From 82e161923480b4bc6116d9fef23127783dcd28cd Mon Sep 17 00:00:00 2001 From: "Luiz Max F. Carvalho" Date: Wed, 2 Oct 2019 11:01:37 -0300 Subject: [PATCH 01/14] Delete GTR-coalescent.stan --- src/GTR-coalescent.stan | 156 ---------------------------------------- 1 file changed, 156 deletions(-) delete mode 100755 src/GTR-coalescent.stan diff --git a/src/GTR-coalescent.stan b/src/GTR-coalescent.stan deleted file mode 100755 index d9e8c96..0000000 --- a/src/GTR-coalescent.stan +++ /dev/null @@ -1,156 +0,0 @@ -functions{ - real coalescent_log(real []x, real pop){ - real p; - real n; - real l; - int i; - real temp; - n = size(x); - p = 0; - l = n + 1.0; - i = 1; - - while(i <= floor(n)){ - temp = ((l*(l-1.0))/2.0)/pop; - p = p + log(temp) - (temp * x[i]); - l = l - 1.0; - i = i + 1; - } - return p; - } - - real oneOnX_log(real x){ - return -log(x); - } -} - -data { - int L; // alignment length - int S; // number of tips - real tipdata[S,L,4]; - int peel[S-1,3]; // list of nodes for peeling - vector[4] frequencies_alpha; - vector[6] rates_alpha; - int map[S-1,S]; -} - -transformed data { - int bcount; // number of branches - int tauCount; - bcount = 2*S-2; - tauCount = S-1; -} - -parameters { - real taus[tauCount]; // intercoalescent times - simplex[4] freqs; - simplex[6] rates; - real theta; -} - - -model { - vector[4] partials[2*S,L]; // partial probabilities for the S tips and S-1 internal nodes - matrix[4,4] fttm[bcount]; // finite-time transition matrices for each branch - matrix[4,4] R; // symmetric rate matrix - matrix[4,4] Q; // rate matrix - matrix[4,4] P2; // diagonal sqrt frequencies - matrix[4,4] P2inv; // diagonal inverse sqrt frequencies - matrix[4,4] A; // another symmetric matrix - vector[4] eigenvalues; - matrix[4,4] eigenvectors; - matrix[4,4] m1; - matrix[4,4] m2; - real s; - vector [bcount] blens; // branch lengths - - // set some branch length priors - theta ~ oneOnX(); - - taus ~ coalescent(theta); - - freqs ~ dirichlet(frequencies_alpha); - - rates ~ dirichlet(rates_alpha); - - - R[2,1] = rates[1]; - R[1,2] = R[2,1]; - R[3,1] = rates[2]; - R[1,3] = R[3,1]; - R[4,1] = rates[3]; - R[1,4] = R[4,1]; - R[3,2] = rates[4]; - R[2,3] = R[3,2]; - R[4,2] = rates[5]; - R[2,4] = R[4,2]; - R[4,3] = rates[6]; - R[3,4] = R[4,3]; - - P2 = rep_matrix(0,4,4); - P2inv = rep_matrix(0,4,4); - - for (i in 1:4) { - R[i,i] = 0.0; - P2[i,i] = sqrt(freqs[i]); - P2inv[i,i] = sqrt(1.0/freqs[i]); - } - - Q = R * diag_matrix(freqs); - s = 0; - for (i in 1:4) { - Q[i,i] = 0.0; - Q[i,i] = -sum(Q[i,1:4]); - s = s + Q[i,i] * freqs[i]; - } - Q = -Q/s; - - A = P2 * Q * P2inv; - - eigenvalues = eigenvalues_sym(A); - eigenvectors = eigenvectors_sym(A); - - m1 = P2inv * eigenvectors; - m2 = eigenvectors' * P2; - - - for( b in 1:bcount ){ - blens[b] = 0; - } - - for( i in 1:tauCount ){ - for( j in 1:S ){ - if(map[i,j] > 0){ - blens[map[i,j]] = blens[map[i,j]] + taus[i]; - } - } - } - - for( b in 1:bcount ){ - fttm[b] = m1 * diag_matrix(exp(eigenvalues*blens[b])) * m2; - } - - // copy tip data into node probability vector - for( n in 1:S ) { - for( i in 1:L ) { - for( a in 1:4 ) { - partials[n,i][a] = tipdata[n,i,a]; - } - } - } - - // calculate tree likelihood for the topology encoded in peel - for( i in 1:L ) { - for( n in 1:(S-1) ) { - //partials[peel[n,3],i] = (fttm[n*2-1]*partials[peel[n,1],i]) .* (fttm[n*2]*partials[peel[n,2],i]); - partials[peel[n,3],i] = (fttm[peel[n,1]]*partials[peel[n,1],i]) .* (fttm[peel[n,2]]*partials[peel[n,2],i]); - } - - // multiply by background nt freqs (assuming uniform here) - for(j in 1:4){ - partials[2*S,i][j] = partials[peel[S-1,3],i][j] * freqs[j]; - } - // add the site log likelihood - target += log(sum(partials[2*S,i])); - } -} From db5b65798c14b2f93dbcc8859808ef181b786b18 Mon Sep 17 00:00:00 2001 From: "Luiz Max F. Carvalho" Date: Wed, 2 Oct 2019 11:01:45 -0300 Subject: [PATCH 02/14] Delete GTR-uniform.stan --- src/GTR-uniform.stan | 119 ------------------------------------------- 1 file changed, 119 deletions(-) delete mode 100644 src/GTR-uniform.stan diff --git a/src/GTR-uniform.stan b/src/GTR-uniform.stan deleted file mode 100644 index ce88827..0000000 --- a/src/GTR-uniform.stan +++ /dev/null @@ -1,119 +0,0 @@ - -data { - int L; // alignment length - int S; // number of tips - real tipdata[S,L,4]; - int peel[S-1,3]; // list of nodes for peeling - vector[4] frequencies_alpha; - vector[6] rates_alpha; -} - -transformed data { - int bcount; // number of branches - int alphalen; - bcount = 2*S-2; - alphalen=4; // assume DNA -} - -parameters { - vector [bcount-1] blens; // branch lengths - simplex[6] rates; - simplex[4] freqs; -} - - -model { - vector[4] node[2*S,L]; // partial probabilities for the S tips and S-1 internal nodes - - matrix[4,4] fttm[bcount]; // finite-time transition matrices for each branch - matrix[4,4] R; // symmetric rate matrix - matrix[4,4] Q; // rate matrix - matrix[4,4] P2; // diagonal sqrt frequencies - matrix[4,4] P2inv; // diagonal inverse sqrt frequencies - matrix[4,4] A; // another symmetric matrix - vector[4] eigenvalues; - matrix[4,4] eigenvectors; - matrix[4,4] m1; - matrix[4,4] m2; - real s; - - // Priors - blens ~ exponential(20); - //rates ~ gamma(0.05,10); - rates ~ dirichlet(rates_alpha); - freqs ~ dirichlet(frequencies_alpha); - - // calculate finite time transition matrices for each branch - // under the GTR model - R[2,1] = rates[1]; - R[1,2] = R[2,1]; - R[3,1] = rates[2]; - R[1,3] = R[3,1]; - R[4,1] = rates[3]; - R[1,4] = R[4,1]; - R[3,2] = rates[4]; - R[2,3] = R[3,2]; - R[4,2] = rates[5]; - R[2,4] = R[4,2]; - R[4,3] = rates[6]; - R[3,4] = R[4,3]; - - P2 = rep_matrix(0,4,4); - P2inv = rep_matrix(0,4,4); - - for (i in 1:4) { - R[i,i] = 0.0; - P2[i,i] = sqrt(freqs[i]); - P2inv[i,i] = sqrt(1.0/freqs[i]); - } - - Q = R * diag_matrix(freqs); - s = 0; - for (i in 1:4) { - Q[i,i] = 0.0; - Q[i,i] = -sum(Q[i,1:4]); - s = s + Q[i,i] * freqs[i]; - } - Q = -Q/s; - - A = P2 * Q * P2inv; - - eigenvalues = eigenvalues_sym(A); - eigenvectors = eigenvectors_sym(A); - - m1 = P2inv * eigenvectors; - m2 = eigenvectors' * P2; - - for( b in 1:bcount-1 ){ - fttm[b] = m1 * diag_matrix(exp(eigenvalues*blens[b])) * m2; - } - - // zero-length root branch identity matrix - fttm[bcount] = rep_matrix(0,4,4); - for( i in 1:4 ) { - fttm[bcount][i,i] = 1; - } - - // copy tip data into node probability vector - for( n in 1:S ) { - for( i in 1:L ) { - for( a in 1:alphalen ) { - node[n,i][a] = tipdata[n,i,a]; - } - } - } - - // calculate tree likelihood for the topology encoded in peel - for( i in 1:L ) { - for( n in 1:(S-1) ) { - node[peel[n,3],i] = (fttm[n*2-1]*node[peel[n,1],i]) .* (fttm[n*2]*node[peel[n,2],i]); - } - for(j in 1:4){ - node[2*S,i][j] = node[peel[S-1,3],i][j] * freqs[j]; - } - - // add the site log likelihood - target += log(sum(node[2*S,i])); - } - -} From d0e4a69cc6eea688003468e90994ea3100f297ec Mon Sep 17 00:00:00 2001 From: "Luiz Max F. Carvalho" Date: Wed, 2 Oct 2019 11:01:52 -0300 Subject: [PATCH 03/14] Delete HKY-coalescent.stan --- src/HKY-coalescent.stan | 148 ---------------------------------------- 1 file changed, 148 deletions(-) delete mode 100755 src/HKY-coalescent.stan diff --git a/src/HKY-coalescent.stan b/src/HKY-coalescent.stan deleted file mode 100755 index 6dd26c4..0000000 --- a/src/HKY-coalescent.stan +++ /dev/null @@ -1,148 +0,0 @@ -functions{ - real coalescent_log(real []x, real pop){ - real p; - real n; - real l; - int i; - real temp; - n = size(x); - p = 0; - l = n + 1.0; - i = 1; - - while(i <= floor(n)){ - temp = ((l*(l-1.0))/2.0)/pop; - p = p + log(temp) - (temp * x[i]); - l = l - 1.0; - i = i + 1; - } - return p; - } - - real oneOnX_log(real x){ - return -log(x); - } -} - -data { - int L; // alignment length - int S; // number of tips - real tipdata[S,L,4]; - int peel[S-1,3]; // list of nodes for peeling - vector[4] frequencies_alpha; - int map[S-1,S]; -} - -transformed data { - int bcount; // number of branches - int tauCount; - bcount = 2*S-2; - tauCount = S-1; -} - -parameters { - real taus[tauCount]; // intercoalescent times - simplex[4] freqs; - real kappa; - real theta; -} - - -model { - vector[4] partials[2*S,L]; // partial probabilities for the S tips and S-1 internal nodes - matrix[4,4] fttm[bcount]; // finite-time transition matrices for each branch - real R; - real Y; - real k1; - real k2; - real r; - real exp1; - real exp22; - real exp21; - vector [bcount] blens; // branch lengths - - // set some branch length priors - theta ~ oneOnX(); - - taus ~ coalescent(theta); - - freqs ~ dirichlet(frequencies_alpha); - - kappa ~ uniform(0,100); - //kappa ~ lognormal(1.0,1.25); - - for( b in 1:bcount ){ - blens[b] = 0; - } - - for( i in 1:tauCount ){ - for( j in 1:S ){ - if(map[i,j] > 0){ - blens[map[i,j]] = blens[map[i,j]] + taus[i]; - } - } - } - - R = freqs[1] + freqs[3]; - Y = freqs[4] + freqs[2]; - k1 = kappa * Y + R; - k2 = kappa * R + Y; - - r = 1.0 / (2.0 * (freqs[1] * freqs[2] + freqs[2] * freqs[3] + freqs[1] * freqs[4] + freqs[3] * freqs[4] + kappa * (freqs[2] * freqs[4] + freqs[1] * freqs[3]))); - - for( b in 1:bcount ){ - - exp1 = exp(-blens[b]*r); - exp22 = exp(-k2 * blens[b] * r); - exp21 = exp(-k1 * blens[b] * r); - - //A - fttm[b][1,1] = freqs[1] * (1. + (Y/R) * exp1) + (freqs[3]/R) * exp22; //A - fttm[b][1,2] = freqs[2] * (1. - exp1); //C - fttm[b][1,3] = freqs[3] * (1. + (Y/R) * exp1) - (freqs[3]/R) * exp22; //G - fttm[b][1,4] = freqs[4] * (1. - exp1); //T, U - - //C - fttm[b][2,1] = freqs[1] * (1. - exp1); //A - fttm[b][2,2] = freqs[2] * (1. + (R/Y) * exp1) + (freqs[4]/Y) * exp21; //C - fttm[b][2,3] = freqs[3] * (1. - exp1); //G - fttm[b][2,4] = freqs[4] * (1. + (R/Y) * exp1) - (freqs[4]/Y) * exp21; //T, U - - //G - fttm[b][3,1] = freqs[1] * (1. + (Y/R) * exp1) - (freqs[1]/R) * exp22; //A - fttm[b][3,2] = freqs[2] * (1. - exp1); //C - fttm[b][3,3] = freqs[3] * (1. + (Y/R) * exp1) + (freqs[1]/R) * exp22; //G - fttm[b][3,4] = freqs[4] * (1. - exp1); //T, U - - //T, U - fttm[b][4,1] = freqs[1] * (1. - exp1); //A - fttm[b][4,2] = freqs[2] * (1. + (R/Y) * exp1) - (freqs[2]/Y) * exp21; //C - fttm[b][4,3] = freqs[3] * (1. - exp1); //G - fttm[b][4,4] = freqs[4] * (1. + (R/Y) * exp1) + (freqs[2]/Y) * exp21; //T, U - } - - - // copy tip data into node probability vector - for( n in 1:S ) { - for( i in 1:L ) { - for( a in 1:4 ) { - partials[n,i][a] = tipdata[n,i,a]; - } - } - } - - // calculate tree likelihood for the topology encoded in peel - for( i in 1:L ) { - for( n in 1:(S-1) ) { - //partials[peel[n,3],i] = (fttm[n*2-1]*partials[peel[n,1],i]) .* (fttm[n*2]*partials[peel[n,2],i]); - partials[peel[n,3],i] = (fttm[peel[n,1]]*partials[peel[n,1],i]) .* (fttm[peel[n,2]]*partials[peel[n,2],i]); - } - - // multiply by background nt freqs (assuming uniform here) - for(j in 1:4){ - partials[2*S,i][j] = partials[peel[S-1,3],i][j] * freqs[j]; - } - // add the site log likelihood - target += log(sum(partials[2*S,i])); - } -} From ddc0bffc7e3a72f57adfec25f7146c182e6c03f2 Mon Sep 17 00:00:00 2001 From: "Luiz Max F. Carvalho" Date: Wed, 2 Oct 2019 11:01:59 -0300 Subject: [PATCH 04/14] Delete JC69-GTR.stan --- src/JC69-GTR.stan | 148 ---------------------------------------------- 1 file changed, 148 deletions(-) delete mode 100644 src/JC69-GTR.stan diff --git a/src/JC69-GTR.stan b/src/JC69-GTR.stan deleted file mode 100644 index f4f565a..0000000 --- a/src/JC69-GTR.stan +++ /dev/null @@ -1,148 +0,0 @@ - -data { - int L; // alignment length - int S; // number of tips - real tipdata[S,L,4]; - int peel[S-1,3]; // list of nodes for peeling - real weights[L]; - vector[4] frequencies_alpha; - vector[6] rates_alpha; - vector[2] thetas_alpha; -} - -transformed data { - int bcount; // number of branches - int root; - bcount = 2*S-2; - root = peel[S-1,3]; // root is the final peeling -} - -parameters { - vector [bcount-1] blens; // branch lengths - // For GTR model - simplex[6] rates; - simplex[4] freqs; - simplex[2] theta; -} - - -model { - vector[4] node[2,2*S,L]; // partial probabilities for the S tips and S-1 internal nodes - matrix[4,4] fttm[2,bcount]; // finite-time transition matrices for each branch, plus zero-length root branch - real ps[2]; - - // For GTR - matrix[4,4] R; // symmetric rate matrix - matrix[4,4] Q; // rate matrix - matrix[4,4] P2; // diagonal sqrt frequencies - matrix[4,4] P2inv; // diagonal inverse sqrt frequencies - matrix[4,4] A; // another symmetric matrix - vector[4] eigenvalues; - matrix[4,4] eigenvectors; - matrix[4,4] m1; - matrix[4,4] m2; - real s; - - // set some branch length priors - blens ~ exponential(20); - rates ~ dirichlet(rates_alpha); - freqs ~ dirichlet(frequencies_alpha); - theta ~ dirichlet(thetas_alpha); - - // calculate finite time transition matrices for each branch - // under the Jukes-Cantor model - for( b in 1:bcount-1 ) { - for( i in 1:4 ) { - for( j in 1:4 ) { - fttm[1,b][i,j] = 0.25 - 0.25*exp(-4*blens[b]/3); - } - fttm[1,b][i,i] = 0.25 + 0.75*exp(-4*blens[b]/3); - } - } - // GTR model - R[2,1] = rates[1]; - R[1,2] = R[2,1]; - R[3,1] = rates[2]; - R[1,3] = R[3,1]; - R[4,1] = rates[3]; - R[1,4] = R[4,1]; - R[3,2] = rates[4]; - R[2,3] = R[3,2]; - R[4,2] = rates[5]; - R[2,4] = R[4,2]; - R[4,3] = rates[6]; - R[3,4] = R[4,3]; - - P2 = rep_matrix(0,4,4); - P2inv = rep_matrix(0,4,4); - - for (i in 1:4) { - R[i,i] = 0.0; - P2[i,i] = sqrt(freqs[i]); - P2inv[i,i] = sqrt(1.0/freqs[i]); - } - - Q = R * diag_matrix(freqs); - s = 0; - for (i in 1:4) { - Q[i,i] = 0.0; - Q[i,i] = -sum(Q[i,1:4]); - s = s + Q[i,i] * freqs[i]; - } - Q = -Q/s; - - A = P2 * Q * P2inv; - - eigenvalues = eigenvalues_sym(A); - eigenvectors = eigenvectors_sym(A); - - m1 = P2inv * eigenvectors; - m2 = eigenvectors' * P2; - - for( b in 1:bcount-1 ){ - fttm[2,b] = m1 * diag_matrix(exp(eigenvalues*blens[b])) * m2; - } - - // zero-length root branch identity matrix - fttm[1,bcount] = rep_matrix(0,4,4); - fttm[2,bcount] = rep_matrix(0,4,4); - for( i in 1:4 ) { - fttm[1,bcount][i,i] = 1; - fttm[2,bcount][i,i] = 1; - } - - // copy tip data into node probability vector - for( n in 1:S ) { - for( i in 1:L ) { - for( a in 1:4 ) { - node[1,n,i][a] = tipdata[n,i,a]; - node[2,n,i][a] = tipdata[n,i,a]; - } - } - } - - // calculate tree likelihood for the topology encoded in peel - for( i in 1:L ) { - - for( n in 1:(S-1) ) { - for( m in 1:2){ - node[m,peel[n,3],i] = (fttm[m,n*2-1]*node[m,peel[n,1],i]) .* (fttm[m,n*2]*node[m,peel[n,2],i]); - } - } - - // multiply by background nt freqs (assuming uniform here) - node[1,2*S,i] = node[1,root,i] * 0.25; - - for(j in 1:4){ - node[2,2*S,i][j] = node[2,peel[S-1,3],i][j] * freqs[j]; - } - - // add the site log likelihood - for( m in 1:2){ - ps[m] = log(theta[m]) + log(sum(node[m,2*S,i])); - } - - target += log_sum_exp(ps)*weights[i]; - } - -} From 80f53a9c4e5394841d875e34978caaea04697b10 Mon Sep 17 00:00:00 2001 From: "Luiz Max F. Carvalho" Date: Wed, 2 Oct 2019 11:02:21 -0300 Subject: [PATCH 05/14] Delete JC69-HKY-GTR.stan --- src/JC69-HKY-GTR.stan | 210 ------------------------------------------ 1 file changed, 210 deletions(-) delete mode 100644 src/JC69-HKY-GTR.stan diff --git a/src/JC69-HKY-GTR.stan b/src/JC69-HKY-GTR.stan deleted file mode 100644 index f7982f4..0000000 --- a/src/JC69-HKY-GTR.stan +++ /dev/null @@ -1,210 +0,0 @@ - -data { - int L; // alignment length - int S; // number of tips - real tipdata[S,L,4]; - int peel[S-1,3]; // list of nodes for peeling - real weights[L]; - vector[4] frequencies_alpha; - vector[6] rates_alpha; - vector[3] thetas_alpha; -} - -transformed data { - int bcount; // number of branches - int root; - int M; // number of substitution models - bcount = 2*S-2; - root = peel[S-1,3]; // root is the final peeling - M = 3; -} - -parameters { - vector [bcount-1] blens; // branch lengths - // For GTR model - simplex[6] rates; - simplex[4] freqs; - // HKY - //simplex[4] freqs_hky; - real kappa; - - simplex[M] theta; -} - - -model { - vector[4] node[M,2*S,L]; // partial probabilities for the S tips and S-1 internal nodes - matrix[4,4] fttm[M,bcount]; // finite-time transition matrices for each branch, plus zero-length root branch - real ps[M]; - - // For GTR - matrix[4,4] R; // symmetric rate matrix - matrix[4,4] Q; // rate matrix - matrix[4,4] P2; // diagonal sqrt frequencies - matrix[4,4] P2inv; // diagonal inverse sqrt frequencies - matrix[4,4] A; // another symmetric matrix - vector[4] eigenvalues; - matrix[4,4] eigenvectors; - matrix[4,4] m1; - matrix[4,4] m2; - real s; - - // For HKY - real RR; - real Y; - real k1; - real k2; - real r; - real exp1; - real exp22; - real exp21; - - // set some branch length priors - blens ~ exponential(20); - rates ~ dirichlet(rates_alpha); - freqs ~ dirichlet(frequencies_alpha); - //freqs_hky ~ dirichlet(frequencies_alpha); - kappa ~ uniform(0,100); - theta ~ dirichlet(thetas_alpha); - - // calculate finite time transition matrices for each branch - // under the Jukes-Cantor model - for( b in 1:bcount-1 ) { - for( i in 1:4 ) { - for( j in 1:4 ) { - fttm[1,b][i,j] = 0.25 - 0.25*exp(-4*blens[b]/3); - } - fttm[1,b][i,i] = 0.25 + 0.75*exp(-4*blens[b]/3); - } - } - // GTR model - R[2,1] = rates[1]; - R[1,2] = R[2,1]; - R[3,1] = rates[2]; - R[1,3] = R[3,1]; - R[4,1] = rates[3]; - R[1,4] = R[4,1]; - R[3,2] = rates[4]; - R[2,3] = R[3,2]; - R[4,2] = rates[5]; - R[2,4] = R[4,2]; - R[4,3] = rates[6]; - R[3,4] = R[4,3]; - - P2 = rep_matrix(0,4,4); - P2inv = rep_matrix(0,4,4); - - for (i in 1:4) { - R[i,i] = 0.0; - P2[i,i] = sqrt(freqs[i]); - P2inv[i,i] = sqrt(1.0/freqs[i]); - } - - Q = R * diag_matrix(freqs); - s = 0; - for (i in 1:4) { - Q[i,i] = 0.0; - Q[i,i] = -sum(Q[i,1:4]); - s = s + Q[i,i] * freqs[i]; - } - Q = -Q/s; - - A = P2 * Q * P2inv; - - eigenvalues = eigenvalues_sym(A); - eigenvectors = eigenvectors_sym(A); - - m1 = P2inv * eigenvectors; - m2 = eigenvectors' * P2; - - for( b in 1:bcount-1 ){ - fttm[2,b] = m1 * diag_matrix(exp(eigenvalues*blens[b])) * m2; - } - - // HKY model - RR = freqs[1] + freqs[3]; - Y = freqs[4] + freqs[2]; - k1 = kappa * Y + RR; - k2 = kappa * RR + Y; - - r = 1.0 / (2.0 * (freqs[1] * freqs[2] + freqs[2] * freqs[3] + freqs[1] * freqs[4] + freqs[3] * freqs[4] + kappa * (freqs[2] * freqs[4] + freqs[1] * freqs[3]))); - - for( b in 1:bcount-1 ){ - - exp1 = exp(-blens[b]*r); - exp22 = exp(-k2 * blens[b] * r); - exp21 = exp(-k1 * blens[b] * r); - - //A - fttm[3,b][1,1] = freqs[1] * (1. + (Y/RR) * exp1) + (freqs[3]/RR) * exp22; //A - fttm[3,b][1,2] = freqs[2] * (1. - exp1); //C - fttm[3,b][1,3] = freqs[3] * (1. + (Y/RR) * exp1) - (freqs[3]/RR) * exp22; //G - fttm[3,b][1,4] = freqs[4] * (1. - exp1); //T, U - - //C - fttm[3,b][2,1] = freqs[1] * (1. - exp1); //A - fttm[3,b][2,2] = freqs[2] * (1. + (RR/Y) * exp1) + (freqs[4]/Y) * exp21; //C - fttm[3,b][2,3] = freqs[3] * (1. - exp1); //G - fttm[3,b][2,4] = freqs[4] * (1. + (RR/Y) * exp1) - (freqs[4]/Y) * exp21; //T, U - - //G - fttm[3,b][3,1] = freqs[1] * (1. + (Y/RR) * exp1) - (freqs[1]/RR) * exp22; //A - fttm[3,b][3,2] = freqs[2] * (1. - exp1); //C - fttm[3,b][3,3] = freqs[3] * (1. + (Y/RR) * exp1) + (freqs[1]/RR) * exp22; //G - fttm[3,b][3,4] = freqs[4] * (1. - exp1); //T, U - - //T, U - fttm[3,b][4,1] = freqs[1] * (1. - exp1); //A - fttm[3,b][4,2] = freqs[2] * (1. + (RR/Y) * exp1) - (freqs[2]/Y) * exp21; //C - fttm[3,b][4,3] = freqs[3] * (1. - exp1); //G - fttm[3,b][4,4] = freqs[4] * (1. + (RR/Y) * exp1) + (freqs[2]/Y) * exp21; //T, U - } - - // zero-length root branch identity matrix - for( m in 1:M ) { - fttm[m,bcount] = rep_matrix(0,4,4); - } - for( i in 1:4 ) { - for( m in 1:M ) { - fttm[m,bcount][i,i] = 1; - } - } - - // copy tip data into node probability vector - for( n in 1:S ) { - for( i in 1:L ) { - for( a in 1:4 ) { - for( m in 1:M ) { - node[m,n,i][a] = tipdata[n,i,a]; - } - } - } - } - - // calculate tree likelihood for the topology encoded in peel - for( i in 1:L ) { - - for( n in 1:(S-1) ) { - for( m in 1:M){ - node[m,peel[n,3],i] = (fttm[m,n*2-1]*node[m,peel[n,1],i]) .* (fttm[m,n*2]*node[m,peel[n,2],i]); - } - } - - // JC69 - node[1,2*S,i] = node[1,root,i] * 0.25; - - // GTR and HKY - for(j in 1:4){ - node[2,2*S,i][j] = node[2,peel[S-1,3],i][j] * freqs[j]; - node[3,2*S,i][j] = node[3,peel[S-1,3],i][j] * freqs[j]; - } - - // add the site log likelihood - for( m in 1:M){ - ps[m] = log(theta[m]) + log(sum(node[m,2*S,i])); - } - - target += log_sum_exp(ps)*weights[i]; - } - -} From 0c2f914a3f190fca1cbcb3baa03b3dce4cd6332e Mon Sep 17 00:00:00 2001 From: "Luiz Max F. Carvalho" Date: Wed, 2 Oct 2019 11:02:28 -0300 Subject: [PATCH 06/14] Delete JC69-coalescent.stan --- src/JC69-coalescent.stan | 102 --------------------------------------- 1 file changed, 102 deletions(-) delete mode 100755 src/JC69-coalescent.stan diff --git a/src/JC69-coalescent.stan b/src/JC69-coalescent.stan deleted file mode 100755 index dd04f50..0000000 --- a/src/JC69-coalescent.stan +++ /dev/null @@ -1,102 +0,0 @@ -functions{ - real coalescent_log(real []x, real pop){ - real p; - real n; - real l; - int i; - real temp; - n = size(x); - p = 0; - l = n + 1.0; - i = 1; - - while(i <= floor(n)){ - temp = ((l*(l-1.0))/2.0)/pop; - p = p + log(temp) - (temp * x[i]); - l = l - 1.0; - i = i + 1; - } - return p; - } - - real oneOnX_log(real x){ - return -log(x); - } -} - -data { - int L; // alignment length - int S; // number of tips - real tipdata[S,L,4]; - int peel[S-1,3]; // list of nodes for peeling - int map[S-1,S]; -} - -transformed data { - int bcount; // number of branches - int tauCount; - bcount = 2*S-2; - tauCount = S-1; -} - -parameters { - real taus[tauCount]; // intercoalescent times - real theta; -} - - -model { - vector[4] partials[2*S,L]; // partial probabilities for the S tips and S-1 internal nodes - matrix[4,4] fttm[bcount]; // finite-time transition matrices for each branch - vector [bcount] blens; // branch lengths - - // set some branch length priors - theta ~ oneOnX(); - - taus ~ coalescent(theta); - - for( b in 1:bcount ){ - blens[b] = 0; - } - - for( i in 1:tauCount ){ - for( j in 1:S ){ - if(map[i,j] > 0){ - blens[map[i,j]] = blens[map[i,j]] + taus[i]; - } - } - } - - for( b in 1:bcount ) { - for( i in 1:4 ) { - for( j in 1:4 ) { - fttm[b][i,j] = 0.25 - 0.25*exp(-4*blens[b]/3); - } - fttm[b][i,i] = 0.25 + 0.75*exp(-4*blens[b]/3); - } - } - - - // copy tip data into node probability vector - for( n in 1:S ) { - for( i in 1:L ) { - for( a in 1:4 ) { - partials[n,i][a] = tipdata[n,i,a]; - } - } - } - - // calculate tree likelihood for the topology encoded in peel - for( i in 1:L ) { - for( n in 1:(S-1) ) { - partials[peel[n,3],i] = (fttm[peel[n,1]]*partials[peel[n,1],i]) .* (fttm[peel[n,2]]*partials[peel[n,2],i]); - } - - // multiply by background nt freqs (assuming uniform here) - for(j in 1:4){ - partials[2*S,i][j] = partials[peel[S-1,3],i][j] * 0.25; - } - // add the site log likelihood - target += log(sum(partials[2*S,i])); - } -} From 78d53dbccd5a80bb0dd7caea3cb9471219cde28c Mon Sep 17 00:00:00 2001 From: "Luiz Max F. Carvalho" Date: Wed, 2 Oct 2019 11:02:35 -0300 Subject: [PATCH 07/14] Delete JC69-mixture.stan --- src/JC69-mixture.stan | 90 ------------------------------------------- 1 file changed, 90 deletions(-) delete mode 100644 src/JC69-mixture.stan diff --git a/src/JC69-mixture.stan b/src/JC69-mixture.stan deleted file mode 100644 index 311718f..0000000 --- a/src/JC69-mixture.stan +++ /dev/null @@ -1,90 +0,0 @@ - -data { - int T; // number of trees - int L; // alignment length - int S; // number of tips - real tipdata[S,L,4]; - int peel[T,(S-1),3]; // list of nodes for peeling - real weights[L]; -} - -transformed data { - int bcount; // number of branches - int pcount; - int alphalen; - int root; - vector[T] alpha; // could be moved to data - - bcount = 2*S-2; // number of branches - pcount = 2*S-3; // number of branch parameters - alphalen=4; // assume DNA - for(i in 1:T){ - alpha[i] = 1; - } - -} - -parameters { - vector [pcount] blens[T]; // branch lengths - simplex[T] theta; -} - - -model { - vector[alphalen] node[T,2*S,L]; // partial probabilities for the S tips and S-1 internal nodes - matrix[alphalen,alphalen] fttm[T,bcount]; // finite-time transition matrices for each branch, plus zero-length root branch - real ps[T]; - - // set some branch length priors - for( t in 1:T){ - blens[t] ~ exponential(20); - } - - theta ~ dirichlet(alpha); - - // calculate finite time transition matrices for each branch - // under the Jukes-Cantor model - for( t in 1:T){ - for( b in 1:pcount ) { - for( i in 1:alphalen ) { - for( j in 1:alphalen ) { - fttm[t,b][i,j] = 0.25 - 0.25*exp(-4*blens[t,b]/3); - } - fttm[t,b][i,i] = 0.25 + 0.75*exp(-4*blens[t,b]/3); - } - } - - // zero-length root branch identity matrix - fttm[t,bcount] = rep_matrix(0,alphalen,alphalen); - for( i in 1:alphalen ) { - fttm[t,bcount][i,i] = 1; - } - } - - - // copy tip data into node probability vector - for( t in 1:T ) { - for( n in 1:S ) { - for( i in 1:L ) { - for( a in 1:alphalen ) { - node[t,n,i][a] = tipdata[n,i,a]; - } - } - } - } - - // calculate tree likelihood for the topology encoded in peel - for( i in 1:L ) { - for( t in 1:T ) { - for( n in 1:(S-1) ) { - node[t,peel[t,n,3],i] = (fttm[t,n*2-1]*node[t,peel[t,n,1],i]) .* (fttm[t,n*2]*node[t,peel[t,n,2],i]); - } - // multiply by background nt freqs (assuming uniform here) - node[t,2*S,i] = node[t,peel[t,S-1,3],i] / alphalen; - - // add the site log likelihood - ps[t] = log(theta[t]) + log(sum(node[t,2*S,i])); - } - target += log_sum_exp(ps)*weights[i]; - } -} From 8faacf0fe3dc83daab5e6b49c9ef9e7b150957a2 Mon Sep 17 00:00:00 2001 From: "Luiz Max F. Carvalho" Date: Wed, 2 Oct 2019 11:02:42 -0300 Subject: [PATCH 08/14] Delete JC69-mixture2.stan --- src/JC69-mixture2.stan | 130 ----------------------------------------- 1 file changed, 130 deletions(-) delete mode 100644 src/JC69-mixture2.stan diff --git a/src/JC69-mixture2.stan b/src/JC69-mixture2.stan deleted file mode 100644 index 44fc9a7..0000000 --- a/src/JC69-mixture2.stan +++ /dev/null @@ -1,130 +0,0 @@ - -data { - int T; // number of trees - int L; // alignment length - int S; // number of tips - int B; // number of independent branches (not including one of the children of root) - real tipdata[S,L,4]; - int peel[T,(S-1),3]; // list of nodes for peeling - int indexes[(2*S-3)*T]; // -3 because we do not count one of the children of root - real weights[L]; -} - -transformed data { - int bcount; // number of branches - int pcount; - int alphalen; - int root; - vector[T] alpha; // could be moved to data - - bcount = 2*S-2; - pcount = 2*S-3; - alphalen=4; // assume DNA - for(i in 1:T){ - alpha[i] = 1; - } - -} - -parameters { - //vector [B] blens[T]; // branch lengths - vector [B] blens; // branch lengths (independent) - simplex[T] theta; -} - - -model { - vector[alphalen] node[T,2*S,L]; // partial probabilities for the S tips and S-1 internal nodes - matrix[alphalen,alphalen] fttm[B+1]; // finite-time transition matrices for each branch, plus zero-length root branch - real ps[T]; - int counter; - - counter = 1; - - // set some branch length priors - blens ~ exponential(20); - - theta ~ dirichlet(alpha); - - // calculate finite time transition matrices for each branch - // under the Jukes-Cantor model - for( b in 1:B){ - for( i in 1:4 ) { - for( j in 1:4 ) { - fttm[b][i,j] = 0.25 - 0.25*exp(-4*blens[b]/3); - } - fttm[b][i,i] = 0.25 + 0.75*exp(-4*blens[b]/3); - } - } - fttm[B+1] = rep_matrix(0,alphalen,alphalen); - for( i in 1:alphalen ) { - fttm[B+1][i,i] = 1; - } - - /*for( t in 1:T){ - for( b in 1:bcount-1 ) { - for( i in 1:alphalen ) { - for( j in 1:alphalen ) { - //fttm[t,b][i,j] = 0.25 - 0.25*exp(-4*blens[t,b]/3); - fttm[t,b][i,j] = 0.25 - 0.25*exp(-4*blens[indexes[counter]]/3); - } - //fttm[t,b][i,i] = 0.25 + 0.75*exp(-4*blens[t,b]/3); - fttm[t,b][i,i] = 0.25 + 0.75*exp(-4*blens[indexes[counter]]/3); - } - counter = counter + 1; - } - - // zero-length root branch identity matrix - fttm[t,bcount] = rep_matrix(0,alphalen,alphalen); - for( i in 1:alphalen ) { - fttm[t,bcount][i,i] = 1; - } - }*/ - - - // copy tip data into node probability vector - for( t in 1:T ) { - for( n in 1:S ) { - for( i in 1:L ) { - for( a in 1:alphalen ) { - node[t,n,i][a] = tipdata[n,i,a]; - } - } - } - } - - // calculate tree likelihood for the topology encoded in peel - /*for( t in 1:T ) { - ps[t] = log(theta[t]); - for( i in 1:L ) { - for( n in 1:(S-1) ) { - node[t,peel[t,n,3],i] = (fttm[t,n*2-1]*node[t,peel[t,n,1],i]) .* (fttm[t,n*2]*node[t,peel[t,n,2],i]); - } - // multiply by background nt freqs (assuming uniform here) - node[t,2*S,i] = node[t,peel[t,S-1,3],i] / alphalen; - - // add the site log likelihood - ps[t] = ps[t] + log(sum(node[t,2*S,i]))*weights[i]; - } - } - target += log_sum_exp(ps);*/ - - for( i in 1:L ) { - counter = 1; - for( t in 1:T ) { - for( n in 1:(S-2) ) { - node[t,peel[t,n,3],i] = (fttm[indexes[counter]]*node[t,peel[t,n,1],i]) .* (fttm[indexes[counter+1]]*node[t,peel[t,n,2],i]); - counter = counter + 2; - } - node[t,peel[t,S-1,3],i] = (fttm[indexes[counter]]*node[t,peel[t,S-1,1],i]) .* (fttm[indexes[B+1]]*node[t,peel[t,S-1,2],i]); - counter = counter + 1; - // multiply by background nt freqs (assuming uniform here) - node[t,2*S,i] = node[t,peel[t,S-1,3],i] / alphalen; - - // add the site log likelihood - ps[t] = log(theta[t]) + log(sum(node[t,2*S,i])); - } - target += log_sum_exp(ps)*weights[i]; - } - -} From 8793c9ce82f19a496607d102f465a4d9b1709ff4 Mon Sep 17 00:00:00 2001 From: "Luiz Max F. Carvalho" Date: Wed, 2 Oct 2019 11:02:49 -0300 Subject: [PATCH 09/14] Delete JC69-uniform.stan --- src/JC69-uniform.stan | 65 ------------------------------------------- 1 file changed, 65 deletions(-) delete mode 100755 src/JC69-uniform.stan diff --git a/src/JC69-uniform.stan b/src/JC69-uniform.stan deleted file mode 100755 index bfa6b60..0000000 --- a/src/JC69-uniform.stan +++ /dev/null @@ -1,65 +0,0 @@ - -data { - int L; // alignment length - int S; // number of tips - real tipdata[S,L,4]; - int peel[S-1,3]; // list of nodes for peeling -} - -transformed data { - int bcount; // number of branches - int root; - bcount = 2*S-2; - root = peel[S-1,3]; // root is the final peeling -} - -parameters { - vector [bcount-1] blens; // branch lengths -} - - -model { - vector[4] node[2*S,L]; // partial probabilities for the S tips and S-1 internal nodes - matrix[4,4] fttm[bcount]; // finite-time transition matrices for each branch, plus zero-length root branch - - // set some branch length priors - blens ~ exponential(20); - - // calculate finite time transition matrices for each branch - // under the Jukes-Cantor model - for( b in 1:bcount-1 ) { - for( i in 1:4 ) { - for( j in 1:4 ) { - fttm[b][i,j] = 0.25 - 0.25*exp(-4*blens[b]/3); - } - fttm[b][i,i] = 0.25 + 0.75*exp(-4*blens[b]/3); - } - } - // zero-length root branch identity matrix - fttm[bcount] = rep_matrix(0,4,4); - for( i in 1:4 ) { - fttm[bcount][i,i] = 1; - } - - // copy tip data into node probability vector - for( n in 1:S ) { - for( i in 1:L ) { - for( a in 1:4 ) { - node[n,i][a] = tipdata[n,i,a]; - } - } - } - - // calculate tree likelihood for the topology encoded in peel - for( i in 1:L ) { - for( n in 1:(S-1) ) { - node[peel[n,3],i] = (fttm[n*2-1]*node[peel[n,1],i]) .* (fttm[n*2]*node[peel[n,2],i]); - } - // multiply by background nt freqs (assuming uniform here) - node[2*S,i] = node[root,i] * 0.25; - - // add the site log likelihood - target += log(sum(node[2*S,i])); - } - -} From 5e0aa9c19a65b75566b4888ad0f96e326aa5b254 Mon Sep 17 00:00:00 2001 From: "Luiz Max F. Carvalho" Date: Wed, 2 Oct 2019 11:02:56 -0300 Subject: [PATCH 10/14] Delete K80-coalescent.stan --- src/K80-coalescent.stan | 134 ---------------------------------------- 1 file changed, 134 deletions(-) delete mode 100755 src/K80-coalescent.stan diff --git a/src/K80-coalescent.stan b/src/K80-coalescent.stan deleted file mode 100755 index e072fa5..0000000 --- a/src/K80-coalescent.stan +++ /dev/null @@ -1,134 +0,0 @@ -functions{ - real coalescent_log(real []x, real pop){ - real p; - real n; - real l; - int i; - real temp; - n = size(x); - p = 0; - l = n + 1.0; - i = 1; - - while(i <= floor(n)){ - temp = ((l*(l-1.0))/2.0)/pop; - p = p + log(temp) - (temp * x[i]); - l = l - 1.0; - i = i + 1; - } - return p; - } - - real oneOnX_log(real x){ - return -log(x); - } -} - -data { - int L; // alignment length - int S; // number of tips - real tipdata[S,L,4]; - int peel[S-1,3]; // list of nodes for peeling - int map[S-1,S]; -} - -transformed data { - int bcount; // number of branches - int tauCount; - bcount = 2*S-2; - tauCount = S-1; -} - -parameters { - real taus[tauCount]; // intercoalescent times - real kappa; - real theta; -} - - -model { - vector[4] partials[2*S,L]; // partial probabilities for the S tips and S-1 internal nodes - matrix[4,4] fttm[bcount]; // finite-time transition matrices for each branch - real k; - real r; - real exp1; - real exp22; - vector [bcount] blens; // branch lengths - - // set some branch length priors - theta ~ oneOnX(); - - taus ~ coalescent(theta); - - kappa ~ uniform(0,100); - //kappa ~ lognormal(1.0,1.25); - - for( b in 1:bcount ){ - blens[b] = 0; - } - - for( i in 1:tauCount ){ - for( j in 1:S ){ - if(map[i,j] > 0){ - blens[map[i,j]] = blens[map[i,j]] + taus[i]; - } - } - } - - k = (kappa + 1.0)/2.0; - r = 4.0 / (kappa + 2.0); - - for( b in 1:bcount ){ - - exp1 = exp(-blens[b]*r); - exp22 = exp(-k * blens[b]*r); - - //A - fttm[b][1,1] = 0.25 * (1. + exp1) + 0.5 * exp22; //A - fttm[b][1,2] = 0.25 * (1. - exp1); //C - fttm[b][1,3] = 0.25 * (1. + exp1) - 0.5 * exp22; //G - fttm[b][1,4] = 0.25 * (1. - exp1); //T, U - - //C - fttm[b][2,1] = 0.25 * (1. - exp1); //A - fttm[b][2,2] = 0.25 * (1. + exp1) + 0.5 * exp22; //C - fttm[b][2,3] = 0.25 * (1. - exp1); //G - fttm[b][2,4] = 0.25 * (1. + exp1) - 0.5 * exp22; //T, U - - //G - fttm[b][3,1] = 0.25 * (1. + exp1) - 0.5 * exp22; //A - fttm[b][3,2] = 0.25 * (1. - exp1); //C - fttm[b][3,3] = 0.25 * (1. + exp1) + 0.5 * exp22; //G - fttm[b][3,4] = 0.25 * (1. - exp1); //T, U - - //T, U - fttm[b][4,1] = 0.25 * (1. - exp1); //A - fttm[b][4,2] = 0.25 * (1. + exp1) - 0.5 * exp22; //C - fttm[b][4,3] = 0.25 * (1. - exp1); //G - fttm[b][4,4] = 0.25 * (1. + exp1) + 0.5 * exp22; //T, U - } - - - // copy tip data into node probability vector - for( n in 1:S ) { - for( i in 1:L ) { - for( a in 1:4 ) { - partials[n,i][a] = tipdata[n,i,a]; - } - } - } - - // calculate tree likelihood for the topology encoded in peel - for( i in 1:L ) { - for( n in 1:(S-1) ) { - partials[peel[n,3],i] = (fttm[peel[n,1]]*partials[peel[n,1],i]) .* (fttm[peel[n,2]]*partials[peel[n,2],i]); - } - - // multiply by background nt freqs (assuming uniform here) - for(j in 1:4){ - partials[2*S,i][j] = partials[peel[S-1,3],i][j] * 0.25; - } - // add the site log likelihood - target += log(sum(partials[2*S,i])); - } -} From 9b43c647fd5d7a3cef6e753bb28c3babdfcbbc4f Mon Sep 17 00:00:00 2001 From: Luiz Max Carvalho Date: Fri, 4 Oct 2019 10:37:19 -0300 Subject: [PATCH 11/14] intermediate work, not fluent in Python AT ALL --- examples/fluA/.Rhistory | 512 ++++++++++++++++ examples/fluA/clean | 1 + examples/fluA/fluA.trees | 1075 ++++++++++++++++++++++++++++++++++ phylostan/generate_script.py | 80 ++- phylostan/phylostan.py | 4 +- phylostan/utils.py | 1 - src/GTR-coalescent.stan | 156 ----- src/GTR-uniform.stan | 119 ---- src/HKY-coalescent.stan | 148 ----- src/JC69-GTR.stan | 148 ----- src/JC69-HKY-GTR.stan | 210 ------- src/JC69-coalescent.stan | 102 ---- src/JC69-mixture.stan | 90 --- src/JC69-mixture2.stan | 130 ---- src/JC69-uniform.stan | 65 -- src/K80-coalescent.stan | 134 ----- 16 files changed, 1668 insertions(+), 1307 deletions(-) create mode 100644 examples/fluA/.Rhistory create mode 100755 examples/fluA/clean create mode 100644 examples/fluA/fluA.trees delete mode 100755 src/GTR-coalescent.stan delete mode 100644 src/GTR-uniform.stan delete mode 100755 src/HKY-coalescent.stan delete mode 100644 src/JC69-GTR.stan delete mode 100644 src/JC69-HKY-GTR.stan delete mode 100755 src/JC69-coalescent.stan delete mode 100644 src/JC69-mixture.stan delete mode 100644 src/JC69-mixture2.stan delete mode 100755 src/JC69-uniform.stan delete mode 100755 src/K80-coalescent.stan diff --git a/examples/fluA/.Rhistory b/examples/fluA/.Rhistory new file mode 100644 index 0000000..0de97cd --- /dev/null +++ b/examples/fluA/.Rhistory @@ -0,0 +1,512 @@ +} +# mm <- .7 +# dd <- .2 +# pars <- elicit_beta_median_iq(m = mm, d = dd) +# qbeta(.5, shape1 = pars$a, shape2 = pars$b) +# qbeta(.9, shape1 = pars$a, shape2 = pars$b) +# curve(dbeta(x,shape1 = pars$a, shape2 = pars$b), lwd = 2) +get_parameter_vectors_median_iq <- function(iq_correct, +iq_wrong = c(.15, .25, .35, .45) ){ +pars_0 <- elicit_beta_median_iq(m = .5, iq = iq_wrong[1]) +pars_1 <- elicit_beta_mean_cv(m0 = .5, iq = iq_wrong[2]) +pars_2 <- elicit_beta_mean_cv(m0 = .5, iq = iq_correct) # big shot +pars_3 <- elicit_beta_mean_cv(m0 = .5, iq = iq_wrong[3]) +pars_4 <- elicit_beta_mean_cv(m0 = .5, iq = iq_wrong[4]) +av <- unlist( c(pars_0[1], pars_1[1], pars_2[1], pars_3[1], pars_4[1]) ) +bv <- unlist( c(pars_0[2], pars_1[2], pars_2[2], pars_3[2], pars_4[2]) ) +return(list( +av = as.numeric(av), +bv = as.numeric(bv) +)) +} +get_parameter_vectors_median_iq(iq_correct = .1) +## Here is a simple method-of-moments based elicitation procedure for the Beta distribution. +## This function will take either +## (i) prior mean and variance m_0 and v_0, respectively, or; +## (ii) prior mean and coefficient of variation m_0 and c, respectively. +elicit_beta_mean_cv <- function(m0, v0 = NULL, cv = 1){ +if(!is.null(v0)){ +a <- -(m0*v0 + m0^3 - m0^2)/v0 +b <- ((m0-1)*v0 + m0^3 - 2*m0^2 + m0)/v0 +}else{ +a <- -(m0*(cv*m0)^2 + m0^3 - m0^2)/(cv*m0)^2 +b <- ((m0-1)*(cv*m0)^2 + m0^3 - 2*m0^2 + m0)/(cv*m0)^2 +} +if(a < 0 || b <0) warning("Warning: at least one of the obtained parameters is not valid") +return(list(a = a, b = b)) +} +## +# Testing +# m <- .15 +# v <- 0.019 +# c0 <- 2 +# elicit_beta_mean_cv(m0 = m, v0 = v) +# elicit_beta_mean_cv(m0 = m, cv = c0) +get_parameter_vectors_mean_cv <- function(cv_correct, cv_wrong = .1){ +pars_0 <- elicit_beta_mean_cv(m0 = .1, cv = cv_wrong) +pars_1 <- elicit_beta_mean_cv(m0 = .2, cv = cv_wrong) +pars_2 <- elicit_beta_mean_cv(m0 = .5, cv = cv_correct) # big shot +pars_3 <- elicit_beta_mean_cv(m0 = .8, cv = cv_wrong) +pars_4 <- elicit_beta_mean_cv(m0 = .9, cv = cv_wrong) +av <- unlist( c(pars_0[1], pars_1[1], pars_2[1], pars_3[1], pars_4[1]) ) +bv <- unlist( c(pars_0[2], pars_1[2], pars_2[2], pars_3[2], pars_4[2]) ) +return(list( +av = as.numeric(av), +bv = as.numeric(bv) +)) +} +# +elicit_beta_median_iq <- function(m, d, q = .90){ +u <- m + d +loss <- function(x){ +a <- x[1] +b <- x[2] +m.hat <- qbeta(.5, shape1 = a, shape2 = b) +u.hat <- qbeta(q, shape1 = a, shape2 = b) +error <- .5 * (m.hat - m)^2 + .5*(u.hat-u)^2 +return(error) +} +opt <- suppressWarnings( optim(loss, par = c(1, 1)) ) +a <- opt$par[1] +b <- opt$par[2] +if(a < 0 || b <0) warning("Warning: at least one of the obtained parameters is not valid") +return(list(a = a, b = b)) +} +# mm <- .7 +# dd <- .2 +# pars <- elicit_beta_median_iq(m = mm, d = dd) +# qbeta(.5, shape1 = pars$a, shape2 = pars$b) +# qbeta(.9, shape1 = pars$a, shape2 = pars$b) +# curve(dbeta(x,shape1 = pars$a, shape2 = pars$b), lwd = 2) +get_parameter_vectors_median_iq <- function(iq_correct, +iq_wrong = c(.15, .25, .35, .45) ){ +pars_0 <- elicit_beta_median_iq(m = .5, q = iq_wrong[1]) +pars_1 <- elicit_beta_median_iq(m = .5, q = iq_wrong[2]) +pars_2 <- elicit_beta_median_iq(m = .5, q = iq_correct) # big shot +pars_3 <- elicit_beta_median_iq(m = .5, q = iq_wrong[3]) +pars_4 <- elicit_beta_median_iq(m = .5, q = iq_wrong[4]) +av <- unlist( c(pars_0[1], pars_1[1], pars_2[1], pars_3[1], pars_4[1]) ) +bv <- unlist( c(pars_0[2], pars_1[2], pars_2[2], pars_3[2], pars_4[2]) ) +return(list( +av = as.numeric(av), +bv = as.numeric(bv) +)) +} +# +plot_densities <- function(pars){ +av <- pars$av +bv <- pars$bv +K <- length(av) +curve(dbeta(x, av[1], bv[1]), lwd = 2) +for(k in 2:K){ +curve(dbeta(x, av[k], bv[k]), lwd = 2, col = k, add = TRUE) +} +} +get_parameter_vectors_median_iq(iq_correct = .1) +get_parameter_vectors_median_iq <- function(iq_correct, +iq_wrong = c(.15, .25, .35, .45) ){ +pars_0 <- elicit_beta_median_iq(m = .5, d = iq_wrong[1]) +pars_1 <- elicit_beta_median_iq(m = .5, d = iq_wrong[2]) +pars_2 <- elicit_beta_median_iq(m = .5, d = iq_correct) # big shot +pars_3 <- elicit_beta_median_iq(m = .5, d = iq_wrong[3]) +pars_4 <- elicit_beta_median_iq(m = .5, d = iq_wrong[4]) +av <- unlist( c(pars_0[1], pars_1[1], pars_2[1], pars_3[1], pars_4[1]) ) +bv <- unlist( c(pars_0[2], pars_1[2], pars_2[2], pars_3[2], pars_4[2]) ) +return(list( +av = as.numeric(av), +bv = as.numeric(bv) +)) +} +# +plot_densities <- function(pars){ +av <- pars$av +bv <- pars$bv +K <- length(av) +curve(dbeta(x, av[1], bv[1]), lwd = 2) +for(k in 2:K){ +curve(dbeta(x, av[k], bv[k]), lwd = 2, col = k, add = TRUE) +} +} +get_parameter_vectors_median_iq(iq_correct = .1) +plot_densities(get_parameter_vectors_median_iq(iq_correct = .1)) +get_parameter_vectors_median_iq <- function(iq_correct, +iq_wrong = c(.1, .15, .25, .35) ){ +pars_0 <- elicit_beta_median_iq(m = .5, d = iq_wrong[1]) +pars_1 <- elicit_beta_median_iq(m = .5, d = iq_wrong[2]) +pars_2 <- elicit_beta_median_iq(m = .5, d = iq_correct) # big shot +pars_3 <- elicit_beta_median_iq(m = .5, d = iq_wrong[3]) +pars_4 <- elicit_beta_median_iq(m = .5, d = iq_wrong[4]) +av <- unlist( c(pars_0[1], pars_1[1], pars_2[1], pars_3[1], pars_4[1]) ) +bv <- unlist( c(pars_0[2], pars_1[2], pars_2[2], pars_3[2], pars_4[2]) ) +return(list( +av = as.numeric(av), +bv = as.numeric(bv) +)) +} +plot_densities(get_parameter_vectors_median_iq(iq_correct = .05)) +get_parameter_vectors_median_iq(iq_correct = .05) +elicit_beta_median_iq <- function(m, d, q = .90){ +u <- m + d +loss <- function(x){ +a <- x[1] +b <- x[2] +m.hat <- qbeta(.5, shape1 = a, shape2 = b) +u.hat <- qbeta(q, shape1 = a, shape2 = b) +error <- .5 * (m.hat - m)^2 + .5*(u.hat-u)^2 +return(error) +} +opt <- suppressWarnings( optim(loss, par = c(1, 1), lower = c(0, 0)) ) +a <- opt$par[1] +b <- opt$par[2] +if(a < 0 || b <0) warning("Warning: at least one of the obtained parameters is not valid") +return(list(a = a, b = b)) +} +# mm <- .7 +# dd <- .2 +# pars <- elicit_beta_median_iq(m = mm, d = dd) +# qbeta(.5, shape1 = pars$a, shape2 = pars$b) +# qbeta(.9, shape1 = pars$a, shape2 = pars$b) +# curve(dbeta(x,shape1 = pars$a, shape2 = pars$b), lwd = 2) +get_parameter_vectors_median_iq <- function(iq_correct, +iq_wrong = c(.1, .15, .25, .35) ){ +pars_0 <- elicit_beta_median_iq(m = .5, d = iq_wrong[1]) +pars_1 <- elicit_beta_median_iq(m = .5, d = iq_wrong[2]) +pars_2 <- elicit_beta_median_iq(m = .5, d = iq_correct) # big shot +pars_3 <- elicit_beta_median_iq(m = .5, d = iq_wrong[3]) +pars_4 <- elicit_beta_median_iq(m = .5, d = iq_wrong[4]) +av <- unlist( c(pars_0[1], pars_1[1], pars_2[1], pars_3[1], pars_4[1]) ) +bv <- unlist( c(pars_0[2], pars_1[2], pars_2[2], pars_3[2], pars_4[2]) ) +return(list( +av = as.numeric(av), +bv = as.numeric(bv) +)) +} +# +plot_densities <- function(pars){ +av <- pars$av +bv <- pars$bv +K <- length(av) +curve(dbeta(x, av[1], bv[1]), lwd = 2) +for(k in 2:K){ +curve(dbeta(x, av[k], bv[k]), lwd = 2, col = k, add = TRUE) +} +} +get_parameter_vectors_median_iq <- function(iq_correct, +iq_wrong = c(.0125, .025, .05, .1) ){ +pars_0 <- elicit_beta_median_iq(m = .5, d = iq_wrong[1]) +pars_1 <- elicit_beta_median_iq(m = .5, d = iq_wrong[2]) +pars_2 <- elicit_beta_median_iq(m = .5, d = iq_correct) # big shot +pars_3 <- elicit_beta_median_iq(m = .5, d = iq_wrong[3]) +pars_4 <- elicit_beta_median_iq(m = .5, d = iq_wrong[4]) +av <- unlist( c(pars_0[1], pars_1[1], pars_2[1], pars_3[1], pars_4[1]) ) +bv <- unlist( c(pars_0[2], pars_1[2], pars_2[2], pars_3[2], pars_4[2]) ) +return(list( +av = as.numeric(av), +bv = as.numeric(bv) +)) +} +# +plot_densities <- function(pars){ +av <- pars$av +bv <- pars$bv +K <- length(av) +curve(dbeta(x, av[1], bv[1]), lwd = 2) +for(k in 2:K){ +curve(dbeta(x, av[k], bv[k]), lwd = 2, col = k, add = TRUE) +} +} +get_parameter_vectors_median_iq(iq_correct = .005) +plot_densities(get_parameter_vectors_median_iq(iq_correct = .005)) +get_parameter_vectors_median_iq <- function(med = 0.5, +iq_correct, +iq_wrong = c(.0125, .025, .05, .1) ){ +pars_0 <- elicit_beta_median_iq(m = med, d = iq_wrong[1]) +pars_1 <- elicit_beta_median_iq(m = med, d = iq_wrong[2]) +pars_2 <- elicit_beta_median_iq(m = med, d = iq_correct) # big shot +pars_3 <- elicit_beta_median_iq(m = med, d = iq_wrong[3]) +pars_4 <- elicit_beta_median_iq(m = med, d = iq_wrong[4]) +av <- unlist( c(pars_0[1], pars_1[1], pars_2[1], pars_3[1], pars_4[1]) ) +bv <- unlist( c(pars_0[2], pars_1[2], pars_2[2], pars_3[2], pars_4[2]) ) +return(list( +av = as.numeric(av), +bv = as.numeric(bv) +)) +} +# +plot_densities <- function(pars){ +av <- pars$av +bv <- pars$bv +K <- length(av) +curve(dbeta(x, av[1], bv[1]), lwd = 2) +for(k in 2:K){ +curve(dbeta(x, av[k], bv[k]), lwd = 2, col = k, add = TRUE) +} +} +plot_densities(get_parameter_vectors_median_iq(iq_correct = .005)) +plot_densities(get_parameter_vectors_median_iq(iq_correct = .005, med = .8)) +plot_densities(get_parameter_vectors_median_iq(iq_correct = .005, med = .7)) +plot_densities(get_parameter_vectors_median_iq(iq_correct = .15, med = .7)) +plot_densities <- function(pars, lg = TRUE){ +av <- pars$av +bv <- pars$bv +K <- length(av) +curve(dbeta(x, av[1], bv[1]), lwd = 2) +for(k in 2:K){ +curve(dbeta(x, av[k], bv[k]), lwd = 2, col = k, add = TRUE) +} +if(lg){ +legend(x = "top", col = 1:K, lwd = 2, lty = 1, bty = 'n', legend = paste("Expert_", 1:K, sep = "") ) +} +} +plot_densities(get_parameter_vectors_median_iq(iq_correct = .15, med = .7)) +plot_densities <- function(pars, lg = TRUE){ +av <- pars$av +bv <- pars$bv +K <- length(av) +curve(dbeta(x, av[1], bv[1]), lwd = 2) +for(k in 2:K){ +curve(dbeta(x, av[k], bv[k]), lwd = 2, col = k, add = TRUE) +} +if(lg){ +legend(x = "top", col = 1:K, lwd = 2, lty = 1, bty = 'n', legend = paste("Expert_", (1:K)-1, sep = "") ) +} +} +plot_densities(get_parameter_vectors_median_iq(iq_correct = .15, med = .7)) +plot_densities(get_parameter_vectors_median_iq(iq_correct = .25, med = .7)) +mm <- .7 +dd <- .25 +pars <- elicit_beta_median_iq(m = mm, d = dd) +qbeta(.5, shape1 = pars$a, shape2 = pars$b) +qbeta(.9, shape1 = pars$a, shape2 = pars$b) +curve(dbeta(x,shape1 = pars$a, shape2 = pars$b), lwd = 2) +plot_densities(get_parameter_vectors_median_iq(iq_correct = .25, med = .3)) +get_parameter_vectors_median_iq(iq_correct = .25, med = .3) +elicit_beta_median_iq <- function(m, d, q = .90){ +u <- m + d +loss <- function(x){ +a <- x[1] +b <- x[2] +m.hat <- qbeta(.5, shape1 = a, shape2 = b) +u.hat <- qbeta(q, shape1 = a, shape2 = b) +error <- .5 * (m.hat - m)^2 + .5*(u.hat-u)^2 +return(error) +} +opt <- suppressWarnings( optim(loss, par = c(1, 1), lower = c(1E-3, 1E-3)) ) +a <- opt$par[1] +b <- opt$par[2] +if(a < 0 || b <0) warning("Warning: at least one of the obtained parameters is not valid") +return(list(a = a, b = b)) +} +# mm <- .7 +# dd <- .25 +# pars <- elicit_beta_median_iq(m = mm, d = dd) +# qbeta(.5, shape1 = pars$a, shape2 = pars$b) +# qbeta(.9, shape1 = pars$a, shape2 = pars$b) +# curve(dbeta(x,shape1 = pars$a, shape2 = pars$b), lwd = 2) +get_parameter_vectors_median_iq <- function(med = 0.5, +iq_correct, +iq_wrong = c(.0125, .025, .05, .1) ){ +pars_0 <- elicit_beta_median_iq(m = med, d = iq_wrong[1]) +pars_1 <- elicit_beta_median_iq(m = med, d = iq_wrong[2]) +pars_2 <- elicit_beta_median_iq(m = med, d = iq_correct) # big shot +pars_3 <- elicit_beta_median_iq(m = med, d = iq_wrong[3]) +pars_4 <- elicit_beta_median_iq(m = med, d = iq_wrong[4]) +av <- unlist( c(pars_0[1], pars_1[1], pars_2[1], pars_3[1], pars_4[1]) ) +bv <- unlist( c(pars_0[2], pars_1[2], pars_2[2], pars_3[2], pars_4[2]) ) +return(list( +av = as.numeric(av), +bv = as.numeric(bv) +)) +} +# +plot_densities <- function(pars, lg = TRUE){ +av <- pars$av +bv <- pars$bv +K <- length(av) +curve(dbeta(x, av[1], bv[1]), lwd = 2) +for(k in 2:K){ +curve(dbeta(x, av[k], bv[k]), lwd = 2, col = k, add = TRUE) +} +if(lg){ +legend(x = "top", col = 1:K, lwd = 2, lty = 1, bty = 'n', legend = paste("Expert_", (1:K)-1, sep = "") ) +} +} +get_parameter_vectors_median_iq(iq_correct = .25, med = .3) +plot_densities(get_parameter_vectors_median_iq(iq_correct = .25, med = .3)) +plot_densities(get_parameter_vectors_median_iq(iq_correct = .2, med = .3)) +plot_densities(get_parameter_vectors_median_iq(iq_correct = .12, med = .3)) +get_parameter_vectors_median_iq(iq_correct = .25, med = .3) +get_parameter_vectors_median_iq(iq_correct = .12, med = .3) +get_parameter_vectors_median_iq(iq_correct = .12, med = .4) +plot_densities(get_parameter_vectors_median_iq(iq_correct = .12, med = .4)) +plot_densities(get_parameter_vectors_median_iq(iq_correct = .2, med = .4)) +get_parameter_vectors_median_iq(iq_correct = .2, med = .4) +rank(1:5) +rank(1:5)[2] +get_parameter_vectors_median_iq(iq_correct = .4, med = .4) +plot(get_parameter_vectors_median_iq(iq_correct = .4, med = .4)) +plot_densities(get_parameter_vectors_median_iq(iq_correct = .4, med = .4)) +rstan:::rstudio_stanc("DUMP/phylostan/examples/fluA/fluA-GTR-W4_InvGamma.stan") +rstan:::rstudio_stanc("DUMP/phylostan/examples/fluA/integrated_prior.stan") +rstan:::rstudio_stanc("DUMP/phylostan/examples/fluA/integrated_prior.stan") +rstan:::rstudio_stanc("DUMP/phylostan/examples/fluA/integrated_prior.stan") +rstan:::rstudio_stanc("DUMP/phylostan/examples/fluA/integrated_prior.stan") +rstan:::rstudio_stanc("DUMP/phylostan/examples/fluA/integrated_prior.stan") +rstan:::rstudio_stanc("DUMP/phylostan/examples/fluA/integrated_prior.stan") +setwd("~/DUMP/phylostan/examples/fluA") +library(rstan) +rstan_options(auto_write = TRUE) +options(mc.cores = 4) +compiled.model <- stan_model("integrated_prior.stan") +expose_stan_functions(compiled.model) +integrated_density(t = 0, choose(5, 2), u = 1000) +integrated_density(t = 2, choose(5, 2), u = 1000) +integrated_density(t = 2, choose(5, 2), u = 10) +integrated_density(t = .2, choose(5, 2), u = 1000) +integrated_density(t = .2, kappa = choose(5, 2), u = 1000) +u <- 1000 +kappa <- choose(10, 2) +kappa <- choose(5, 2) +t <- 2 +square <- function(x) x*x +2 *square(u + kappa * t) + 4*kappa*t*u + 3*square(kappa*t) - 3*log(kappa*t) * square(u + kappa * t) - 3 * square(u + kappa*t); +Sum = 2 *square(u + kappa * t) + 4*kappa*t*u + 3*square(kappa*t) - 3*log(kappa*t) * square(u + kappa * t) - 3 * square(u + kappa*t); +k <- 2 +# ff <- function(time, n, theta){ +# delta <- choose(n, 2)* time +# return(theta^-2 * exp(-delta/theta)) +# } +# +# integrate(function(x) ff(time = tk, n = k, theta = x), 0, Inf) ## confirming +# 1/(choose(k, 2)*tk) +############### +# alpha <- 1.2 +# beta <- 2 +# ff <- function(time, n, theta){ +# delta <- choose(n, 2)* time +# return(theta^-1 * exp(-delta/theta) * MCMCpack::dinvgamma(theta, shape = alpha, scale = beta)) +# } +# tk <- 1.5 +# integrate(function(x) ff(time = tk, n = k, theta = x), 0, Inf) ## confirming +# (alpha * beta^alpha)/(choose(k, 2)*tk + beta)^{alpha + 1} ## correct +################ +marginal_Jeffreys <- function(tt, n){ +2/(n*(n-1)*tt) +} +marginal_Jeffreys <- Vectorize(marginal_Jeffreys) +### +marginal_invgamma <- function(tt, n, a, b){ +choose(n, 2)*(a * b^a)/(choose(n, 2)*tt + b)^{a + 1} +} +marginal_invgamma <- Vectorize(marginal_invgamma) +### +marginal_lognormal <- function(tt, n, mu0 = 0, sd0 = 1){ +fn <- function(time, theta, log = FALSE){ +delta <- choose(n, 2)* time +dens <- -log(theta) -delta/theta + dlnorm(x = theta, mu0, sd0, log = TRUE) +if(!log) dens <- exp(dens) +return(dens) +} +integrate(function(x) fn(time = tt, theta = x), 0, Inf)$value +} +marginal_lognormal <- Vectorize(marginal_lognormal) +marginal_lognormal_normalised <- function(tt, n, mu0 = 0, sd0 = 1){ +norm_const <- integrate(function(x) marginal_lognormal(x, n, mu0, sd0), +0, Inf)$value +ans <- marginal_lognormal(tt, n, mu0, sd0) +return(ans/norm_const) +} +marginal_lognormal_normalised <- Vectorize(marginal_lognormal_normalised) +################# +################# +curve(marginal_Jeffreys(x, n = k), 0, 50, +main = paste("k =", k), +lwd = 2, xlab = expression(t[k]), ylab = "Density") +curve(marginal_invgamma(x, n = k, a = 1.2, b = 2), col = 3, add = TRUE) +curve(marginal_lognormal_normalised(x, n = k, mu0 = -0.004975165, sd0 = 2.14823), +0, 50, add = TRUE, col = 2, lty = 2, lwd = 2)## mean Ne = 10, sd = 100 +int_density <- function(t, kappa, u, log = FALSE){ +z <- kappa*t +w <- square(z + u) +lnum <- log( +2*w*log(u + z) + 3*square(z) + 4*u*z - w*(2*log(z) + 3) +) +ldenom <- log(2) + log(w) +ans <- log(2) + log(kappa) + lnum - ldenom +if(!log) ans <- exp(ans) +return(ans) +} +int_density(t= 2, kappa = choose(5, 2), u = 1000) +square <- function(x) x*x +int_density <- function(t, kappa, u, log = FALSE){ +z <- kappa*t +w <- square(z + u) +lnum <- log( +2*w*log(u + z) + 3*square(z) + 4*u*z - w*(2*log(z) + 3) +) +ldenom <- log(2) + log(w) +ans <- log(2) + log(kappa) + lnum - ldenom +if(!log) ans <- exp(ans) +return(ans) +} +int_density(t= 2, kappa = choose(5, 2), u = 1000) +int_density <- Vectorize(int_density) +int_density(t= 2, kappa = choose(5, 2), u = 1000) +curve(int_density(x, kappa = choose(5, 2), u = 1000), 0, 1000) +integrate(int_density(x, kappa = choose(5, 2), u = 1000), 0, Inf) +integrate(function(x) int_density(x, kappa = choose(5, 2), u = 1000), 0, Inf) +choose(5, 2) +square <- function(x) x*x +int_density <- function(t, kappa, u, log = FALSE){ +z <- kappa*t +w <- square(z + u) +lnum <- log( +2*w*log(u + z) + 3*square(z) + 4*u*z - w*(2*log(z) + 3) +) +ldenom <- log(2) + log(w) +ans <- log(2) + log(kappa) + lnum - ldenom +if(!log) ans <- exp(ans) +return(ans) +} +int_density <- Vectorize(int_density) +int_density(t = 2, kappa = choose(5, 2), u = 1000) +curve(int_density(x, kappa = choose(5, 2), u = 1000), 0, 1000) +integrate(function(x) int_density(x, kappa = choose(5, 2), u = 1000), 0, Inf) +integrate(function(x) int_density(x, kappa = choose(5, 2), u = 10), 0, Inf) +square <- function(x) x*x +int_density <- function(t, kappa, u, log = FALSE){ +z <- kappa*t +w <- square(z + u) +lnum <- log( +2*w*log(u + z) + 3*square(z) + 4*u*z - w*(2*log(z) + 3) +) +ldenom <- log(2) + log(w) +ans <- log(2) + log(kappa) + lnum - ldenom -log(u) +if(!log) ans <- exp(ans) +return(ans) +} +int_density <- Vectorize(int_density) +int_density(t = 2, kappa = choose(5, 2), u = 1000) +curve(int_density(x, kappa = choose(5, 2), u = 1000), 0, 1000) +integrate(function(x) int_density(x, kappa = choose(5, 2), u = 10), 0, Inf) +library(rstan) +rstan_options(auto_write = TRUE) +options(mc.cores = 4) +compiled.model <- stan_model("integrated_prior.stan") +expose_stan_functions(compiled.model) +integrated_density(t = 0, kappa = choose(5, 2), u = 1000) +integrated_density(t = 1, kappa = choose(5, 2), u = 1000) +integrated_density(t = 10, kappa = choose(5, 2), u = 1000) +integrated_density(t = 100, kappa = choose(5, 2), u = 1000) +curve(integrated_density(t = x, kappa = choose(5, 2), u = 1000), 0, 1000) +curve(function(x) integrated_density(t = x, kappa = choose(5, 2), u = 1000), 0, 1000) +curve(fn, 0, 1000) +fn <- function(x) integrated_density(t = x, kappa = choose(5, 2), u = 1000); fn <- Vectorize(fn) +curve(fn, 0, 1000) +lfn <- function(x) integrated_density(t = x, kappa = choose(5, 2), u = 1000); fn <- Vectorize(fn) +fn <- function(x) exp(lfn(x)); fn <- Vectorize(fn) +fn <- function(x) exp(lfn(x)); fn <- Vectorize(fn) +integrate(fn, 0, Inf) +rstan:::rstudio_stanc("~/DUMP/phylostan/examples/fluA/fluA-GTR-W4.stan") +rstan:::rstudio_stanc("~/DUMP/phylostan/examples/fluA/fluA-GTR-W4.stan") +rstan:::rstudio_stanc("~/DUMP/phylostan/examples/fluA/fluA-GTR-W4.stan") diff --git a/examples/fluA/clean b/examples/fluA/clean new file mode 100755 index 0000000..43fdcad --- /dev/null +++ b/examples/fluA/clean @@ -0,0 +1 @@ +rm *.pkl fluA *.diag diff --git a/examples/fluA/fluA.trees b/examples/fluA/fluA.trees new file mode 100644 index 0000000..2126b40 --- /dev/null +++ b/examples/fluA/fluA.trees @@ -0,0 +1,1075 @@ +#NEXUS +Begin trees; +Translate +1 A_Belgium_2_1981, +2 A_ChristHospital_231_1982, +3 A_Baylor1B_1983, +4 A_Texas_17988_1984, +5 A_Caen_1_1984, +6 A_Oita_3_1983, +7 A_Alaska_8_1984, +8 A_Texas_12764_1983, +9 A_Wellington_4_1985, +10 A_Tonga_23_1985, +11 A_Qingdao_10_1987, +12 A_Guizhou_1_1987, +13 A_Sydney_1_1987, +14 A_Tokyo_1275_1987, +15 A_LosAngeles_1987, +16 A_Guangdong_9_1987, +17 A_Sichuan_2_1987, +18 A_Victoria_7_1987, +19 A_Perth_1_1992, +20 A_Tianjin_33_1992, +21 A_Sapporo_304_1992, +22 A_Argentina_3779_1994, +23 A_Johannesburg_33_1994, +24 A_England_67_1994, +25 A_HongKong_1_1994, +26 A_Pennsylvania_7_1994, +27 A_Switzerland_7729_1998, +28 A_Neuquen_V541_1998, +29 A_JOHANNESBURG_3_1998, +30 A_Seoul_37_1998, +31 A_PERTH_24_1998, +32 A_MALMO_1_1998, +33 A_Greece_103_1998, +34 A_Tucuman_V425_1998, +35 A_Cordoba_V185_1998, +36 A_Waikato_12_1998, +37 A_Christchurch_45_1998, +38 A_Ushuaia_R127_1998, +39 A_Nagasaki_76_1998, +40 A_Pusan_68_1998, +41 A_Athens_1_1998, +42 A_Aichi_69_1994, +43 A_Shangdong_5_1994, +44 A_Santiago_7198_1994, +45 A_Romania_160_1994, +46 A_Vermont_3_1994, +47 A_Akita_1_1994, +48 A_Singapore_7_1994, +49 A_Thailand_75_1994, +50 A_Harbin_15_1992, +51 A_France_1109_1994, +52 A_California_271_1992, +53 A_Qingdao_53_1992, +54 A_Hawaii_3_1992, +55 A_Alaska_9_1992, +56 A_Beijing_32_1992, +57 A_Umea_1_1992, +58 A_Indonesia_3946_1992, +59 A_Victoria_29_1992, +60 A_Wellington_66_1992, +61 A_Mexico_3255_1994, +62 A_Finland_205_1992, +63 A_SouthAustralia_36_1992, +64 A_Shanghai_11_1987, +65 A_Colorado_2_1987, +66 A_Memphis_6_1986, +67 A_Czechoslovakia_4_1986, +68 A_Leningrad_360_1986, +69 A_Philippines_2_1982 +; +tree 1 = ((1[&height=17.0,rate=0.0035648]:1.8452,(2[&height=16.0,rate=0.0035648]:1.8994,4[&height=15.0,rate=0.0035648]:2.8994)[&height=17.8994,rate=0.0035648]:0.9458)[&height=18.8452,rate=0.0035648]:1.4708,(((9[&height=14.0,rate=0.0035648]:2.1781,(8[&height=14.0,rate=0.0035648]:1.4365,5[&height=15.0,rate=0.0035648]:0.4365)[&height=15.4365,rate=0.0035648]:0.7416)[&height=16.1781,rate=0.0035648]:0.2602,(7[&height=14.0,rate=0.0035648]:1.9892,(6[&height=15.0,rate=0.0035648]:0.4865,((68[&height=13.0,rate=0.0035648]:1.0566,69[&height=13.0,rate=0.0035648]:1.0566)[&height=14.0566,rate=0.0035648]:0.2731,((((14[&height=11.0,rate=0.0035648]:0.9712,12[&height=11.0,rate=0.0035648]:0.9712)[&height=11.9712,rate=0.0035648]:0.2189,(17[&height=11.0,rate=0.0035648]:0.7648,18[&height=11.0,rate=0.0035648]:0.7648)[&height=11.7648,rate=0.0035648]:0.4253)[&height=12.1901,rate=0.0035648]:0.2786,((((13[&height=11.0,rate=0.0035648]:0.6232,(11[&height=11.0,rate=0.0035648]:0.1508,16[&height=11.0,rate=0.0035648]:0.1508)[&height=11.1508,rate=0.0035648]:0.4724)[&height=11.6232,rate=0.0035648]:0.3546,(19[&height=11.0,rate=0.0035648]:0.7383,((27[&height=6.0,rate=0.0035648]:3.18379,((31[&height=6.0,rate=0.0035648]:1.95881,(29[&height=6.0,rate=0.0035648]:1.60454,((((37[&height=4.0,rate=0.0035648]:1.35417,41[&height=4.0,rate=0.0035648]:1.35417)[&height=5.35417,rate=0.0035648]:0.26695,((38[&height=4.0,rate=0.0035648]:1.28745,40[&height=4.0,rate=0.0035648]:1.28745)[&height=5.28745,rate=0.0035648]:0.1134,43[&height=4.0,rate=0.0035648]:1.40085)[&height=5.40085,rate=0.0035648]:0.22027)[&height=5.62112,rate=0.0035648]:1.53785,(((((((61[&height=0.0,rate=0.0035648]:1.06548,((57[&height=0.0,rate=0.0035648]:0.682901,(54[&height=0.0,rate=0.0035648]:0.417271,60[&height=0.0,rate=0.0035648]:0.417271)[&height=0.417271,rate=0.0035648]:0.26563)[&height=0.682901,rate=0.0035648]:0.260523,58[&height=0.0,rate=0.0035648]:0.943424)[&height=0.943424,rate=0.0035648]:0.122056)[&height=1.06548,rate=0.0035648]:0.38397,55[&height=0.0,rate=0.0035648]:1.44945)[&height=1.44945,rate=0.0035648]:0.1704,53[&height=0.0,rate=0.0035648]:1.61985)[&height=1.61985,rate=0.0035648]:0.06105,(((62[&height=0.0,rate=0.0035648]:0.904506,52[&height=0.0,rate=0.0035648]:0.904506)[&height=0.904506,rate=0.0035648]:0.335844,(((64[&height=0.0,rate=0.0035648]:0.199891,51[&height=0.0,rate=0.0035648]:0.199891)[&height=0.199891,rate=0.0035648]:0.60556,63[&height=0.0,rate=0.0035648]:0.805451)[&height=0.805451,rate=0.0035648]:0.287289,56[&height=0.0,rate=0.0035648]:1.09274)[&height=1.09274,rate=0.0035648]:0.14761)[&height=1.24035,rate=0.0035648]:0.15287,59[&height=0.0,rate=0.0035648]:1.39322)[&height=1.39322,rate=0.0035648]:0.28768)[&height=1.6809,rate=0.0035648]:0.93153,50[&height=0.0,rate=0.0035648]:2.61243)[&height=2.61243,rate=0.0035648]:2.90405,(35[&height=4.0,rate=0.0035648]:1.38311,46[&height=4.0,rate=0.0035648]:1.38311)[&height=5.38311,rate=0.0035648]:0.13337)[&height=5.51648,rate=0.0035648]:1.57739,((45[&height=4.0,rate=0.0035648]:1.7916,(44[&height=4.0,rate=0.0035648]:1.49306,(49[&height=4.0,rate=0.0035648]:1.11344,36[&height=4.0,rate=0.0035648]:1.11344)[&height=5.11344,rate=0.0035648]:0.37962)[&height=5.49306,rate=0.0035648]:0.29854)[&height=5.7916,rate=0.0035648]:1.17486,(47[&height=4.0,rate=0.0035648]:1.50888,48[&height=4.0,rate=0.0035648]:1.50888)[&height=5.50888,rate=0.0035648]:1.45758)[&height=6.96646,rate=0.0035648]:0.12741)[&height=7.09387,rate=0.0035648]:0.0651)[&height=7.15897,rate=0.0035648]:0.28758,24[&height=6.0,rate=0.0035648]:1.44655)[&height=7.44655,rate=0.0035648]:0.15799)[&height=7.60454,rate=0.0035648]:0.35427)[&height=7.95881,rate=0.0035648]:0.08838,(((39[&height=4.0,rate=0.0035648]:3.01242,22[&height=6.0,rate=0.0035648]:1.01242)[&height=7.01242,rate=0.0035648]:0.48782,(28[&height=6.0,rate=0.0035648]:1.32075,(25[&height=6.0,rate=0.0035648]:1.12612,20[&height=6.0,rate=0.0035648]:1.12612)[&height=7.12612,rate=0.0035648]:0.19463)[&height=7.32075,rate=0.0035648]:0.17949)[&height=7.50024,rate=0.0035648]:0.36768,21[&height=6.0,rate=0.0035648]:1.86792)[&height=7.86792,rate=0.0035648]:0.17927)[&height=8.04719,rate=0.0035648]:1.1366)[&height=9.18379,rate=0.0035648]:0.76883,(((32[&height=6.0,rate=0.0035648]:0.64126,26[&height=6.0,rate=0.0035648]:0.64126)[&height=6.64126,rate=0.0035648]:0.3249,(33[&height=6.0,rate=0.0035648]:0.63583,34[&height=6.0,rate=0.0035648]:0.63583)[&height=6.63583,rate=0.0035648]:0.33033)[&height=6.96616,rate=0.0035648]:1.89046,((42[&height=4.0,rate=0.0035648]:2.53621,23[&height=6.0,rate=0.0035648]:0.53621)[&height=6.53621,rate=0.0035648]:0.41549,30[&height=6.0,rate=0.0035648]:0.9517)[&height=6.9517,rate=0.0035648]:1.90492)[&height=8.85662,rate=0.0035648]:1.096)[&height=9.95262,rate=0.0035648]:1.78568)[&height=11.7383,rate=0.0035648]:0.2395)[&height=11.9778,rate=0.0035648]:0.0879,15[&height=11.0,rate=0.0035648]:1.0657)[&height=12.0657,rate=0.0035648]:0.1904,10[&height=11.0,rate=0.0035648]:1.2561)[&height=12.2561,rate=0.0035648]:0.2126)[&height=12.4687,rate=0.0035648]:1.6011,((67[&height=12.0,rate=0.0035648]:0.9109,65[&height=12.0,rate=0.0035648]:0.9109)[&height=12.9109,rate=0.0035648]:0.3685,66[&height=12.0,rate=0.0035648]:1.2794)[&height=13.2794,rate=0.0035648]:0.7904)[&height=14.0698,rate=0.0035648]:0.2599)[&height=14.3297,rate=0.0035648]:1.1568)[&height=15.4865,rate=0.0035648]:0.5027)[&height=15.9892,rate=0.0035648]:0.4491)[&height=16.4383,rate=0.0035648]:1.6305,3[&height=16.0,rate=0.0035648]:2.0688)[&height=18.0688,rate=0.0035648]:2.2472)[&height=20.316]; +tree 2 = ((1[&height=17.0,rate=0.00388474]:1.8212,(2[&height=16.0,rate=0.00388474]:2.2818,4[&height=15.0,rate=0.00388474]:3.2818)[&height=18.2818,rate=0.00388474]:0.5394)[&height=18.8212,rate=0.00388474]:1.5797,(((9[&height=14.0,rate=0.00388474]:2.0817,(8[&height=14.0,rate=0.00388474]:1.1685,5[&height=15.0,rate=0.00388474]:0.1685)[&height=15.1685,rate=0.00388474]:0.9132)[&height=16.0817,rate=0.00388474]:0.1017,(7[&height=14.0,rate=0.00388474]:1.9184,(6[&height=15.0,rate=0.00388474]:0.4242,((68[&height=13.0,rate=0.00388474]:0.4881,69[&height=13.0,rate=0.00388474]:0.4881)[&height=13.4881,rate=0.00388474]:0.1485,((((14[&height=11.0,rate=0.00388474]:0.6266,12[&height=11.0,rate=0.00388474]:0.6266)[&height=11.6266,rate=0.00388474]:0.0419,(17[&height=11.0,rate=0.00388474]:0.3771,18[&height=11.0,rate=0.00388474]:0.3771)[&height=11.3771,rate=0.00388474]:0.2914)[&height=11.6685,rate=0.00388474]:0.7546,((((13[&height=11.0,rate=0.00388474]:0.6893,(11[&height=11.0,rate=0.00388474]:0.1221,16[&height=11.0,rate=0.00388474]:0.1221)[&height=11.1221,rate=0.00388474]:0.5672)[&height=11.6893,rate=0.00388474]:0.2301,(19[&height=11.0,rate=0.00388474]:0.8274,((27[&height=6.0,rate=0.00388474]:3.30391,((31[&height=6.0,rate=0.00388474]:1.97982,(29[&height=6.0,rate=0.00388474]:1.0997,((((37[&height=4.0,rate=0.00388474]:1.12637,41[&height=4.0,rate=0.00388474]:1.12637)[&height=5.12637,rate=0.00388474]:0.41633,((38[&height=4.0,rate=0.00388474]:1.08232,40[&height=4.0,rate=0.00388474]:1.08232)[&height=5.08232,rate=0.00388474]:0.06676,43[&height=4.0,rate=0.00388474]:1.14908)[&height=5.14908,rate=0.00388474]:0.39362)[&height=5.5427,rate=0.00388474]:1.31469,(((((((61[&height=0.0,rate=0.00388474]:1.83788,((57[&height=0.0,rate=0.00388474]:0.312117,(54[&height=0.0,rate=0.00388474]:0.020817,60[&height=0.0,rate=0.00388474]:0.020817)[&height=0.020817,rate=0.00388474]:0.2913)[&height=0.312117,rate=0.00388474]:1.272543,58[&height=0.0,rate=0.00388474]:1.58466)[&height=1.58466,rate=0.00388474]:0.25322)[&height=1.83788,rate=0.00388474]:0.42911,55[&height=0.0,rate=0.00388474]:2.26699)[&height=2.26699,rate=0.00388474]:0.18497,53[&height=0.0,rate=0.00388474]:2.45196)[&height=2.45196,rate=0.00388474]:0.11572,(((62[&height=0.0,rate=0.00388474]:1.20758,52[&height=0.0,rate=0.00388474]:1.20758)[&height=1.20758,rate=0.00388474]:0.38346,(((64[&height=0.0,rate=0.00388474]:0.387681,51[&height=0.0,rate=0.00388474]:0.387681)[&height=0.387681,rate=0.00388474]:0.456152,63[&height=0.0,rate=0.00388474]:0.843833)[&height=0.843833,rate=0.00388474]:0.304577,56[&height=0.0,rate=0.00388474]:1.14841)[&height=1.14841,rate=0.00388474]:0.44263)[&height=1.59104,rate=0.00388474]:0.0565,59[&height=0.0,rate=0.00388474]:1.64754)[&height=1.64754,rate=0.00388474]:0.92014)[&height=2.56768,rate=0.00388474]:0.91357,50[&height=0.0,rate=0.00388474]:3.48125)[&height=3.48125,rate=0.00388474]:2.48481,(35[&height=4.0,rate=0.00388474]:1.73578,46[&height=4.0,rate=0.00388474]:1.73578)[&height=5.73578,rate=0.00388474]:0.23028)[&height=5.96606,rate=0.00388474]:0.86772,((45[&height=4.0,rate=0.00388474]:1.48623,(44[&height=4.0,rate=0.00388474]:0.90423,(49[&height=4.0,rate=0.00388474]:0.7718,36[&height=4.0,rate=0.00388474]:0.7718)[&height=4.7718,rate=0.00388474]:0.13243)[&height=4.90423,rate=0.00388474]:0.582)[&height=5.48623,rate=0.00388474]:1.30962,(47[&height=4.0,rate=0.00388474]:1.02422,48[&height=4.0,rate=0.00388474]:1.02422)[&height=5.02422,rate=0.00388474]:1.77163)[&height=6.79585,rate=0.00388474]:0.03793)[&height=6.83378,rate=0.00388474]:0.02361)[&height=6.85739,rate=0.00388474]:0.21322,24[&height=6.0,rate=0.00388474]:1.07061)[&height=7.07061,rate=0.00388474]:0.02909)[&height=7.0997,rate=0.00388474]:0.88012)[&height=7.97982,rate=0.00388474]:0.06683,(((39[&height=4.0,rate=0.00388474]:3.38892,22[&height=6.0,rate=0.00388474]:1.38892)[&height=7.38892,rate=0.00388474]:0.17626,(28[&height=6.0,rate=0.00388474]:1.17709,(25[&height=6.0,rate=0.00388474]:0.60859,20[&height=6.0,rate=0.00388474]:0.60859)[&height=6.60859,rate=0.00388474]:0.5685)[&height=7.17709,rate=0.00388474]:0.38809)[&height=7.56518,rate=0.00388474]:0.39277,21[&height=6.0,rate=0.00388474]:1.95795)[&height=7.95795,rate=0.00388474]:0.0887)[&height=8.04665,rate=0.00388474]:1.25726)[&height=9.30391,rate=0.00388474]:0.55952,(((32[&height=6.0,rate=0.00388474]:0.23482,26[&height=6.0,rate=0.00388474]:0.23482)[&height=6.23482,rate=0.00388474]:0.01737,(33[&height=6.0,rate=0.00388474]:0.22513,34[&height=6.0,rate=0.00388474]:0.22513)[&height=6.22513,rate=0.00388474]:0.02706)[&height=6.25219,rate=0.00388474]:1.82813,((42[&height=4.0,rate=0.00388474]:2.51204,23[&height=6.0,rate=0.00388474]:0.51204)[&height=6.51204,rate=0.00388474]:0.18481,30[&height=6.0,rate=0.00388474]:0.69685)[&height=6.69685,rate=0.00388474]:1.38347)[&height=8.08032,rate=0.00388474]:1.78311)[&height=9.86343,rate=0.00388474]:1.96397)[&height=11.8274,rate=0.00388474]:0.092)[&height=11.9194,rate=0.00388474]:0.2045,15[&height=11.0,rate=0.00388474]:1.1239)[&height=12.1239,rate=0.00388474]:0.0543,1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+tree 3 = ((1[&height=17.0,rate=0.00337074]:3.0546,(2[&height=16.0,rate=0.00337074]:2.9268,4[&height=15.0,rate=0.00337074]:3.9268)[&height=18.9268,rate=0.00337074]:1.1278)[&height=20.0546,rate=0.00337074]:1.5276,(((9[&height=14.0,rate=0.00337074]:1.4082,(8[&height=14.0,rate=0.00337074]:1.1507,5[&height=15.0,rate=0.00337074]:0.1507)[&height=15.1507,rate=0.00337074]:0.2575)[&height=15.4082,rate=0.00337074]:0.8667,(7[&height=14.0,rate=0.00337074]:1.8296,(6[&height=15.0,rate=0.00337074]:0.4798,((68[&height=13.0,rate=0.00337074]:1.4327,69[&height=13.0,rate=0.00337074]:1.4327)[&height=14.4327,rate=0.00337074]:0.2282,((((14[&height=11.0,rate=0.00337074]:1.4307,12[&height=11.0,rate=0.00337074]:1.4307)[&height=12.4307,rate=0.00337074]:0.0967,(17[&height=11.0,rate=0.00337074]:0.9297,18[&height=11.0,rate=0.00337074]:0.9297)[&height=11.9297,rate=0.00337074]:0.5977)[&height=12.5274,rate=0.00337074]:0.1245,((((13[&height=11.0,rate=0.00337074]:0.5692,(11[&height=11.0,rate=0.00337074]:0.1424,16[&height=11.0,rate=0.00337074]:0.1424)[&height=11.1424,rate=0.00337074]:0.4268)[&height=11.5692,rate=0.00337074]:0.5536,(19[&height=11.0,rate=0.00337074]:1.0543,((27[&height=6.0,rate=0.00337074]:4.1422,((31[&height=6.0,rate=0.00337074]:2.53085,(29[&height=6.0,rate=0.00337074]:2.00541,((((37[&height=4.0,rate=0.00337074]:1.57497,41[&height=4.0,rate=0.00337074]:1.57497)[&height=5.57497,rate=0.00337074]:0.07395,((38[&height=4.0,rate=0.00337074]:1.25255,40[&height=4.0,rate=0.00337074]:1.25255)[&height=5.25255,rate=0.00337074]:0.31835,43[&height=4.0,rate=0.00337074]:1.5709)[&height=5.5709,rate=0.00337074]:0.07802)[&height=5.64892,rate=0.00337074]:2.07474,(((((((61[&height=0.0,rate=0.00337074]:0.47104,((57[&height=0.0,rate=0.00337074]:0.372661,(54[&height=0.0,rate=0.00337074]:0.292296,60[&height=0.0,rate=0.00337074]:0.292296)[&height=0.292296,rate=0.00337074]:0.080365)[&height=0.372661,rate=0.00337074]:0.006021,58[&height=0.0,rate=0.00337074]:0.378682)[&height=0.378682,rate=0.00337074]:0.092358)[&height=0.47104,rate=0.00337074]:0.203423,55[&height=0.0,rate=0.00337074]:0.674463)[&height=0.674463,rate=0.00337074]:1.269297,53[&height=0.0,rate=0.00337074]:1.94376)[&height=1.94376,rate=0.00337074]:0.17795,(((62[&height=0.0,rate=0.00337074]:0.627024,52[&height=0.0,rate=0.00337074]:0.627024)[&height=0.627024,rate=0.00337074]:0.729636,(((64[&height=0.0,rate=0.00337074]:0.469359,51[&height=0.0,rate=0.00337074]:0.469359)[&height=0.469359,rate=0.00337074]:0.208878,63[&height=0.0,rate=0.00337074]:0.678237)[&height=0.678237,rate=0.00337074]:0.074122,56[&height=0.0,rate=0.00337074]:0.752359)[&height=0.752359,rate=0.00337074]:0.604301)[&height=1.35666,rate=0.00337074]:0.1846,59[&height=0.0,rate=0.00337074]:1.54126)[&height=1.54126,rate=0.00337074]:0.58045)[&height=2.12171,rate=0.00337074]:0.99795,50[&height=0.0,rate=0.00337074]:3.11966)[&height=3.11966,rate=0.00337074]:2.7903,(35[&height=4.0,rate=0.00337074]:1.5306,46[&height=4.0,rate=0.00337074]:1.5306)[&height=5.5306,rate=0.00337074]:0.37936)[&height=5.90996,rate=0.00337074]:1.78275,((45[&height=4.0,rate=0.00337074]:2.57312,(44[&height=4.0,rate=0.00337074]:2.44963,(49[&height=4.0,rate=0.00337074]:0.37245,36[&height=4.0,rate=0.00337074]:0.37245)[&height=4.37245,rate=0.00337074]:2.07718)[&height=6.44963,rate=0.00337074]:0.12349)[&height=6.57312,rate=0.00337074]:1.05044,(47[&height=4.0,rate=0.00337074]:2.09675,48[&height=4.0,rate=0.00337074]:2.09675)[&height=6.09675,rate=0.00337074]:1.52681)[&height=7.62356,rate=0.00337074]:0.06915)[&height=7.69271,rate=0.00337074]:0.03095)[&height=7.72366,rate=0.00337074]:0.19281,24[&height=6.0,rate=0.00337074]:1.91647)[&height=7.91647,rate=0.00337074]:0.08894)[&height=8.00541,rate=0.00337074]:0.52544)[&height=8.53085,rate=0.00337074]:0.21072,(((39[&height=4.0,rate=0.00337074]:2.82713,22[&height=6.0,rate=0.00337074]:0.82713)[&height=6.82713,rate=0.00337074]:0.85082,(28[&height=6.0,rate=0.00337074]:1.04064,(25[&height=6.0,rate=0.00337074]:1.0216,20[&height=6.0,rate=0.00337074]:1.0216)[&height=7.0216,rate=0.00337074]:0.01904)[&height=7.04064,rate=0.00337074]:0.63731)[&height=7.67795,rate=0.00337074]:0.34709,21[&height=6.0,rate=0.00337074]:2.02504)[&height=8.02504,rate=0.00337074]:0.71653)[&height=8.74157,rate=0.00337074]:1.40063)[&height=10.1422,rate=0.00337074]:0.7448,(((32[&height=6.0,rate=0.00337074]:0.77767,26[&height=6.0,rate=0.00337074]:0.77767)[&height=6.77767,rate=0.00337074]:0.0453,(33[&height=6.0,rate=0.00337074]:0.68489,34[&height=6.0,rate=0.00337074]:0.68489)[&height=6.68489,rate=0.00337074]:0.13808)[&height=6.82297,rate=0.00337074]:2.53548,((42[&height=4.0,rate=0.00337074]:2.99973,23[&height=6.0,rate=0.00337074]:0.99973)[&height=6.99973,rate=0.00337074]:0.23694,30[&height=6.0,rate=0.00337074]:1.23667)[&height=7.23667,rate=0.00337074]:2.12178)[&height=9.35845,rate=0.00337074]:1.52855)[&height=10.887,rate=0.00337074]:1.1673)[&height=12.0543,rate=0.00337074]:0.0685)[&height=12.1228,rate=0.00337074]:0.1642,15[&height=11.0,rate=0.00337074]:1.287)[&height=12.287,rate=0.0033707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+tree 4 = ((1[&height=17.0,rate=0.0035357]:2.4487,(2[&height=16.0,rate=0.0035357]:2.5825,4[&height=15.0,rate=0.0035357]:3.5825)[&height=18.5825,rate=0.0035357]:0.8662)[&height=19.4487,rate=0.0035357]:1.1513,(((9[&height=14.0,rate=0.0035357]:2.6347,(8[&height=14.0,rate=0.0035357]:2.019,5[&height=15.0,rate=0.0035357]:1.019)[&height=16.019,rate=0.0035357]:0.6157)[&height=16.6347,rate=0.0035357]:0.2002,(7[&height=14.0,rate=0.0035357]:2.2538,(6[&height=15.0,rate=0.0035357]:0.8753,((68[&height=13.0,rate=0.0035357]:1.0554,69[&height=13.0,rate=0.0035357]:1.0554)[&height=14.0554,rate=0.0035357]:0.1193,((((14[&height=11.0,rate=0.0035357]:0.5348,12[&height=11.0,rate=0.0035357]:0.5348)[&height=11.5348,rate=0.0035357]:0.5014,(17[&height=11.0,rate=0.0035357]:0.537,18[&height=11.0,rate=0.0035357]:0.537)[&height=11.537,rate=0.0035357]:0.4992)[&height=12.0362,rate=0.0035357]:0.3726,((((13[&height=11.0,rate=0.0035357]:0.6987,(11[&height=11.0,rate=0.0035357]:0.0433,16[&height=11.0,rate=0.0035357]:0.0433)[&height=11.0433,rate=0.0035357]:0.6554)[&height=11.6987,rate=0.0035357]:0.3997,(19[&height=11.0,rate=0.0035357]:0.9855,((27[&height=6.0,rate=0.0035357]:3.57909,((31[&height=6.0,rate=0.0035357]:2.26449,(29[&height=6.0,rate=0.0035357]:1.96735,((((37[&height=4.0,rate=0.0035357]:2.11778,41[&height=4.0,rate=0.0035357]:2.11778)[&height=6.11778,rate=0.0035357]:0.3158,((38[&height=4.0,rate=0.0035357]:1.92795,40[&height=4.0,rate=0.0035357]:1.92795)[&height=5.92795,rate=0.0035357]:0.04531,43[&height=4.0,rate=0.0035357]:1.97326)[&height=5.97326,rate=0.0035357]:0.46032)[&height=6.43358,rate=0.0035357]:1.28048,(((((((61[&height=0.0,rate=0.0035357]:1.05409,((57[&height=0.0,rate=0.0035357]:0.0899211,(54[&height=0.0,rate=0.0035357]:0.0879187,60[&height=0.0,rate=0.0035357]:0.0879187)[&height=0.0879187,rate=0.0035357]:0.0020024)[&height=0.0899211,rate=0.0035357]:0.4975369,58[&height=0.0,rate=0.0035357]:0.587458)[&height=0.587458,rate=0.0035357]:0.466632)[&height=1.05409,rate=0.0035357]:0.22046,55[&height=0.0,rate=0.0035357]:1.27455)[&height=1.27455,rate=0.0035357]:0.08409,53[&height=0.0,rate=0.0035357]:1.35864)[&height=1.35864,rate=0.0035357]:0.18031,(((62[&height=0.0,rate=0.0035357]:0.637312,52[&height=0.0,rate=0.0035357]:0.637312)[&height=0.637312,rate=0.0035357]:0.307428,(((64[&height=0.0,rate=0.0035357]:0.0544888,51[&height=0.0,rate=0.0035357]:0.0544888)[&height=0.0544888,rate=0.0035357]:0.4997922,63[&height=0.0,rate=0.0035357]:0.554281)[&height=0.554281,rate=0.0035357]:0.159148,56[&height=0.0,rate=0.0035357]:0.713429)[&height=0.713429,rate=0.0035357]:0.231311)[&height=0.94474,rate=0.0035357]:0.11352,59[&height=0.0,rate=0.0035357]:1.05826)[&height=1.05826,rate=0.0035357]:0.48069)[&height=1.53895,rate=0.0035357]:0.67084,50[&height=0.0,rate=0.0035357]:2.20979)[&height=2.20979,rate=0.0035357]:3.25569,(35[&height=4.0,rate=0.0035357]:1.4329,46[&height=4.0,rate=0.0035357]:1.4329)[&height=5.4329,rate=0.0035357]:0.03258)[&height=5.46548,rate=0.0035357]:2.19673,((45[&height=4.0,rate=0.0035357]:1.93654,(44[&height=4.0,rate=0.0035357]:1.76679,(49[&height=4.0,rate=0.0035357]:1.70334,36[&height=4.0,rate=0.0035357]:1.70334)[&height=5.70334,rate=0.0035357]:0.06345)[&height=5.76679,rate=0.0035357]:0.16975)[&height=5.93654,rate=0.0035357]:1.60571,(47[&height=4.0,rate=0.0035357]:1.63417,48[&height=4.0,rate=0.0035357]:1.63417)[&height=5.63417,rate=0.0035357]:1.90808)[&height=7.54225,rate=0.0035357]:0.11996)[&height=7.66221,rate=0.0035357]:0.05185)[&height=7.71406,rate=0.0035357]:0.16055,24[&height=6.0,rate=0.0035357]:1.87461)[&height=7.87461,rate=0.0035357]:0.09274)[&height=7.96735,rate=0.0035357]:0.29714)[&height=8.26449,rate=0.0035357]:0.07859,(((39[&height=4.0,rate=0.0035357]:3.28241,22[&height=6.0,rate=0.0035357]:1.28241)[&height=7.28241,rate=0.0035357]:0.13087,(28[&height=6.0,rate=0.0035357]:1.35486,(25[&height=6.0,rate=0.0035357]:0.66386,20[&height=6.0,rate=0.0035357]:0.66386)[&height=6.66386,rate=0.0035357]:0.691)[&height=7.35486,rate=0.0035357]:0.05842)[&height=7.41328,rate=0.0035357]:0.85864,21[&height=6.0,rate=0.0035357]:2.27192)[&height=8.27192,rate=0.0035357]:0.07116)[&height=8.34308,rate=0.0035357]:1.23601)[&height=9.57909,rate=0.0035357]:1.01671,(((32[&height=6.0,rate=0.0035357]:1.14197,26[&height=6.0,rate=0.0035357]:1.14197)[&height=7.14197,rate=0.0035357]:0.23859,(33[&height=6.0,rate=0.0035357]:1.09888,34[&height=6.0,rate=0.0035357]:1.09888)[&height=7.09888,rate=0.0035357]:0.28168)[&height=7.38056,rate=0.0035357]:2.54234,((42[&height=4.0,rate=0.0035357]:2.59532,23[&height=6.0,rate=0.0035357]:0.59532)[&height=6.59532,rate=0.0035357]:0.65782,30[&height=6.0,rate=0.0035357]:1.25314)[&height=7.25314,rate=0.0035357]:2.66976)[&height=9.9229,rate=0.0035357]:0.6729)[&height=10.5958,rate=0.0035357]:1.3897)[&height=11.9855,rate=0.0035357]:0.1129)[&height=12.0984,rate=0.0035357]:0.0088,15[&height=11.0,rate=0.0035357]:1.1072)[&height=12.1072,rate=0.0035357]:0.0494,10[&height=11.0,rate=0.0035357]:1.1566)[&height=12.1566,rate=0.0035357]:0.2522)[&height=12.4088,rate=0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+tree 5 = ((1[&height=17.0,rate=0.0038716]:1.7057,(2[&height=16.0,rate=0.0038716]:1.3385,4[&height=15.0,rate=0.0038716]:2.3385)[&height=17.3385,rate=0.0038716]:1.3672)[&height=18.7057,rate=0.0038716]:0.5537,(((9[&height=14.0,rate=0.0038716]:1.8579,(8[&height=14.0,rate=0.0038716]:1.7126,5[&height=15.0,rate=0.0038716]:0.7126)[&height=15.7126,rate=0.0038716]:0.1453)[&height=15.8579,rate=0.0038716]:0.22,(7[&height=14.0,rate=0.0038716]:1.6365,(6[&height=15.0,rate=0.0038716]:0.4496,((68[&height=13.0,rate=0.0038716]:0.723,69[&height=13.0,rate=0.0038716]:0.723)[&height=13.723,rate=0.0038716]:0.5313,((((14[&height=11.0,rate=0.0038716]:0.5305,12[&height=11.0,rate=0.0038716]:0.5305)[&height=11.5305,rate=0.0038716]:0.7214,(17[&height=11.0,rate=0.0038716]:0.5536,18[&height=11.0,rate=0.0038716]:0.5536)[&height=11.5536,rate=0.0038716]:0.6983)[&height=12.2519,rate=0.0038716]:0.2121,((((13[&height=11.0,rate=0.0038716]:0.4242,(11[&height=11.0,rate=0.0038716]:0.0576,16[&height=11.0,rate=0.0038716]:0.0576)[&height=11.0576,rate=0.0038716]:0.3666)[&height=11.4242,rate=0.0038716]:0.3832,(19[&height=11.0,rate=0.0038716]:0.7897,((27[&height=6.0,rate=0.0038716]:3.19859,((31[&height=6.0,rate=0.0038716]:1.75511,(29[&height=6.0,rate=0.0038716]:1.58368,((((37[&height=4.0,rate=0.0038716]:1.40986,41[&height=4.0,rate=0.0038716]:1.40986)[&height=5.40986,rate=0.0038716]:0.18202,((38[&height=4.0,rate=0.0038716]:0.85037,40[&height=4.0,rate=0.0038716]:0.85037)[&height=4.85037,rate=0.0038716]:0.51142,43[&height=4.0,rate=0.0038716]:1.36179)[&height=5.36179,rate=0.0038716]:0.23009)[&height=5.59188,rate=0.0038716]:1.60047,(((((((61[&height=0.0,rate=0.0038716]:1.16979,((57[&height=0.0,rate=0.0038716]:0.395247,(54[&height=0.0,rate=0.0038716]:0.163636,60[&height=0.0,rate=0.0038716]:0.163636)[&height=0.163636,rate=0.0038716]:0.231611)[&height=0.395247,rate=0.0038716]:0.635813,58[&height=0.0,rate=0.0038716]:1.03106)[&height=1.03106,rate=0.0038716]:0.13873)[&height=1.16979,rate=0.0038716]:0.38294,55[&height=0.0,rate=0.0038716]:1.55273)[&height=1.55273,rate=0.0038716]:0.04976,53[&height=0.0,rate=0.0038716]:1.60249)[&height=1.60249,rate=0.0038716]:0.30648,(((62[&height=0.0,rate=0.0038716]:1.25004,52[&height=0.0,rate=0.0038716]:1.25004)[&height=1.25004,rate=0.0038716]:0.27174,(((64[&height=0.0,rate=0.0038716]:0.234969,51[&height=0.0,rate=0.0038716]:0.234969)[&height=0.234969,rate=0.0038716]:0.991241,63[&height=0.0,rate=0.0038716]:1.22621)[&height=1.22621,rate=0.0038716]:0.14836,56[&height=0.0,rate=0.0038716]:1.37457)[&height=1.37457,rate=0.0038716]:0.14721)[&height=1.52178,rate=0.0038716]:0.1923,59[&height=0.0,rate=0.0038716]:1.71408)[&height=1.71408,rate=0.0038716]:0.19489)[&height=1.90897,rate=0.0038716]:0.81128,50[&height=0.0,rate=0.0038716]:2.72025)[&height=2.72025,rate=0.0038716]:2.49861,(35[&height=4.0,rate=0.0038716]:1.13416,46[&height=4.0,rate=0.0038716]:1.13416)[&height=5.13416,rate=0.0038716]:0.0847)[&height=5.21886,rate=0.0038716]:1.95057,((45[&height=4.0,rate=0.0038716]:1.66576,(44[&height=4.0,rate=0.0038716]:1.4688,(49[&height=4.0,rate=0.0038716]:1.20752,36[&height=4.0,rate=0.0038716]:1.20752)[&height=5.20752,rate=0.0038716]:0.26128)[&height=5.4688,rate=0.0038716]:0.19696)[&height=5.66576,rate=0.0038716]:1.34223,(47[&height=4.0,rate=0.0038716]:1.59871,48[&height=4.0,rate=0.0038716]:1.59871)[&height=5.59871,rate=0.0038716]:1.40928)[&height=7.00799,rate=0.0038716]:0.16144)[&height=7.16943,rate=0.0038716]:0.02292)[&height=7.19235,rate=0.0038716]:0.30086,24[&height=6.0,rate=0.0038716]:1.49321)[&height=7.49321,rate=0.0038716]:0.09047)[&height=7.58368,rate=0.0038716]:0.17143)[&height=7.75511,rate=0.0038716]:0.04954,(((39[&height=4.0,rate=0.0038716]:3.0419,22[&height=6.0,rate=0.0038716]:1.0419)[&height=7.0419,rate=0.0038716]:0.37186,(28[&height=6.0,rate=0.0038716]:1.22465,(25[&height=6.0,rate=0.0038716]:0.95316,20[&height=6.0,rate=0.0038716]:0.95316)[&height=6.95316,rate=0.0038716]:0.27149)[&height=7.22465,rate=0.0038716]:0.18911)[&height=7.41376,rate=0.0038716]:0.19776,21[&height=6.0,rate=0.0038716]:1.61152)[&height=7.61152,rate=0.0038716]:0.19313)[&height=7.80465,rate=0.0038716]:1.39394)[&height=9.19859,rate=0.0038716]:0.87951,(((32[&height=6.0,rate=0.0038716]:0.39854,26[&height=6.0,rate=0.0038716]:0.39854)[&height=6.39854,rate=0.0038716]:0.25858,(33[&height=6.0,rate=0.0038716]:0.39828,34[&height=6.0,rate=0.0038716]:0.39828)[&height=6.39828,rate=0.0038716]:0.25884)[&height=6.65712,rate=0.0038716]:2.34055,((42[&height=4.0,rate=0.0038716]:2.76243,23[&height=6.0,rate=0.0038716]:0.76243)[&height=6.76243,rate=0.0038716]:0.16804,30[&height=6.0,rate=0.0038716]:0.93047)[&height=6.93047,rate=0.0038716]:2.0672)[&height=8.99767,rate=0.0038716]:1.08043)[&height=10.0781,rate=0.0038716]:1.7116)[&height=11.7897,rate=0.0038716]:0.0177)[&height=11.8074,rate=0.0038716]:0.0266,15[&height=11.0,rate=0.0038716]:0.834)[&height=11.834,rate=0.0038716]:0.1531,10[&height=11.0,rate=0.0038716]:0.9871)[&height=11.9871,rate=0.0038716]:0.4769)[&height=12.464,rate=0.0038716]:1.6293,((67[&height=12.0,rate=0.0038716]:0.6857,65[&height=12.0,rate=0.0038716]:0.6857)[&height=12.6857,rate=0.0038716]:0.4708,66[&height=12.0,rate=0.0038716]:1.1565)[&height=13.1565,rate=0.0038716]:0.9368)[&height=14.0933,rate=0.0038716]:0.161)[&height=14.2543,rate=0.0038716]:1.1953)[&height=15.4496,rate=0.0038716]:0.1869)[&height=15.6365,rate=0.0038716]:0.4414)[&height=16.0779,rate=0.0038716]:1.7133,3[&height=16.0,rate=0.0038716]:1.7912)[&height=17.7912,rate=0.0038716]:1.4682)[&height=19.2594]; +tree 6 = ((1[&height=17.0,rate=0.00382886]:2.1362,(2[&height=16.0,rate=0.00382886]:2.1772,4[&height=15.0,rate=0.00382886]:3.1772)[&height=18.1772,rate=0.00382886]:0.959)[&height=19.1362,rate=0.00382886]:0.893,(((9[&height=14.0,rate=0.00382886]:1.8816,(8[&height=14.0,rate=0.00382886]:1.2028,5[&height=15.0,rate=0.00382886]:0.2028)[&height=15.2028,rate=0.00382886]:0.6788)[&height=15.8816,rate=0.00382886]:0.0501,(7[&height=14.0,rate=0.00382886]:1.7276,(6[&height=15.0,rate=0.00382886]:0.377,((68[&height=13.0,rate=0.00382886]:1.4389,69[&height=13.0,rate=0.00382886]:1.4389)[&height=14.4389,rate=0.00382886]:0.135,((((14[&height=11.0,rate=0.00382886]:0.9665,12[&height=11.0,rate=0.00382886]:0.9665)[&height=11.9665,rate=0.00382886]:0.1071,(17[&height=11.0,rate=0.00382886]:0.6316,18[&height=11.0,rate=0.00382886]:0.6316)[&height=11.6316,rate=0.00382886]:0.442)[&height=12.0736,rate=0.00382886]:0.2628,((((13[&height=11.0,rate=0.00382886]:0.5508,(11[&height=11.0,rate=0.00382886]:0.0424,16[&height=11.0,rate=0.00382886]:0.0424)[&height=11.0424,rate=0.00382886]:0.5084)[&height=11.5508,rate=0.00382886]:0.2969,(19[&height=11.0,rate=0.00382886]:0.5225,((27[&height=6.0,rate=0.00382886]:2.98473,((31[&height=6.0,rate=0.00382886]:1.85323,(29[&height=6.0,rate=0.00382886]:1.48297,((((37[&height=4.0,rate=0.00382886]:1.43059,41[&height=4.0,rate=0.00382886]:1.43059)[&height=5.43059,rate=0.00382886]:0.04173,((38[&height=4.0,rate=0.00382886]:1.00159,40[&height=4.0,rate=0.00382886]:1.00159)[&height=5.00159,rate=0.00382886]:0.07959,43[&height=4.0,rate=0.00382886]:1.08118)[&height=5.08118,rate=0.00382886]:0.39114)[&height=5.47232,rate=0.00382886]:1.6133,(((((((61[&height=0.0,rate=0.00382886]:0.751599,((57[&height=0.0,rate=0.00382886]:0.512373,(54[&height=0.0,rate=0.00382886]:0.135718,60[&height=0.0,rate=0.00382886]:0.135718)[&height=0.135718,rate=0.00382886]:0.376655)[&height=0.512373,rate=0.00382886]:0.07612,58[&height=0.0,rate=0.00382886]:0.588493)[&height=0.588493,rate=0.00382886]:0.163106)[&height=0.751599,rate=0.00382886]:0.229211,55[&height=0.0,rate=0.00382886]:0.98081)[&height=0.98081,rate=0.00382886]:0.56263,53[&height=0.0,rate=0.00382886]:1.54344)[&height=1.54344,rate=0.00382886]:0.06365,(((62[&height=0.0,rate=0.00382886]:0.929056,52[&height=0.0,rate=0.00382886]:0.929056)[&height=0.929056,rate=0.00382886]:0.420184,(((64[&height=0.0,rate=0.00382886]:0.115414,51[&height=0.0,rate=0.00382886]:0.115414)[&height=0.115414,rate=0.00382886]:0.85369,63[&height=0.0,rate=0.00382886]:0.969104)[&height=0.969104,rate=0.00382886]:0.114206,56[&height=0.0,rate=0.00382886]:1.08331)[&height=1.08331,rate=0.00382886]:0.26593)[&height=1.34924,rate=0.00382886]:0.18126,59[&height=0.0,rate=0.00382886]:1.5305)[&height=1.5305,rate=0.00382886]:0.07659)[&height=1.60709,rate=0.00382886]:1.01817,50[&height=0.0,rate=0.00382886]:2.62526)[&height=2.62526,rate=0.00382886]:2.42535,(35[&height=4.0,rate=0.00382886]:0.69053,46[&height=4.0,rate=0.00382886]:0.69053)[&height=4.69053,rate=0.00382886]:0.36008)[&height=5.05061,rate=0.00382886]:1.95801,((45[&height=4.0,rate=0.00382886]:1.85711,(44[&height=4.0,rate=0.00382886]:1.76881,(49[&height=4.0,rate=0.00382886]:1.58888,36[&height=4.0,rate=0.00382886]:1.58888)[&height=5.58888,rate=0.00382886]:0.17993)[&height=5.76881,rate=0.00382886]:0.0883)[&height=5.85711,rate=0.00382886]:0.61849,(47[&height=4.0,rate=0.00382886]:1.45127,48[&height=4.0,rate=0.00382886]:1.45127)[&height=5.45127,rate=0.00382886]:1.02433)[&height=6.4756,rate=0.00382886]:0.53302)[&height=7.00862,rate=0.00382886]:0.077)[&height=7.08562,rate=0.00382886]:0.21369,24[&height=6.0,rate=0.00382886]:1.29931)[&height=7.29931,rate=0.00382886]:0.18366)[&height=7.48297,rate=0.00382886]:0.37026)[&height=7.85323,rate=0.00382886]:0.13259,(((39[&height=4.0,rate=0.00382886]:3.13689,22[&height=6.0,rate=0.00382886]:1.13689)[&height=7.13689,rate=0.00382886]:0.21626,(28[&height=6.0,rate=0.00382886]:1.1261,(25[&height=6.0,rate=0.00382886]:1.10225,20[&height=6.0,rate=0.00382886]:1.10225)[&height=7.10225,rate=0.00382886]:0.02385)[&height=7.1261,rate=0.00382886]:0.22705)[&height=7.35315,rate=0.00382886]:0.56291,21[&height=6.0,rate=0.00382886]:1.91606)[&height=7.91606,rate=0.00382886]:0.06976)[&height=7.98582,rate=0.00382886]:0.99891)[&height=8.98473,rate=0.00382886]:0.67623,(((32[&height=6.0,rate=0.00382886]:0.22036,26[&height=6.0,rate=0.00382886]:0.22036)[&height=6.22036,rate=0.00382886]:0.44667,(33[&height=6.0,rate=0.00382886]:0.53074,34[&height=6.0,rate=0.00382886]:0.53074)[&height=6.53074,rate=0.00382886]:0.13629)[&height=6.66703,rate=0.00382886]:1.97719,((42[&height=4.0,rate=0.00382886]:2.16732,23[&height=6.0,rate=0.00382886]:0.16732)[&height=6.16732,rate=0.00382886]:0.81869,30[&height=6.0,rate=0.00382886]:0.98601)[&height=6.98601,rate=0.00382886]:1.65821)[&height=8.64422,rate=0.00382886]:1.01674)[&height=9.66096,rate=0.00382886]:1.86154)[&height=11.5225,rate=0.00382886]:0.3252)[&height=11.8477,rate=0.00382886]:0.048,15[&height=11.0,rate=0.00382886]:0.8957)[&height=11.8957,rate=0.00382886]:0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+tree 7 = ((1[&height=17.0,rate=0.0036384]:1.9661,(2[&height=16.0,rate=0.0036384]:2.3467,4[&height=15.0,rate=0.0036384]:3.3467)[&height=18.3467,rate=0.0036384]:0.6194)[&height=18.9661,rate=0.0036384]:2.0538,(((9[&height=14.0,rate=0.0036384]:1.5807,(8[&height=14.0,rate=0.0036384]:1.302,5[&height=15.0,rate=0.0036384]:0.302)[&height=15.302,rate=0.0036384]:0.2787)[&height=15.5807,rate=0.0036384]:0.4825,(7[&height=14.0,rate=0.0036384]:1.8664,(6[&height=15.0,rate=0.0036384]:0.2377,((68[&height=13.0,rate=0.0036384]:0.6946,69[&height=13.0,rate=0.0036384]:0.6946)[&height=13.6946,rate=0.0036384]:0.4183,((((14[&height=11.0,rate=0.0036384]:0.867,12[&height=11.0,rate=0.0036384]:0.867)[&height=11.867,rate=0.0036384]:0.3154,(17[&height=11.0,rate=0.0036384]:0.9969,18[&height=11.0,rate=0.0036384]:0.9969)[&height=11.9969,rate=0.0036384]:0.1855)[&height=12.1824,rate=0.0036384]:0.1122,((((13[&height=11.0,rate=0.0036384]:0.3487,(11[&height=11.0,rate=0.0036384]:0.0659,16[&height=11.0,rate=0.0036384]:0.0659)[&height=11.0659,rate=0.0036384]:0.2828)[&height=11.3487,rate=0.0036384]:0.3484,(19[&height=11.0,rate=0.0036384]:0.5942,((27[&height=6.0,rate=0.0036384]:2.65646,((31[&height=6.0,rate=0.0036384]:1.40356,(29[&height=6.0,rate=0.0036384]:1.29494,((((37[&height=4.0,rate=0.0036384]:0.89285,41[&height=4.0,rate=0.0036384]:0.89285)[&height=4.89285,rate=0.0036384]:0.35935,((38[&height=4.0,rate=0.0036384]:1.12703,40[&height=4.0,rate=0.0036384]:1.12703)[&height=5.12703,rate=0.0036384]:0.00525,43[&height=4.0,rate=0.0036384]:1.13228)[&height=5.13228,rate=0.0036384]:0.11992)[&height=5.2522,rate=0.0036384]:1.19805,(((((((61[&height=0.0,rate=0.0036384]:1.09897,((57[&height=0.0,rate=0.0036384]:0.44787,(54[&height=0.0,rate=0.0036384]:0.198506,60[&height=0.0,rate=0.0036384]:0.198506)[&height=0.198506,rate=0.0036384]:0.249364)[&height=0.44787,rate=0.0036384]:0.63094,58[&height=0.0,rate=0.0036384]:1.07881)[&height=1.07881,rate=0.0036384]:0.02016)[&height=1.09897,rate=0.0036384]:0.21126,55[&height=0.0,rate=0.0036384]:1.31023)[&height=1.31023,rate=0.0036384]:0.05224,53[&height=0.0,rate=0.0036384]:1.36247)[&height=1.36247,rate=0.0036384]:0.12601,(((62[&height=0.0,rate=0.0036384]:0.71721,52[&height=0.0,rate=0.0036384]:0.71721)[&height=0.71721,rate=0.0036384]:0.115215,(((64[&height=0.0,rate=0.0036384]:0.0119392,51[&height=0.0,rate=0.0036384]:0.0119392)[&height=0.0119392,rate=0.0036384]:0.2035888,63[&height=0.0,rate=0.0036384]:0.215528)[&height=0.215528,rate=0.0036384]:0.517545,56[&height=0.0,rate=0.0036384]:0.733073)[&height=0.733073,rate=0.0036384]:0.099352)[&height=0.832425,rate=0.0036384]:0.045919,59[&height=0.0,rate=0.0036384]:0.878344)[&height=0.878344,rate=0.0036384]:0.610136)[&height=1.48848,rate=0.0036384]:1.01767,50[&height=0.0,rate=0.0036384]:2.50615)[&height=2.50615,rate=0.0036384]:2.91931,(35[&height=4.0,rate=0.0036384]:1.31147,46[&height=4.0,rate=0.0036384]:1.31147)[&height=5.31147,rate=0.0036384]:0.11399)[&height=5.42546,rate=0.0036384]:0.99788,((45[&height=4.0,rate=0.0036384]:1.44435,(44[&height=4.0,rate=0.0036384]:1.20274,(49[&height=4.0,rate=0.0036384]:0.63166,36[&height=4.0,rate=0.0036384]:0.63166)[&height=4.63166,rate=0.0036384]:0.57108)[&height=5.20274,rate=0.0036384]:0.24161)[&height=5.44435,rate=0.0036384]:0.88941,(47[&height=4.0,rate=0.0036384]:0.93313,48[&height=4.0,rate=0.0036384]:0.93313)[&height=4.93313,rate=0.0036384]:1.40063)[&height=6.33376,rate=0.0036384]:0.08958)[&height=6.42334,rate=0.0036384]:0.02691)[&height=6.45025,rate=0.0036384]:0.3438,24[&height=6.0,rate=0.0036384]:0.79405)[&height=6.79405,rate=0.0036384]:0.50089)[&height=7.29494,rate=0.0036384]:0.10862)[&height=7.40356,rate=0.0036384]:0.12152,(((39[&height=4.0,rate=0.0036384]:2.76843,22[&height=6.0,rate=0.0036384]:0.76843)[&height=6.76843,rate=0.0036384]:0.27712,(28[&height=6.0,rate=0.0036384]:1.00019,(25[&height=6.0,rate=0.0036384]:0.91318,20[&height=6.0,rate=0.0036384]:0.91318)[&height=6.91318,rate=0.0036384]:0.08701)[&height=7.00019,rate=0.0036384]:0.04536)[&height=7.04555,rate=0.0036384]:0.25383,21[&height=6.0,rate=0.0036384]:1.29938)[&height=7.29938,rate=0.0036384]:0.2257)[&height=7.52508,rate=0.0036384]:1.13138)[&height=8.65646,rate=0.0036384]:1.02225,(((32[&height=6.0,rate=0.0036384]:0.51273,26[&height=6.0,rate=0.0036384]:0.51273)[&height=6.51273,rate=0.0036384]:0.42174,(33[&height=6.0,rate=0.0036384]:0.64386,34[&height=6.0,rate=0.0036384]:0.64386)[&height=6.64386,rate=0.0036384]:0.29061)[&height=6.93447,rate=0.0036384]:1.96389,((42[&height=4.0,rate=0.0036384]:2.35026,23[&height=6.0,rate=0.0036384]:0.35026)[&height=6.35026,rate=0.0036384]:0.94937,30[&height=6.0,rate=0.0036384]:1.29963)[&height=7.29963,rate=0.0036384]:1.59873)[&height=8.89836,rate=0.0036384]:0.78035)[&height=9.67871,rate=0.0036384]:1.91549)[&height=11.5942,rate=0.0036384]:0.1029)[&height=11.6971,rate=0.0036384]:0.0215,15[&height=11.0,rate=0.0036384]:0.7186)[&height=11.7186,rate=0.0036384]:0.0637,10[&height=11.0,rate=0.0036384]:0.7823)[&height=11.7823,rate=0.0036384]:0.5123)[&height=12.2946,rate=0.0036384]:1.5096,((67[&height=12.0,rate=0.0036384]:1.091,65[&height=12.0,rate=0.0036384]:1.091)[&height=13.091,rate=0.0036384]:0.0744,66[&height=12.0,rate=0.0036384]:1.1654)[&height=13.1654,rate=0.0036384]:0.6388)[&height=13.8042,rate=0.0036384]:0.3087)[&height=14.1129,rate=0.0036384]:1.1248)[&height=15.2377,rate=0.0036384]:0.6287)[&height=15.8664,rate=0.0036384]:0.1968)[&height=16.0632,rate=0.0036384]:2.918,3[&height=16.0,rate=0.0036384]:2.9812)[&height=18.9812,rate=0.0036384]:2.0387)[&height=21.0199]; +tree 8 = ((1[&height=17.0,rate=0.00372602]:2.3519,(2[&height=16.0,rate=0.00372602]:1.9741,4[&height=15.0,rate=0.00372602]:2.9741)[&height=17.9741,rate=0.00372602]:1.3778)[&height=19.3519,rate=0.00372602]:1.214,(((9[&height=14.0,rate=0.00372602]:2.5656,(8[&height=14.0,rate=0.00372602]:1.1056,5[&height=15.0,rate=0.00372602]:0.1056)[&height=15.1056,rate=0.00372602]:1.46)[&height=16.5656,rate=0.00372602]:0.1057,(7[&height=14.0,rate=0.00372602]:2.2373,(6[&height=15.0,rate=0.00372602]:0.2213,((68[&height=13.0,rate=0.00372602]:0.7385,69[&height=13.0,rate=0.00372602]:0.7385)[&height=13.7385,rate=0.00372602]:0.4739,((((14[&height=11.0,rate=0.00372602]:0.5409,12[&height=11.0,rate=0.00372602]:0.5409)[&height=11.5409,rate=0.00372602]:0.212,(17[&height=11.0,rate=0.00372602]:0.3457,18[&height=11.0,rate=0.00372602]:0.3457)[&height=11.3457,rate=0.00372602]:0.4072)[&height=11.7529,rate=0.00372602]:0.1724,((((13[&height=11.0,rate=0.00372602]:0.5138,(11[&height=11.0,rate=0.00372602]:0.0653,16[&height=11.0,rate=0.00372602]:0.0653)[&height=11.0653,rate=0.00372602]:0.4485)[&height=11.5138,rate=0.00372602]:0.1287,(19[&height=11.0,rate=0.00372602]:0.4182,((27[&height=6.0,rate=0.00372602]:2.95286,((31[&height=6.0,rate=0.00372602]:1.44854,(29[&height=6.0,rate=0.00372602]:1.20312,((((37[&height=4.0,rate=0.00372602]:1.34777,41[&height=4.0,rate=0.00372602]:1.34777)[&height=5.34777,rate=0.00372602]:0.43737,((38[&height=4.0,rate=0.00372602]:0.58214,40[&height=4.0,rate=0.00372602]:0.58214)[&height=4.58214,rate=0.00372602]:0.85342,43[&height=4.0,rate=0.00372602]:1.43556)[&height=5.43556,rate=0.00372602]:0.34958)[&height=5.78514,rate=0.00372602]:1.06857,(((((((61[&height=0.0,rate=0.00372602]:1.15439,((57[&height=0.0,rate=0.00372602]:0.799473,(54[&height=0.0,rate=0.00372602]:0.015682,60[&height=0.0,rate=0.00372602]:0.015682)[&height=0.015682,rate=0.00372602]:0.783791)[&height=0.799473,rate=0.00372602]:0.207057,58[&height=0.0,rate=0.00372602]:1.00653)[&height=1.00653,rate=0.00372602]:0.14786)[&height=1.15439,rate=0.00372602]:0.37378,55[&height=0.0,rate=0.00372602]:1.52817)[&height=1.52817,rate=0.00372602]:0.26842,53[&height=0.0,rate=0.00372602]:1.79659)[&height=1.79659,rate=0.00372602]:0.02742,(((62[&height=0.0,rate=0.00372602]:0.985837,52[&height=0.0,rate=0.00372602]:0.985837)[&height=0.985837,rate=0.00372602]:0.419053,(((64[&height=0.0,rate=0.00372602]:0.577059,51[&height=0.0,rate=0.00372602]:0.577059)[&height=0.577059,rate=0.00372602]:0.401805,63[&height=0.0,rate=0.00372602]:0.978864)[&height=0.978864,rate=0.00372602]:0.326906,56[&height=0.0,rate=0.00372602]:1.30577)[&height=1.30577,rate=0.00372602]:0.09912)[&height=1.40489,rate=0.00372602]:0.0871,59[&height=0.0,rate=0.00372602]:1.49199)[&height=1.49199,rate=0.00372602]:0.33202)[&height=1.82401,rate=0.00372602]:1.31252,50[&height=0.0,rate=0.00372602]:3.13653)[&height=3.13653,rate=0.00372602]:2.85146,(35[&height=4.0,rate=0.00372602]:1.96066,46[&height=4.0,rate=0.00372602]:1.96066)[&height=5.96066,rate=0.00372602]:0.02733)[&height=5.98799,rate=0.00372602]:0.83911,((45[&height=4.0,rate=0.00372602]:1.25855,(44[&height=4.0,rate=0.00372602]:1.15225,(49[&height=4.0,rate=0.00372602]:0.37531,36[&height=4.0,rate=0.00372602]:0.37531)[&height=4.37531,rate=0.00372602]:0.77694)[&height=5.15225,rate=0.00372602]:0.1063)[&height=5.25855,rate=0.00372602]:1.40068,(47[&height=4.0,rate=0.00372602]:1.33696,48[&height=4.0,rate=0.00372602]:1.33696)[&height=5.33696,rate=0.00372602]:1.32227)[&height=6.65923,rate=0.00372602]:0.16787)[&height=6.8271,rate=0.00372602]:0.02661)[&height=6.85371,rate=0.00372602]:0.13856,24[&height=6.0,rate=0.00372602]:0.99227)[&height=6.99227,rate=0.00372602]:0.21085)[&height=7.20312,rate=0.00372602]:0.24542)[&height=7.44854,rate=0.00372602]:0.06682,(((39[&height=4.0,rate=0.00372602]:2.92191,22[&height=6.0,rate=0.00372602]:0.92191)[&height=6.92191,rate=0.00372602]:0.28221,(28[&height=6.0,rate=0.00372602]:1.09614,(25[&height=6.0,rate=0.00372602]:1.06944,20[&height=6.0,rate=0.00372602]:1.06944)[&height=7.06944,rate=0.00372602]:0.0267)[&height=7.09614,rate=0.00372602]:0.10798)[&height=7.20412,rate=0.00372602]:0.24612,21[&height=6.0,rate=0.00372602]:1.45024)[&height=7.45024,rate=0.00372602]:0.06512)[&height=7.51536,rate=0.00372602]:1.4375)[&height=8.95286,rate=0.00372602]:0.85119,(((32[&height=6.0,rate=0.00372602]:0.61683,26[&height=6.0,rate=0.00372602]:0.61683)[&height=6.61683,rate=0.00372602]:0.4801,(33[&height=6.0,rate=0.00372602]:0.79414,34[&height=6.0,rate=0.00372602]:0.79414)[&height=6.79414,rate=0.00372602]:0.30279)[&height=7.09693,rate=0.00372602]:2.19729,((42[&height=4.0,rate=0.00372602]:2.41575,23[&height=6.0,rate=0.00372602]:0.41575)[&height=6.41575,rate=0.00372602]:0.59542,30[&height=6.0,rate=0.00372602]:1.01117)[&height=7.01117,rate=0.00372602]:2.28305)[&height=9.29422,rate=0.00372602]:0.50983)[&height=9.80405,rate=0.00372602]:1.61415)[&height=11.4182,rate=0.00372602]:0.2243)[&height=11.6425,rate=0.00372602]:0.0359,15[&height=11.0,rate=0.00372602]:0.6784)[&height=11.6784,rate=0.00372602]:0.0645,10[&height=11.0,rate=0.00372602]:0.7429)[&height=11.7429,rate=0.00372602]:0.1824)[&height=11.9253,rate=0.00372602]:1.9861,((67[&height=12.0,rate=0.00372602]:0.8641,65[&height=12.0,rate=0.00372602]:0.8641)[&height=12.8641,rate=0.00372602]:0.3533,66[&height=12.0,rate=0.00372602]:1.2174)[&height=13.2174,rate=0.00372602]:0.694)[&height=13.9114,rate=0.00372602]:0.301)[&height=14.2124,rate=0.00372602]:1.0089)[&height=15.2213,rate=0.00372602]:1.016)[&height=16.2373,rate=0.00372602]:0.434)[&height=16.6713,rate=0.00372602]:1.8262,3[&height=16.0,rate=0.00372602]:2.4975)[&height=18.4975,rate=0.00372602]:2.0684)[&height=20.5659]; +tree 9 = ((1[&height=17.0,rate=0.00350319]:2.2424,(2[&height=16.0,rate=0.00350319]:2.0394,4[&height=15.0,rate=0.00350319]:3.0394)[&height=18.0394,rate=0.00350319]:1.203)[&height=19.2424,rate=0.00350319]:1.2676,(((9[&height=14.0,rate=0.00350319]:2.2819,(8[&height=14.0,rate=0.00350319]:1.2958,5[&height=15.0,rate=0.00350319]:0.2958)[&height=15.2958,rate=0.00350319]:0.9861)[&height=16.2819,rate=0.00350319]:0.0821,(7[&height=14.0,rate=0.00350319]:1.781,(6[&height=15.0,rate=0.00350319]:0.1825,((68[&height=13.0,rate=0.00350319]:0.7696,69[&height=13.0,rate=0.00350319]:0.7696)[&height=13.7696,rate=0.00350319]:0.2124,((((14[&height=11.0,rate=0.00350319]:1.3098,12[&height=11.0,rate=0.00350319]:1.3098)[&height=12.3098,rate=0.00350319]:0.137,(17[&height=11.0,rate=0.00350319]:0.8277,18[&height=11.0,rate=0.00350319]:0.8277)[&height=11.8277,rate=0.00350319]:0.6191)[&height=12.4468,rate=0.00350319]:0.223,((((13[&height=11.0,rate=0.00350319]:0.9092,(11[&height=11.0,rate=0.00350319]:0.37,16[&height=11.0,rate=0.00350319]:0.37)[&height=11.37,rate=0.00350319]:0.5392)[&height=11.9092,rate=0.00350319]:0.5424,(19[&height=11.0,rate=0.00350319]:1.0156,((27[&height=6.0,rate=0.00350319]:3.83867,((31[&height=6.0,rate=0.00350319]:2.0717,(29[&height=6.0,rate=0.00350319]:1.4391,((((37[&height=4.0,rate=0.00350319]:0.71944,41[&height=4.0,rate=0.00350319]:0.71944)[&height=4.71944,rate=0.00350319]:0.98752,((38[&height=4.0,rate=0.00350319]:1.29915,40[&height=4.0,rate=0.00350319]:1.29915)[&height=5.29915,rate=0.00350319]:0.04928,43[&height=4.0,rate=0.00350319]:1.34843)[&height=5.34843,rate=0.00350319]:0.35853)[&height=5.70696,rate=0.00350319]:0.92212,(((((((61[&height=0.0,rate=0.00350319]:1.35284,((57[&height=0.0,rate=0.00350319]:0.687948,(54[&height=0.0,rate=0.00350319]:0.426267,60[&height=0.0,rate=0.00350319]:0.426267)[&height=0.426267,rate=0.00350319]:0.261681)[&height=0.687948,rate=0.00350319]:0.113566,58[&height=0.0,rate=0.00350319]:0.801514)[&height=0.801514,rate=0.00350319]:0.551326)[&height=1.35284,rate=0.00350319]:0.57609,55[&height=0.0,rate=0.00350319]:1.92893)[&height=1.92893,rate=0.00350319]:0.02821,53[&height=0.0,rate=0.00350319]:1.95714)[&height=1.95714,rate=0.00350319]:0.11184,(((62[&height=0.0,rate=0.00350319]:1.12983,52[&height=0.0,rate=0.00350319]:1.12983)[&height=1.12983,rate=0.00350319]:0.45496,(((64[&height=0.0,rate=0.00350319]:0.763303,51[&height=0.0,rate=0.00350319]:0.763303)[&height=0.763303,rate=0.00350319]:0.540997,63[&height=0.0,rate=0.00350319]:1.3043)[&height=1.3043,rate=0.00350319]:0.19537,56[&height=0.0,rate=0.00350319]:1.49967)[&height=1.49967,rate=0.00350319]:0.08512)[&height=1.58479,rate=0.00350319]:0.29121,59[&height=0.0,rate=0.00350319]:1.876)[&height=1.876,rate=0.00350319]:0.19298)[&height=2.06898,rate=0.00350319]:1.03281,50[&height=0.0,rate=0.00350319]:3.10179)[&height=3.10179,rate=0.00350319]:2.34866,(35[&height=4.0,rate=0.00350319]:1.39035,46[&height=4.0,rate=0.00350319]:1.39035)[&height=5.39035,rate=0.00350319]:0.0601)[&height=5.45045,rate=0.00350319]:1.06316,((45[&height=4.0,rate=0.00350319]:1.55322,(44[&height=4.0,rate=0.00350319]:1.46338,(49[&height=4.0,rate=0.00350319]:1.3122,36[&height=4.0,rate=0.00350319]:1.3122)[&height=5.3122,rate=0.00350319]:0.15118)[&height=5.46338,rate=0.00350319]:0.08984)[&height=5.55322,rate=0.00350319]:0.95594,(47[&height=4.0,rate=0.00350319]:0.92924,48[&height=4.0,rate=0.00350319]:0.92924)[&height=4.92924,rate=0.00350319]:1.57992)[&height=6.50916,rate=0.00350319]:0.00445)[&height=6.51361,rate=0.00350319]:0.11547)[&height=6.62908,rate=0.00350319]:0.43288,24[&height=6.0,rate=0.00350319]:1.06196)[&height=7.06196,rate=0.00350319]:0.37714)[&height=7.4391,rate=0.00350319]:0.6326)[&height=8.0717,rate=0.00350319]:0.18404,(((39[&height=4.0,rate=0.00350319]:3.60515,22[&height=6.0,rate=0.00350319]:1.60515)[&height=7.60515,rate=0.00350319]:0.27245,(28[&height=6.0,rate=0.00350319]:1.20191,(25[&height=6.0,rate=0.00350319]:1.10513,20[&height=6.0,rate=0.00350319]:1.10513)[&height=7.10513,rate=0.00350319]:0.09678)[&height=7.20191,rate=0.00350319]:0.67569)[&height=7.8776,rate=0.00350319]:0.16741,21[&height=6.0,rate=0.00350319]:2.04501)[&height=8.04501,rate=0.00350319]:0.21073)[&height=8.25574,rate=0.00350319]:1.58293)[&height=9.83867,rate=0.00350319]:0.76523,(((32[&height=6.0,rate=0.00350319]:0.58088,26[&height=6.0,rate=0.00350319]:0.58088)[&height=6.58088,rate=0.00350319]:0.40137,(33[&height=6.0,rate=0.00350319]:0.76885,34[&height=6.0,rate=0.00350319]:0.76885)[&height=6.76885,rate=0.00350319]:0.2134)[&height=6.98225,rate=0.00350319]:2.49342,((42[&height=4.0,rate=0.00350319]:3.05775,23[&height=6.0,rate=0.00350319]:1.05775)[&height=7.05775,rate=0.00350319]:0.32768,30[&height=6.0,rate=0.00350319]:1.38543)[&height=7.38543,rate=0.00350319]:2.09024)[&height=9.47567,rate=0.00350319]:1.12823)[&height=10.6039,rate=0.00350319]:1.4117)[&height=12.0156,rate=0.00350319]:0.436)[&height=12.4516,rate=0.00350319]:0.0862,15[&height=11.0,rate=0.00350319]:1.5378)[&height=12.5378,rate=0.00350319]:0.0609,10[&height=11.0,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+tree 10 = ((1[&height=17.0,rate=0.00326235]:2.1237,(2[&height=16.0,rate=0.00326235]:1.5932,4[&height=15.0,rate=0.00326235]:2.5932)[&height=17.5932,rate=0.00326235]:1.5305)[&height=19.1237,rate=0.00326235]:1.9148,(((9[&height=14.0,rate=0.00326235]:3.2716,(8[&height=14.0,rate=0.00326235]:2.7132,5[&height=15.0,rate=0.00326235]:1.7132)[&height=16.7132,rate=0.00326235]:0.5584)[&height=17.2716,rate=0.00326235]:0.1388,(7[&height=14.0,rate=0.00326235]:2.712,(6[&height=15.0,rate=0.00326235]:1.1648,((68[&height=13.0,rate=0.00326235]:1.4584,69[&height=13.0,rate=0.00326235]:1.4584)[&height=14.4584,rate=0.00326235]:0.3181,((((14[&height=11.0,rate=0.00326235]:1.0985,12[&height=11.0,rate=0.00326235]:1.0985)[&height=12.0985,rate=0.00326235]:0.1588,(17[&height=11.0,rate=0.00326235]:0.7519,18[&height=11.0,rate=0.00326235]:0.7519)[&height=11.7519,rate=0.00326235]:0.5054)[&height=12.2573,rate=0.00326235]:0.2979,((((13[&height=11.0,rate=0.00326235]:0.5471,(11[&height=11.0,rate=0.00326235]:0.2177,16[&height=11.0,rate=0.00326235]:0.2177)[&height=11.2177,rate=0.00326235]:0.3294)[&height=11.5471,rate=0.00326235]:0.3259,(19[&height=11.0,rate=0.00326235]:0.6888,((27[&height=6.0,rate=0.00326235]:2.85293,((31[&height=6.0,rate=0.00326235]:1.74563,(29[&height=6.0,rate=0.00326235]:1.5408,((((37[&height=4.0,rate=0.00326235]:0.82436,41[&height=4.0,rate=0.00326235]:0.82436)[&height=4.82436,rate=0.00326235]:0.50623,((38[&height=4.0,rate=0.00326235]:0.6077,40[&height=4.0,rate=0.00326235]:0.6077)[&height=4.6077,rate=0.00326235]:0.62737,43[&height=4.0,rate=0.00326235]:1.23507)[&height=5.23507,rate=0.00326235]:0.09552)[&height=5.33059,rate=0.00326235]:1.60544,(((((((61[&height=0.0,rate=0.00326235]:0.778206,((57[&height=0.0,rate=0.00326235]:0.476057,(54[&height=0.0,rate=0.00326235]:0.220195,60[&height=0.0,rate=0.00326235]:0.220195)[&height=0.220195,rate=0.00326235]:0.255862)[&height=0.476057,rate=0.00326235]:0.280106,58[&height=0.0,rate=0.00326235]:0.756163)[&height=0.756163,rate=0.00326235]:0.022043)[&height=0.778206,rate=0.00326235]:0.318504,55[&height=0.0,rate=0.00326235]:1.09671)[&height=1.09671,rate=0.00326235]:0.56878,53[&height=0.0,rate=0.00326235]:1.66549)[&height=1.66549,rate=0.00326235]:0.03072,(((62[&height=0.0,rate=0.00326235]:1.24027,52[&height=0.0,rate=0.00326235]:1.24027)[&height=1.24027,rate=0.00326235]:0.08831,(((64[&height=0.0,rate=0.00326235]:0.0280089,51[&height=0.0,rate=0.00326235]:0.0280089)[&height=0.0280089,rate=0.00326235]:0.3918781,63[&height=0.0,rate=0.00326235]:0.419887)[&height=0.419887,rate=0.00326235]:0.831603,56[&height=0.0,rate=0.00326235]:1.25149)[&height=1.25149,rate=0.00326235]:0.07709)[&height=1.32858,rate=0.00326235]:0.15601,59[&height=0.0,rate=0.00326235]:1.48459)[&height=1.48459,rate=0.00326235]:0.21162)[&height=1.69621,rate=0.00326235]:0.4408,50[&height=0.0,rate=0.00326235]:2.13701)[&height=2.13701,rate=0.00326235]:2.99069,(35[&height=4.0,rate=0.00326235]:1.07704,46[&height=4.0,rate=0.00326235]:1.07704)[&height=5.07704,rate=0.00326235]:0.05066)[&height=5.1277,rate=0.00326235]:1.37576,((45[&height=4.0,rate=0.00326235]:1.70598,(44[&height=4.0,rate=0.00326235]:1.02275,(49[&height=4.0,rate=0.00326235]:0.67924,36[&height=4.0,rate=0.00326235]:0.67924)[&height=4.67924,rate=0.00326235]:0.34351)[&height=5.02275,rate=0.00326235]:0.68323)[&height=5.70598,rate=0.00326235]:0.77104,(47[&height=4.0,rate=0.00326235]:1.20315,48[&height=4.0,rate=0.00326235]:1.20315)[&height=5.20315,rate=0.00326235]:1.27387)[&height=6.47702,rate=0.00326235]:0.02644)[&height=6.50346,rate=0.00326235]:0.43257)[&height=6.93603,rate=0.00326235]:0.26756,24[&height=6.0,rate=0.00326235]:1.20359)[&height=7.20359,rate=0.00326235]:0.33721)[&height=7.5408,rate=0.00326235]:0.20483)[&height=7.74563,rate=0.00326235]:0.07336,(((39[&height=4.0,rate=0.00326235]:3.03262,22[&height=6.0,rate=0.00326235]:1.03262)[&height=7.03262,rate=0.00326235]:0.4154,(28[&height=6.0,rate=0.00326235]:0.66336,(25[&height=6.0,rate=0.00326235]:0.60086,20[&height=6.0,rate=0.00326235]:0.60086)[&height=6.60086,rate=0.00326235]:0.0625)[&height=6.66336,rate=0.00326235]:0.78466)[&height=7.44802,rate=0.00326235]:0.19462,21[&height=6.0,rate=0.00326235]:1.64264)[&height=7.64264,rate=0.00326235]:0.17635)[&height=7.81899,rate=0.00326235]:1.03394)[&height=8.85293,rate=0.00326235]:0.55156,(((32[&height=6.0,rate=0.00326235]:0.32925,26[&height=6.0,rate=0.00326235]:0.32925)[&height=6.32925,rate=0.00326235]:0.46313,(33[&height=6.0,rate=0.00326235]:0.53248,34[&height=6.0,rate=0.00326235]:0.53248)[&height=6.53248,rate=0.00326235]:0.2599)[&height=6.79238,rate=0.00326235]:1.58368,((42[&height=4.0,rate=0.00326235]:2.2669,23[&height=6.0,rate=0.00326235]:0.2669)[&height=6.2669,rate=0.00326235]:0.30008,30[&height=6.0,rate=0.00326235]:0.56698)[&height=6.56698,rate=0.00326235]:1.80908)[&height=8.37606,rate=0.00326235]:1.02843)[&height=9.40449,rate=0.00326235]:2.28431)[&height=11.6888,rate=0.00326235]:0.1842)[&height=11.873,rate=0.00326235]:0.026,15[&height=11.0,rate=0.00326235]:0.899)[&height=11.899,rate=0.00326235]:0.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+tree 11 = ((1[&height=17.0,rate=0.00336313]:1.9062,(2[&height=16.0,rate=0.00336313]:1.8486,4[&height=15.0,rate=0.00336313]:2.8486)[&height=17.8486,rate=0.00336313]:1.0576)[&height=18.9062,rate=0.00336313]:1.6089,(((9[&height=14.0,rate=0.00336313]:1.8804,(8[&height=14.0,rate=0.00336313]:1.3013,5[&height=15.0,rate=0.00336313]:0.3013)[&height=15.3013,rate=0.00336313]:0.5791)[&height=15.8804,rate=0.00336313]:0.3688,(7[&height=14.0,rate=0.00336313]:1.8006,(6[&height=15.0,rate=0.00336313]:0.2056,((68[&height=13.0,rate=0.00336313]:0.7649,69[&height=13.0,rate=0.00336313]:0.7649)[&height=13.7649,rate=0.00336313]:0.2395,((((14[&height=11.0,rate=0.00336313]:0.8552,12[&height=11.0,rate=0.00336313]:0.8552)[&height=11.8552,rate=0.00336313]:0.1514,(17[&height=11.0,rate=0.00336313]:0.8066,18[&height=11.0,rate=0.00336313]:0.8066)[&height=11.8066,rate=0.00336313]:0.2)[&height=12.0066,rate=0.00336313]:0.3875,((((13[&height=11.0,rate=0.00336313]:0.7404,(11[&height=11.0,rate=0.00336313]:0.2188,16[&height=11.0,rate=0.00336313]:0.2188)[&height=11.2188,rate=0.00336313]:0.5216)[&height=11.7404,rate=0.00336313]:0.089,(19[&height=11.0,rate=0.00336313]:0.593,((27[&height=6.0,rate=0.00336313]:3.49534,((31[&height=6.0,rate=0.00336313]:2.15923,(29[&height=6.0,rate=0.00336313]:1.86511,((((37[&height=4.0,rate=0.00336313]:1.44709,41[&height=4.0,rate=0.00336313]:1.44709)[&height=5.44709,rate=0.00336313]:0.30209,((38[&height=4.0,rate=0.00336313]:0.78071,40[&height=4.0,rate=0.00336313]:0.78071)[&height=4.78071,rate=0.00336313]:0.49379,43[&height=4.0,rate=0.00336313]:1.2745)[&height=5.2745,rate=0.00336313]:0.47468)[&height=5.74918,rate=0.00336313]:1.42957,(((((((61[&height=0.0,rate=0.00336313]:0.800016,((57[&height=0.0,rate=0.00336313]:0.564435,(54[&height=0.0,rate=0.00336313]:0.121149,60[&height=0.0,rate=0.00336313]:0.121149)[&height=0.121149,rate=0.00336313]:0.443286)[&height=0.564435,rate=0.00336313]:0.232642,58[&height=0.0,rate=0.00336313]:0.797077)[&height=0.797077,rate=0.00336313]:0.002939)[&height=0.800016,rate=0.00336313]:0.294564,55[&height=0.0,rate=0.00336313]:1.09458)[&height=1.09458,rate=0.00336313]:0.15253,53[&height=0.0,rate=0.00336313]:1.24711)[&height=1.24711,rate=0.00336313]:0.02504,(((62[&height=0.0,rate=0.00336313]:0.780341,52[&height=0.0,rate=0.00336313]:0.780341)[&height=0.780341,rate=0.00336313]:0.335579,(((64[&height=0.0,rate=0.00336313]:0.105745,51[&height=0.0,rate=0.00336313]:0.105745)[&height=0.105745,rate=0.00336313]:0.639751,63[&height=0.0,rate=0.00336313]:0.745496)[&height=0.745496,rate=0.00336313]:0.069451,56[&height=0.0,rate=0.00336313]:0.814947)[&height=0.814947,rate=0.00336313]:0.300973)[&height=1.11592,rate=0.00336313]:0.02174,59[&height=0.0,rate=0.00336313]:1.13766)[&height=1.13766,rate=0.00336313]:0.13449)[&height=1.27215,rate=0.00336313]:0.91408,50[&height=0.0,rate=0.00336313]:2.18623)[&height=2.18623,rate=0.00336313]:3.17636,(35[&height=4.0,rate=0.00336313]:0.22991,46[&height=4.0,rate=0.00336313]:0.22991)[&height=4.22991,rate=0.00336313]:1.13268)[&height=5.36259,rate=0.00336313]:1.76552,((45[&height=4.0,rate=0.00336313]:1.61661,(44[&height=4.0,rate=0.00336313]:1.29999,(49[&height=4.0,rate=0.00336313]:1.0212,36[&height=4.0,rate=0.00336313]:1.0212)[&height=5.0212,rate=0.00336313]:0.27879)[&height=5.29999,rate=0.00336313]:0.31662)[&height=5.61661,rate=0.00336313]:1.14473,(47[&height=4.0,rate=0.00336313]:1.79337,48[&height=4.0,rate=0.00336313]:1.79337)[&height=5.79337,rate=0.00336313]:0.96797)[&height=6.76134,rate=0.00336313]:0.36677)[&height=7.12811,rate=0.00336313]:0.05064)[&height=7.17875,rate=0.00336313]:0.22448,24[&height=6.0,rate=0.00336313]:1.40323)[&height=7.40323,rate=0.00336313]:0.46188)[&height=7.86511,rate=0.00336313]:0.29412)[&height=8.15923,rate=0.00336313]:0.0663,(((39[&height=4.0,rate=0.00336313]:2.88592,22[&height=6.0,rate=0.00336313]:0.88592)[&height=6.88592,rate=0.00336313]:0.95179,(28[&height=6.0,rate=0.00336313]:0.45101,(25[&height=6.0,rate=0.00336313]:0.39313,20[&height=6.0,rate=0.00336313]:0.39313)[&height=6.39313,rate=0.00336313]:0.05788)[&height=6.45101,rate=0.00336313]:1.3867)[&height=7.83771,rate=0.00336313]:0.18952,21[&height=6.0,rate=0.00336313]:2.02723)[&height=8.02723,rate=0.00336313]:0.1983)[&height=8.22553,rate=0.00336313]:1.26981)[&height=9.49534,rate=0.00336313]:0.38232,(((32[&height=6.0,rate=0.00336313]:0.65934,26[&height=6.0,rate=0.00336313]:0.65934)[&height=6.65934,rate=0.00336313]:0.13989,(33[&height=6.0,rate=0.00336313]:0.53305,34[&height=6.0,rate=0.00336313]:0.53305)[&height=6.53305,rate=0.00336313]:0.26618)[&height=6.79923,rate=0.00336313]:2.1435,((42[&height=4.0,rate=0.00336313]:2.78782,23[&height=6.0,rate=0.00336313]:0.78782)[&height=6.78782,rate=0.00336313]:0.12459,30[&height=6.0,rate=0.00336313]:0.91241)[&height=6.91241,rate=0.00336313]:2.03032)[&height=8.94273,rate=0.00336313]:0.93493)[&height=9.87766,rate=0.00336313]:1.71534)[&height=11.593,rate=0.00336313]:0.2364)[&height=11.8294,rate=0.00336313]:0.074,15[&height=11.0,rate=0.00336313]:0.9034)[&height=11.9034,rate=0.0033631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+tree 12 = ((1[&height=17.0,rate=0.00360542]:1.5962,(2[&height=16.0,rate=0.00360542]:2.0161,4[&height=15.0,rate=0.00360542]:3.0161)[&height=18.0161,rate=0.00360542]:0.5801)[&height=18.5962,rate=0.00360542]:1.0795,(((9[&height=14.0,rate=0.00360542]:2.2633,(8[&height=14.0,rate=0.00360542]:1.4496,5[&height=15.0,rate=0.00360542]:0.4496)[&height=15.4496,rate=0.00360542]:0.8137)[&height=16.2633,rate=0.00360542]:0.5776,(7[&height=14.0,rate=0.00360542]:2.2776,(6[&height=15.0,rate=0.00360542]:0.4131,((68[&height=13.0,rate=0.00360542]:1.1862,69[&height=13.0,rate=0.00360542]:1.1862)[&height=14.1862,rate=0.00360542]:0.177,((((14[&height=11.0,rate=0.00360542]:0.9235,12[&height=11.0,rate=0.00360542]:0.9235)[&height=11.9235,rate=0.00360542]:0.3789,(17[&height=11.0,rate=0.00360542]:1.0694,18[&height=11.0,rate=0.00360542]:1.0694)[&height=12.0694,rate=0.00360542]:0.233)[&height=12.3024,rate=0.00360542]:0.2027,((((13[&height=11.0,rate=0.00360542]:0.5542,(11[&height=11.0,rate=0.00360542]:0.0379,16[&height=11.0,rate=0.00360542]:0.0379)[&height=11.0379,rate=0.00360542]:0.5163)[&height=11.5542,rate=0.00360542]:0.4857,(19[&height=11.0,rate=0.00360542]:0.8433,((27[&height=6.0,rate=0.00360542]:2.93949,((31[&height=6.0,rate=0.00360542]:1.74685,(29[&height=6.0,rate=0.00360542]:1.49944,((((37[&height=4.0,rate=0.00360542]:1.09509,41[&height=4.0,rate=0.00360542]:1.09509)[&height=5.09509,rate=0.00360542]:0.37306,((38[&height=4.0,rate=0.00360542]:0.92157,40[&height=4.0,rate=0.00360542]:0.92157)[&height=4.92157,rate=0.00360542]:0.01919,43[&height=4.0,rate=0.00360542]:0.94076)[&height=4.94076,rate=0.00360542]:0.52739)[&height=5.46815,rate=0.00360542]:1.69683,(((((((61[&height=0.0,rate=0.00360542]:1.25778,((57[&height=0.0,rate=0.00360542]:0.655975,(54[&height=0.0,rate=0.00360542]:0.419106,60[&height=0.0,rate=0.00360542]:0.419106)[&height=0.419106,rate=0.00360542]:0.236869)[&height=0.655975,rate=0.00360542]:0.25971,58[&height=0.0,rate=0.00360542]:0.915685)[&height=0.915685,rate=0.00360542]:0.342095)[&height=1.25778,rate=0.00360542]:0.29616,55[&height=0.0,rate=0.00360542]:1.55394)[&height=1.55394,rate=0.00360542]:0.52582,53[&height=0.0,rate=0.00360542]:2.07976)[&height=2.07976,rate=0.00360542]:0.03559,(((62[&height=0.0,rate=0.00360542]:1.04312,52[&height=0.0,rate=0.00360542]:1.04312)[&height=1.04312,rate=0.00360542]:0.37718,(((64[&height=0.0,rate=0.00360542]:0.237905,51[&height=0.0,rate=0.00360542]:0.237905)[&height=0.237905,rate=0.00360542]:0.832035,63[&height=0.0,rate=0.00360542]:1.06994)[&height=1.06994,rate=0.00360542]:0.28267,56[&height=0.0,rate=0.00360542]:1.35261)[&height=1.35261,rate=0.00360542]:0.06769)[&height=1.4203,rate=0.00360542]:0.58978,59[&height=0.0,rate=0.00360542]:2.01008)[&height=2.01008,rate=0.00360542]:0.10527)[&height=2.11535,rate=0.00360542]:1.25724,50[&height=0.0,rate=0.00360542]:3.37259)[&height=3.37259,rate=0.00360542]:2.21157,(35[&height=4.0,rate=0.00360542]:1.24495,46[&height=4.0,rate=0.00360542]:1.24495)[&height=5.24495,rate=0.00360542]:0.33921)[&height=5.58416,rate=0.00360542]:1.53415,((45[&height=4.0,rate=0.00360542]:1.84736,(44[&height=4.0,rate=0.00360542]:1.68709,(49[&height=4.0,rate=0.00360542]:1.53955,36[&height=4.0,rate=0.00360542]:1.53955)[&height=5.53955,rate=0.00360542]:0.14754)[&height=5.68709,rate=0.00360542]:0.16027)[&height=5.84736,rate=0.00360542]:0.9237,(47[&height=4.0,rate=0.00360542]:1.4045,48[&height=4.0,rate=0.00360542]:1.4045)[&height=5.4045,rate=0.00360542]:1.36656)[&height=6.77106,rate=0.00360542]:0.34725)[&height=7.11831,rate=0.00360542]:0.04667)[&height=7.16498,rate=0.00360542]:0.26948,24[&height=6.0,rate=0.00360542]:1.43446)[&height=7.43446,rate=0.00360542]:0.06498)[&height=7.49944,rate=0.00360542]:0.24741)[&height=7.74685,rate=0.00360542]:0.11192,(((39[&height=4.0,rate=0.00360542]:2.75197,22[&height=6.0,rate=0.00360542]:0.75197)[&height=6.75197,rate=0.00360542]:0.54233,(28[&height=6.0,rate=0.00360542]:0.46799,(25[&height=6.0,rate=0.00360542]:0.16836,20[&height=6.0,rate=0.00360542]:0.16836)[&height=6.16836,rate=0.00360542]:0.29963)[&height=6.46799,rate=0.00360542]:0.82631)[&height=7.2943,rate=0.00360542]:0.53844,21[&height=6.0,rate=0.00360542]:1.83274)[&height=7.83274,rate=0.00360542]:0.02603)[&height=7.85877,rate=0.00360542]:1.08072)[&height=8.93949,rate=0.00360542]:0.64186,(((32[&height=6.0,rate=0.00360542]:0.44877,26[&height=6.0,rate=0.00360542]:0.44877)[&height=6.44877,rate=0.00360542]:0.09982,(33[&height=6.0,rate=0.00360542]:0.20976,34[&height=6.0,rate=0.00360542]:0.20976)[&height=6.20976,rate=0.00360542]:0.33883)[&height=6.54859,rate=0.00360542]:1.53727,((42[&height=4.0,rate=0.00360542]:2.40497,23[&height=6.0,rate=0.00360542]:0.40497)[&height=6.40497,rate=0.00360542]:0.17659,30[&height=6.0,rate=0.00360542]:0.58156)[&height=6.58156,rate=0.00360542]:1.5043)[&height=8.08586,rate=0.00360542]:1.49549)[&height=9.58135,rate=0.00360542]:2.26195)[&height=11.8433,rate=0.00360542]:0.1966)[&height=12.0399,rate=0.00360542]:0.0497,15[&height=11.0,rate=0.00360542]:1.0896)[&height=12.0896,rate=0.00360542]:0.07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+tree 13 = ((1[&height=17.0,rate=0.00352297]:1.0207,(2[&height=16.0,rate=0.00352297]:1.3638,4[&height=15.0,rate=0.00352297]:2.3638)[&height=17.3638,rate=0.00352297]:0.6569)[&height=18.0207,rate=0.00352297]:1.3726,(((9[&height=14.0,rate=0.00352297]:1.7738,(8[&height=14.0,rate=0.00352297]:1.0229,5[&height=15.0,rate=0.00352297]:0.0229)[&height=15.0229,rate=0.00352297]:0.7509)[&height=15.7738,rate=0.00352297]:0.1629,(7[&height=14.0,rate=0.00352297]:1.5173,(6[&height=15.0,rate=0.00352297]:0.2463,((68[&height=13.0,rate=0.00352297]:0.6369,69[&height=13.0,rate=0.00352297]:0.6369)[&height=13.6369,rate=0.00352297]:0.3084,((((14[&height=11.0,rate=0.00352297]:0.8518,12[&height=11.0,rate=0.00352297]:0.8518)[&height=11.8518,rate=0.00352297]:0.3858,(17[&height=11.0,rate=0.00352297]:1.067,18[&height=11.0,rate=0.00352297]:1.067)[&height=12.067,rate=0.00352297]:0.1706)[&height=12.2376,rate=0.00352297]:0.4032,((((13[&height=11.0,rate=0.00352297]:0.4908,(11[&height=11.0,rate=0.00352297]:0.2466,16[&height=11.0,rate=0.00352297]:0.2466)[&height=11.2466,rate=0.00352297]:0.2442)[&height=11.4908,rate=0.00352297]:0.1804,(19[&height=11.0,rate=0.00352297]:0.5797,((27[&height=6.0,rate=0.00352297]:3.27107,((31[&height=6.0,rate=0.00352297]:2.13969,(29[&height=6.0,rate=0.00352297]:0.97875,((((37[&height=4.0,rate=0.00352297]:1.11761,41[&height=4.0,rate=0.00352297]:1.11761)[&height=5.11761,rate=0.00352297]:0.11181,((38[&height=4.0,rate=0.00352297]:0.90165,40[&height=4.0,rate=0.00352297]:0.90165)[&height=4.90165,rate=0.00352297]:0.20704,43[&height=4.0,rate=0.00352297]:1.10869)[&height=5.10869,rate=0.00352297]:0.12073)[&height=5.22942,rate=0.00352297]:1.07839,(((((((61[&height=0.0,rate=0.00352297]:0.545704,((57[&height=0.0,rate=0.00352297]:0.0645394,(54[&height=0.0,rate=0.00352297]:0.0515738,60[&height=0.0,rate=0.00352297]:0.0515738)[&height=0.0515738,rate=0.00352297]:0.0129656)[&height=0.0645394,rate=0.00352297]:0.3780966,58[&height=0.0,rate=0.00352297]:0.442636)[&height=0.442636,rate=0.00352297]:0.103068)[&height=0.545704,rate=0.00352297]:0.32609,55[&height=0.0,rate=0.00352297]:0.871794)[&height=0.871794,rate=0.00352297]:0.421946,53[&height=0.0,rate=0.00352297]:1.29374)[&height=1.29374,rate=0.00352297]:0.14569,(((62[&height=0.0,rate=0.00352297]:1.11445,52[&height=0.0,rate=0.00352297]:1.11445)[&height=1.11445,rate=0.00352297]:0.14352,(((64[&height=0.0,rate=0.00352297]:0.168121,51[&height=0.0,rate=0.00352297]:0.168121)[&height=0.168121,rate=0.00352297]:0.180135,63[&height=0.0,rate=0.00352297]:0.348256)[&height=0.348256,rate=0.00352297]:0.906544,56[&height=0.0,rate=0.00352297]:1.2548)[&height=1.2548,rate=0.00352297]:0.00317)[&height=1.25797,rate=0.00352297]:0.03727,59[&height=0.0,rate=0.00352297]:1.29524)[&height=1.29524,rate=0.00352297]:0.14419)[&height=1.43943,rate=0.00352297]:0.52769,50[&height=0.0,rate=0.00352297]:1.96712)[&height=1.96712,rate=0.00352297]:2.97496,(35[&height=4.0,rate=0.00352297]:0.73582,46[&height=4.0,rate=0.00352297]:0.73582)[&height=4.73582,rate=0.00352297]:0.20626)[&height=4.94208,rate=0.00352297]:1.34651,((45[&height=4.0,rate=0.00352297]:0.90873,(44[&height=4.0,rate=0.00352297]:0.75889,(49[&height=4.0,rate=0.00352297]:0.68875,36[&height=4.0,rate=0.00352297]:0.68875)[&height=4.68875,rate=0.00352297]:0.07014)[&height=4.75889,rate=0.00352297]:0.14984)[&height=4.90873,rate=0.00352297]:0.96919,(47[&height=4.0,rate=0.00352297]:0.90099,48[&height=4.0,rate=0.00352297]:0.90099)[&height=4.90099,rate=0.00352297]:0.97693)[&height=5.87792,rate=0.00352297]:0.41067)[&height=6.28859,rate=0.00352297]:0.01922)[&height=6.30781,rate=0.00352297]:0.28196,24[&height=6.0,rate=0.00352297]:0.58977)[&height=6.58977,rate=0.00352297]:0.38898)[&height=6.97875,rate=0.00352297]:1.16094)[&height=8.13969,rate=0.00352297]:0.13491,(((39[&height=4.0,rate=0.00352297]:3.49299,22[&height=6.0,rate=0.00352297]:1.49299)[&height=7.49299,rate=0.00352297]:0.07714,(28[&height=6.0,rate=0.00352297]:0.57117,(25[&height=6.0,rate=0.00352297]:0.44461,20[&height=6.0,rate=0.00352297]:0.44461)[&height=6.44461,rate=0.00352297]:0.12656)[&height=6.57117,rate=0.00352297]:0.99896)[&height=7.57013,rate=0.00352297]:0.46621,21[&height=6.0,rate=0.00352297]:2.03634)[&height=8.03634,rate=0.00352297]:0.23826)[&height=8.2746,rate=0.00352297]:0.99647)[&height=9.27107,rate=0.00352297]:0.80153,(((32[&height=6.0,rate=0.00352297]:0.74492,26[&height=6.0,rate=0.00352297]:0.74492)[&height=6.74492,rate=0.00352297]:0.55418,(33[&height=6.0,rate=0.00352297]:0.94226,34[&height=6.0,rate=0.00352297]:0.94226)[&height=6.94226,rate=0.00352297]:0.35684)[&height=7.2991,rate=0.00352297]:1.2896,((42[&height=4.0,rate=0.00352297]:2.73831,23[&height=6.0,rate=0.00352297]:0.73831)[&height=6.73831,rate=0.00352297]:0.43037,30[&height=6.0,rate=0.00352297]:1.16868)[&height=7.16868,rate=0.00352297]:1.42002)[&height=8.5887,rate=0.00352297]:1.4839)[&height=10.0726,rate=0.00352297]:1.5071)[&height=11.5797,rate=0.00352297]:0.0915)[&height=11.6712,rate=0.00352297]:0.0725,15[&height=11.0,rate=0.00352297]:0.7437)[&height=11.7437,rate=0.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+tree 14 = ((1[&height=17.0,rate=0.00359808]:1.4101,(2[&height=16.0,rate=0.00359808]:1.2189,4[&height=15.0,rate=0.00359808]:2.2189)[&height=17.2189,rate=0.00359808]:1.1912)[&height=18.4101,rate=0.00359808]:1.5085,(((9[&height=14.0,rate=0.00359808]:2.3283,(8[&height=14.0,rate=0.00359808]:1.4872,5[&height=15.0,rate=0.00359808]:0.4872)[&height=15.4872,rate=0.00359808]:0.8411)[&height=16.3283,rate=0.00359808]:0.201,(7[&height=14.0,rate=0.00359808]:2.1588,(6[&height=15.0,rate=0.00359808]:0.6452,((68[&height=13.0,rate=0.00359808]:1.2932,69[&height=13.0,rate=0.00359808]:1.2932)[&height=14.2932,rate=0.00359808]:0.1393,((((14[&height=11.0,rate=0.00359808]:1.421,12[&height=11.0,rate=0.00359808]:1.421)[&height=12.421,rate=0.00359808]:0.1204,(17[&height=11.0,rate=0.00359808]:1.1365,18[&height=11.0,rate=0.00359808]:1.1365)[&height=12.1365,rate=0.00359808]:0.4049)[&height=12.5414,rate=0.00359808]:0.0703,((((13[&height=11.0,rate=0.00359808]:0.6824,(11[&height=11.0,rate=0.00359808]:0.1863,16[&height=11.0,rate=0.00359808]:0.1863)[&height=11.1863,rate=0.00359808]:0.4961)[&height=11.6824,rate=0.00359808]:0.5688,(19[&height=11.0,rate=0.00359808]:0.6502,((27[&height=6.0,rate=0.00359808]:2.88138,((31[&height=6.0,rate=0.00359808]:1.40288,(29[&height=6.0,rate=0.00359808]:1.24187,((((37[&height=4.0,rate=0.00359808]:0.87088,41[&height=4.0,rate=0.00359808]:0.87088)[&height=4.87088,rate=0.00359808]:0.47045,((38[&height=4.0,rate=0.00359808]:1.02425,40[&height=4.0,rate=0.00359808]:1.02425)[&height=5.02425,rate=0.00359808]:0.055,43[&height=4.0,rate=0.00359808]:1.07925)[&height=5.07925,rate=0.00359808]:0.26208)[&height=5.34133,rate=0.00359808]:1.56607,(((((((61[&height=0.0,rate=0.00359808]:0.997873,((57[&height=0.0,rate=0.00359808]:0.576809,(54[&height=0.0,rate=0.00359808]:0.271274,60[&height=0.0,rate=0.00359808]:0.271274)[&height=0.271274,rate=0.00359808]:0.305535)[&height=0.576809,rate=0.00359808]:0.30956,58[&height=0.0,rate=0.00359808]:0.886369)[&height=0.886369,rate=0.00359808]:0.111504)[&height=0.997873,rate=0.00359808]:0.393987,55[&height=0.0,rate=0.00359808]:1.39186)[&height=1.39186,rate=0.00359808]:0.07066,53[&height=0.0,rate=0.00359808]:1.46252)[&height=1.46252,rate=0.00359808]:0.11123,(((62[&height=0.0,rate=0.00359808]:0.8674,52[&height=0.0,rate=0.00359808]:0.8674)[&height=0.8674,rate=0.00359808]:0.17105,(((64[&height=0.0,rate=0.00359808]:0.174429,51[&height=0.0,rate=0.00359808]:0.174429)[&height=0.174429,rate=0.00359808]:0.36665,63[&height=0.0,rate=0.00359808]:0.541079)[&height=0.541079,rate=0.00359808]:0.287067,56[&height=0.0,rate=0.00359808]:0.828146)[&height=0.828146,rate=0.00359808]:0.210304)[&height=1.03845,rate=0.00359808]:0.21439,59[&height=0.0,rate=0.00359808]:1.25284)[&height=1.25284,rate=0.00359808]:0.32091)[&height=1.57375,rate=0.00359808]:1.02366,50[&height=0.0,rate=0.00359808]:2.59741)[&height=2.59741,rate=0.00359808]:3.16354,(35[&height=4.0,rate=0.00359808]:1.66025,46[&height=4.0,rate=0.00359808]:1.66025)[&height=5.66025,rate=0.00359808]:0.1007)[&height=5.76095,rate=0.00359808]:0.79091,((45[&height=4.0,rate=0.00359808]:1.51167,(44[&height=4.0,rate=0.00359808]:1.28134,(49[&height=4.0,rate=0.00359808]:1.19431,36[&height=4.0,rate=0.00359808]:1.19431)[&height=5.19431,rate=0.00359808]:0.08703)[&height=5.28134,rate=0.00359808]:0.23033)[&height=5.51167,rate=0.00359808]:0.9605,(47[&height=4.0,rate=0.00359808]:1.12485,48[&height=4.0,rate=0.00359808]:1.12485)[&height=5.12485,rate=0.00359808]:1.34732)[&height=6.47217,rate=0.00359808]:0.07969)[&height=6.55186,rate=0.00359808]:0.35554)[&height=6.9074,rate=0.00359808]:0.30518,24[&height=6.0,rate=0.00359808]:1.21258)[&height=7.21258,rate=0.00359808]:0.02929)[&height=7.24187,rate=0.00359808]:0.16101)[&height=7.40288,rate=0.00359808]:0.58552,(((39[&height=4.0,rate=0.00359808]:2.31676,22[&height=6.0,rate=0.00359808]:0.31676)[&height=6.31676,rate=0.00359808]:0.80253,(28[&height=6.0,rate=0.00359808]:1.05668,(25[&height=6.0,rate=0.00359808]:0.29762,20[&height=6.0,rate=0.00359808]:0.29762)[&height=6.29762,rate=0.00359808]:0.75906)[&height=7.05668,rate=0.00359808]:0.06261)[&height=7.11929,rate=0.00359808]:0.69976,21[&height=6.0,rate=0.00359808]:1.81905)[&height=7.81905,rate=0.00359808]:0.16935)[&height=7.9884,rate=0.00359808]:0.89298)[&height=8.88138,rate=0.00359808]:0.82821,(((32[&height=6.0,rate=0.00359808]:0.78772,26[&height=6.0,rate=0.00359808]:0.78772)[&height=6.78772,rate=0.00359808]:0.38037,(33[&height=6.0,rate=0.00359808]:0.7436,34[&height=6.0,rate=0.00359808]:0.7436)[&height=6.7436,rate=0.00359808]:0.42449)[&height=7.16809,rate=0.00359808]:1.64291,((42[&height=4.0,rate=0.00359808]:2.24222,23[&height=6.0,rate=0.00359808]:0.24222)[&height=6.24222,rate=0.00359808]:0.32111,30[&height=6.0,rate=0.00359808]:0.56333)[&height=6.56333,rate=0.00359808]:2.24767)[&height=8.811,rate=0.00359808]:0.89859)[&height=9.70959,rate=0.00359808]:1.94061)[&height=11.6502,rate=0.00359808]:0.601)[&height=12.2512,rate=0.00359808]:0.1224,15[&height=11.0,rate=0.00359808]:1.3736)[&height=12.3736,rate=0.00359808]:0.1345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+tree 15 = ((1[&height=17.0,rate=0.00382155]:2.0912,(2[&height=16.0,rate=0.00382155]:2.2069,4[&height=15.0,rate=0.00382155]:3.2069)[&height=18.2069,rate=0.00382155]:0.8843)[&height=19.0912,rate=0.00382155]:2.0012,(((9[&height=14.0,rate=0.00382155]:2.8227,(8[&height=14.0,rate=0.00382155]:1.2668,5[&height=15.0,rate=0.00382155]:0.2668)[&height=15.2668,rate=0.00382155]:1.5559)[&height=16.8227,rate=0.00382155]:0.7796,(7[&height=14.0,rate=0.00382155]:2.2381,(6[&height=15.0,rate=0.00382155]:0.3853,((68[&height=13.0,rate=0.00382155]:1.3111,69[&height=13.0,rate=0.00382155]:1.3111)[&height=14.3111,rate=0.00382155]:0.1287,((((14[&height=11.0,rate=0.00382155]:0.8987,12[&height=11.0,rate=0.00382155]:0.8987)[&height=11.8987,rate=0.00382155]:0.4156,(17[&height=11.0,rate=0.00382155]:0.74,18[&height=11.0,rate=0.00382155]:0.74)[&height=11.74,rate=0.00382155]:0.5743)[&height=12.3143,rate=0.00382155]:0.5845,((((13[&height=11.0,rate=0.00382155]:0.4153,(11[&height=11.0,rate=0.00382155]:0.1952,16[&height=11.0,rate=0.00382155]:0.1952)[&height=11.1952,rate=0.00382155]:0.2201)[&height=11.4153,rate=0.00382155]:0.5739,(19[&height=11.0,rate=0.00382155]:0.2531,((27[&height=6.0,rate=0.00382155]:2.7314,((31[&height=6.0,rate=0.00382155]:1.82221,(29[&height=6.0,rate=0.00382155]:1.43229,((((37[&height=4.0,rate=0.00382155]:1.22202,41[&height=4.0,rate=0.00382155]:1.22202)[&height=5.22202,rate=0.00382155]:0.43282,((38[&height=4.0,rate=0.00382155]:1.40031,40[&height=4.0,rate=0.00382155]:1.40031)[&height=5.40031,rate=0.00382155]:0.03787,43[&height=4.0,rate=0.00382155]:1.43818)[&height=5.43818,rate=0.00382155]:0.21666)[&height=5.65484,rate=0.00382155]:1.57481,(((((((61[&height=0.0,rate=0.00382155]:1.05153,((57[&height=0.0,rate=0.00382155]:0.748179,(54[&height=0.0,rate=0.00382155]:0.54991,60[&height=0.0,rate=0.00382155]:0.54991)[&height=0.54991,rate=0.00382155]:0.198269)[&height=0.748179,rate=0.00382155]:0.228782,58[&height=0.0,rate=0.00382155]:0.976961)[&height=0.976961,rate=0.00382155]:0.074569)[&height=1.05153,rate=0.00382155]:0.56908,55[&height=0.0,rate=0.00382155]:1.62061)[&height=1.62061,rate=0.00382155]:0.012,53[&height=0.0,rate=0.00382155]:1.63261)[&height=1.63261,rate=0.00382155]:0.05341,(((62[&height=0.0,rate=0.00382155]:0.496681,52[&height=0.0,rate=0.00382155]:0.496681)[&height=0.496681,rate=0.00382155]:0.299623,(((64[&height=0.0,rate=0.00382155]:0.339496,51[&height=0.0,rate=0.00382155]:0.339496)[&height=0.339496,rate=0.00382155]:0.379792,63[&height=0.0,rate=0.00382155]:0.719288)[&height=0.719288,rate=0.00382155]:0.047854,56[&height=0.0,rate=0.00382155]:0.767142)[&height=0.767142,rate=0.00382155]:0.029162)[&height=0.796304,rate=0.00382155]:0.606036,59[&height=0.0,rate=0.00382155]:1.40234)[&height=1.40234,rate=0.00382155]:0.28368)[&height=1.68602,rate=0.00382155]:0.9873,50[&height=0.0,rate=0.00382155]:2.67332)[&height=2.67332,rate=0.00382155]:3.23243,(35[&height=4.0,rate=0.00382155]:1.74809,46[&height=4.0,rate=0.00382155]:1.74809)[&height=5.74809,rate=0.00382155]:0.15766)[&height=5.90575,rate=0.00382155]:1.28657,((45[&height=4.0,rate=0.00382155]:0.95619,(44[&height=4.0,rate=0.00382155]:0.87943,(49[&height=4.0,rate=0.00382155]:0.2178,36[&height=4.0,rate=0.00382155]:0.2178)[&height=4.2178,rate=0.00382155]:0.66163)[&height=4.87943,rate=0.00382155]:0.07676)[&height=4.95619,rate=0.00382155]:1.86083,(47[&height=4.0,rate=0.00382155]:1.12023,48[&height=4.0,rate=0.00382155]:1.12023)[&height=5.12023,rate=0.00382155]:1.69679)[&height=6.81702,rate=0.00382155]:0.3753)[&height=7.19232,rate=0.00382155]:0.03733)[&height=7.22965,rate=0.00382155]:0.14535,24[&height=6.0,rate=0.00382155]:1.375)[&height=7.375,rate=0.00382155]:0.05729)[&height=7.43229,rate=0.00382155]:0.38992)[&height=7.82221,rate=0.00382155]:0.13346,(((39[&height=4.0,rate=0.00382155]:3.36299,22[&height=6.0,rate=0.00382155]:1.36299)[&height=7.36299,rate=0.00382155]:0.38017,(28[&height=6.0,rate=0.00382155]:1.65793,(25[&height=6.0,rate=0.00382155]:1.37966,20[&height=6.0,rate=0.00382155]:1.37966)[&height=7.37966,rate=0.00382155]:0.27827)[&height=7.65793,rate=0.00382155]:0.08523)[&height=7.74316,rate=0.00382155]:0.13786,21[&height=6.0,rate=0.00382155]:1.88102)[&height=7.88102,rate=0.00382155]:0.07465)[&height=7.95567,rate=0.00382155]:0.77573)[&height=8.7314,rate=0.00382155]:0.92217,(((32[&height=6.0,rate=0.00382155]:0.41618,26[&height=6.0,rate=0.00382155]:0.41618)[&height=6.41618,rate=0.00382155]:0.66206,(33[&height=6.0,rate=0.00382155]:0.75462,34[&height=6.0,rate=0.00382155]:0.75462)[&height=6.75462,rate=0.00382155]:0.32362)[&height=7.07824,rate=0.00382155]:1.49232,((42[&height=4.0,rate=0.00382155]:2.72511,23[&height=6.0,rate=0.00382155]:0.72511)[&height=6.72511,rate=0.00382155]:0.38051,30[&height=6.0,rate=0.00382155]:1.10562)[&height=7.10562,rate=0.00382155]:1.46494)[&height=8.57056,rate=0.00382155]:1.08301)[&height=9.65357,rate=0.00382155]:1.59953)[&height=11.2531,rate=0.00382155]:0.7361)[&height=11.9892,rate=0.00382155]:0.6736,15[&height=11.0,rate=0.00382155]:1.6628)[&height=12.6628,rate=0.00382155]:0.18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+tree 16 = 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+tree 18 = 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+tree 19 = 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+tree 20 = 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+tree 21 = 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+tree 22 = 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+tree 24 = 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+tree 25 = 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+tree 26 = 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+tree 40 = 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+tree 61 = ((1[&height=17.0,rate=0.00349861]:2.2158,(2[&height=16.0,rate=0.00349861]:1.7727,4[&height=15.0,rate=0.00349861]:2.7727)[&height=17.7727,rate=0.00349861]:1.4431)[&height=19.2158,rate=0.00349861]:1.5028,(((9[&height=14.0,rate=0.00349861]:2.3038,(8[&height=14.0,rate=0.00349861]:2.0249,5[&height=15.0,rate=0.00349861]:1.0249)[&height=16.0249,rate=0.00349861]:0.2789)[&height=16.3038,rate=0.00349861]:0.3368,(7[&height=14.0,rate=0.00349861]:2.1802,(6[&height=15.0,rate=0.00349861]:0.7136,((68[&height=13.0,rate=0.00349861]:1.1388,69[&height=13.0,rate=0.00349861]:1.1388)[&height=14.1388,rate=0.00349861]:0.6077,((((14[&height=11.0,rate=0.00349861]:1.4642,12[&height=11.0,rate=0.00349861]:1.4642)[&height=12.4642,rate=0.00349861]:0.0725,(17[&height=11.0,rate=0.00349861]:0.9716,18[&height=11.0,rate=0.00349861]:0.9716)[&height=11.9716,rate=0.00349861]:0.5651)[&height=12.5367,rate=0.00349861]:0.3412,((((13[&height=11.0,rate=0.00349861]:0.3857,(11[&height=11.0,rate=0.00349861]:0.1369,16[&height=11.0,rate=0.00349861]:0.1369)[&height=11.1369,rate=0.00349861]:0.2488)[&height=11.3857,rate=0.00349861]:0.3888,(19[&height=11.0,rate=0.00349861]:0.1914,((27[&height=6.0,rate=0.00349861]:3.17431,((31[&height=6.0,rate=0.00349861]:1.97833,(29[&height=6.0,rate=0.00349861]:1.84449,((((37[&height=4.0,rate=0.00349861]:1.68791,41[&height=4.0,rate=0.00349861]:1.68791)[&height=5.68791,rate=0.00349861]:0.06553,((38[&height=4.0,rate=0.00349861]:1.45191,40[&height=4.0,rate=0.00349861]:1.45191)[&height=5.45191,rate=0.00349861]:0.16551,43[&height=4.0,rate=0.00349861]:1.61742)[&height=5.61742,rate=0.00349861]:0.13602)[&height=5.75344,rate=0.00349861]:1.53772,(((((((61[&height=0.0,rate=0.00349861]:1.26796,((57[&height=0.0,rate=0.00349861]:0.877625,(54[&height=0.0,rate=0.00349861]:0.67964,60[&height=0.0,rate=0.00349861]:0.67964)[&height=0.67964,rate=0.00349861]:0.197985)[&height=0.877625,rate=0.00349861]:0.296835,58[&height=0.0,rate=0.00349861]:1.17446)[&height=1.17446,rate=0.00349861]:0.0935)[&height=1.26796,rate=0.00349861]:0.24581,55[&height=0.0,rate=0.00349861]:1.51377)[&height=1.51377,rate=0.00349861]:0.13474,53[&height=0.0,rate=0.00349861]:1.64851)[&height=1.64851,rate=0.00349861]:0.12236,(((62[&height=0.0,rate=0.00349861]:0.943973,52[&height=0.0,rate=0.00349861]:0.943973)[&height=0.943973,rate=0.00349861]:0.414157,(((64[&height=0.0,rate=0.00349861]:0.0868278,51[&height=0.0,rate=0.00349861]:0.0868278)[&height=0.0868278,rate=0.00349861]:0.1618202,63[&height=0.0,rate=0.00349861]:0.248648)[&height=0.248648,rate=0.00349861]:0.550168,56[&height=0.0,rate=0.00349861]:0.798816)[&height=0.798816,rate=0.00349861]:0.559314)[&height=1.35813,rate=0.00349861]:0.11933,59[&height=0.0,rate=0.00349861]:1.47746)[&height=1.47746,rate=0.00349861]:0.29341)[&height=1.77087,rate=0.00349861]:1.54797,50[&height=0.0,rate=0.00349861]:3.31884)[&height=3.31884,rate=0.00349861]:2.40885,(35[&height=4.0,rate=0.00349861]:1.30779,46[&height=4.0,rate=0.00349861]:1.30779)[&height=5.30779,rate=0.00349861]:0.4199)[&height=5.72769,rate=0.00349861]:1.42042,((45[&height=4.0,rate=0.00349861]:1.88037,(44[&height=4.0,rate=0.00349861]:1.73518,(49[&height=4.0,rate=0.00349861]:0.52313,36[&height=4.0,rate=0.00349861]:0.52313)[&height=4.52313,rate=0.00349861]:1.21205)[&height=5.73518,rate=0.00349861]:0.14519)[&height=5.88037,rate=0.00349861]:1.1669,(47[&height=4.0,rate=0.00349861]:1.69643,48[&height=4.0,rate=0.00349861]:1.69643)[&height=5.69643,rate=0.00349861]:1.35084)[&height=7.04727,rate=0.00349861]:0.10084)[&height=7.14811,rate=0.00349861]:0.14305)[&height=7.29116,rate=0.00349861]:0.40881,24[&height=6.0,rate=0.00349861]:1.69997)[&height=7.69997,rate=0.00349861]:0.14452)[&height=7.84449,rate=0.00349861]:0.13384)[&height=7.97833,rate=0.00349861]:0.1861,(((39[&height=4.0,rate=0.00349861]:3.04693,22[&height=6.0,rate=0.00349861]:1.04693)[&height=7.04693,rate=0.00349861]:0.37951,(28[&height=6.0,rate=0.00349861]:0.98223,(25[&height=6.0,rate=0.00349861]:0.51929,20[&height=6.0,rate=0.00349861]:0.51929)[&height=6.51929,rate=0.00349861]:0.46294)[&height=6.98223,rate=0.00349861]:0.44421)[&height=7.42644,rate=0.00349861]:0.52937,21[&height=6.0,rate=0.00349861]:1.95581)[&height=7.95581,rate=0.00349861]:0.20862)[&height=8.16443,rate=0.00349861]:1.00988)[&height=9.17431,rate=0.00349861]:0.26035,(((32[&height=6.0,rate=0.00349861]:0.49761,26[&height=6.0,rate=0.00349861]:0.49761)[&height=6.49761,rate=0.00349861]:0.453,(33[&height=6.0,rate=0.00349861]:0.44436,34[&height=6.0,rate=0.00349861]:0.44436)[&height=6.44436,rate=0.00349861]:0.50625)[&height=6.95061,rate=0.00349861]:1.49842,((42[&height=4.0,rate=0.00349861]:2.358,23[&height=6.0,rate=0.00349861]:0.358)[&height=6.358,rate=0.00349861]:0.167,30[&height=6.0,rate=0.00349861]:0.525)[&height=6.525,rate=0.00349861]:1.92403)[&height=8.44903,rate=0.00349861]:0.98563)[&height=9.43466,rate=0.00349861]:1.75674)[&height=11.1914,rate=0.00349861]:0.5831)[&height=11.7745,rate=0.00349861]:0.5872,15[&height=11.0,rate=0.00349861]:1.3617)[&height=12.3617,rate=0.00349861]:0.41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+tree 109 = ((1[&height=17.0,rate=0.00349056]:1.7035,(2[&height=16.0,rate=0.00349056]:2.232,4[&height=15.0,rate=0.00349056]:3.232)[&height=18.232,rate=0.00349056]:0.4715)[&height=18.7035,rate=0.00349056]:1.4414,(((9[&height=14.0,rate=0.00349056]:1.9991,(8[&height=14.0,rate=0.00349056]:1.3515,5[&height=15.0,rate=0.00349056]:0.3515)[&height=15.3515,rate=0.00349056]:0.6476)[&height=15.9991,rate=0.00349056]:1.1542,(7[&height=14.0,rate=0.00349056]:2.1463,(6[&height=15.0,rate=0.00349056]:0.3937,((68[&height=13.0,rate=0.00349056]:0.8603,69[&height=13.0,rate=0.00349056]:0.8603)[&height=13.8603,rate=0.00349056]:0.292,((((14[&height=11.0,rate=0.00349056]:0.7819,12[&height=11.0,rate=0.00349056]:0.7819)[&height=11.7819,rate=0.00349056]:0.361,(17[&height=11.0,rate=0.00349056]:0.4782,18[&height=11.0,rate=0.00349056]:0.4782)[&height=11.4782,rate=0.00349056]:0.6647)[&height=12.1429,rate=0.00349056]:0.0884,((((13[&height=11.0,rate=0.00349056]:0.5408,(11[&height=11.0,rate=0.00349056]:0.1581,16[&height=11.0,rate=0.00349056]:0.1581)[&height=11.1581,rate=0.00349056]:0.3827)[&height=11.5408,rate=0.00349056]:0.3179,(19[&height=11.0,rate=0.00349056]:0.5176,((27[&height=6.0,rate=0.00349056]:3.30922,((31[&height=6.0,rate=0.00349056]:1.59914,(29[&height=6.0,rate=0.00349056]:1.44577,((((37[&height=4.0,rate=0.00349056]:1.6142,41[&height=4.0,rate=0.00349056]:1.6142)[&height=5.6142,rate=0.00349056]:0.0494,((38[&height=4.0,rate=0.00349056]:1.14096,40[&height=4.0,rate=0.00349056]:1.14096)[&height=5.14096,rate=0.00349056]:0.16701,43[&height=4.0,rate=0.00349056]:1.30797)[&height=5.30797,rate=0.00349056]:0.35563)[&height=5.6636,rate=0.00349056]:1.15085,(((((((61[&height=0.0,rate=0.00349056]:0.357015,((57[&height=0.0,rate=0.00349056]:0.115594,(54[&height=0.0,rate=0.00349056]:0.111632,60[&height=0.0,rate=0.00349056]:0.111632)[&height=0.111632,rate=0.00349056]:0.003962)[&height=0.115594,rate=0.00349056]:0.216582,58[&height=0.0,rate=0.00349056]:0.332176)[&height=0.332176,rate=0.00349056]:0.024839)[&height=0.357015,rate=0.00349056]:0.274854,55[&height=0.0,rate=0.00349056]:0.631869)[&height=0.631869,rate=0.00349056]:1.435841,53[&height=0.0,rate=0.00349056]:2.06771)[&height=2.06771,rate=0.00349056]:0.37132,(((62[&height=0.0,rate=0.00349056]:0.554233,52[&height=0.0,rate=0.00349056]:0.554233)[&height=0.554233,rate=0.00349056]:0.651067,(((64[&height=0.0,rate=0.00349056]:0.284123,51[&height=0.0,rate=0.00349056]:0.284123)[&height=0.284123,rate=0.00349056]:0.552267,63[&height=0.0,rate=0.00349056]:0.83639)[&height=0.83639,rate=0.00349056]:0.105161,56[&height=0.0,rate=0.00349056]:0.941551)[&height=0.941551,rate=0.00349056]:0.263749)[&height=1.2053,rate=0.00349056]:0.03137,59[&height=0.0,rate=0.00349056]:1.23667)[&height=1.23667,rate=0.00349056]:1.20236)[&height=2.43903,rate=0.00349056]:0.7345,50[&height=0.0,rate=0.00349056]:3.17353)[&height=3.17353,rate=0.00349056]:2.29195,(35[&height=4.0,rate=0.00349056]:1.43174,46[&height=4.0,rate=0.00349056]:1.43174)[&height=5.43174,rate=0.00349056]:0.03374)[&height=5.46548,rate=0.00349056]:1.26582,((45[&height=4.0,rate=0.00349056]:1.21839,(44[&height=4.0,rate=0.00349056]:1.11271,(49[&height=4.0,rate=0.00349056]:0.74596,36[&height=4.0,rate=0.00349056]:0.74596)[&height=4.74596,rate=0.00349056]:0.36675)[&height=5.11271,rate=0.00349056]:0.10568)[&height=5.21839,rate=0.00349056]:1.11588,(47[&height=4.0,rate=0.00349056]:1.15997,48[&height=4.0,rate=0.00349056]:1.15997)[&height=5.15997,rate=0.00349056]:1.1743)[&height=6.33427,rate=0.00349056]:0.39703)[&height=6.7313,rate=0.00349056]:0.08315)[&height=6.81445,rate=0.00349056]:0.49595,24[&height=6.0,rate=0.00349056]:1.3104)[&height=7.3104,rate=0.00349056]:0.13537)[&height=7.44577,rate=0.00349056]:0.15337)[&height=7.59914,rate=0.00349056]:0.22936,(((39[&height=4.0,rate=0.00349056]:2.18902,22[&height=6.0,rate=0.00349056]:0.18902)[&height=6.18902,rate=0.00349056]:0.70019,(28[&height=6.0,rate=0.00349056]:0.87532,(25[&height=6.0,rate=0.00349056]:0.65436,20[&height=6.0,rate=0.00349056]:0.65436)[&height=6.65436,rate=0.00349056]:0.22096)[&height=6.87532,rate=0.00349056]:0.01389)[&height=6.88921,rate=0.00349056]:0.45852,21[&height=6.0,rate=0.00349056]:1.34773)[&height=7.34773,rate=0.00349056]:0.48077)[&height=7.8285,rate=0.00349056]:1.48072)[&height=9.30922,rate=0.00349056]:0.56848,(((32[&height=6.0,rate=0.00349056]:0.09761,26[&height=6.0,rate=0.00349056]:0.09761)[&height=6.09761,rate=0.00349056]:0.64881,(33[&height=6.0,rate=0.00349056]:0.49157,34[&height=6.0,rate=0.00349056]:0.49157)[&height=6.49157,rate=0.00349056]:0.25485)[&height=6.74642,rate=0.00349056]:1.79674,((42[&height=4.0,rate=0.00349056]:2.87957,23[&height=6.0,rate=0.00349056]:0.87957)[&height=6.87957,rate=0.00349056]:0.58137,30[&height=6.0,rate=0.00349056]:1.46094)[&height=7.46094,rate=0.00349056]:1.08222)[&height=8.54316,rate=0.00349056]:1.33454)[&height=9.8777,rate=0.00349056]:1.6399)[&height=11.5176,rate=0.00349056]:0.3411)[&height=11.8587,rate=0.00349056]:0.0325,15[&height=11.0,rate=0.00349056]:0.8912)[&height=11.8912,rate=0.00349056]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+tree 620 = 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+tree 621 = ((1[&height=17.0,rate=0.00344017]:2.7149,(2[&height=16.0,rate=0.00344017]:2.5897,4[&height=15.0,rate=0.00344017]:3.5897)[&height=18.5897,rate=0.00344017]:1.1252)[&height=19.7149,rate=0.00344017]:0.8466,(((9[&height=14.0,rate=0.00344017]:2.1245,(8[&height=14.0,rate=0.00344017]:1.1184,5[&height=15.0,rate=0.00344017]:0.1184)[&height=15.1184,rate=0.00344017]:1.0061)[&height=16.1245,rate=0.00344017]:0.0297,(7[&height=14.0,rate=0.00344017]:1.9704,(6[&height=15.0,rate=0.00344017]:0.5175,((68[&height=13.0,rate=0.00344017]:0.9509,69[&height=13.0,rate=0.00344017]:0.9509)[&height=13.9509,rate=0.00344017]:0.184,((((14[&height=11.0,rate=0.00344017]:0.7293,12[&height=11.0,rate=0.00344017]:0.7293)[&height=11.7293,rate=0.00344017]:0.2323,(17[&height=11.0,rate=0.00344017]:0.6641,18[&height=11.0,rate=0.00344017]:0.6641)[&height=11.6641,rate=0.00344017]:0.2975)[&height=11.9616,rate=0.00344017]:0.0507,((((13[&height=11.0,rate=0.00344017]:0.2502,(11[&height=11.0,rate=0.00344017]:0.1197,16[&height=11.0,rate=0.00344017]:0.1197)[&height=11.1197,rate=0.00344017]:0.1305)[&height=11.2502,rate=0.00344017]:0.5295,(19[&height=11.0,rate=0.00344017]:0.2853,((27[&height=6.0,rate=0.00344017]:2.94864,((31[&height=6.0,rate=0.00344017]:1.92315,(29[&height=6.0,rate=0.00344017]:1.42873,((((37[&height=4.0,rate=0.00344017]:0.76279,41[&height=4.0,rate=0.00344017]:0.76279)[&height=4.76279,rate=0.00344017]:0.39037,((38[&height=4.0,rate=0.00344017]:0.97886,40[&height=4.0,rate=0.00344017]:0.97886)[&height=4.97886,rate=0.00344017]:0.07692,43[&height=4.0,rate=0.00344017]:1.05578)[&height=5.05578,rate=0.00344017]:0.09738)[&height=5.15316,rate=0.00344017]:1.35989,(((((((61[&height=0.0,rate=0.00344017]:0.827798,((57[&height=0.0,rate=0.00344017]:0.0317804,(54[&height=0.0,rate=0.00344017]:0.0199657,60[&height=0.0,rate=0.00344017]:0.0199657)[&height=0.0199657,rate=0.00344017]:0.0118147)[&height=0.0317804,rate=0.00344017]:0.2991596,58[&height=0.0,rate=0.00344017]:0.33094)[&height=0.33094,rate=0.00344017]:0.496858)[&height=0.827798,rate=0.00344017]:0.831632,55[&height=0.0,rate=0.00344017]:1.65943)[&height=1.65943,rate=0.00344017]:0.13186,53[&height=0.0,rate=0.00344017]:1.79129)[&height=1.79129,rate=0.00344017]:0.11844,(((62[&height=0.0,rate=0.00344017]:0.996406,52[&height=0.0,rate=0.00344017]:0.996406)[&height=0.996406,rate=0.00344017]:0.339764,(((64[&height=0.0,rate=0.00344017]:0.557318,51[&height=0.0,rate=0.00344017]:0.557318)[&height=0.557318,rate=0.00344017]:0.40529,63[&height=0.0,rate=0.00344017]:0.962608)[&height=0.962608,rate=0.00344017]:0.273382,56[&height=0.0,rate=0.00344017]:1.23599)[&height=1.23599,rate=0.00344017]:0.10018)[&height=1.33617,rate=0.00344017]:0.16751,59[&height=0.0,rate=0.00344017]:1.50368)[&height=1.50368,rate=0.00344017]:0.40605)[&height=1.90973,rate=0.00344017]:0.51679,50[&height=0.0,rate=0.00344017]:2.42652)[&height=2.42652,rate=0.00344017]:2.47346,(35[&height=4.0,rate=0.00344017]:0.80948,46[&height=4.0,rate=0.00344017]:0.80948)[&height=4.80948,rate=0.00344017]:0.0905)[&height=4.89998,rate=0.00344017]:1.57768,((45[&height=4.0,rate=0.00344017]:1.67024,(44[&height=4.0,rate=0.00344017]:1.44134,(49[&height=4.0,rate=0.00344017]:1.03314,36[&height=4.0,rate=0.00344017]:1.03314)[&height=5.03314,rate=0.00344017]:0.4082)[&height=5.44134,rate=0.00344017]:0.2289)[&height=5.67024,rate=0.00344017]:0.75054,(47[&height=4.0,rate=0.00344017]:1.28197,48[&height=4.0,rate=0.00344017]:1.28197)[&height=5.28197,rate=0.00344017]:1.13881)[&height=6.42078,rate=0.00344017]:0.05688)[&height=6.47766,rate=0.00344017]:0.03539)[&height=6.51305,rate=0.00344017]:0.66085,24[&height=6.0,rate=0.00344017]:1.1739)[&height=7.1739,rate=0.00344017]:0.25483)[&height=7.42873,rate=0.00344017]:0.49442)[&height=7.92315,rate=0.00344017]:0.05484,(((39[&height=4.0,rate=0.00344017]:2.56684,22[&height=6.0,rate=0.00344017]:0.56684)[&height=6.56684,rate=0.00344017]:0.76495,(28[&height=6.0,rate=0.00344017]:1.29864,(25[&height=6.0,rate=0.00344017]:1.24126,20[&height=6.0,rate=0.00344017]:1.24126)[&height=7.24126,rate=0.00344017]:0.05738)[&height=7.29864,rate=0.00344017]:0.03315)[&height=7.33179,rate=0.00344017]:0.3032,21[&height=6.0,rate=0.00344017]:1.63499)[&height=7.63499,rate=0.00344017]:0.343)[&height=7.97799,rate=0.00344017]:0.97065)[&height=8.94864,rate=0.00344017]:0.52205,(((32[&height=6.0,rate=0.00344017]:0.21656,26[&height=6.0,rate=0.00344017]:0.21656)[&height=6.21656,rate=0.00344017]:0.53885,(33[&height=6.0,rate=0.00344017]:0.45943,34[&height=6.0,rate=0.00344017]:0.45943)[&height=6.45943,rate=0.00344017]:0.29598)[&height=6.75541,rate=0.00344017]:1.91503,((42[&height=4.0,rate=0.00344017]:2.40918,23[&height=6.0,rate=0.00344017]:0.40918)[&height=6.40918,rate=0.00344017]:0.32053,30[&height=6.0,rate=0.00344017]:0.72971)[&height=6.72971,rate=0.00344017]:1.94073)[&height=8.67044,rate=0.00344017]:0.80025)[&height=9.47069,rate=0.00344017]:1.81461)[&height=11.2853,rate=0.00344017]:0.4944)[&height=11.7797,rate=0.00344017]:0.1808,15[&height=11.0,rate=0.00344017]:0.9605)[&height=11.9605,rate=0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+tree 622 = 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+tree 650 = 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+tree 810 = 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+tree 812 = 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+tree 824 = 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+tree 910 = 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+tree 911 = 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+tree 912 = 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+tree 913 = ((1[&height=17.0,rate=0.00324811]:2.2329,(2[&height=16.0,rate=0.00324811]:1.7921,4[&height=15.0,rate=0.00324811]:2.7921)[&height=17.7921,rate=0.00324811]:1.4408)[&height=19.2329,rate=0.00324811]:0.7133,(((9[&height=14.0,rate=0.00324811]:2.363,(8[&height=14.0,rate=0.00324811]:1.1439,5[&height=15.0,rate=0.00324811]:0.1439)[&height=15.1439,rate=0.00324811]:1.2191)[&height=16.363,rate=0.00324811]:0.0769,(7[&height=14.0,rate=0.00324811]:2.0425,(6[&height=15.0,rate=0.00324811]:0.4297,((68[&height=13.0,rate=0.00324811]:1.203,69[&height=13.0,rate=0.00324811]:1.203)[&height=14.203,rate=0.00324811]:0.3969,((((14[&height=11.0,rate=0.00324811]:0.7985,12[&height=11.0,rate=0.00324811]:0.7985)[&height=11.7985,rate=0.00324811]:0.2104,(17[&height=11.0,rate=0.00324811]:0.7385,18[&height=11.0,rate=0.00324811]:0.7385)[&height=11.7385,rate=0.00324811]:0.2704)[&height=12.0089,rate=0.00324811]:0.3402,((((13[&height=11.0,rate=0.00324811]:0.1776,(11[&height=11.0,rate=0.00324811]:0.0216,16[&height=11.0,rate=0.00324811]:0.0216)[&height=11.0216,rate=0.00324811]:0.156)[&height=11.1776,rate=0.00324811]:0.1041,(19[&height=11.0,rate=0.00324811]:0.0974,((27[&height=6.0,rate=0.00324811]:1.77983,((31[&height=6.0,rate=0.00324811]:1.02778,(29[&height=6.0,rate=0.00324811]:0.50927,((((37[&height=4.0,rate=0.00324811]:1.26282,41[&height=4.0,rate=0.00324811]:1.26282)[&height=5.26282,rate=0.00324811]:0.08484,((38[&height=4.0,rate=0.00324811]:1.10887,40[&height=4.0,rate=0.00324811]:1.10887)[&height=5.10887,rate=0.00324811]:0.21503,43[&height=4.0,rate=0.00324811]:1.3239)[&height=5.3239,rate=0.00324811]:0.02376)[&height=5.34766,rate=0.00324811]:0.9642,(((((((61[&height=0.0,rate=0.00324811]:0.812963,((57[&height=0.0,rate=0.00324811]:0.366633,(54[&height=0.0,rate=0.00324811]:0.326315,60[&height=0.0,rate=0.00324811]:0.326315)[&height=0.326315,rate=0.00324811]:0.040318)[&height=0.366633,rate=0.00324811]:0.153848,58[&height=0.0,rate=0.00324811]:0.520481)[&height=0.520481,rate=0.00324811]:0.292482)[&height=0.812963,rate=0.00324811]:0.193827,55[&height=0.0,rate=0.00324811]:1.00679)[&height=1.00679,rate=0.00324811]:0.0977,53[&height=0.0,rate=0.00324811]:1.10449)[&height=1.10449,rate=0.00324811]:0.11826,(((62[&height=0.0,rate=0.00324811]:0.751686,52[&height=0.0,rate=0.00324811]:0.751686)[&height=0.751686,rate=0.00324811]:0.200085,(((64[&height=0.0,rate=0.00324811]:0.12836,51[&height=0.0,rate=0.00324811]:0.12836)[&height=0.12836,rate=0.00324811]:0.65323,63[&height=0.0,rate=0.00324811]:0.78159)[&height=0.78159,rate=0.00324811]:0.035804,56[&height=0.0,rate=0.00324811]:0.817394)[&height=0.817394,rate=0.00324811]:0.134377)[&height=0.951771,rate=0.00324811]:0.068069,59[&height=0.0,rate=0.00324811]:1.01984)[&height=1.01984,rate=0.00324811]:0.20291)[&height=1.22275,rate=0.00324811]:0.65552,50[&height=0.0,rate=0.00324811]:1.87827)[&height=1.87827,rate=0.00324811]:3.15358,(35[&height=4.0,rate=0.00324811]:0.97375,46[&height=4.0,rate=0.00324811]:0.97375)[&height=4.97375,rate=0.00324811]:0.0581)[&height=5.03185,rate=0.00324811]:1.26002,((45[&height=4.0,rate=0.00324811]:1.63575,(44[&height=4.0,rate=0.00324811]:0.79518,(49[&height=4.0,rate=0.00324811]:0.5083,36[&height=4.0,rate=0.00324811]:0.5083)[&height=4.5083,rate=0.00324811]:0.28688)[&height=4.79518,rate=0.00324811]:0.84057)[&height=5.63575,rate=0.00324811]:0.44215,(47[&height=4.0,rate=0.00324811]:1.22307,48[&height=4.0,rate=0.00324811]:1.22307)[&height=5.22307,rate=0.00324811]:0.85483)[&height=6.0779,rate=0.00324811]:0.21397)[&height=6.29187,rate=0.00324811]:0.01999)[&height=6.31186,rate=0.00324811]:0.16979,24[&height=6.0,rate=0.00324811]:0.48165)[&height=6.48165,rate=0.00324811]:0.02762)[&height=6.50927,rate=0.00324811]:0.51851)[&height=7.02778,rate=0.00324811]:0.1367,(((39[&height=4.0,rate=0.00324811]:2.61586,22[&height=6.0,rate=0.00324811]:0.61586)[&height=6.61586,rate=0.00324811]:0.24641,(28[&height=6.0,rate=0.00324811]:0.81391,(25[&height=6.0,rate=0.00324811]:0.648,20[&height=6.0,rate=0.00324811]:0.648)[&height=6.648,rate=0.00324811]:0.16591)[&height=6.81391,rate=0.00324811]:0.04836)[&height=6.86227,rate=0.00324811]:0.27491,21[&height=6.0,rate=0.00324811]:1.13718)[&height=7.13718,rate=0.00324811]:0.0273)[&height=7.16448,rate=0.00324811]:0.61535)[&height=7.77983,rate=0.00324811]:0.58046,(((32[&height=6.0,rate=0.00324811]:0.14743,26[&height=6.0,rate=0.00324811]:0.14743)[&height=6.14743,rate=0.00324811]:0.42833,(33[&height=6.0,rate=0.00324811]:0.37884,34[&height=6.0,rate=0.00324811]:0.37884)[&height=6.37884,rate=0.00324811]:0.19692)[&height=6.57576,rate=0.00324811]:1.273,((42[&height=4.0,rate=0.00324811]:2.23028,23[&height=6.0,rate=0.00324811]:0.23028)[&height=6.23028,rate=0.00324811]:0.47579,30[&height=6.0,rate=0.00324811]:0.70607)[&height=6.70607,rate=0.00324811]:1.14269)[&height=7.84876,rate=0.00324811]:0.51153)[&height=8.36029,rate=0.00324811]:2.73711)[&height=11.0974,rate=0.00324811]:0.1843)[&height=11.2817,rate=0.00324811]:0.1442,15[&height=11.0,rate=0.00324811]:0.4259)[&height=11.4259,rate=0.00324811]:0.5713,10[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+tree 914 = 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+tree 1000 = ((1[&height=17.0,rate=0.00351926]:1.9959,(2[&height=16.0,rate=0.00351926]:2.3339,4[&height=15.0,rate=0.00351926]:3.3339)[&height=18.3339,rate=0.00351926]:0.662)[&height=18.9959,rate=0.00351926]:1.0991,(((9[&height=14.0,rate=0.00351926]:2.4114,(8[&height=14.0,rate=0.00351926]:1.2407,5[&height=15.0,rate=0.00351926]:0.2407)[&height=15.2407,rate=0.00351926]:1.1707)[&height=16.4114,rate=0.00351926]:0.1159,(7[&height=14.0,rate=0.00351926]:2.0611,(6[&height=15.0,rate=0.00351926]:0.5934,((68[&height=13.0,rate=0.00351926]:1.8954,69[&height=13.0,rate=0.00351926]:1.8954)[&height=14.8954,rate=0.00351926]:0.114,((((14[&height=11.0,rate=0.00351926]:1.0725,12[&height=11.0,rate=0.00351926]:1.0725)[&height=12.0725,rate=0.00351926]:0.4371,(17[&height=11.0,rate=0.00351926]:0.7516,18[&height=11.0,rate=0.00351926]:0.7516)[&height=11.7516,rate=0.00351926]:0.758)[&height=12.5096,rate=0.00351926]:0.1094,((((13[&height=11.0,rate=0.00351926]:0.5701,(11[&height=11.0,rate=0.00351926]:0.2432,16[&height=11.0,rate=0.00351926]:0.2432)[&height=11.2432,rate=0.00351926]:0.3269)[&height=11.5701,rate=0.00351926]:0.1092,(19[&height=11.0,rate=0.00351926]:0.5462,((27[&height=6.0,rate=0.00351926]:3.61902,((31[&height=6.0,rate=0.00351926]:2.29576,(29[&height=6.0,rate=0.00351926]:2.2341,((((37[&height=4.0,rate=0.00351926]:1.70963,41[&height=4.0,rate=0.00351926]:1.70963)[&height=5.70963,rate=0.00351926]:0.36071,((38[&height=4.0,rate=0.00351926]:1.62485,40[&height=4.0,rate=0.00351926]:1.62485)[&height=5.62485,rate=0.00351926]:0.12412,43[&height=4.0,rate=0.00351926]:1.74897)[&height=5.74897,rate=0.00351926]:0.32137)[&height=6.07034,rate=0.00351926]:1.4494,(((((((61[&height=0.0,rate=0.00351926]:0.2729,((57[&height=0.0,rate=0.00351926]:0.23826,(54[&height=0.0,rate=0.00351926]:0.156589,60[&height=0.0,rate=0.00351926]:0.156589)[&height=0.156589,rate=0.00351926]:0.081671)[&height=0.23826,rate=0.00351926]:0.030936,58[&height=0.0,rate=0.00351926]:0.269196)[&height=0.269196,rate=0.00351926]:0.003704)[&height=0.2729,rate=0.00351926]:0.78609,55[&height=0.0,rate=0.00351926]:1.05899)[&height=1.05899,rate=0.00351926]:0.11283,53[&height=0.0,rate=0.00351926]:1.17182)[&height=1.17182,rate=0.00351926]:0.03998,(((62[&height=0.0,rate=0.00351926]:0.530523,52[&height=0.0,rate=0.00351926]:0.530523)[&height=0.530523,rate=0.00351926]:0.340864,(((64[&height=0.0,rate=0.00351926]:0.138744,51[&height=0.0,rate=0.00351926]:0.138744)[&height=0.138744,rate=0.00351926]:0.514805,63[&height=0.0,rate=0.00351926]:0.653549)[&height=0.653549,rate=0.00351926]:0.143475,56[&height=0.0,rate=0.00351926]:0.797024)[&height=0.797024,rate=0.00351926]:0.074363)[&height=0.871387,rate=0.00351926]:0.050681,59[&height=0.0,rate=0.00351926]:0.922068)[&height=0.922068,rate=0.00351926]:0.289732)[&height=1.2118,rate=0.00351926]:1.31072,50[&height=0.0,rate=0.00351926]:2.52252)[&height=2.52252,rate=0.00351926]:3.13863,(35[&height=4.0,rate=0.00351926]:1.21726,46[&height=4.0,rate=0.00351926]:1.21726)[&height=5.21726,rate=0.00351926]:0.44389)[&height=5.66115,rate=0.00351926]:1.74069,((45[&height=4.0,rate=0.00351926]:1.98301,(44[&height=4.0,rate=0.00351926]:1.68351,(49[&height=4.0,rate=0.00351926]:1.55787,36[&height=4.0,rate=0.00351926]:1.55787)[&height=5.55787,rate=0.00351926]:0.12564)[&height=5.68351,rate=0.00351926]:0.2995)[&height=5.98301,rate=0.00351926]:1.27716,(47[&height=4.0,rate=0.00351926]:1.68464,48[&height=4.0,rate=0.00351926]:1.68464)[&height=5.68464,rate=0.00351926]:1.57553)[&height=7.26017,rate=0.00351926]:0.14167)[&height=7.40184,rate=0.00351926]:0.1179)[&height=7.51974,rate=0.00351926]:0.32449,24[&height=6.0,rate=0.00351926]:1.84423)[&height=7.84423,rate=0.00351926]:0.38987)[&height=8.2341,rate=0.00351926]:0.06166)[&height=8.29576,rate=0.00351926]:0.1283,(((39[&height=4.0,rate=0.00351926]:3.07439,22[&height=6.0,rate=0.00351926]:1.07439)[&height=7.07439,rate=0.00351926]:0.61238,(28[&height=6.0,rate=0.00351926]:1.15448,(25[&height=6.0,rate=0.00351926]:0.86348,20[&height=6.0,rate=0.00351926]:0.86348)[&height=6.86348,rate=0.00351926]:0.291)[&height=7.15448,rate=0.00351926]:0.53229)[&height=7.68677,rate=0.00351926]:0.15723,21[&height=6.0,rate=0.00351926]:1.844)[&height=7.844,rate=0.00351926]:0.58006)[&height=8.42406,rate=0.00351926]:1.19496)[&height=9.61902,rate=0.00351926]:0.36657,(((32[&height=6.0,rate=0.00351926]:0.54985,26[&height=6.0,rate=0.00351926]:0.54985)[&height=6.54985,rate=0.00351926]:0.11733,(33[&height=6.0,rate=0.00351926]:0.55263,34[&height=6.0,rate=0.00351926]:0.55263)[&height=6.55263,rate=0.00351926]:0.11455)[&height=6.66718,rate=0.00351926]:1.50365,((42[&height=4.0,rate=0.00351926]:2.41699,23[&height=6.0,rate=0.00351926]:0.41699)[&height=6.41699,rate=0.00351926]:0.21255,30[&height=6.0,rate=0.00351926]:0.62954)[&height=6.62954,rate=0.00351926]:1.54129)[&height=8.17083,rate=0.00351926]:1.81476)[&height=9.98559,rate=0.00351926]:1.56061)[&height=11.5462,rate=0.00351926]:0.1331)[&height=11.6793,rate=0.00351926]:0.0676,15[&height=11.0,rate=0.00351926]:0.7469)[&height=11.7469,rate=0.00351926]:0.4912,10[&height=11.0,rate=0.00351926]:1.2381)[&height=12.2381,rate=0.00351926]:0.3809)[&height=12.619,rate=0.00351926]:1.7685,((67[&height=12.0,rate=0.00351926]:1.5136,65[&height=12.0,rate=0.00351926]:1.5136)[&height=13.5136,rate=0.00351926]:0.1053,66[&height=12.0,rate=0.00351926]:1.6189)[&height=13.6189,rate=0.00351926]:0.7686)[&height=14.3875,rate=0.00351926]:0.6219)[&height=15.0094,rate=0.00351926]:0.584)[&height=15.5934,rate=0.00351926]:0.4677)[&height=16.0611,rate=0.00351926]:0.4662)[&height=16.5273,rate=0.00351926]:1.5662,3[&height=16.0,rate=0.00351926]:2.0935)[&height=18.0935,rate=0.00351926]:2.0015)[&height=20.095]; +tree 1001 = ((1[&height=17.0,rate=0.00348736]:2.3526,(2[&height=16.0,rate=0.00348736]:2.2091,4[&height=15.0,rate=0.00348736]:3.2091)[&height=18.2091,rate=0.00348736]:1.1435)[&height=19.3526,rate=0.00348736]:0.7107,(((9[&height=14.0,rate=0.00348736]:2.8324,(8[&height=14.0,rate=0.00348736]:1.2561,5[&height=15.0,rate=0.00348736]:0.2561)[&height=15.2561,rate=0.00348736]:1.5763)[&height=16.8324,rate=0.00348736]:0.4493,(7[&height=14.0,rate=0.00348736]:2.9095,(6[&height=15.0,rate=0.00348736]:0.9787,((68[&height=13.0,rate=0.00348736]:1.1805,69[&height=13.0,rate=0.00348736]:1.1805)[&height=14.1805,rate=0.00348736]:0.2923,((((14[&height=11.0,rate=0.00348736]:1.1477,12[&height=11.0,rate=0.00348736]:1.1477)[&height=12.1477,rate=0.00348736]:0.1559,(17[&height=11.0,rate=0.00348736]:1.1408,18[&height=11.0,rate=0.00348736]:1.1408)[&height=12.1408,rate=0.00348736]:0.1628)[&height=12.3036,rate=0.00348736]:0.4157,((((13[&height=11.0,rate=0.00348736]:0.2264,(11[&height=11.0,rate=0.00348736]:0.0608,16[&height=11.0,rate=0.00348736]:0.0608)[&height=11.0608,rate=0.00348736]:0.1656)[&height=11.2264,rate=0.00348736]:0.6012,(19[&height=11.0,rate=0.00348736]:0.6757,((27[&height=6.0,rate=0.00348736]:3.45625,((31[&height=6.0,rate=0.00348736]:1.67235,(29[&height=6.0,rate=0.00348736]:1.41872,((((37[&height=4.0,rate=0.00348736]:1.79436,41[&height=4.0,rate=0.00348736]:1.79436)[&height=5.79436,rate=0.00348736]:0.0546,((38[&height=4.0,rate=0.00348736]:1.13717,40[&height=4.0,rate=0.00348736]:1.13717)[&height=5.13717,rate=0.00348736]:0.50855,43[&height=4.0,rate=0.00348736]:1.64572)[&height=5.64572,rate=0.00348736]:0.20324)[&height=5.84896,rate=0.00348736]:1.24999,(((((((61[&height=0.0,rate=0.00348736]:0.911735,((57[&height=0.0,rate=0.00348736]:0.351971,(54[&height=0.0,rate=0.00348736]:0.274024,60[&height=0.0,rate=0.00348736]:0.274024)[&height=0.274024,rate=0.00348736]:0.077947)[&height=0.351971,rate=0.00348736]:0.523822,58[&height=0.0,rate=0.00348736]:0.875793)[&height=0.875793,rate=0.00348736]:0.035942)[&height=0.911735,rate=0.00348736]:0.307165,55[&height=0.0,rate=0.00348736]:1.2189)[&height=1.2189,rate=0.00348736]:0.1431,53[&height=0.0,rate=0.00348736]:1.362)[&height=1.362,rate=0.00348736]:0.00835,(((62[&height=0.0,rate=0.00348736]:0.805893,52[&height=0.0,rate=0.00348736]:0.805893)[&height=0.805893,rate=0.00348736]:0.308297,(((64[&height=0.0,rate=0.00348736]:0.108831,51[&height=0.0,rate=0.00348736]:0.108831)[&height=0.108831,rate=0.00348736]:0.31384,63[&height=0.0,rate=0.00348736]:0.422671)[&height=0.422671,rate=0.00348736]:0.546862,56[&height=0.0,rate=0.00348736]:0.969533)[&height=0.969533,rate=0.00348736]:0.144657)[&height=1.11419,rate=0.00348736]:0.1556,59[&height=0.0,rate=0.00348736]:1.26979)[&height=1.26979,rate=0.00348736]:0.10056)[&height=1.37035,rate=0.00348736]:0.63055,50[&height=0.0,rate=0.00348736]:2.0009)[&height=2.0009,rate=0.00348736]:2.84709,(35[&height=4.0,rate=0.00348736]:0.82937,46[&height=4.0,rate=0.00348736]:0.82937)[&height=4.82937,rate=0.00348736]:0.01862)[&height=4.84799,rate=0.00348736]:2.21695,((45[&height=4.0,rate=0.00348736]:1.54369,(44[&height=4.0,rate=0.00348736]:1.10833,(49[&height=4.0,rate=0.00348736]:0.32709,36[&height=4.0,rate=0.00348736]:0.32709)[&height=4.32709,rate=0.00348736]:0.78124)[&height=5.10833,rate=0.00348736]:0.43536)[&height=5.54369,rate=0.00348736]:1.30126,(47[&height=4.0,rate=0.00348736]:1.8399,48[&height=4.0,rate=0.00348736]:1.8399)[&height=5.8399,rate=0.00348736]:1.00505)[&height=6.84495,rate=0.00348736]:0.21999)[&height=7.06494,rate=0.00348736]:0.03401)[&height=7.09895,rate=0.00348736]:0.24997,24[&height=6.0,rate=0.00348736]:1.34892)[&height=7.34892,rate=0.00348736]:0.0698)[&height=7.41872,rate=0.00348736]:0.25363)[&height=7.67235,rate=0.00348736]:0.01517,(((39[&height=4.0,rate=0.00348736]:2.30211,22[&height=6.0,rate=0.00348736]:0.30211)[&height=6.30211,rate=0.00348736]:0.8801,(28[&height=6.0,rate=0.00348736]:1.13751,(25[&height=6.0,rate=0.00348736]:0.95398,20[&height=6.0,rate=0.00348736]:0.95398)[&height=6.95398,rate=0.00348736]:0.18353)[&height=7.13751,rate=0.00348736]:0.0447)[&height=7.18221,rate=0.00348736]:0.31646,21[&height=6.0,rate=0.00348736]:1.49867)[&height=7.49867,rate=0.00348736]:0.18885)[&height=7.68752,rate=0.00348736]:1.76873)[&height=9.45625,rate=0.00348736]:0.55885,(((32[&height=6.0,rate=0.00348736]:0.56324,26[&height=6.0,rate=0.00348736]:0.56324)[&height=6.56324,rate=0.00348736]:0.10832,(33[&height=6.0,rate=0.00348736]:0.31419,34[&height=6.0,rate=0.00348736]:0.31419)[&height=6.31419,rate=0.00348736]:0.35737)[&height=6.67156,rate=0.00348736]:2.16482,((42[&height=4.0,rate=0.00348736]:2.97414,23[&height=6.0,rate=0.00348736]:0.97414)[&height=6.97414,rate=0.00348736]:0.29523,30[&height=6.0,rate=0.00348736]:1.26937)[&height=7.26937,rate=0.00348736]:1.56701)[&height=8.83638,rate=0.00348736]:1.17872)[&height=10.0151,rate=0.00348736]:1.6606)[&height=11.6757,rate=0.00348736]:0.1519)[&height=11.8276,rate=0.00348736]:0.2431,15[&height=11.0,rate=0.00348736]:1.0707)[&height=12.0707,rate=0.00348736]: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+END; \ No newline at end of file diff --git a/phylostan/generate_script.py b/phylostan/generate_script.py index 704a1dd..b55b63e 100755 --- a/phylostan/generate_script.py +++ b/phylostan/generate_script.py @@ -133,6 +133,76 @@ def constant_coalescent(heterochronous=False): else: return constant_coalescent_str.format('', '0') +def integrated_constant_coalescent(heterochronous=False): + integrated_constant_coalescent_str = """ + real integrated_density(real t, real kappa, real u){{ + real z = kappa*t; + real w = square(z + u); + real lnum = log(2*w*log(u + z) + 3*square(z) + 4*u*z - w*(2*log(z) + 3)); + real ldenom = log(2) + log(w); + return(log(2) + log(kappa) + lnum - ldenom -log(u)); + }} + real integrated_constant_coalescent_log(real[] heights, real U, int[,] map{0}){{ + int S = size(heights) + 1; // number of leaves from the number of internal nodes + int nodeCount = size(heights) + S; + + real logP = 0.0; + real lineageCount = 0.0; // first 2 intervals are sampling events + + int indices[nodeCount]; + int childCounts[nodeCount]; + real times[nodeCount]; + + real start; + real finish; + real interval; + + for( i in 1:nodeCount ){ + // internal node: transform + if(map[i, 1] > S){ + times[map[i, 1]] = heights[map[i, 1]-S]; + childCounts[map[i, 1]] = 2; + } + else{ + times[map[i, 1]] = lowers[map[i, 1]]; + childCounts[map[i, 1]] = 0; + } + } + + // calculate intervals + indices = sort_indices_asc(times); + + // first tip + start = times[indices[1]]; + + for (i in 1:nodeCount) { + finish = times[indices[i]]; + + interval = finish - start; + // print("Interval = ", interval, " node = ", i, " lincount =", lineageCount, " logP = ", logP); + + if(interval != 0.0 && childCounts[indices[i]] != 0 ){ + logP += integrated_density(interval, lineageCount*(lineageCount-1.0)/2.0, U); + } + // sampling event + if (childCounts[indices[i]] == 0) { + lineageCount += 1.0; + } + // coalescent event + else { + lineageCount -= 1.0; + } + start = finish; + } + + return logP; + }} + """ + + if heterochronous: + return integrated_constant_coalescent_str.format(', real[] lowers', 'lowers[map[i,1]]') + else: + return integrated_constant_coalescent_str.format('', '0') def skyride_coalescent(heterochronous): skyride_coalescent_str = """ @@ -779,7 +849,13 @@ def get_model(params): model_priors.append('heights ~ constant_coalescent(theta, map, lowers);') else: model_priors.append('heights ~ constant_coalescent(theta, map);') - elif params.coalescent == 'skyride': + elif params.coalescent == 'integrated': + functions_block.append(integrated_constant_coalescent(params.heterochronous)) + if params.heterochronous: + model_priors.append('heights ~ integrated_constant_coalescent(map, 1000.0, lowers);') # picking u = 1E3 + else: + model_priors.append('heights ~ integrated_constant_coalescent(map, 1000.0);') + elif params.coalescent == 'skyride': functions_block.append(skyride_coalescent(params.heterochronous)) functions_block.append(GMRF()) # functions_block.append(GMRF_time_aware(params.heterochronous)) @@ -798,7 +874,7 @@ def get_model(params): model_priors.append('thetas ~ gmrf(tau);') model_priors.append('tau ~ gamma(0.001, 0.001);') - elif params.coalescent == 'skygrid': + elif params.coalescent == 'skygrid': functions_block.append(skygrid_coalescent(params.heterochronous)) functions_block.append(GMRF()) diff --git a/phylostan/phylostan.py b/phylostan/phylostan.py index 4bdc048..c90b7fb 100755 --- a/phylostan/phylostan.py +++ b/phylostan/phylostan.py @@ -76,8 +76,8 @@ def create_build_parser(subprasers, prog, help): parser.add_argument('--clock', required=False, choices=['strict', 'autocorrelated', 'uncorrelated'], default=None, help="""Type of clock""") parser.add_argument('--estimate_rate', action='store_true', help="""Estimate substitution rate""") - parser.add_argument('-c', '--coalescent', choices=['constant', 'skyride', 'skygrid'], default=None, - help="""Type of coalescent (constant or skyride)""") + parser.add_argument('-c', '--coalescent', choices=['constant', 'integrated', 'skyride', 'skygrid'], default=None, + help="""Type of coalescent (constant, integrated, skyride or skygrid)""") parser.add_argument('--grid', metavar='I', required=False, type=int, help="""Number of grid points in skygrid""") parser.add_argument('--cutoff', metavar='G', required=False, type=float, help="""a cutoff for skygrid""") parser.add_argument('--compile', action="store_true", help="""Compile Stan script""") diff --git a/phylostan/utils.py b/phylostan/utils.py index 9e646ee..b166cc8 100644 --- a/phylostan/utils.py +++ b/phylostan/utils.py @@ -1,5 +1,4 @@ import numpy -import math def get_peeling_order(tree): peeling = [] diff --git a/src/GTR-coalescent.stan b/src/GTR-coalescent.stan deleted file mode 100755 index d9e8c96..0000000 --- a/src/GTR-coalescent.stan +++ /dev/null @@ -1,156 +0,0 @@ -functions{ - real coalescent_log(real []x, real pop){ - real p; - real n; - real l; - int i; - real temp; - n = size(x); - p = 0; - l = n + 1.0; - i = 1; - - while(i <= floor(n)){ - temp = ((l*(l-1.0))/2.0)/pop; - p = p + log(temp) - (temp * x[i]); - l = l - 1.0; - i = i + 1; - } - return p; - } - - real oneOnX_log(real x){ - return -log(x); - } -} - -data { - int L; // alignment length - int S; // number of tips - real tipdata[S,L,4]; - int peel[S-1,3]; // list of nodes for peeling - vector[4] frequencies_alpha; - vector[6] rates_alpha; - int map[S-1,S]; -} - -transformed data { - int bcount; // number of branches - int tauCount; - bcount = 2*S-2; - tauCount = S-1; -} - -parameters { - real taus[tauCount]; // intercoalescent times - simplex[4] freqs; - simplex[6] rates; - real theta; -} - - -model { - vector[4] partials[2*S,L]; // partial probabilities for the S tips and S-1 internal nodes - matrix[4,4] fttm[bcount]; // finite-time transition matrices for each branch - matrix[4,4] R; // symmetric rate matrix - matrix[4,4] Q; // rate matrix - matrix[4,4] P2; // diagonal sqrt frequencies - matrix[4,4] P2inv; // diagonal inverse sqrt frequencies - matrix[4,4] A; // another symmetric matrix - vector[4] eigenvalues; - matrix[4,4] eigenvectors; - matrix[4,4] m1; - matrix[4,4] m2; - real s; - vector [bcount] blens; // branch lengths - - // set some branch length priors - theta ~ oneOnX(); - - taus ~ coalescent(theta); - - freqs ~ dirichlet(frequencies_alpha); - - rates ~ dirichlet(rates_alpha); - - - R[2,1] = rates[1]; - R[1,2] = R[2,1]; - R[3,1] = rates[2]; - R[1,3] = R[3,1]; - R[4,1] = rates[3]; - R[1,4] = R[4,1]; - R[3,2] = rates[4]; - R[2,3] = R[3,2]; - R[4,2] = rates[5]; - R[2,4] = R[4,2]; - R[4,3] = rates[6]; - R[3,4] = R[4,3]; - - P2 = rep_matrix(0,4,4); - P2inv = rep_matrix(0,4,4); - - for (i in 1:4) { - R[i,i] = 0.0; - P2[i,i] = sqrt(freqs[i]); - P2inv[i,i] = sqrt(1.0/freqs[i]); - } - - Q = R * diag_matrix(freqs); - s = 0; - for (i in 1:4) { - Q[i,i] = 0.0; - Q[i,i] = -sum(Q[i,1:4]); - s = s + Q[i,i] * freqs[i]; - } - Q = -Q/s; - - A = P2 * Q * P2inv; - - eigenvalues = eigenvalues_sym(A); - eigenvectors = eigenvectors_sym(A); - - m1 = P2inv * eigenvectors; - m2 = eigenvectors' * P2; - - - for( b in 1:bcount ){ - blens[b] = 0; - } - - for( i in 1:tauCount ){ - for( j in 1:S ){ - if(map[i,j] > 0){ - blens[map[i,j]] = blens[map[i,j]] + taus[i]; - } - } - } - - for( b in 1:bcount ){ - fttm[b] = m1 * diag_matrix(exp(eigenvalues*blens[b])) * m2; - } - - // copy tip data into node probability vector - for( n in 1:S ) { - for( i in 1:L ) { - for( a in 1:4 ) { - partials[n,i][a] = tipdata[n,i,a]; - } - } - } - - // calculate tree likelihood for the topology encoded in peel - for( i in 1:L ) { - for( n in 1:(S-1) ) { - //partials[peel[n,3],i] = (fttm[n*2-1]*partials[peel[n,1],i]) .* (fttm[n*2]*partials[peel[n,2],i]); - partials[peel[n,3],i] = (fttm[peel[n,1]]*partials[peel[n,1],i]) .* (fttm[peel[n,2]]*partials[peel[n,2],i]); - } - - // multiply by background nt freqs (assuming uniform here) - for(j in 1:4){ - partials[2*S,i][j] = partials[peel[S-1,3],i][j] * freqs[j]; - } - // add the site log likelihood - target += log(sum(partials[2*S,i])); - } -} diff --git a/src/GTR-uniform.stan b/src/GTR-uniform.stan deleted file mode 100644 index ce88827..0000000 --- a/src/GTR-uniform.stan +++ /dev/null @@ -1,119 +0,0 @@ - -data { - int L; // alignment length - int S; // number of tips - real tipdata[S,L,4]; - int peel[S-1,3]; // list of nodes for peeling - vector[4] frequencies_alpha; - vector[6] rates_alpha; -} - -transformed data { - int bcount; // number of branches - int alphalen; - bcount = 2*S-2; - alphalen=4; // assume DNA -} - -parameters { - vector [bcount-1] blens; // branch lengths - simplex[6] rates; - simplex[4] freqs; -} - - -model { - vector[4] node[2*S,L]; // partial probabilities for the S tips and S-1 internal nodes - - matrix[4,4] fttm[bcount]; // finite-time transition matrices for each branch - matrix[4,4] R; // symmetric rate matrix - matrix[4,4] Q; // rate matrix - matrix[4,4] P2; // diagonal sqrt frequencies - matrix[4,4] P2inv; // diagonal inverse sqrt frequencies - matrix[4,4] A; // another symmetric matrix - vector[4] eigenvalues; - matrix[4,4] eigenvectors; - matrix[4,4] m1; - matrix[4,4] m2; - real s; - - // Priors - blens ~ exponential(20); - //rates ~ gamma(0.05,10); - rates ~ dirichlet(rates_alpha); - freqs ~ dirichlet(frequencies_alpha); - - // calculate finite time transition matrices for each branch - // under the GTR model - R[2,1] = rates[1]; - R[1,2] = R[2,1]; - R[3,1] = rates[2]; - R[1,3] = R[3,1]; - R[4,1] = rates[3]; - R[1,4] = R[4,1]; - R[3,2] = rates[4]; - R[2,3] = R[3,2]; - R[4,2] = rates[5]; - R[2,4] = R[4,2]; - R[4,3] = rates[6]; - R[3,4] = R[4,3]; - - P2 = rep_matrix(0,4,4); - P2inv = rep_matrix(0,4,4); - - for (i in 1:4) { - R[i,i] = 0.0; - P2[i,i] = sqrt(freqs[i]); - P2inv[i,i] = sqrt(1.0/freqs[i]); - } - - Q = R * diag_matrix(freqs); - s = 0; - for (i in 1:4) { - Q[i,i] = 0.0; - Q[i,i] = -sum(Q[i,1:4]); - s = s + Q[i,i] * freqs[i]; - } - Q = -Q/s; - - A = P2 * Q * P2inv; - - eigenvalues = eigenvalues_sym(A); - eigenvectors = eigenvectors_sym(A); - - m1 = P2inv * eigenvectors; - m2 = eigenvectors' * P2; - - for( b in 1:bcount-1 ){ - fttm[b] = m1 * diag_matrix(exp(eigenvalues*blens[b])) * m2; - } - - // zero-length root branch identity matrix - fttm[bcount] = rep_matrix(0,4,4); - for( i in 1:4 ) { - fttm[bcount][i,i] = 1; - } - - // copy tip data into node probability vector - for( n in 1:S ) { - for( i in 1:L ) { - for( a in 1:alphalen ) { - node[n,i][a] = tipdata[n,i,a]; - } - } - } - - // calculate tree likelihood for the topology encoded in peel - for( i in 1:L ) { - for( n in 1:(S-1) ) { - node[peel[n,3],i] = (fttm[n*2-1]*node[peel[n,1],i]) .* (fttm[n*2]*node[peel[n,2],i]); - } - for(j in 1:4){ - node[2*S,i][j] = node[peel[S-1,3],i][j] * freqs[j]; - } - - // add the site log likelihood - target += log(sum(node[2*S,i])); - } - -} diff --git a/src/HKY-coalescent.stan b/src/HKY-coalescent.stan deleted file mode 100755 index 6dd26c4..0000000 --- a/src/HKY-coalescent.stan +++ /dev/null @@ -1,148 +0,0 @@ -functions{ - real coalescent_log(real []x, real pop){ - real p; - real n; - real l; - int i; - real temp; - n = size(x); - p = 0; - l = n + 1.0; - i = 1; - - while(i <= floor(n)){ - temp = ((l*(l-1.0))/2.0)/pop; - p = p + log(temp) - (temp * x[i]); - l = l - 1.0; - i = i + 1; - } - return p; - } - - real oneOnX_log(real x){ - return -log(x); - } -} - -data { - int L; // alignment length - int S; // number of tips - real tipdata[S,L,4]; - int peel[S-1,3]; // list of nodes for peeling - vector[4] frequencies_alpha; - int map[S-1,S]; -} - -transformed data { - int bcount; // number of branches - int tauCount; - bcount = 2*S-2; - tauCount = S-1; -} - -parameters { - real taus[tauCount]; // intercoalescent times - simplex[4] freqs; - real kappa; - real theta; -} - - -model { - vector[4] partials[2*S,L]; // partial probabilities for the S tips and S-1 internal nodes - matrix[4,4] fttm[bcount]; // finite-time transition matrices for each branch - real R; - real Y; - real k1; - real k2; - real r; - real exp1; - real exp22; - real exp21; - vector [bcount] blens; // branch lengths - - // set some branch length priors - theta ~ oneOnX(); - - taus ~ coalescent(theta); - - freqs ~ dirichlet(frequencies_alpha); - - kappa ~ uniform(0,100); - //kappa ~ lognormal(1.0,1.25); - - for( b in 1:bcount ){ - blens[b] = 0; - } - - for( i in 1:tauCount ){ - for( j in 1:S ){ - if(map[i,j] > 0){ - blens[map[i,j]] = blens[map[i,j]] + taus[i]; - } - } - } - - R = freqs[1] + freqs[3]; - Y = freqs[4] + freqs[2]; - k1 = kappa * Y + R; - k2 = kappa * R + Y; - - r = 1.0 / (2.0 * (freqs[1] * freqs[2] + freqs[2] * freqs[3] + freqs[1] * freqs[4] + freqs[3] * freqs[4] + kappa * (freqs[2] * freqs[4] + freqs[1] * freqs[3]))); - - for( b in 1:bcount ){ - - exp1 = exp(-blens[b]*r); - exp22 = exp(-k2 * blens[b] * r); - exp21 = exp(-k1 * blens[b] * r); - - //A - fttm[b][1,1] = freqs[1] * (1. + (Y/R) * exp1) + (freqs[3]/R) * exp22; //A - fttm[b][1,2] = freqs[2] * (1. - exp1); //C - fttm[b][1,3] = freqs[3] * (1. + (Y/R) * exp1) - (freqs[3]/R) * exp22; //G - fttm[b][1,4] = freqs[4] * (1. - exp1); //T, U - - //C - fttm[b][2,1] = freqs[1] * (1. - exp1); //A - fttm[b][2,2] = freqs[2] * (1. + (R/Y) * exp1) + (freqs[4]/Y) * exp21; //C - fttm[b][2,3] = freqs[3] * (1. - exp1); //G - fttm[b][2,4] = freqs[4] * (1. + (R/Y) * exp1) - (freqs[4]/Y) * exp21; //T, U - - //G - fttm[b][3,1] = freqs[1] * (1. + (Y/R) * exp1) - (freqs[1]/R) * exp22; //A - fttm[b][3,2] = freqs[2] * (1. - exp1); //C - fttm[b][3,3] = freqs[3] * (1. + (Y/R) * exp1) + (freqs[1]/R) * exp22; //G - fttm[b][3,4] = freqs[4] * (1. - exp1); //T, U - - //T, U - fttm[b][4,1] = freqs[1] * (1. - exp1); //A - fttm[b][4,2] = freqs[2] * (1. + (R/Y) * exp1) - (freqs[2]/Y) * exp21; //C - fttm[b][4,3] = freqs[3] * (1. - exp1); //G - fttm[b][4,4] = freqs[4] * (1. + (R/Y) * exp1) + (freqs[2]/Y) * exp21; //T, U - } - - - // copy tip data into node probability vector - for( n in 1:S ) { - for( i in 1:L ) { - for( a in 1:4 ) { - partials[n,i][a] = tipdata[n,i,a]; - } - } - } - - // calculate tree likelihood for the topology encoded in peel - for( i in 1:L ) { - for( n in 1:(S-1) ) { - //partials[peel[n,3],i] = (fttm[n*2-1]*partials[peel[n,1],i]) .* (fttm[n*2]*partials[peel[n,2],i]); - partials[peel[n,3],i] = (fttm[peel[n,1]]*partials[peel[n,1],i]) .* (fttm[peel[n,2]]*partials[peel[n,2],i]); - } - - // multiply by background nt freqs (assuming uniform here) - for(j in 1:4){ - partials[2*S,i][j] = partials[peel[S-1,3],i][j] * freqs[j]; - } - // add the site log likelihood - target += log(sum(partials[2*S,i])); - } -} diff --git a/src/JC69-GTR.stan b/src/JC69-GTR.stan deleted file mode 100644 index f4f565a..0000000 --- a/src/JC69-GTR.stan +++ /dev/null @@ -1,148 +0,0 @@ - -data { - int L; // alignment length - int S; // number of tips - real tipdata[S,L,4]; - int peel[S-1,3]; // list of nodes for peeling - real weights[L]; - vector[4] frequencies_alpha; - vector[6] rates_alpha; - vector[2] thetas_alpha; -} - -transformed data { - int bcount; // number of branches - int root; - bcount = 2*S-2; - root = peel[S-1,3]; // root is the final peeling -} - -parameters { - vector [bcount-1] blens; // branch lengths - // For GTR model - simplex[6] rates; - simplex[4] freqs; - simplex[2] theta; -} - - -model { - vector[4] node[2,2*S,L]; // partial probabilities for the S tips and S-1 internal nodes - matrix[4,4] fttm[2,bcount]; // finite-time transition matrices for each branch, plus zero-length root branch - real ps[2]; - - // For GTR - matrix[4,4] R; // symmetric rate matrix - matrix[4,4] Q; // rate matrix - matrix[4,4] P2; // diagonal sqrt frequencies - matrix[4,4] P2inv; // diagonal inverse sqrt frequencies - matrix[4,4] A; // another symmetric matrix - vector[4] eigenvalues; - matrix[4,4] eigenvectors; - matrix[4,4] m1; - matrix[4,4] m2; - real s; - - // set some branch length priors - blens ~ exponential(20); - rates ~ dirichlet(rates_alpha); - freqs ~ dirichlet(frequencies_alpha); - theta ~ dirichlet(thetas_alpha); - - // calculate finite time transition matrices for each branch - // under the Jukes-Cantor model - for( b in 1:bcount-1 ) { - for( i in 1:4 ) { - for( j in 1:4 ) { - fttm[1,b][i,j] = 0.25 - 0.25*exp(-4*blens[b]/3); - } - fttm[1,b][i,i] = 0.25 + 0.75*exp(-4*blens[b]/3); - } - } - // GTR model - R[2,1] = rates[1]; - R[1,2] = R[2,1]; - R[3,1] = rates[2]; - R[1,3] = R[3,1]; - R[4,1] = rates[3]; - R[1,4] = R[4,1]; - R[3,2] = rates[4]; - R[2,3] = R[3,2]; - R[4,2] = rates[5]; - R[2,4] = R[4,2]; - R[4,3] = rates[6]; - R[3,4] = R[4,3]; - - P2 = rep_matrix(0,4,4); - P2inv = rep_matrix(0,4,4); - - for (i in 1:4) { - R[i,i] = 0.0; - P2[i,i] = sqrt(freqs[i]); - P2inv[i,i] = sqrt(1.0/freqs[i]); - } - - Q = R * diag_matrix(freqs); - s = 0; - for (i in 1:4) { - Q[i,i] = 0.0; - Q[i,i] = -sum(Q[i,1:4]); - s = s + Q[i,i] * freqs[i]; - } - Q = -Q/s; - - A = P2 * Q * P2inv; - - eigenvalues = eigenvalues_sym(A); - eigenvectors = eigenvectors_sym(A); - - m1 = P2inv * eigenvectors; - m2 = eigenvectors' * P2; - - for( b in 1:bcount-1 ){ - fttm[2,b] = m1 * diag_matrix(exp(eigenvalues*blens[b])) * m2; - } - - // zero-length root branch identity matrix - fttm[1,bcount] = rep_matrix(0,4,4); - fttm[2,bcount] = rep_matrix(0,4,4); - for( i in 1:4 ) { - fttm[1,bcount][i,i] = 1; - fttm[2,bcount][i,i] = 1; - } - - // copy tip data into node probability vector - for( n in 1:S ) { - for( i in 1:L ) { - for( a in 1:4 ) { - node[1,n,i][a] = tipdata[n,i,a]; - node[2,n,i][a] = tipdata[n,i,a]; - } - } - } - - // calculate tree likelihood for the topology encoded in peel - for( i in 1:L ) { - - for( n in 1:(S-1) ) { - for( m in 1:2){ - node[m,peel[n,3],i] = (fttm[m,n*2-1]*node[m,peel[n,1],i]) .* (fttm[m,n*2]*node[m,peel[n,2],i]); - } - } - - // multiply by background nt freqs (assuming uniform here) - node[1,2*S,i] = node[1,root,i] * 0.25; - - for(j in 1:4){ - node[2,2*S,i][j] = node[2,peel[S-1,3],i][j] * freqs[j]; - } - - // add the site log likelihood - for( m in 1:2){ - ps[m] = log(theta[m]) + log(sum(node[m,2*S,i])); - } - - target += log_sum_exp(ps)*weights[i]; - } - -} diff --git a/src/JC69-HKY-GTR.stan b/src/JC69-HKY-GTR.stan deleted file mode 100644 index f7982f4..0000000 --- a/src/JC69-HKY-GTR.stan +++ /dev/null @@ -1,210 +0,0 @@ - -data { - int L; // alignment length - int S; // number of tips - real tipdata[S,L,4]; - int peel[S-1,3]; // list of nodes for peeling - real weights[L]; - vector[4] frequencies_alpha; - vector[6] rates_alpha; - vector[3] thetas_alpha; -} - -transformed data { - int bcount; // number of branches - int root; - int M; // number of substitution models - bcount = 2*S-2; - root = peel[S-1,3]; // root is the final peeling - M = 3; -} - -parameters { - vector [bcount-1] blens; // branch lengths - // For GTR model - simplex[6] rates; - simplex[4] freqs; - // HKY - //simplex[4] freqs_hky; - real kappa; - - simplex[M] theta; -} - - -model { - vector[4] node[M,2*S,L]; // partial probabilities for the S tips and S-1 internal nodes - matrix[4,4] fttm[M,bcount]; // finite-time transition matrices for each branch, plus zero-length root branch - real ps[M]; - - // For GTR - matrix[4,4] R; // symmetric rate matrix - matrix[4,4] Q; // rate matrix - matrix[4,4] P2; // diagonal sqrt frequencies - matrix[4,4] P2inv; // diagonal inverse sqrt frequencies - matrix[4,4] A; // another symmetric matrix - vector[4] eigenvalues; - matrix[4,4] eigenvectors; - matrix[4,4] m1; - matrix[4,4] m2; - real s; - - // For HKY - real RR; - real Y; - real k1; - real k2; - real r; - real exp1; - real exp22; - real exp21; - - // set some branch length priors - blens ~ exponential(20); - rates ~ dirichlet(rates_alpha); - freqs ~ dirichlet(frequencies_alpha); - //freqs_hky ~ dirichlet(frequencies_alpha); - kappa ~ uniform(0,100); - theta ~ dirichlet(thetas_alpha); - - // calculate finite time transition matrices for each branch - // under the Jukes-Cantor model - for( b in 1:bcount-1 ) { - for( i in 1:4 ) { - for( j in 1:4 ) { - fttm[1,b][i,j] = 0.25 - 0.25*exp(-4*blens[b]/3); - } - fttm[1,b][i,i] = 0.25 + 0.75*exp(-4*blens[b]/3); - } - } - // GTR model - R[2,1] = rates[1]; - R[1,2] = R[2,1]; - R[3,1] = rates[2]; - R[1,3] = R[3,1]; - R[4,1] = rates[3]; - R[1,4] = R[4,1]; - R[3,2] = rates[4]; - R[2,3] = R[3,2]; - R[4,2] = rates[5]; - R[2,4] = R[4,2]; - R[4,3] = rates[6]; - R[3,4] = R[4,3]; - - P2 = rep_matrix(0,4,4); - P2inv = rep_matrix(0,4,4); - - for (i in 1:4) { - R[i,i] = 0.0; - P2[i,i] = sqrt(freqs[i]); - P2inv[i,i] = sqrt(1.0/freqs[i]); - } - - Q = R * diag_matrix(freqs); - s = 0; - for (i in 1:4) { - Q[i,i] = 0.0; - Q[i,i] = -sum(Q[i,1:4]); - s = s + Q[i,i] * freqs[i]; - } - Q = -Q/s; - - A = P2 * Q * P2inv; - - eigenvalues = eigenvalues_sym(A); - eigenvectors = eigenvectors_sym(A); - - m1 = P2inv * eigenvectors; - m2 = eigenvectors' * P2; - - for( b in 1:bcount-1 ){ - fttm[2,b] = m1 * diag_matrix(exp(eigenvalues*blens[b])) * m2; - } - - // HKY model - RR = freqs[1] + freqs[3]; - Y = freqs[4] + freqs[2]; - k1 = kappa * Y + RR; - k2 = kappa * RR + Y; - - r = 1.0 / (2.0 * (freqs[1] * freqs[2] + freqs[2] * freqs[3] + freqs[1] * freqs[4] + freqs[3] * freqs[4] + kappa * (freqs[2] * freqs[4] + freqs[1] * freqs[3]))); - - for( b in 1:bcount-1 ){ - - exp1 = exp(-blens[b]*r); - exp22 = exp(-k2 * blens[b] * r); - exp21 = exp(-k1 * blens[b] * r); - - //A - fttm[3,b][1,1] = freqs[1] * (1. + (Y/RR) * exp1) + (freqs[3]/RR) * exp22; //A - fttm[3,b][1,2] = freqs[2] * (1. - exp1); //C - fttm[3,b][1,3] = freqs[3] * (1. + (Y/RR) * exp1) - (freqs[3]/RR) * exp22; //G - fttm[3,b][1,4] = freqs[4] * (1. - exp1); //T, U - - //C - fttm[3,b][2,1] = freqs[1] * (1. - exp1); //A - fttm[3,b][2,2] = freqs[2] * (1. + (RR/Y) * exp1) + (freqs[4]/Y) * exp21; //C - fttm[3,b][2,3] = freqs[3] * (1. - exp1); //G - fttm[3,b][2,4] = freqs[4] * (1. + (RR/Y) * exp1) - (freqs[4]/Y) * exp21; //T, U - - //G - fttm[3,b][3,1] = freqs[1] * (1. + (Y/RR) * exp1) - (freqs[1]/RR) * exp22; //A - fttm[3,b][3,2] = freqs[2] * (1. - exp1); //C - fttm[3,b][3,3] = freqs[3] * (1. + (Y/RR) * exp1) + (freqs[1]/RR) * exp22; //G - fttm[3,b][3,4] = freqs[4] * (1. - exp1); //T, U - - //T, U - fttm[3,b][4,1] = freqs[1] * (1. - exp1); //A - fttm[3,b][4,2] = freqs[2] * (1. + (RR/Y) * exp1) - (freqs[2]/Y) * exp21; //C - fttm[3,b][4,3] = freqs[3] * (1. - exp1); //G - fttm[3,b][4,4] = freqs[4] * (1. + (RR/Y) * exp1) + (freqs[2]/Y) * exp21; //T, U - } - - // zero-length root branch identity matrix - for( m in 1:M ) { - fttm[m,bcount] = rep_matrix(0,4,4); - } - for( i in 1:4 ) { - for( m in 1:M ) { - fttm[m,bcount][i,i] = 1; - } - } - - // copy tip data into node probability vector - for( n in 1:S ) { - for( i in 1:L ) { - for( a in 1:4 ) { - for( m in 1:M ) { - node[m,n,i][a] = tipdata[n,i,a]; - } - } - } - } - - // calculate tree likelihood for the topology encoded in peel - for( i in 1:L ) { - - for( n in 1:(S-1) ) { - for( m in 1:M){ - node[m,peel[n,3],i] = (fttm[m,n*2-1]*node[m,peel[n,1],i]) .* (fttm[m,n*2]*node[m,peel[n,2],i]); - } - } - - // JC69 - node[1,2*S,i] = node[1,root,i] * 0.25; - - // GTR and HKY - for(j in 1:4){ - node[2,2*S,i][j] = node[2,peel[S-1,3],i][j] * freqs[j]; - node[3,2*S,i][j] = node[3,peel[S-1,3],i][j] * freqs[j]; - } - - // add the site log likelihood - for( m in 1:M){ - ps[m] = log(theta[m]) + log(sum(node[m,2*S,i])); - } - - target += log_sum_exp(ps)*weights[i]; - } - -} diff --git a/src/JC69-coalescent.stan b/src/JC69-coalescent.stan deleted file mode 100755 index dd04f50..0000000 --- a/src/JC69-coalescent.stan +++ /dev/null @@ -1,102 +0,0 @@ -functions{ - real coalescent_log(real []x, real pop){ - real p; - real n; - real l; - int i; - real temp; - n = size(x); - p = 0; - l = n + 1.0; - i = 1; - - while(i <= floor(n)){ - temp = ((l*(l-1.0))/2.0)/pop; - p = p + log(temp) - (temp * x[i]); - l = l - 1.0; - i = i + 1; - } - return p; - } - - real oneOnX_log(real x){ - return -log(x); - } -} - -data { - int L; // alignment length - int S; // number of tips - real tipdata[S,L,4]; - int peel[S-1,3]; // list of nodes for peeling - int map[S-1,S]; -} - -transformed data { - int bcount; // number of branches - int tauCount; - bcount = 2*S-2; - tauCount = S-1; -} - -parameters { - real taus[tauCount]; // intercoalescent times - real theta; -} - - -model { - vector[4] partials[2*S,L]; // partial probabilities for the S tips and S-1 internal nodes - matrix[4,4] fttm[bcount]; // finite-time transition matrices for each branch - vector [bcount] blens; // branch lengths - - // set some branch length priors - theta ~ oneOnX(); - - taus ~ coalescent(theta); - - for( b in 1:bcount ){ - blens[b] = 0; - } - - for( i in 1:tauCount ){ - for( j in 1:S ){ - if(map[i,j] > 0){ - blens[map[i,j]] = blens[map[i,j]] + taus[i]; - } - } - } - - for( b in 1:bcount ) { - for( i in 1:4 ) { - for( j in 1:4 ) { - fttm[b][i,j] = 0.25 - 0.25*exp(-4*blens[b]/3); - } - fttm[b][i,i] = 0.25 + 0.75*exp(-4*blens[b]/3); - } - } - - - // copy tip data into node probability vector - for( n in 1:S ) { - for( i in 1:L ) { - for( a in 1:4 ) { - partials[n,i][a] = tipdata[n,i,a]; - } - } - } - - // calculate tree likelihood for the topology encoded in peel - for( i in 1:L ) { - for( n in 1:(S-1) ) { - partials[peel[n,3],i] = (fttm[peel[n,1]]*partials[peel[n,1],i]) .* (fttm[peel[n,2]]*partials[peel[n,2],i]); - } - - // multiply by background nt freqs (assuming uniform here) - for(j in 1:4){ - partials[2*S,i][j] = partials[peel[S-1,3],i][j] * 0.25; - } - // add the site log likelihood - target += log(sum(partials[2*S,i])); - } -} diff --git a/src/JC69-mixture.stan b/src/JC69-mixture.stan deleted file mode 100644 index 311718f..0000000 --- a/src/JC69-mixture.stan +++ /dev/null @@ -1,90 +0,0 @@ - -data { - int T; // number of trees - int L; // alignment length - int S; // number of tips - real tipdata[S,L,4]; - int peel[T,(S-1),3]; // list of nodes for peeling - real weights[L]; -} - -transformed data { - int bcount; // number of branches - int pcount; - int alphalen; - int root; - vector[T] alpha; // could be moved to data - - bcount = 2*S-2; // number of branches - pcount = 2*S-3; // number of branch parameters - alphalen=4; // assume DNA - for(i in 1:T){ - alpha[i] = 1; - } - -} - -parameters { - vector [pcount] blens[T]; // branch lengths - simplex[T] theta; -} - - -model { - vector[alphalen] node[T,2*S,L]; // partial probabilities for the S tips and S-1 internal nodes - matrix[alphalen,alphalen] fttm[T,bcount]; // finite-time transition matrices for each branch, plus zero-length root branch - real ps[T]; - - // set some branch length priors - for( t in 1:T){ - blens[t] ~ exponential(20); - } - - theta ~ dirichlet(alpha); - - // calculate finite time transition matrices for each branch - // under the Jukes-Cantor model - for( t in 1:T){ - for( b in 1:pcount ) { - for( i in 1:alphalen ) { - for( j in 1:alphalen ) { - fttm[t,b][i,j] = 0.25 - 0.25*exp(-4*blens[t,b]/3); - } - fttm[t,b][i,i] = 0.25 + 0.75*exp(-4*blens[t,b]/3); - } - } - - // zero-length root branch identity matrix - fttm[t,bcount] = rep_matrix(0,alphalen,alphalen); - for( i in 1:alphalen ) { - fttm[t,bcount][i,i] = 1; - } - } - - - // copy tip data into node probability vector - for( t in 1:T ) { - for( n in 1:S ) { - for( i in 1:L ) { - for( a in 1:alphalen ) { - node[t,n,i][a] = tipdata[n,i,a]; - } - } - } - } - - // calculate tree likelihood for the topology encoded in peel - for( i in 1:L ) { - for( t in 1:T ) { - for( n in 1:(S-1) ) { - node[t,peel[t,n,3],i] = (fttm[t,n*2-1]*node[t,peel[t,n,1],i]) .* (fttm[t,n*2]*node[t,peel[t,n,2],i]); - } - // multiply by background nt freqs (assuming uniform here) - node[t,2*S,i] = node[t,peel[t,S-1,3],i] / alphalen; - - // add the site log likelihood - ps[t] = log(theta[t]) + log(sum(node[t,2*S,i])); - } - target += log_sum_exp(ps)*weights[i]; - } -} diff --git a/src/JC69-mixture2.stan b/src/JC69-mixture2.stan deleted file mode 100644 index 44fc9a7..0000000 --- a/src/JC69-mixture2.stan +++ /dev/null @@ -1,130 +0,0 @@ - -data { - int T; // number of trees - int L; // alignment length - int S; // number of tips - int B; // number of independent branches (not including one of the children of root) - real tipdata[S,L,4]; - int peel[T,(S-1),3]; // list of nodes for peeling - int indexes[(2*S-3)*T]; // -3 because we do not count one of the children of root - real weights[L]; -} - -transformed data { - int bcount; // number of branches - int pcount; - int alphalen; - int root; - vector[T] alpha; // could be moved to data - - bcount = 2*S-2; - pcount = 2*S-3; - alphalen=4; // assume DNA - for(i in 1:T){ - alpha[i] = 1; - } - -} - -parameters { - //vector [B] blens[T]; // branch lengths - vector [B] blens; // branch lengths (independent) - simplex[T] theta; -} - - -model { - vector[alphalen] node[T,2*S,L]; // partial probabilities for the S tips and S-1 internal nodes - matrix[alphalen,alphalen] fttm[B+1]; // finite-time transition matrices for each branch, plus zero-length root branch - real ps[T]; - int counter; - - counter = 1; - - // set some branch length priors - blens ~ exponential(20); - - theta ~ dirichlet(alpha); - - // calculate finite time transition matrices for each branch - // under the Jukes-Cantor model - for( b in 1:B){ - for( i in 1:4 ) { - for( j in 1:4 ) { - fttm[b][i,j] = 0.25 - 0.25*exp(-4*blens[b]/3); - } - fttm[b][i,i] = 0.25 + 0.75*exp(-4*blens[b]/3); - } - } - fttm[B+1] = rep_matrix(0,alphalen,alphalen); - for( i in 1:alphalen ) { - fttm[B+1][i,i] = 1; - } - - /*for( t in 1:T){ - for( b in 1:bcount-1 ) { - for( i in 1:alphalen ) { - for( j in 1:alphalen ) { - //fttm[t,b][i,j] = 0.25 - 0.25*exp(-4*blens[t,b]/3); - fttm[t,b][i,j] = 0.25 - 0.25*exp(-4*blens[indexes[counter]]/3); - } - //fttm[t,b][i,i] = 0.25 + 0.75*exp(-4*blens[t,b]/3); - fttm[t,b][i,i] = 0.25 + 0.75*exp(-4*blens[indexes[counter]]/3); - } - counter = counter + 1; - } - - // zero-length root branch identity matrix - fttm[t,bcount] = rep_matrix(0,alphalen,alphalen); - for( i in 1:alphalen ) { - fttm[t,bcount][i,i] = 1; - } - }*/ - - - // copy tip data into node probability vector - for( t in 1:T ) { - for( n in 1:S ) { - for( i in 1:L ) { - for( a in 1:alphalen ) { - node[t,n,i][a] = tipdata[n,i,a]; - } - } - } - } - - // calculate tree likelihood for the topology encoded in peel - /*for( t in 1:T ) { - ps[t] = log(theta[t]); - for( i in 1:L ) { - for( n in 1:(S-1) ) { - node[t,peel[t,n,3],i] = (fttm[t,n*2-1]*node[t,peel[t,n,1],i]) .* (fttm[t,n*2]*node[t,peel[t,n,2],i]); - } - // multiply by background nt freqs (assuming uniform here) - node[t,2*S,i] = node[t,peel[t,S-1,3],i] / alphalen; - - // add the site log likelihood - ps[t] = ps[t] + log(sum(node[t,2*S,i]))*weights[i]; - } - } - target += log_sum_exp(ps);*/ - - for( i in 1:L ) { - counter = 1; - for( t in 1:T ) { - for( n in 1:(S-2) ) { - node[t,peel[t,n,3],i] = (fttm[indexes[counter]]*node[t,peel[t,n,1],i]) .* (fttm[indexes[counter+1]]*node[t,peel[t,n,2],i]); - counter = counter + 2; - } - node[t,peel[t,S-1,3],i] = (fttm[indexes[counter]]*node[t,peel[t,S-1,1],i]) .* (fttm[indexes[B+1]]*node[t,peel[t,S-1,2],i]); - counter = counter + 1; - // multiply by background nt freqs (assuming uniform here) - node[t,2*S,i] = node[t,peel[t,S-1,3],i] / alphalen; - - // add the site log likelihood - ps[t] = log(theta[t]) + log(sum(node[t,2*S,i])); - } - target += log_sum_exp(ps)*weights[i]; - } - -} diff --git a/src/JC69-uniform.stan b/src/JC69-uniform.stan deleted file mode 100755 index bfa6b60..0000000 --- a/src/JC69-uniform.stan +++ /dev/null @@ -1,65 +0,0 @@ - -data { - int L; // alignment length - int S; // number of tips - real tipdata[S,L,4]; - int peel[S-1,3]; // list of nodes for peeling -} - -transformed data { - int bcount; // number of branches - int root; - bcount = 2*S-2; - root = peel[S-1,3]; // root is the final peeling -} - -parameters { - vector [bcount-1] blens; // branch lengths -} - - -model { - vector[4] node[2*S,L]; // partial probabilities for the S tips and S-1 internal nodes - matrix[4,4] fttm[bcount]; // finite-time transition matrices for each branch, plus zero-length root branch - - // set some branch length priors - blens ~ exponential(20); - - // calculate finite time transition matrices for each branch - // under the Jukes-Cantor model - for( b in 1:bcount-1 ) { - for( i in 1:4 ) { - for( j in 1:4 ) { - fttm[b][i,j] = 0.25 - 0.25*exp(-4*blens[b]/3); - } - fttm[b][i,i] = 0.25 + 0.75*exp(-4*blens[b]/3); - } - } - // zero-length root branch identity matrix - fttm[bcount] = rep_matrix(0,4,4); - for( i in 1:4 ) { - fttm[bcount][i,i] = 1; - } - - // copy tip data into node probability vector - for( n in 1:S ) { - for( i in 1:L ) { - for( a in 1:4 ) { - node[n,i][a] = tipdata[n,i,a]; - } - } - } - - // calculate tree likelihood for the topology encoded in peel - for( i in 1:L ) { - for( n in 1:(S-1) ) { - node[peel[n,3],i] = (fttm[n*2-1]*node[peel[n,1],i]) .* (fttm[n*2]*node[peel[n,2],i]); - } - // multiply by background nt freqs (assuming uniform here) - node[2*S,i] = node[root,i] * 0.25; - - // add the site log likelihood - target += log(sum(node[2*S,i])); - } - -} diff --git a/src/K80-coalescent.stan b/src/K80-coalescent.stan deleted file mode 100755 index e072fa5..0000000 --- a/src/K80-coalescent.stan +++ /dev/null @@ -1,134 +0,0 @@ -functions{ - real coalescent_log(real []x, real pop){ - real p; - real n; - real l; - int i; - real temp; - n = size(x); - p = 0; - l = n + 1.0; - i = 1; - - while(i <= floor(n)){ - temp = ((l*(l-1.0))/2.0)/pop; - p = p + log(temp) - (temp * x[i]); - l = l - 1.0; - i = i + 1; - } - return p; - } - - real oneOnX_log(real x){ - return -log(x); - } -} - -data { - int L; // alignment length - int S; // number of tips - real tipdata[S,L,4]; - int peel[S-1,3]; // list of nodes for peeling - int map[S-1,S]; -} - -transformed data { - int bcount; // number of branches - int tauCount; - bcount = 2*S-2; - tauCount = S-1; -} - -parameters { - real taus[tauCount]; // intercoalescent times - real kappa; - real theta; -} - - -model { - vector[4] partials[2*S,L]; // partial probabilities for the S tips and S-1 internal nodes - matrix[4,4] fttm[bcount]; // finite-time transition matrices for each branch - real k; - real r; - real exp1; - real exp22; - vector [bcount] blens; // branch lengths - - // set some branch length priors - theta ~ oneOnX(); - - taus ~ coalescent(theta); - - kappa ~ uniform(0,100); - //kappa ~ lognormal(1.0,1.25); - - for( b in 1:bcount ){ - blens[b] = 0; - } - - for( i in 1:tauCount ){ - for( j in 1:S ){ - if(map[i,j] > 0){ - blens[map[i,j]] = blens[map[i,j]] + taus[i]; - } - } - } - - k = (kappa + 1.0)/2.0; - r = 4.0 / (kappa + 2.0); - - for( b in 1:bcount ){ - - exp1 = exp(-blens[b]*r); - exp22 = exp(-k * blens[b]*r); - - //A - fttm[b][1,1] = 0.25 * (1. + exp1) + 0.5 * exp22; //A - fttm[b][1,2] = 0.25 * (1. - exp1); //C - fttm[b][1,3] = 0.25 * (1. + exp1) - 0.5 * exp22; //G - fttm[b][1,4] = 0.25 * (1. - exp1); //T, U - - //C - fttm[b][2,1] = 0.25 * (1. - exp1); //A - fttm[b][2,2] = 0.25 * (1. + exp1) + 0.5 * exp22; //C - fttm[b][2,3] = 0.25 * (1. - exp1); //G - fttm[b][2,4] = 0.25 * (1. + exp1) - 0.5 * exp22; //T, U - - //G - fttm[b][3,1] = 0.25 * (1. + exp1) - 0.5 * exp22; //A - fttm[b][3,2] = 0.25 * (1. - exp1); //C - fttm[b][3,3] = 0.25 * (1. + exp1) + 0.5 * exp22; //G - fttm[b][3,4] = 0.25 * (1. - exp1); //T, U - - //T, U - fttm[b][4,1] = 0.25 * (1. - exp1); //A - fttm[b][4,2] = 0.25 * (1. + exp1) - 0.5 * exp22; //C - fttm[b][4,3] = 0.25 * (1. - exp1); //G - fttm[b][4,4] = 0.25 * (1. + exp1) + 0.5 * exp22; //T, U - } - - - // copy tip data into node probability vector - for( n in 1:S ) { - for( i in 1:L ) { - for( a in 1:4 ) { - partials[n,i][a] = tipdata[n,i,a]; - } - } - } - - // calculate tree likelihood for the topology encoded in peel - for( i in 1:L ) { - for( n in 1:(S-1) ) { - partials[peel[n,3],i] = (fttm[peel[n,1]]*partials[peel[n,1],i]) .* (fttm[peel[n,2]]*partials[peel[n,2],i]); - } - - // multiply by background nt freqs (assuming uniform here) - for(j in 1:4){ - partials[2*S,i][j] = partials[peel[S-1,3],i][j] * 0.25; - } - // add the site log likelihood - target += log(sum(partials[2*S,i])); - } -} From 844b41bd1b605d3b932834529fe10dd8bb2ff51a Mon Sep 17 00:00:00 2001 From: Luiz Max Carvalho Date: Fri, 4 Oct 2019 17:31:48 -0300 Subject: [PATCH 12/14] Think we're ready for a first look at the integrated prior --- examples/fluA/.Rhistory | 512 ----------- examples/fluA/clean | 1 - phylostan/generate_script.py | 1685 +++++++++++++++++----------------- 3 files changed, 842 insertions(+), 1356 deletions(-) delete mode 100644 examples/fluA/.Rhistory delete mode 100755 examples/fluA/clean diff --git a/examples/fluA/.Rhistory b/examples/fluA/.Rhistory deleted file mode 100644 index 0de97cd..0000000 --- a/examples/fluA/.Rhistory +++ /dev/null @@ -1,512 +0,0 @@ -} -# mm <- .7 -# dd <- .2 -# pars <- elicit_beta_median_iq(m = mm, d = dd) -# qbeta(.5, shape1 = pars$a, shape2 = pars$b) -# qbeta(.9, shape1 = pars$a, shape2 = pars$b) -# curve(dbeta(x,shape1 = pars$a, shape2 = pars$b), lwd = 2) -get_parameter_vectors_median_iq <- function(iq_correct, -iq_wrong = c(.15, .25, .35, .45) ){ -pars_0 <- elicit_beta_median_iq(m = .5, iq = iq_wrong[1]) -pars_1 <- elicit_beta_mean_cv(m0 = .5, iq = iq_wrong[2]) -pars_2 <- elicit_beta_mean_cv(m0 = .5, iq = iq_correct) # big shot -pars_3 <- elicit_beta_mean_cv(m0 = .5, iq = iq_wrong[3]) -pars_4 <- elicit_beta_mean_cv(m0 = .5, iq = iq_wrong[4]) -av <- unlist( c(pars_0[1], pars_1[1], pars_2[1], pars_3[1], pars_4[1]) ) -bv <- unlist( c(pars_0[2], pars_1[2], pars_2[2], pars_3[2], pars_4[2]) ) -return(list( -av = as.numeric(av), -bv = as.numeric(bv) -)) -} -get_parameter_vectors_median_iq(iq_correct = .1) -## Here is a simple method-of-moments based elicitation procedure for the Beta distribution. -## This function will take either -## (i) prior mean and variance m_0 and v_0, respectively, or; -## (ii) prior mean and coefficient of variation m_0 and c, respectively. -elicit_beta_mean_cv <- function(m0, v0 = NULL, cv = 1){ -if(!is.null(v0)){ -a <- -(m0*v0 + m0^3 - m0^2)/v0 -b <- ((m0-1)*v0 + m0^3 - 2*m0^2 + m0)/v0 -}else{ -a <- -(m0*(cv*m0)^2 + m0^3 - m0^2)/(cv*m0)^2 -b <- ((m0-1)*(cv*m0)^2 + m0^3 - 2*m0^2 + m0)/(cv*m0)^2 -} -if(a < 0 || b <0) warning("Warning: at least one of the obtained parameters is not valid") -return(list(a = a, b = b)) -} -## -# Testing -# m <- .15 -# v <- 0.019 -# c0 <- 2 -# elicit_beta_mean_cv(m0 = m, v0 = v) -# elicit_beta_mean_cv(m0 = m, cv = c0) -get_parameter_vectors_mean_cv <- function(cv_correct, cv_wrong = .1){ -pars_0 <- elicit_beta_mean_cv(m0 = .1, cv = cv_wrong) -pars_1 <- elicit_beta_mean_cv(m0 = .2, cv = cv_wrong) -pars_2 <- elicit_beta_mean_cv(m0 = .5, cv = cv_correct) # big shot -pars_3 <- elicit_beta_mean_cv(m0 = .8, cv = cv_wrong) -pars_4 <- elicit_beta_mean_cv(m0 = .9, cv = cv_wrong) -av <- unlist( c(pars_0[1], pars_1[1], pars_2[1], pars_3[1], pars_4[1]) ) -bv <- unlist( c(pars_0[2], pars_1[2], pars_2[2], pars_3[2], pars_4[2]) ) -return(list( -av = as.numeric(av), -bv = as.numeric(bv) -)) -} -# -elicit_beta_median_iq <- function(m, d, q = .90){ -u <- m + d -loss <- function(x){ -a <- x[1] -b <- x[2] -m.hat <- qbeta(.5, shape1 = a, shape2 = b) -u.hat <- qbeta(q, shape1 = a, shape2 = b) -error <- .5 * (m.hat - m)^2 + .5*(u.hat-u)^2 -return(error) -} -opt <- suppressWarnings( optim(loss, par = c(1, 1)) ) -a <- opt$par[1] -b <- opt$par[2] -if(a < 0 || b <0) warning("Warning: at least one of the obtained parameters is not valid") -return(list(a = a, b = b)) -} -# mm <- .7 -# dd <- .2 -# pars <- elicit_beta_median_iq(m = mm, d = dd) -# qbeta(.5, shape1 = pars$a, shape2 = pars$b) -# qbeta(.9, shape1 = pars$a, shape2 = pars$b) -# curve(dbeta(x,shape1 = pars$a, shape2 = pars$b), lwd = 2) -get_parameter_vectors_median_iq <- function(iq_correct, -iq_wrong = c(.15, .25, .35, .45) ){ -pars_0 <- elicit_beta_median_iq(m = .5, q = iq_wrong[1]) -pars_1 <- elicit_beta_median_iq(m = .5, q = iq_wrong[2]) -pars_2 <- elicit_beta_median_iq(m = .5, q = iq_correct) # big shot -pars_3 <- elicit_beta_median_iq(m = .5, q = iq_wrong[3]) -pars_4 <- elicit_beta_median_iq(m = .5, q = iq_wrong[4]) -av <- unlist( c(pars_0[1], pars_1[1], pars_2[1], pars_3[1], pars_4[1]) ) -bv <- unlist( c(pars_0[2], pars_1[2], pars_2[2], pars_3[2], pars_4[2]) ) -return(list( -av = as.numeric(av), -bv = as.numeric(bv) -)) -} -# -plot_densities <- function(pars){ -av <- pars$av -bv <- pars$bv -K <- length(av) -curve(dbeta(x, av[1], bv[1]), lwd = 2) -for(k in 2:K){ -curve(dbeta(x, av[k], bv[k]), lwd = 2, col = k, add = TRUE) -} -} -get_parameter_vectors_median_iq(iq_correct = .1) -get_parameter_vectors_median_iq <- function(iq_correct, -iq_wrong = c(.15, .25, .35, .45) ){ -pars_0 <- elicit_beta_median_iq(m = .5, d = iq_wrong[1]) -pars_1 <- elicit_beta_median_iq(m = .5, d = iq_wrong[2]) -pars_2 <- elicit_beta_median_iq(m = .5, d = iq_correct) # big shot -pars_3 <- elicit_beta_median_iq(m = .5, d = iq_wrong[3]) -pars_4 <- elicit_beta_median_iq(m = .5, d = iq_wrong[4]) -av <- unlist( c(pars_0[1], pars_1[1], pars_2[1], pars_3[1], pars_4[1]) ) -bv <- unlist( c(pars_0[2], pars_1[2], pars_2[2], pars_3[2], pars_4[2]) ) -return(list( -av = as.numeric(av), -bv = as.numeric(bv) -)) -} -# -plot_densities <- function(pars){ -av <- pars$av -bv <- pars$bv -K <- length(av) -curve(dbeta(x, av[1], bv[1]), lwd = 2) -for(k in 2:K){ -curve(dbeta(x, av[k], bv[k]), lwd = 2, col = k, add = TRUE) -} -} -get_parameter_vectors_median_iq(iq_correct = .1) -plot_densities(get_parameter_vectors_median_iq(iq_correct = .1)) -get_parameter_vectors_median_iq <- function(iq_correct, -iq_wrong = c(.1, .15, .25, .35) ){ -pars_0 <- elicit_beta_median_iq(m = .5, d = iq_wrong[1]) -pars_1 <- elicit_beta_median_iq(m = .5, d = iq_wrong[2]) -pars_2 <- elicit_beta_median_iq(m = .5, d = iq_correct) # big shot -pars_3 <- elicit_beta_median_iq(m = .5, d = iq_wrong[3]) -pars_4 <- elicit_beta_median_iq(m = .5, d = iq_wrong[4]) -av <- unlist( c(pars_0[1], pars_1[1], pars_2[1], pars_3[1], pars_4[1]) ) -bv <- unlist( c(pars_0[2], pars_1[2], pars_2[2], pars_3[2], pars_4[2]) ) -return(list( -av = as.numeric(av), -bv = as.numeric(bv) -)) -} -plot_densities(get_parameter_vectors_median_iq(iq_correct = .05)) -get_parameter_vectors_median_iq(iq_correct = .05) -elicit_beta_median_iq <- function(m, d, q = .90){ -u <- m + d -loss <- function(x){ -a <- x[1] -b <- x[2] -m.hat <- qbeta(.5, shape1 = a, shape2 = b) -u.hat <- qbeta(q, shape1 = a, shape2 = b) -error <- .5 * (m.hat - m)^2 + .5*(u.hat-u)^2 -return(error) -} -opt <- suppressWarnings( optim(loss, par = c(1, 1), lower = c(0, 0)) ) -a <- opt$par[1] -b <- opt$par[2] -if(a < 0 || b <0) warning("Warning: at least one of the obtained parameters is not valid") -return(list(a = a, b = b)) -} -# mm <- .7 -# dd <- .2 -# pars <- elicit_beta_median_iq(m = mm, d = dd) -# qbeta(.5, shape1 = pars$a, shape2 = pars$b) -# qbeta(.9, shape1 = pars$a, shape2 = pars$b) -# curve(dbeta(x,shape1 = pars$a, shape2 = pars$b), lwd = 2) -get_parameter_vectors_median_iq <- function(iq_correct, -iq_wrong = c(.1, .15, .25, .35) ){ -pars_0 <- elicit_beta_median_iq(m = .5, d = iq_wrong[1]) -pars_1 <- elicit_beta_median_iq(m = .5, d = iq_wrong[2]) -pars_2 <- elicit_beta_median_iq(m = .5, d = iq_correct) # big shot -pars_3 <- elicit_beta_median_iq(m = .5, d = iq_wrong[3]) -pars_4 <- elicit_beta_median_iq(m = .5, d = iq_wrong[4]) -av <- unlist( c(pars_0[1], pars_1[1], pars_2[1], pars_3[1], pars_4[1]) ) -bv <- unlist( c(pars_0[2], pars_1[2], pars_2[2], pars_3[2], pars_4[2]) ) -return(list( -av = as.numeric(av), -bv = as.numeric(bv) -)) -} -# -plot_densities <- function(pars){ -av <- pars$av -bv <- pars$bv -K <- length(av) -curve(dbeta(x, av[1], bv[1]), lwd = 2) -for(k in 2:K){ -curve(dbeta(x, av[k], bv[k]), lwd = 2, col = k, add = TRUE) -} -} -get_parameter_vectors_median_iq <- function(iq_correct, -iq_wrong = c(.0125, .025, .05, .1) ){ -pars_0 <- elicit_beta_median_iq(m = .5, d = iq_wrong[1]) -pars_1 <- elicit_beta_median_iq(m = .5, d = iq_wrong[2]) -pars_2 <- elicit_beta_median_iq(m = .5, d = iq_correct) # big shot -pars_3 <- elicit_beta_median_iq(m = .5, d = iq_wrong[3]) -pars_4 <- elicit_beta_median_iq(m = .5, d = iq_wrong[4]) -av <- unlist( c(pars_0[1], pars_1[1], pars_2[1], pars_3[1], pars_4[1]) ) -bv <- unlist( c(pars_0[2], pars_1[2], pars_2[2], pars_3[2], pars_4[2]) ) -return(list( -av = as.numeric(av), -bv = as.numeric(bv) -)) -} -# -plot_densities <- function(pars){ -av <- pars$av -bv <- pars$bv -K <- length(av) -curve(dbeta(x, av[1], bv[1]), lwd = 2) -for(k in 2:K){ -curve(dbeta(x, av[k], bv[k]), lwd = 2, col = k, add = TRUE) -} -} -get_parameter_vectors_median_iq(iq_correct = .005) -plot_densities(get_parameter_vectors_median_iq(iq_correct = .005)) -get_parameter_vectors_median_iq <- function(med = 0.5, -iq_correct, -iq_wrong = c(.0125, .025, .05, .1) ){ -pars_0 <- elicit_beta_median_iq(m = med, d = iq_wrong[1]) -pars_1 <- elicit_beta_median_iq(m = med, d = iq_wrong[2]) -pars_2 <- elicit_beta_median_iq(m = med, d = iq_correct) # big shot -pars_3 <- elicit_beta_median_iq(m = med, d = iq_wrong[3]) -pars_4 <- elicit_beta_median_iq(m = med, d = iq_wrong[4]) -av <- unlist( c(pars_0[1], pars_1[1], pars_2[1], pars_3[1], pars_4[1]) ) -bv <- unlist( c(pars_0[2], pars_1[2], pars_2[2], pars_3[2], pars_4[2]) ) -return(list( -av = as.numeric(av), -bv = as.numeric(bv) -)) -} -# -plot_densities <- function(pars){ -av <- pars$av -bv <- pars$bv -K <- length(av) -curve(dbeta(x, av[1], bv[1]), lwd = 2) -for(k in 2:K){ -curve(dbeta(x, av[k], bv[k]), lwd = 2, col = k, add = TRUE) -} -} -plot_densities(get_parameter_vectors_median_iq(iq_correct = .005)) -plot_densities(get_parameter_vectors_median_iq(iq_correct = .005, med = .8)) -plot_densities(get_parameter_vectors_median_iq(iq_correct = .005, med = .7)) -plot_densities(get_parameter_vectors_median_iq(iq_correct = .15, med = .7)) -plot_densities <- function(pars, lg = TRUE){ -av <- pars$av -bv <- pars$bv -K <- length(av) -curve(dbeta(x, av[1], bv[1]), lwd = 2) -for(k in 2:K){ -curve(dbeta(x, av[k], bv[k]), lwd = 2, col = k, add = TRUE) -} -if(lg){ -legend(x = "top", col = 1:K, lwd = 2, lty = 1, bty = 'n', legend = paste("Expert_", 1:K, sep = "") ) -} -} -plot_densities(get_parameter_vectors_median_iq(iq_correct = .15, med = .7)) -plot_densities <- function(pars, lg = TRUE){ -av <- pars$av -bv <- pars$bv -K <- length(av) -curve(dbeta(x, av[1], bv[1]), lwd = 2) -for(k in 2:K){ -curve(dbeta(x, av[k], bv[k]), lwd = 2, col = k, add = TRUE) -} -if(lg){ -legend(x = "top", col = 1:K, lwd = 2, lty = 1, bty = 'n', legend = paste("Expert_", (1:K)-1, sep = "") ) -} -} -plot_densities(get_parameter_vectors_median_iq(iq_correct = .15, med = .7)) -plot_densities(get_parameter_vectors_median_iq(iq_correct = .25, med = .7)) -mm <- .7 -dd <- .25 -pars <- elicit_beta_median_iq(m = mm, d = dd) -qbeta(.5, shape1 = pars$a, shape2 = pars$b) -qbeta(.9, shape1 = pars$a, shape2 = pars$b) -curve(dbeta(x,shape1 = pars$a, shape2 = pars$b), lwd = 2) -plot_densities(get_parameter_vectors_median_iq(iq_correct = .25, med = .3)) -get_parameter_vectors_median_iq(iq_correct = .25, med = .3) -elicit_beta_median_iq <- function(m, d, q = .90){ -u <- m + d -loss <- function(x){ -a <- x[1] -b <- x[2] -m.hat <- qbeta(.5, shape1 = a, shape2 = b) -u.hat <- qbeta(q, shape1 = a, shape2 = b) -error <- .5 * (m.hat - m)^2 + .5*(u.hat-u)^2 -return(error) -} -opt <- suppressWarnings( optim(loss, par = c(1, 1), lower = c(1E-3, 1E-3)) ) -a <- opt$par[1] -b <- opt$par[2] -if(a < 0 || b <0) warning("Warning: at least one of the obtained parameters is not valid") -return(list(a = a, b = b)) -} -# mm <- .7 -# dd <- .25 -# pars <- elicit_beta_median_iq(m = mm, d = dd) -# qbeta(.5, shape1 = pars$a, shape2 = pars$b) -# qbeta(.9, shape1 = pars$a, shape2 = pars$b) -# curve(dbeta(x,shape1 = pars$a, shape2 = pars$b), lwd = 2) -get_parameter_vectors_median_iq <- function(med = 0.5, -iq_correct, -iq_wrong = c(.0125, .025, .05, .1) ){ -pars_0 <- elicit_beta_median_iq(m = med, d = iq_wrong[1]) -pars_1 <- elicit_beta_median_iq(m = med, d = iq_wrong[2]) -pars_2 <- elicit_beta_median_iq(m = med, d = iq_correct) # big shot -pars_3 <- elicit_beta_median_iq(m = med, d = iq_wrong[3]) -pars_4 <- elicit_beta_median_iq(m = med, d = iq_wrong[4]) -av <- unlist( c(pars_0[1], pars_1[1], pars_2[1], pars_3[1], pars_4[1]) ) -bv <- unlist( c(pars_0[2], pars_1[2], pars_2[2], pars_3[2], pars_4[2]) ) -return(list( -av = as.numeric(av), -bv = as.numeric(bv) -)) -} -# -plot_densities <- function(pars, lg = TRUE){ -av <- pars$av -bv <- pars$bv -K <- length(av) -curve(dbeta(x, av[1], bv[1]), lwd = 2) -for(k in 2:K){ -curve(dbeta(x, av[k], bv[k]), lwd = 2, col = k, add = TRUE) -} -if(lg){ -legend(x = "top", col = 1:K, lwd = 2, lty = 1, bty = 'n', legend = paste("Expert_", (1:K)-1, sep = "") ) -} -} -get_parameter_vectors_median_iq(iq_correct = .25, med = .3) -plot_densities(get_parameter_vectors_median_iq(iq_correct = .25, med = .3)) -plot_densities(get_parameter_vectors_median_iq(iq_correct = .2, med = .3)) -plot_densities(get_parameter_vectors_median_iq(iq_correct = .12, med = .3)) -get_parameter_vectors_median_iq(iq_correct = .25, med = .3) -get_parameter_vectors_median_iq(iq_correct = .12, med = .3) -get_parameter_vectors_median_iq(iq_correct = .12, med = .4) -plot_densities(get_parameter_vectors_median_iq(iq_correct = .12, med = .4)) -plot_densities(get_parameter_vectors_median_iq(iq_correct = .2, med = .4)) -get_parameter_vectors_median_iq(iq_correct = .2, med = .4) -rank(1:5) -rank(1:5)[2] -get_parameter_vectors_median_iq(iq_correct = .4, med = .4) -plot(get_parameter_vectors_median_iq(iq_correct = .4, med = .4)) -plot_densities(get_parameter_vectors_median_iq(iq_correct = .4, med = .4)) -rstan:::rstudio_stanc("DUMP/phylostan/examples/fluA/fluA-GTR-W4_InvGamma.stan") -rstan:::rstudio_stanc("DUMP/phylostan/examples/fluA/integrated_prior.stan") -rstan:::rstudio_stanc("DUMP/phylostan/examples/fluA/integrated_prior.stan") -rstan:::rstudio_stanc("DUMP/phylostan/examples/fluA/integrated_prior.stan") -rstan:::rstudio_stanc("DUMP/phylostan/examples/fluA/integrated_prior.stan") -rstan:::rstudio_stanc("DUMP/phylostan/examples/fluA/integrated_prior.stan") -rstan:::rstudio_stanc("DUMP/phylostan/examples/fluA/integrated_prior.stan") -setwd("~/DUMP/phylostan/examples/fluA") -library(rstan) -rstan_options(auto_write = TRUE) -options(mc.cores = 4) -compiled.model <- stan_model("integrated_prior.stan") -expose_stan_functions(compiled.model) -integrated_density(t = 0, choose(5, 2), u = 1000) -integrated_density(t = 2, choose(5, 2), u = 1000) -integrated_density(t = 2, choose(5, 2), u = 10) -integrated_density(t = .2, choose(5, 2), u = 1000) -integrated_density(t = .2, kappa = choose(5, 2), u = 1000) -u <- 1000 -kappa <- choose(10, 2) -kappa <- choose(5, 2) -t <- 2 -square <- function(x) x*x -2 *square(u + kappa * t) + 4*kappa*t*u + 3*square(kappa*t) - 3*log(kappa*t) * square(u + kappa * t) - 3 * square(u + kappa*t); -Sum = 2 *square(u + kappa * t) + 4*kappa*t*u + 3*square(kappa*t) - 3*log(kappa*t) * square(u + kappa * t) - 3 * square(u + kappa*t); -k <- 2 -# ff <- function(time, n, theta){ -# delta <- choose(n, 2)* time -# return(theta^-2 * exp(-delta/theta)) -# } -# -# integrate(function(x) ff(time = tk, n = k, theta = x), 0, Inf) ## confirming -# 1/(choose(k, 2)*tk) -############### -# alpha <- 1.2 -# beta <- 2 -# ff <- function(time, n, theta){ -# delta <- choose(n, 2)* time -# return(theta^-1 * exp(-delta/theta) * MCMCpack::dinvgamma(theta, shape = alpha, scale = beta)) -# } -# tk <- 1.5 -# integrate(function(x) ff(time = tk, n = k, theta = x), 0, Inf) ## confirming -# (alpha * beta^alpha)/(choose(k, 2)*tk + beta)^{alpha + 1} ## correct -################ -marginal_Jeffreys <- function(tt, n){ -2/(n*(n-1)*tt) -} -marginal_Jeffreys <- Vectorize(marginal_Jeffreys) -### -marginal_invgamma <- function(tt, n, a, b){ -choose(n, 2)*(a * b^a)/(choose(n, 2)*tt + b)^{a + 1} -} -marginal_invgamma <- Vectorize(marginal_invgamma) -### -marginal_lognormal <- function(tt, n, mu0 = 0, sd0 = 1){ -fn <- function(time, theta, log = FALSE){ -delta <- choose(n, 2)* time -dens <- -log(theta) -delta/theta + dlnorm(x = theta, mu0, sd0, log = TRUE) -if(!log) dens <- exp(dens) -return(dens) -} -integrate(function(x) fn(time = tt, theta = x), 0, Inf)$value -} -marginal_lognormal <- Vectorize(marginal_lognormal) -marginal_lognormal_normalised <- function(tt, n, mu0 = 0, sd0 = 1){ -norm_const <- integrate(function(x) marginal_lognormal(x, n, mu0, sd0), -0, Inf)$value -ans <- marginal_lognormal(tt, n, mu0, sd0) -return(ans/norm_const) -} -marginal_lognormal_normalised <- Vectorize(marginal_lognormal_normalised) -################# -################# -curve(marginal_Jeffreys(x, n = k), 0, 50, -main = paste("k =", k), -lwd = 2, xlab = expression(t[k]), ylab = "Density") -curve(marginal_invgamma(x, n = k, a = 1.2, b = 2), col = 3, add = TRUE) -curve(marginal_lognormal_normalised(x, n = k, mu0 = -0.004975165, sd0 = 2.14823), -0, 50, add = TRUE, col = 2, lty = 2, lwd = 2)## mean Ne = 10, sd = 100 -int_density <- function(t, kappa, u, log = FALSE){ -z <- kappa*t -w <- square(z + u) -lnum <- log( -2*w*log(u + z) + 3*square(z) + 4*u*z - w*(2*log(z) + 3) -) -ldenom <- log(2) + log(w) -ans <- log(2) + log(kappa) + lnum - ldenom -if(!log) ans <- exp(ans) -return(ans) -} -int_density(t= 2, kappa = choose(5, 2), u = 1000) -square <- function(x) x*x -int_density <- function(t, kappa, u, log = FALSE){ -z <- kappa*t -w <- square(z + u) -lnum <- log( -2*w*log(u + z) + 3*square(z) + 4*u*z - w*(2*log(z) + 3) -) -ldenom <- log(2) + log(w) -ans <- log(2) + log(kappa) + lnum - ldenom -if(!log) ans <- exp(ans) -return(ans) -} -int_density(t= 2, kappa = choose(5, 2), u = 1000) -int_density <- Vectorize(int_density) -int_density(t= 2, kappa = choose(5, 2), u = 1000) -curve(int_density(x, kappa = choose(5, 2), u = 1000), 0, 1000) -integrate(int_density(x, kappa = choose(5, 2), u = 1000), 0, Inf) -integrate(function(x) int_density(x, kappa = choose(5, 2), u = 1000), 0, Inf) -choose(5, 2) -square <- function(x) x*x -int_density <- function(t, kappa, u, log = FALSE){ -z <- kappa*t -w <- square(z + u) -lnum <- log( -2*w*log(u + z) + 3*square(z) + 4*u*z - w*(2*log(z) + 3) -) -ldenom <- log(2) + log(w) -ans <- log(2) + log(kappa) + lnum - ldenom -if(!log) ans <- exp(ans) -return(ans) -} -int_density <- Vectorize(int_density) -int_density(t = 2, kappa = choose(5, 2), u = 1000) -curve(int_density(x, kappa = choose(5, 2), u = 1000), 0, 1000) -integrate(function(x) int_density(x, kappa = choose(5, 2), u = 1000), 0, Inf) -integrate(function(x) int_density(x, kappa = choose(5, 2), u = 10), 0, Inf) -square <- function(x) x*x -int_density <- function(t, kappa, u, log = FALSE){ -z <- kappa*t -w <- square(z + u) -lnum <- log( -2*w*log(u + z) + 3*square(z) + 4*u*z - w*(2*log(z) + 3) -) -ldenom <- log(2) + log(w) -ans <- log(2) + log(kappa) + lnum - ldenom -log(u) -if(!log) ans <- exp(ans) -return(ans) -} -int_density <- Vectorize(int_density) -int_density(t = 2, kappa = choose(5, 2), u = 1000) -curve(int_density(x, kappa = choose(5, 2), u = 1000), 0, 1000) -integrate(function(x) int_density(x, kappa = choose(5, 2), u = 10), 0, Inf) -library(rstan) -rstan_options(auto_write = TRUE) -options(mc.cores = 4) -compiled.model <- stan_model("integrated_prior.stan") -expose_stan_functions(compiled.model) -integrated_density(t = 0, kappa = choose(5, 2), u = 1000) -integrated_density(t = 1, kappa = choose(5, 2), u = 1000) -integrated_density(t = 10, kappa = choose(5, 2), u = 1000) -integrated_density(t = 100, kappa = choose(5, 2), u = 1000) -curve(integrated_density(t = x, kappa = choose(5, 2), u = 1000), 0, 1000) -curve(function(x) integrated_density(t = x, kappa = choose(5, 2), u = 1000), 0, 1000) -curve(fn, 0, 1000) -fn <- function(x) integrated_density(t = x, kappa = choose(5, 2), u = 1000); fn <- Vectorize(fn) -curve(fn, 0, 1000) -lfn <- function(x) integrated_density(t = x, kappa = choose(5, 2), u = 1000); fn <- Vectorize(fn) -fn <- function(x) exp(lfn(x)); fn <- Vectorize(fn) -fn <- function(x) exp(lfn(x)); fn <- Vectorize(fn) -integrate(fn, 0, Inf) -rstan:::rstudio_stanc("~/DUMP/phylostan/examples/fluA/fluA-GTR-W4.stan") -rstan:::rstudio_stanc("~/DUMP/phylostan/examples/fluA/fluA-GTR-W4.stan") -rstan:::rstudio_stanc("~/DUMP/phylostan/examples/fluA/fluA-GTR-W4.stan") diff --git a/examples/fluA/clean b/examples/fluA/clean deleted file mode 100755 index 43fdcad..0000000 --- a/examples/fluA/clean +++ /dev/null @@ -1 +0,0 @@ -rm *.pkl fluA *.diag diff --git a/phylostan/generate_script.py b/phylostan/generate_script.py index b55b63e..266ec11 100755 --- a/phylostan/generate_script.py +++ b/phylostan/generate_script.py @@ -1,147 +1,147 @@ def autocorrelated_prior(heterochronous): - str = ''' - real logn_autocorrelated_log(real[] rates, real[] heights, int[,] map, real nu{0}){{ - int S = size(heights) + 1; - int nodeCount = S + size(heights); - real logP = 0.0; - // no rate at root and rate of first child is exponentialy distributed - for(i in 3:nodeCount){{ - if(map[i,2] == nodeCount){{ - if(map[i,1] > S){{ - logP += normal_lpdf(log(rates[map[i,1]]) | log(rates[map[2,1]]), nu*(2.0*heights[map[i,2]-S] - heights[map[i,1]-S] - heights[map[2,1]-S])/2.0); - }} - else{{ - logP += normal_lpdf(log(rates[map[i,1]]) | log(rates[map[2,1]]), nu*(2.0*heights[map[i,2]-S]{1} - heights[map[2,1]-S])/2.0); - }} - }} - else if(map[i,1] > S){{ - logP += normal_lpdf(log(rates[map[i,1]]) | log(rates[map[i,2]]), nu*(heights[map[i,2]-S] - heights[map[i,1]-S])/2.0); - }} - else{{ - logP += normal_lpdf(log(rates[map[i,1]]) | log(rates[map[i,2]]), nu*(heights[map[i,2]-S]{1})/2.0); - }} - }} - return logP; - }} + str = ''' + real logn_autocorrelated_log(real[] rates, real[] heights, int[,] map, real nu{0}){{ + int S = size(heights) + 1; + int nodeCount = S + size(heights); + real logP = 0.0; + // no rate at root and rate of first child is exponentialy distributed + for(i in 3:nodeCount){{ + if(map[i,2] == nodeCount){{ + if(map[i,1] > S){{ + logP += normal_lpdf(log(rates[map[i,1]]) | log(rates[map[2,1]]), nu*(2.0*heights[map[i,2]-S] - heights[map[i,1]-S] - heights[map[2,1]-S])/2.0); + }} + else{{ + logP += normal_lpdf(log(rates[map[i,1]]) | log(rates[map[2,1]]), nu*(2.0*heights[map[i,2]-S]{1} - heights[map[2,1]-S])/2.0); + }} + }} + else if(map[i,1] > S){{ + logP += normal_lpdf(log(rates[map[i,1]]) | log(rates[map[i,2]]), nu*(heights[map[i,2]-S] - heights[map[i,1]-S])/2.0); + }} + else{{ + logP += normal_lpdf(log(rates[map[i,1]]) | log(rates[map[i,2]]), nu*(heights[map[i,2]-S]{1})/2.0); + }} + }} + return logP; + }} ''' - if heterochronous: - return str.format(', real[] lowers', ' - lowers[map[i,1]]') - else: - return str.format('', '') + if heterochronous: + return str.format(', real[] lowers', ' - lowers[map[i,1]]') + else: + return str.format('', '') def get_weibull(invariant=False): - weibull_pinv_site_rates = """ - { - real m = 0; - real cat = C - 1; - real pvar = 1.0 - pinv; - rs[1] = 0.0; - ps[1] = pinv; - for(i in 2:C){ - rs[i] = pow(-log(1.0 - (2.0*(i-2)+1.0)/(2.0*cat)), 1.0/wshape); // weibull inverse cdf with lambda=1 - ps[i] = pvar/cat; - } - m = sum(rs)*pvar/cat; - for(i in 2:C){ - rs[i] /= m; - } - } + weibull_pinv_site_rates = """ + { + real m = 0; + real cat = C - 1; + real pvar = 1.0 - pinv; + rs[1] = 0.0; + ps[1] = pinv; + for(i in 2:C){ + rs[i] = pow(-log(1.0 - (2.0*(i-2)+1.0)/(2.0*cat)), 1.0/wshape); // weibull inverse cdf with lambda=1 + ps[i] = pvar/cat; + } + m = sum(rs)*pvar/cat; + for(i in 2:C){ + rs[i] /= m; + } + } """ - weibull_site_rates = """ - { - real m = 0; - for(i in 1:C){ - rs[i] = pow(-log(1.0 - (2.0*(i-1)+1.0)/(2.0*C)), 1.0/wshape); - } - m = sum(rs)/C; - for(i in 1:C){ - rs[i] /= m; - } - } + weibull_site_rates = """ + { + real m = 0; + for(i in 1:C){ + rs[i] = pow(-log(1.0 - (2.0*(i-1)+1.0)/(2.0*C)), 1.0/wshape); + } + m = sum(rs)/C; + for(i in 1:C){ + rs[i] /= m; + } + } """ - if invariant: - return weibull_pinv_site_rates - else: - return weibull_site_rates + if invariant: + return weibull_pinv_site_rates + else: + return weibull_site_rates def constant_coalescent(heterochronous=False): - constant_coalescent_str = """ - real constant_coalescent_log(real[] heights, real popSize, int[,] map{0}){{ - int S = size(heights)+1; // number of leaves from the number of internal nodes - int nodeCount = size(heights) + S; - - real logP = 0.0; - real lineageCount = 0.0; // first 2 intervals are sampling events - - int indices[nodeCount]; - int childCounts[nodeCount]; - real times[nodeCount]; - - real start; - real finish; - real interval; - real logPopSize = log(popSize); - - for( i in 1:nodeCount ){{ - // internal node: transform - if(map[i,1] > S){{ - times[map[i,1]] = heights[map[i,1]-S]; - childCounts[map[i,1]] = 2; - }} - else{{ - times[map[i,1]] = {1}; - childCounts[map[i,1]] = 0; - }} - }} - - // calculate intervals - indices = sort_indices_asc(times); - - // first tip - start = times[indices[1]]; - - for (i in 1:nodeCount) {{ - finish = times[indices[i]]; - - interval = finish - start; - if(interval != 0.0){{ - logP -= interval*((lineageCount*(lineageCount-1.0))/2.0)/popSize; - }} - - // sampling event - if (childCounts[indices[i]] == 0) {{ - lineageCount += 1.0; - }} - // coalescent event - else {{ - lineageCount -= 1.0; - logP -= logPopSize; - }} - - start = finish; - }} - - return logP; - }} - """ - - if heterochronous: - return constant_coalescent_str.format(', real[] lowers', 'lowers[map[i,1]]') - else: - return constant_coalescent_str.format('', '0') + constant_coalescent_str = """ + real constant_coalescent_log(real[] heights, real popSize, int[,] map{0}){{ + int S = size(heights)+1; // number of leaves from the number of internal nodes + int nodeCount = size(heights) + S; + + real logP = 0.0; + real lineageCount = 0.0; // first 2 intervals are sampling events + + int indices[nodeCount]; + int childCounts[nodeCount]; + real times[nodeCount]; + + real start; + real finish; + real interval; + real logPopSize = log(popSize); + + for( i in 1:nodeCount ){{ + // internal node: transform + if(map[i,1] > S){{ + times[map[i,1]] = heights[map[i,1]-S]; + childCounts[map[i,1]] = 2; + }} + else{{ + times[map[i,1]] = {1}; + childCounts[map[i,1]] = 0; + }} + }} + + // calculate intervals + indices = sort_indices_asc(times); + + // first tip + start = times[indices[1]]; + + for (i in 1:nodeCount) {{ + finish = times[indices[i]]; + + interval = finish - start; + if(interval != 0.0){{ + logP -= interval*((lineageCount*(lineageCount-1.0))/2.0)/popSize; + }} + + // sampling event + if (childCounts[indices[i]] == 0) {{ + lineageCount += 1.0; + }} + // coalescent event + else {{ + lineageCount -= 1.0; + logP -= logPopSize; + }} + + start = finish; + }} + + return logP; + }} + """ + + if heterochronous: + return constant_coalescent_str.format(', real[] lowers', 'lowers[map[i,1]]') + else: + return constant_coalescent_str.format('', '0') def integrated_constant_coalescent(heterochronous=False): - integrated_constant_coalescent_str = """ + integrated_constant_coalescent_str = """ real integrated_density(real t, real kappa, real u){{ real z = kappa*t; real w = square(z + u); real lnum = log(2*w*log(u + z) + 3*square(z) + 4*u*z - w*(2*log(z) + 3)); real ldenom = log(2) + log(w); return(log(2) + log(kappa) + lnum - ldenom -log(u)); - }} + }} real integrated_constant_coalescent_log(real[] heights, real U, int[,] map{0}){{ int S = size(heights) + 1; // number of leaves from the number of internal nodes int nodeCount = size(heights) + S; @@ -157,17 +157,17 @@ def integrated_constant_coalescent(heterochronous=False): real finish; real interval; - for( i in 1:nodeCount ){ + for( i in 1:nodeCount ){{ // internal node: transform - if(map[i, 1] > S){ + if(map[i, 1] > S){{ times[map[i, 1]] = heights[map[i, 1]-S]; childCounts[map[i, 1]] = 2; - } - else{ + }} + else{{ times[map[i, 1]] = lowers[map[i, 1]]; childCounts[map[i, 1]] = 0; - } - } + }} + }} // calculate intervals indices = sort_indices_asc(times); @@ -175,794 +175,793 @@ def integrated_constant_coalescent(heterochronous=False): // first tip start = times[indices[1]]; - for (i in 1:nodeCount) { + for (i in 1:nodeCount) {{ finish = times[indices[i]]; interval = finish - start; - // print("Interval = ", interval, " node = ", i, " lincount =", lineageCount, " logP = ", logP); - if(interval != 0.0 && childCounts[indices[i]] != 0 ){ + if(interval != 0.0 && childCounts[indices[i]] != 0 ){{ logP += integrated_density(interval, lineageCount*(lineageCount-1.0)/2.0, U); - } + }} // sampling event - if (childCounts[indices[i]] == 0) { + if (childCounts[indices[i]] == 0) {{ lineageCount += 1.0; - } + }} // coalescent event - else { + else {{ lineageCount -= 1.0; - } + }} start = finish; - } + }} return logP; }} - """ + """ - if heterochronous: - return integrated_constant_coalescent_str.format(', real[] lowers', 'lowers[map[i,1]]') - else: - return integrated_constant_coalescent_str.format('', '0') + if heterochronous: + return integrated_constant_coalescent_str.format(', real[] lowers', 'lowers[map[i,1]]') + else: + return integrated_constant_coalescent_str.format('', '0') def skyride_coalescent(heterochronous): - skyride_coalescent_str = """ - real skyride_coalescent_log(real[] heights, vector pop, int[,] map{0}){{ - int S = size(heights)+1; // number of leaves from the number of internal nodes - int nodeCount = size(heights) + S; - - real logP = 0.0; - int index = 1; - real lineageCount = 0.0; - - int indices[nodeCount]; - int childCounts[nodeCount]; - real times[nodeCount]; - real start; - real finish; - real interval; - - for( i in 1:nodeCount ){{ - // internal node: transform - if(map[i,1] > S){{ - times[i] = heights[map[i,1]-S]; - childCounts[i] = 2; - }} - else{{ - times[i] = {1}; - childCounts[i] = 0; - }} - }} - - // calculate intervals - indices = sort_indices_asc(times); - - // first tip - start = times[indices[1]]; - - for (i in 1:nodeCount) {{ - finish = times[indices[i]]; - - interval = finish - start; - // consecutive sampling events - if(interval != 0.0){{ - logP -= interval*((lineageCount*(lineageCount-1.0))/2.0)/exp(pop[index]); - if (childCounts[indices[i]] != 0) {{ - logP -= pop[index]; - index += 1; - }} - }} - - // sampling event - if (childCounts[indices[i]] == 0) {{ - lineageCount += 1.0; - }} - // coalescent event - else {{ - lineageCount -= 1.0; - }} - - start = finish; - }} - - return logP; - }} + skyride_coalescent_str = """ + real skyride_coalescent_log(real[] heights, vector pop, int[,] map{0}){{ + int S = size(heights)+1; // number of leaves from the number of internal nodes + int nodeCount = size(heights) + S; + + real logP = 0.0; + int index = 1; + real lineageCount = 0.0; + + int indices[nodeCount]; + int childCounts[nodeCount]; + real times[nodeCount]; + real start; + real finish; + real interval; + + for( i in 1:nodeCount ){{ + // internal node: transform + if(map[i,1] > S){{ + times[i] = heights[map[i,1]-S]; + childCounts[i] = 2; + }} + else{{ + times[i] = {1}; + childCounts[i] = 0; + }} + }} + + // calculate intervals + indices = sort_indices_asc(times); + + // first tip + start = times[indices[1]]; + + for (i in 1:nodeCount) {{ + finish = times[indices[i]]; + + interval = finish - start; + // consecutive sampling events + if(interval != 0.0){{ + logP -= interval*((lineageCount*(lineageCount-1.0))/2.0)/exp(pop[index]); + if (childCounts[indices[i]] != 0) {{ + logP -= pop[index]; + index += 1; + }} + }} + + // sampling event + if (childCounts[indices[i]] == 0) {{ + lineageCount += 1.0; + }} + // coalescent event + else {{ + lineageCount -= 1.0; + }} + + start = finish; + }} + + return logP; + }} """ - if heterochronous: - return skyride_coalescent_str.format(', real[] lowers', 'lowers[map[i,1]]') - else: - return skyride_coalescent_str.format('', '0') + if heterochronous: + return skyride_coalescent_str.format(', real[] lowers', 'lowers[map[i,1]]') + else: + return skyride_coalescent_str.format('', '0') def skygrid_coalescent(heterochronous): - skygrid_coalescent_str = """ - real skygrid_coalescent_log(real[] heights, vector pop, int[,] map, vector grid{0}){{ - int G = rows(grid); - int S = size(heights)+1; // number of leaves from the number of internal nodes - int nodeCount = size(heights) + S; - - real logP = 0.0; - int index = 1; - real lineageCount = 0.0; - - int indices[nodeCount]; - int childCounts[nodeCount]; - real times[nodeCount]; - real start; - real finish; - real end; - - real popSize; - real logPopSize; - - for( i in 1:nodeCount ){{ - // internal node: transform - if(map[i,1] > S){{ - times[map[i,1]] = heights[map[i,1]-S]; - childCounts[map[i,1]] = 2; - }} - else{{ - times[map[i,1]] = {1}; - childCounts[map[i,1]] = 0; - }} - }} - - // calculate intervals - indices = sort_indices_asc(times); - - // first tip - start = times[indices[1]]; - logPopSize = pop[index]; - popSize = exp(logPopSize); - - for (i in 1:nodeCount) {{ - finish = times[indices[i]]; - - while(index < G && finish > grid[index]){{ - end = fmin(grid[index], finish); - logP -= (end - start)*((lineageCount*(lineageCount-1.0))/2.0)/popSize; - start = end; - - if(index < G){{ - index += 1; - logPopSize = pop[index]; - popSize = exp(logPopSize); - }} - }} - logP -= (finish - start)*((lineageCount*(lineageCount-1.0))/2.0)/popSize; - if (childCounts[indices[i]] != 0) {{ - logP -= logPopSize; - }} - - // sampling event - if (childCounts[indices[i]] == 0) {{ - lineageCount += 1.0; - }} - // coalescent event - else {{ - lineageCount -= 1.0; - }} - - start = finish; - }} - return logP; - }} + skygrid_coalescent_str = """ + real skygrid_coalescent_log(real[] heights, vector pop, int[,] map, vector grid{0}){{ + int G = rows(grid); + int S = size(heights)+1; // number of leaves from the number of internal nodes + int nodeCount = size(heights) + S; + + real logP = 0.0; + int index = 1; + real lineageCount = 0.0; + + int indices[nodeCount]; + int childCounts[nodeCount]; + real times[nodeCount]; + real start; + real finish; + real end; + + real popSize; + real logPopSize; + + for( i in 1:nodeCount ){{ + // internal node: transform + if(map[i,1] > S){{ + times[map[i,1]] = heights[map[i,1]-S]; + childCounts[map[i,1]] = 2; + }} + else{{ + times[map[i,1]] = {1}; + childCounts[map[i,1]] = 0; + }} + }} + + // calculate intervals + indices = sort_indices_asc(times); + + // first tip + start = times[indices[1]]; + logPopSize = pop[index]; + popSize = exp(logPopSize); + + for (i in 1:nodeCount) {{ + finish = times[indices[i]]; + + while(index < G && finish > grid[index]){{ + end = fmin(grid[index], finish); + logP -= (end - start)*((lineageCount*(lineageCount-1.0))/2.0)/popSize; + start = end; + + if(index < G){{ + index += 1; + logPopSize = pop[index]; + popSize = exp(logPopSize); + }} + }} + logP -= (finish - start)*((lineageCount*(lineageCount-1.0))/2.0)/popSize; + if (childCounts[indices[i]] != 0) {{ + logP -= logPopSize; + }} + + // sampling event + if (childCounts[indices[i]] == 0) {{ + lineageCount += 1.0; + }} + // coalescent event + else {{ + lineageCount -= 1.0; + }} + + start = finish; + }} + return logP; + }} """ - if heterochronous: - return skygrid_coalescent_str.format(', real[] lowers', 'lowers[map[i,1]]') - else: - return skygrid_coalescent_str.format('', '0') + if heterochronous: + return skygrid_coalescent_str.format(', real[] lowers', 'lowers[map[i,1]]') + else: + return skygrid_coalescent_str.format('', '0') def GMRF(): - gmrf_logP = """ - // Not time aware - real gmrf_log(vector logPopSize, real precision){ - int N = rows(logPopSize); - real realN = N; - real s = 0; - for (i in 2:N){ - s += pow(logPopSize[i]-logPopSize[i-1], 2.0); - } - return log(precision)*(realN - 1.0)/2.0 - s*precision/2.0 - (realN - 1.0)/2.0 * log(2.0*pi()); - } + gmrf_logP = """ + // Not time aware + real gmrf_log(vector logPopSize, real precision){ + int N = rows(logPopSize); + real realN = N; + real s = 0; + for (i in 2:N){ + s += pow(logPopSize[i]-logPopSize[i-1], 2.0); + } + return log(precision)*(realN - 1.0)/2.0 - s*precision/2.0 - (realN - 1.0)/2.0 * log(2.0*pi()); + } """ - return gmrf_logP + return gmrf_logP def GMRF_time_aware(heterochronous): - gmrf_logP = """ - // Time aware (mid-point) - real gmrf_log(vector logPopSize, real precision, real[] heights, int[,] mapDEF){ - int S = size(heights)+1; // number of leaves from the number of internal nodes - int nodeCount = size(heights) + S; - int N = S - 1; - real realN = N; - real s = 0; - - int indices[nodeCount]; - real times[nodeCount]; - - for( i in 1:nodeCount ){ - // internal node: transform - if(map[i,1] > S){ - times[i] = heights[map[i,1]-S]; - } - else{ - times[i] = TIP; - } - } - - // calculate intervals - indices = sort_indices_asc(times); - - for (i in 2:N){ - s += pow(logPopSize[i]-logPopSize[i-1], 2.0)*2.0/(times[indices[S+i]] - times[indices[S+i-2]]); - } - return log(precision)*(realN - 1.0)/2.0 - s*precision/2.0 - (realN - 1.0)/2.0 * log(2.0*pi()); - } + gmrf_logP = """ + // Time aware (mid-point) + real gmrf_log(vector logPopSize, real precision, real[] heights, int[,] mapDEF){ + int S = size(heights)+1; // number of leaves from the number of internal nodes + int nodeCount = size(heights) + S; + int N = S - 1; + real realN = N; + real s = 0; + + int indices[nodeCount]; + real times[nodeCount]; + + for( i in 1:nodeCount ){ + // internal node: transform + if(map[i,1] > S){ + times[i] = heights[map[i,1]-S]; + } + else{ + times[i] = TIP; + } + } + + // calculate intervals + indices = sort_indices_asc(times); + + for (i in 2:N){ + s += pow(logPopSize[i]-logPopSize[i-1], 2.0)*2.0/(times[indices[S+i]] - times[indices[S+i-2]]); + } + return log(precision)*(realN - 1.0)/2.0 - s*precision/2.0 - (realN - 1.0)/2.0 * log(2.0*pi()); + } """ - if heterochronous: - return gmrf_logP.replace('DEF', ', real[] lowers').replace('TIP', 'lowers[map[i,1]]') - else: - return gmrf_logP.replace('DEF', '').replace('TIP', '0') + if heterochronous: + return gmrf_logP.replace('DEF', ', real[] lowers').replace('TIP', 'lowers[map[i,1]]') + else: + return gmrf_logP.replace('DEF', '').replace('TIP', '0') def heights_to_blens(heterochronous=False, strict=True): - model_heights_to_blens = """ - // populate blens from heights array in preorder - for( j in 2:(bcount+1) ){{ - // internal node - if(map[j,1] > S){{ - blens[map[j,1]] = rate*(heights[map[j,2]-S] - heights[map[j,1]-S]); - }} - else{{ - blens[map[j,1]] = rate*(heights[map[j,2]-S]{}); - }} - }} + model_heights_to_blens = """ + // populate blens from heights array in preorder + for( j in 2:(bcount+1) ){{ + // internal node + if(map[j,1] > S){{ + blens[map[j,1]] = rate*(heights[map[j,2]-S] - heights[map[j,1]-S]); + }} + else{{ + blens[map[j,1]] = rate*(heights[map[j,2]-S]{}); + }} + }} """ - if heterochronous: - model_heights_to_blens = model_heights_to_blens.format(' - lowers[map[j,1]]') - else: - model_heights_to_blens = model_heights_to_blens.format('') - if not strict: - return model_heights_to_blens.replace('rate', 'substrates[map[j,1]]') - return model_heights_to_blens - + if heterochronous: + model_heights_to_blens = model_heights_to_blens.format(' - lowers[map[j,1]]') + else: + model_heights_to_blens = model_heights_to_blens.format('') + if not strict: + return model_heights_to_blens.replace('rate', 'substrates[map[j,1]]') + return model_heights_to_blens + def transform_heights(heterochronous=False): - transform_str = """ - // transform node heights to proportion, except for the root - real[] transform(real[] p, real rootHeight, int[,] map{0}){{ - int S = size(p)+2; - int nodeCount = S*2-1; - - real heights[S-1]; - int j = 1; - - heights[map[1,1]-S] = rootHeight; - for( i in 2:nodeCount ){{ - // internal node: transform - if(map[i,1] > S){{ - heights[map[i,1]-S] = {1}(heights[map[i,2]-S]{2})*p[j]; - j += 1; - }} - }} - return heights; - }} - """ - - if heterochronous: - return transform_str.format(', real[] lowers', 'lowers[map[i,1]] + ', ' - lowers[map[i,1]]') - else: - return transform_str.format('', '', '') + transform_str = """ + // transform node heights to proportion, except for the root + real[] transform(real[] p, real rootHeight, int[,] map{0}){{ + int S = size(p)+2; + int nodeCount = S*2-1; + + real heights[S-1]; + int j = 1; + + heights[map[1,1]-S] = rootHeight; + for( i in 2:nodeCount ){{ + // internal node: transform + if(map[i,1] > S){{ + heights[map[i,1]-S] = {1}(heights[map[i,2]-S]{2})*p[j]; + j += 1; + }} + }} + return heights; + }} + """ + + if heterochronous: + return transform_str.format(', real[] lowers', 'lowers[map[i,1]] + ', ' - lowers[map[i,1]]') + else: + return transform_str.format('', '', '') def jacobian(heterochronous=False): - log_det_jacobian = """ - // add log det jacobian - for( i in 2:(bcount+1) ){{ - // skip leaves - if(map[i,1] > S ){{ - target += log(heights[map[i,2]-S]{}); - }} - }} + log_det_jacobian = """ + // add log det jacobian + for( i in 2:(bcount+1) ){{ + // skip leaves + if(map[i,1] > S ){{ + target += log(heights[map[i,2]-S]{}); + }} + }} """ - if heterochronous: - return log_det_jacobian.format(' - lowers[map[i,1]]') - else: - return log_det_jacobian.format('') + if heterochronous: + return log_det_jacobian.format(' - lowers[map[i,1]]') + else: + return log_det_jacobian.format('') def JC69(C=1, invariant=False): - jc69_function_str = ''' - matrix[] calculate_jc69_p_matrices(vector blens{0}){{ - {1} - int bcount = rows(blens); - matrix[4,4] pmats[bcount{2}]; // probability matrices - int index = 1; - real d; - {3} - for( b in 1:bcount ) {{ - pmats[index] = rep_matrix(0.25 - 0.25*exp(-blens[b]{4}/0.75), 4, 4); - d = 0.25 + 0.75*exp(-blens[b]{4}/0.75); - for( i in 1:4 ) {{ - pmats[index][i,i] = d; - }} - index += 1; - }} - {5} - return pmats; - }} - ''' - - if C > 1 or invariant: - return jc69_function_str.format(', vector rs', 'int C = rows(rs);', '*C', 'for(c in 1:C){', '*rs[c]', '}') - else: - return jc69_function_str.format(*['']*6) + jc69_function_str = ''' + matrix[] calculate_jc69_p_matrices(vector blens{0}){{ + {1} + int bcount = rows(blens); + matrix[4,4] pmats[bcount{2}]; // probability matrices + int index = 1; + real d; + {3} + for( b in 1:bcount ) {{ + pmats[index] = rep_matrix(0.25 - 0.25*exp(-blens[b]{4}/0.75), 4, 4); + d = 0.25 + 0.75*exp(-blens[b]{4}/0.75); + for( i in 1:4 ) {{ + pmats[index][i,i] = d; + }} + index += 1; + }} + {5} + return pmats; + }} + ''' + + if C > 1 or invariant: + return jc69_function_str.format(', vector rs', 'int C = rows(rs);', '*C', 'for(c in 1:C){', '*rs[c]', '}') + else: + return jc69_function_str.format(*['']*6) def HKY(C=1, invariant=False): - hky_function_str = ''' - matrix[] calculate_hky_p_matrices(vector freqs, real kappa, vector blens{0}){{ - {1} - int bcount = rows(blens); - matrix[4,4] pmats[bcount{2}]; // probability matrices - - matrix[4,4] Q; // rate matrix - matrix[4,4] P2 = diag_matrix(sqrt(freqs)); // diagonal sqrt frequencies - matrix[4,4] P2inv = diag_matrix(1.0 ./ sqrt(freqs)); // diagonal inverse sqrt frequencies - matrix[4,4] A; // another symmetric matrix - vector[4] eigenvalues; - matrix[4,4] eigenvectors; - matrix[4,4] m1; - matrix[4,4] m2; - // symmetric rate matrix - matrix[4,4] R = [[0.0, 1.0, kappa, 1.0], - [1.0, 0.0, 1.0, kappa], - [kappa, 1.0, 0.0, 1.0], - [1.0, kappa, 1.0, 0.0]]; - real s = 0.0; - int index = 1; - - Q = R * diag_matrix(freqs); - for (i in 1:4) {{ - Q[i,i] = 0.0; - Q[i,i] = -sum(Q[i,1:4]); - s -= Q[i,i] * freqs[i]; - }} - Q /= s; - - A = P2 * Q * P2inv; - - eigenvalues = eigenvalues_sym(A); - eigenvectors = eigenvectors_sym(A); - - m1 = P2inv * eigenvectors; - m2 = eigenvectors' * P2; - - {3} - for( b in 1:bcount ){{ - pmats[index] = m1 * diag_matrix(exp(eigenvalues*blens[b]{4})) * m2; - index += 1; - }} - {5} - - return pmats; - }} + hky_function_str = ''' + matrix[] calculate_hky_p_matrices(vector freqs, real kappa, vector blens{0}){{ + {1} + int bcount = rows(blens); + matrix[4,4] pmats[bcount{2}]; // probability matrices + + matrix[4,4] Q; // rate matrix + matrix[4,4] P2 = diag_matrix(sqrt(freqs)); // diagonal sqrt frequencies + matrix[4,4] P2inv = diag_matrix(1.0 ./ sqrt(freqs)); // diagonal inverse sqrt frequencies + matrix[4,4] A; // another symmetric matrix + vector[4] eigenvalues; + matrix[4,4] eigenvectors; + matrix[4,4] m1; + matrix[4,4] m2; + // symmetric rate matrix + matrix[4,4] R = [[0.0, 1.0, kappa, 1.0], + [1.0, 0.0, 1.0, kappa], + [kappa, 1.0, 0.0, 1.0], + [1.0, kappa, 1.0, 0.0]]; + real s = 0.0; + int index = 1; + + Q = R * diag_matrix(freqs); + for (i in 1:4) {{ + Q[i,i] = 0.0; + Q[i,i] = -sum(Q[i,1:4]); + s -= Q[i,i] * freqs[i]; + }} + Q /= s; + + A = P2 * Q * P2inv; + + eigenvalues = eigenvalues_sym(A); + eigenvectors = eigenvectors_sym(A); + + m1 = P2inv * eigenvectors; + m2 = eigenvectors' * P2; + + {3} + for( b in 1:bcount ){{ + pmats[index] = m1 * diag_matrix(exp(eigenvalues*blens[b]{4})) * m2; + index += 1; + }} + {5} + + return pmats; + }} ''' - if C > 1 or invariant: - return hky_function_str.format(', vector rs', 'int C = rows(rs);', '*C', 'for(c in 1:C){', '*rs[c]', '}') - else: - return hky_function_str.format('', '', '', '', '', '') + if C > 1 or invariant: + return hky_function_str.format(', vector rs', 'int C = rows(rs);', '*C', 'for(c in 1:C){', '*rs[c]', '}') + else: + return hky_function_str.format('', '', '', '', '', '') def GTR(C=1, invariant=False): - gtr_function_str = ''' - matrix[] calculate_gtr_p_matrices(vector freqs, vector rates, vector blens{0}){{ - {1} - int bcount = rows(blens); - matrix[4,4] pmats[bcount{2}]; // probability matrices - - matrix[4,4] Q; // rate matrix - matrix[4,4] P2 = diag_matrix(sqrt(freqs)); // diagonal sqrt frequencies - matrix[4,4] P2inv = diag_matrix(1.0 ./ sqrt(freqs)); // diagonal inverse sqrt frequencies - matrix[4,4] A; // another symmetric matrix - vector[4] eigenvalues; - matrix[4,4] eigenvectors; - matrix[4,4] m1; - matrix[4,4] m2; - // symmetric rate matrix - matrix[4,4] R = [[0.0, rates[1], rates[2], rates[3]], - [rates[1], 0.0, rates[4], rates[5]], - [rates[2], rates[4], 0.0, rates[6]], - [rates[3], rates[5], rates[6], 0.0]]; - real s = 0.0; - int index = 1; - - Q = R * diag_matrix(freqs); - for (i in 1:4) {{ - Q[i,i] = 0.0; - Q[i,i] = -sum(Q[i,1:4]); - s -= Q[i,i] * freqs[i]; - }} - Q /= s; - - A = P2 * Q * P2inv; - - eigenvalues = eigenvalues_sym(A); - eigenvectors = eigenvectors_sym(A); - - m1 = P2inv * eigenvectors; - m2 = eigenvectors' * P2; - - {3} - for( b in 1:bcount ){{ - pmats[index] = m1 * diag_matrix(exp(eigenvalues*blens[b]{4})) * m2; - index += 1; - }} - {5} - - return pmats; - }} - ''' - - if C > 1 or invariant: - return gtr_function_str.format(', vector rs', 'int C = rows(rs);', '*C', 'for(c in 1:C){', '*rs[c]', '}') - else: - return gtr_function_str.format('', '', '', '', '', '') + gtr_function_str = ''' + matrix[] calculate_gtr_p_matrices(vector freqs, vector rates, vector blens{0}){{ + {1} + int bcount = rows(blens); + matrix[4,4] pmats[bcount{2}]; // probability matrices + + matrix[4,4] Q; // rate matrix + matrix[4,4] P2 = diag_matrix(sqrt(freqs)); // diagonal sqrt frequencies + matrix[4,4] P2inv = diag_matrix(1.0 ./ sqrt(freqs)); // diagonal inverse sqrt frequencies + matrix[4,4] A; // another symmetric matrix + vector[4] eigenvalues; + matrix[4,4] eigenvectors; + matrix[4,4] m1; + matrix[4,4] m2; + // symmetric rate matrix + matrix[4,4] R = [[0.0, rates[1], rates[2], rates[3]], + [rates[1], 0.0, rates[4], rates[5]], + [rates[2], rates[4], 0.0, rates[6]], + [rates[3], rates[5], rates[6], 0.0]]; + real s = 0.0; + int index = 1; + + Q = R * diag_matrix(freqs); + for (i in 1:4) {{ + Q[i,i] = 0.0; + Q[i,i] = -sum(Q[i,1:4]); + s -= Q[i,i] * freqs[i]; + }} + Q /= s; + + A = P2 * Q * P2inv; + + eigenvalues = eigenvalues_sym(A); + eigenvectors = eigenvectors_sym(A); + + m1 = P2inv * eigenvectors; + m2 = eigenvectors' * P2; + + {3} + for( b in 1:bcount ){{ + pmats[index] = m1 * diag_matrix(exp(eigenvalues*blens[b]{4})) * m2; + index += 1; + }} + {5} + + return pmats; + }} + ''' + + if C > 1 or invariant: + return gtr_function_str.format(', vector rs', 'int C = rows(rs);', '*C', 'for(c in 1:C){', '*rs[c]', '}') + else: + return gtr_function_str.format('', '', '', '', '', '') one_on_X = """ - real oneOnX_log(real x){ - return -log(x); - } + real oneOnX_log(real x){ + return -log(x); + } """ def likelihood(mixture, clock=True): - init_tip_partials = """ - // copy tip data into node probability vector - for( n in 1:S ) { - for( i in 1:L ) { - for( a in 1:4 ) { - partials[n,i][a] = tipdata[n,i,a]; - } - } - } + init_tip_partials = """ + // copy tip data into node probability vector + for( n in 1:S ) { + for( i in 1:L ) { + for( a in 1:4 ) { + partials[n,i][a] = tipdata[n,i,a]; + } + } + } """ - init_tip_partials_mixture=""" - // copy tip data into node probability vector - for( n in 1:S ) { - for( i in 1:L ) { - for( a in 1:4 ) { - for(c in 1:C){ - partials[c,n,i][a] = tipdata[n,i,a]; - } - } - } - } + init_tip_partials_mixture=""" + // copy tip data into node probability vector + for( n in 1:S ) { + for( i in 1:L ) { + for( a in 1:4 ) { + for(c in 1:C){ + partials[c,n,i][a] = tipdata[n,i,a]; + } + } + } + } """ - model_calculate_logP = """ - // calculate tree likelihood - for( i in 1:L ) { - for( n in 1:(S-1) ) { - partials[peel[n,3],i] = (pmats[peel[n,1]]*partials[peel[n,1],i]) .* (pmats[peel[n,2]]*partials[peel[n,2],i]); - } - - for(j in 1:4){ - partials[2*S,i][j] = partials[peel[S-1,3],i][j] * freqs[j]; - } - // add the site log likelihood - target += log(sum(partials[2*S,i]))*weights[i]; - } + model_calculate_logP = """ + // calculate tree likelihood + for( i in 1:L ) { + for( n in 1:(S-1) ) { + partials[peel[n,3],i] = (pmats[peel[n,1]]*partials[peel[n,1],i]) .* (pmats[peel[n,2]]*partials[peel[n,2],i]); + } + + for(j in 1:4){ + partials[2*S,i][j] = partials[peel[S-1,3],i][j] * freqs[j]; + } + // add the site log likelihood + target += log(sum(partials[2*S,i]))*weights[i]; + } """ - model_calculate_mixture_logP = """ - // calculate tree likelihood - for( i in 1:L ) { - for( n in 1:(S-1) ) { - for(c in 1:C){ - partials[c,peel[n,3],i] = (pmats[peel[n,1]+(c-1)*bcount]*partials[c,peel[n,1],i]) .* (pmats[peel[n,2]+(c-1)*bcount]*partials[c,peel[n,2],i]); - } - } - for(c in 1:C){ - probs[c] = ps[c] * sum(partials[c,peel[S-1,3],i] .* freqs); - } - // add the site log likelihood - target += log(sum(probs))*weights[i]; - } + model_calculate_mixture_logP = """ + // calculate tree likelihood + for( i in 1:L ) { + for( n in 1:(S-1) ) { + for(c in 1:C){ + partials[c,peel[n,3],i] = (pmats[peel[n,1]+(c-1)*bcount]*partials[c,peel[n,1],i]) .* (pmats[peel[n,2]+(c-1)*bcount]*partials[c,peel[n,2],i]); + } + } + for(c in 1:C){ + probs[c] = ps[c] * sum(partials[c,peel[S-1,3],i] .* freqs); + } + // add the site log likelihood + target += log(sum(probs))*weights[i]; + } """ - model_calculate_unconstrained_logP = """ - // calculate tree likelihood - for( i in 1:L ) { - for( n in 1:(S-2) ) { - partials[peel[n,3],i] = (pmats[peel[n,1]]*partials[peel[n,1],i]) .* (pmats[peel[n,2]]*partials[peel[n,2],i]); - } - partials[peel[S-1,3],i] = (pmats[peel[S-1,1]]*partials[peel[S-1,1],i]) .* partials[peel[S-1,2],i]; - - // add the site log likelihood - target += log(sum(partials[peel[S-1,3],i] .* freqs))*weights[i]; - } + model_calculate_unconstrained_logP = """ + // calculate tree likelihood + for( i in 1:L ) { + for( n in 1:(S-2) ) { + partials[peel[n,3],i] = (pmats[peel[n,1]]*partials[peel[n,1],i]) .* (pmats[peel[n,2]]*partials[peel[n,2],i]); + } + partials[peel[S-1,3],i] = (pmats[peel[S-1,1]]*partials[peel[S-1,1],i]) .* partials[peel[S-1,2],i]; + + // add the site log likelihood + target += log(sum(partials[peel[S-1,3],i] .* freqs))*weights[i]; + } """ - model_calculate_unconstrained_mixture_logP = """ - // calculate tree likelihood - for( i in 1:L ) { - for( n in 1:(S-2) ) { - for(c in 1:C){ - partials[c,peel[n,3],i] = (pmats[peel[n,1]+(c-1)*bcount]*partials[c,peel[n,1],i]) .* (pmats[peel[n,2]+(c-1)*bcount]*partials[c,peel[n,2],i]); - } - } - for(c in 1:C){ - partials[c,peel[S-1,3],i] = (pmats[peel[S-1,1]+(c-1)*bcount]*partials[c,peel[S-1,1],i]) .* partials[c,peel[S-1,2],i]; - probs[c] = ps[c] * sum(partials[c,peel[S-1,3],i] .* freqs); - } - // add the site log likelihood - target += log(sum(probs))*weights[i]; - } + model_calculate_unconstrained_mixture_logP = """ + // calculate tree likelihood + for( i in 1:L ) { + for( n in 1:(S-2) ) { + for(c in 1:C){ + partials[c,peel[n,3],i] = (pmats[peel[n,1]+(c-1)*bcount]*partials[c,peel[n,1],i]) .* (pmats[peel[n,2]+(c-1)*bcount]*partials[c,peel[n,2],i]); + } + } + for(c in 1:C){ + partials[c,peel[S-1,3],i] = (pmats[peel[S-1,1]+(c-1)*bcount]*partials[c,peel[S-1,1],i]) .* partials[c,peel[S-1,2],i]; + probs[c] = ps[c] * sum(partials[c,peel[S-1,3],i] .* freqs); + } + // add the site log likelihood + target += log(sum(probs))*weights[i]; + } """ - if not mixture: - model = init_tip_partials - if clock: - model += '\n' + model_calculate_logP - else: - model += '\n' + model_calculate_unconstrained_logP - else: - model = init_tip_partials_mixture - if clock: - model += '\n' + model_calculate_mixture_logP - else: - model += '\n' + model_calculate_unconstrained_mixture_logP + if not mixture: + model = init_tip_partials + if clock: + model += '\n' + model_calculate_logP + else: + model += '\n' + model_calculate_unconstrained_logP + else: + model = init_tip_partials_mixture + if clock: + model += '\n' + model_calculate_mixture_logP + else: + model += '\n' + model_calculate_unconstrained_mixture_logP - return model + return model def get_model(params): - functions_block = [] - - data_block = [] - transformed_data_declarations = [] - transformed_data_block = [] - - parameters_block = [] - transformed_parameters_declarations = [] - transformed_parameters_block = [] - - model_block_declarations = [] - model_priors = [] - model_block = [] - - data_block.append('int L; // alignment length') - data_block.append('int S; // number of tips') - data_block.append('real tipdata[S,L,4]; // alignment as partials') - data_block.append('int peel[S-1,3]; // list of nodes for peeling') - data_block.append('real weights[L];') - - if params.clock is None: - transformed_data_declarations.append('int bcount = 2*S-3; // number of branches') - else: - data_block.append('int map[2*S-1,2]; // list of node in preorder [node,parent]') - transformed_data_declarations.append('int bcount = 2*S-2; // number of branches') - - # Site model - if params.invariant or params.categories > 1: - data_block.append('int C;') - model_block_declarations.append('real probs[C];') - model_block_declarations.append('vector[4] partials[C,2*S,L]; // partial probabilities for the S tips and S-1 internal nodes') - model_block_declarations.append('matrix[4,4] pmats[bcount*C]; // finite-time transition matrices for each branch') - else: - model_block_declarations.append('vector[4] partials[2*S,L]; // partial probabilities for the S tips and S-1 internal nodes') - model_block_declarations.append('matrix[4,4] pmats[bcount]; // finite-time transition matrices for each branch') - - if params.categories > 1 and params.heterogeneity == 'weibull': - transformed_parameters_declarations.append('vector[C] ps = rep_vector(1.0/C, C);') - - parameters_block.append('real wshape;') - if params.invariant: - parameters_block.append('real pinv;') - model_priors.append('pinv ~ uniform(0.0,1.0);') - - transformed_parameters_declarations.append('vector[C] rs;') - transformed_parameters_block.append(get_weibull(params.invariant)) - - model_priors.append('wshape ~ exponential(1.0);') - elif params.categories > 1 and not params.invariant: - parameters_block.append('simplex[C] ps;') - parameters_block.append('simplex[C] rate_unscaled;') - - transformed_parameters_declarations.append('vector[C] rs;') - transformed_parameters_declarations.append('simplex[C] constraint;') - - transformed_parameters_block.append('constraint = ps .* rate_unscaled; // not actually a simplex yet') - transformed_parameters_block.append('rs = rate_unscaled / sum(constraint);') - transformed_parameters_block.append('constraint /= sum(constraint); // is now a simplex that equals p .* x ') - elif params.invariant and params.categories == 1: - transformed_data_declarations.append('int C = 2;') - - parameters_block.append('real pinv;') - - transformed_parameters_declarations.append('vector[2] ps;') - transformed_parameters_declarations.append('vector[2] rs;') - - transformed_parameters_block.append('ps[1] = pinv;') - transformed_parameters_block.append('ps[2] = 1.0 - pinv;') - transformed_parameters_block.append('rs[1] = 0.0;') - transformed_parameters_block.append('rs[2] = 1.0/(1.0 - pinv);') - - model_priors.append('pinv ~ uniform(0.0,1.0);') - elif params.invariant and params.categories > 1: - raise ValueError('Cannot use proportion of invariant and discrete rate heterogeneity yet.') - - # Clock model - if params.clock is not None: - model_block_declarations.append('vector [bcount] blens; // branch lengths') - - transformed_data_declarations.append('int pCount = S-2; // number of proportions') - - parameters_block.append('real props[pCount]; // proportions') - transformed_parameters_declarations.append('real heights[S-1];') - - if params.estimate_rate: - if params.clock == 'strict': - parameters_block.append('real rate;') - model_priors.append('rate ~ exponential(1000);') - elif params.clock == 'autocorrelated': - parameters_block.append('real nu;') - parameters_block.append('real substrates[2*S-2];') - functions_block.append(autocorrelated_prior(params.heterochronous)) - if params.heterochronous: - model_priors.append('substrates ~ logn_autocorrelated(heights, map, nu, lowers);') - else: - model_priors.append('substrates ~ logn_autocorrelated(heights, map, nu);') - model_priors.append('substrates[map[2,1]] ~ exponential(1000);') - elif params.clock == 'uncorrelated': - # parameters_block.append('real mu;') - # parameters_block.append('real sigma;') - parameters_block.append('real substrates[2*S-2];') - model_priors.append('substrates ~ exponential(1000);') - # model_priors.append('substrates ~ lognormal(mu, sigma);') - # model_priors.append('mu ~ exponential(1000);') - # model_priors.append('sigma ~ gamma(0.5396, 2.6184);') - - else: - data_block.append('real rate;') - - functions_block.append(transform_heights(params.heterochronous)) - data_block.append('real lower_root;') - if params.heterochronous: - data_block.append('real lowers[2*S-1]; // list of lower bounds for each internal node (for reparametrization)') - parameters_block.append('real height; // root height') - transformed_parameters_block.append('heights = transform(props, height, map, lowers);') - else: - parameters_block.append('real height; // root height') - transformed_parameters_block.append('heights = transform(props, height, map);') - - model_block.append(heights_to_blens(params.heterochronous, params.clock == 'strict' or not params.estimate_rate)) - - # Coalescent - if params.coalescent == 'constant': - functions_block.append(one_on_X) - parameters_block.append('real theta;') - model_priors.append('theta ~ oneOnX();') - functions_block.append(constant_coalescent(params.heterochronous)) - if params.heterochronous: - model_priors.append('heights ~ constant_coalescent(theta, map, lowers);') - else: - model_priors.append('heights ~ constant_coalescent(theta, map);') + functions_block = [] + + data_block = [] + transformed_data_declarations = [] + transformed_data_block = [] + + parameters_block = [] + transformed_parameters_declarations = [] + transformed_parameters_block = [] + + model_block_declarations = [] + model_priors = [] + model_block = [] + + data_block.append('int L; // alignment length') + data_block.append('int S; // number of tips') + data_block.append('real tipdata[S,L,4]; // alignment as partials') + data_block.append('int peel[S-1,3]; // list of nodes for peeling') + data_block.append('real weights[L];') + + if params.clock is None: + transformed_data_declarations.append('int bcount = 2*S-3; // number of branches') + else: + data_block.append('int map[2*S-1,2]; // list of node in preorder [node,parent]') + transformed_data_declarations.append('int bcount = 2*S-2; // number of branches') + + # Site model + if params.invariant or params.categories > 1: + data_block.append('int C;') + model_block_declarations.append('real probs[C];') + model_block_declarations.append('vector[4] partials[C,2*S,L]; // partial probabilities for the S tips and S-1 internal nodes') + model_block_declarations.append('matrix[4,4] pmats[bcount*C]; // finite-time transition matrices for each branch') + else: + model_block_declarations.append('vector[4] partials[2*S,L]; // partial probabilities for the S tips and S-1 internal nodes') + model_block_declarations.append('matrix[4,4] pmats[bcount]; // finite-time transition matrices for each branch') + + if params.categories > 1 and params.heterogeneity == 'weibull': + transformed_parameters_declarations.append('vector[C] ps = rep_vector(1.0/C, C);') + + parameters_block.append('real wshape;') + if params.invariant: + parameters_block.append('real pinv;') + model_priors.append('pinv ~ uniform(0.0,1.0);') + + transformed_parameters_declarations.append('vector[C] rs;') + transformed_parameters_block.append(get_weibull(params.invariant)) + + model_priors.append('wshape ~ exponential(1.0);') + elif params.categories > 1 and not params.invariant: + parameters_block.append('simplex[C] ps;') + parameters_block.append('simplex[C] rate_unscaled;') + + transformed_parameters_declarations.append('vector[C] rs;') + transformed_parameters_declarations.append('simplex[C] constraint;') + + transformed_parameters_block.append('constraint = ps .* rate_unscaled; // not actually a simplex yet') + transformed_parameters_block.append('rs = rate_unscaled / sum(constraint);') + transformed_parameters_block.append('constraint /= sum(constraint); // is now a simplex that equals p .* x ') + elif params.invariant and params.categories == 1: + transformed_data_declarations.append('int C = 2;') + + parameters_block.append('real pinv;') + + transformed_parameters_declarations.append('vector[2] ps;') + transformed_parameters_declarations.append('vector[2] rs;') + + transformed_parameters_block.append('ps[1] = pinv;') + transformed_parameters_block.append('ps[2] = 1.0 - pinv;') + transformed_parameters_block.append('rs[1] = 0.0;') + transformed_parameters_block.append('rs[2] = 1.0/(1.0 - pinv);') + + model_priors.append('pinv ~ uniform(0.0,1.0);') + elif params.invariant and params.categories > 1: + raise ValueError('Cannot use proportion of invariant and discrete rate heterogeneity yet.') + + # Clock model + if params.clock is not None: + model_block_declarations.append('vector [bcount] blens; // branch lengths') + + transformed_data_declarations.append('int pCount = S-2; // number of proportions') + + parameters_block.append('real props[pCount]; // proportions') + transformed_parameters_declarations.append('real heights[S-1];') + + if params.estimate_rate: + if params.clock == 'strict': + parameters_block.append('real rate;') + model_priors.append('rate ~ exponential(1000);') + elif params.clock == 'autocorrelated': + parameters_block.append('real nu;') + parameters_block.append('real substrates[2*S-2];') + functions_block.append(autocorrelated_prior(params.heterochronous)) + if params.heterochronous: + model_priors.append('substrates ~ logn_autocorrelated(heights, map, nu, lowers);') + else: + model_priors.append('substrates ~ logn_autocorrelated(heights, map, nu);') + model_priors.append('substrates[map[2,1]] ~ exponential(1000);') + elif params.clock == 'uncorrelated': + # parameters_block.append('real mu;') + # parameters_block.append('real sigma;') + parameters_block.append('real substrates[2*S-2];') + model_priors.append('substrates ~ exponential(1000);') + # model_priors.append('substrates ~ lognormal(mu, sigma);') + # model_priors.append('mu ~ exponential(1000);') + # model_priors.append('sigma ~ gamma(0.5396, 2.6184);') + + else: + data_block.append('real rate;') + + functions_block.append(transform_heights(params.heterochronous)) + data_block.append('real lower_root;') + if params.heterochronous: + data_block.append('real lowers[2*S-1]; // list of lower bounds for each internal node (for reparametrization)') + parameters_block.append('real height; // root height') + transformed_parameters_block.append('heights = transform(props, height, map, lowers);') + else: + parameters_block.append('real height; // root height') + transformed_parameters_block.append('heights = transform(props, height, map);') + + model_block.append(heights_to_blens(params.heterochronous, params.clock == 'strict' or not params.estimate_rate)) + + # Coalescent + if params.coalescent == 'constant': + functions_block.append(one_on_X) + parameters_block.append('real theta;') + model_priors.append('theta ~ oneOnX();') + functions_block.append(constant_coalescent(params.heterochronous)) + if params.heterochronous: + model_priors.append('heights ~ constant_coalescent(theta, map, lowers);') + else: + model_priors.append('heights ~ constant_coalescent(theta, map);') elif params.coalescent == 'integrated': functions_block.append(integrated_constant_coalescent(params.heterochronous)) if params.heterochronous: - model_priors.append('heights ~ integrated_constant_coalescent(map, 1000.0, lowers);') # picking u = 1E3 + model_priors.append('heights ~ integrated_constant_coalescent(1000.0, map, lowers);') # picking u = 1E3 else: - model_priors.append('heights ~ integrated_constant_coalescent(map, 1000.0);') + model_priors.append('heights ~ integrated_constant_coalescent(1000.0, map);') elif params.coalescent == 'skyride': - functions_block.append(skyride_coalescent(params.heterochronous)) - functions_block.append(GMRF()) - # functions_block.append(GMRF_time_aware(params.heterochronous)) + functions_block.append(skyride_coalescent(params.heterochronous)) + functions_block.append(GMRF()) + # functions_block.append(GMRF_time_aware(params.heterochronous)) - data_block.append('int I; // number of intervals') + data_block.append('int I; // number of intervals') - parameters_block.append('vector[I] thetas; // log space') - parameters_block.append('real tau;') + parameters_block.append('vector[I] thetas; // log space') + parameters_block.append('real tau;') - if params.heterochronous: - model_priors.append('heights ~ skyride_coalescent(thetas, map, lowers);') - # model_priors.append('thetas ~ gmrf(tau, heights, map, lowers);') - else: - model_priors.append('heights ~ skyride_coalescent(thetas, map);') - # model_priors.append('thetas ~ gmrf(tau, heights, map);') + if params.heterochronous: + model_priors.append('heights ~ skyride_coalescent(thetas, map, lowers);') + # model_priors.append('thetas ~ gmrf(tau, heights, map, lowers);') + else: + model_priors.append('heights ~ skyride_coalescent(thetas, map);') + # model_priors.append('thetas ~ gmrf(tau, heights, map);') - model_priors.append('thetas ~ gmrf(tau);') - model_priors.append('tau ~ gamma(0.001, 0.001);') + model_priors.append('thetas ~ gmrf(tau);') + model_priors.append('tau ~ gamma(0.001, 0.001);') elif params.coalescent == 'skygrid': - functions_block.append(skygrid_coalescent(params.heterochronous)) - functions_block.append(GMRF()) - - data_block.append('int G; // number of grid interval') - data_block.append('vector[G] grid;') - - parameters_block.append('vector[G] thetas; // log space') - parameters_block.append('real tau;') - - if params.heterochronous: - model_priors.append('heights ~ skygrid_coalescent(thetas, map, grid, lowers);') - else: - model_priors.append('heights ~ skygrid_coalescent(thetas, map, grid);') - model_priors.append('thetas ~ gmrf(tau);') - model_priors.append('tau ~ gamma(0.001, 0.001);') - else: - parameters_block.append('vector [bcount] blens; // branch lengths') - model_priors.append('blens ~ exponential(10);') - - # Substitution model - if params.model == 'GTR': - data_block.append('vector[4] frequencies_alpha; // parameters of the prior on frequencies') - data_block.append('vector[6] rates_alpha; // parameters of the prior on rates') - - parameters_block.append('simplex[6] rates;') - parameters_block.append('simplex[4] freqs;') - - model_priors.append('rates ~ dirichlet(rates_alpha);') - model_priors.append('freqs ~ dirichlet(frequencies_alpha);') - - functions_block.append(GTR(params.categories, params.invariant)) - if params.invariant or params.categories > 1: - model_block.append('pmats = calculate_gtr_p_matrices(freqs, rates, blens, rs);') - else: - model_block.append('pmats = calculate_gtr_p_matrices(freqs, rates, blens);') - elif params.model == 'HKY': - data_block.append('vector[4] frequencies_alpha; // parameters of the prior on frequencies') - - parameters_block.append('real kappa;') - parameters_block.append('simplex[4] freqs;') - - model_priors.append('kappa ~ lognormal(1.0,1.25);') - model_priors.append('freqs ~ dirichlet(frequencies_alpha);') - - functions_block.append(HKY(params.categories, params.invariant)) - if params.invariant or params.categories > 1: - model_block.append('pmats = calculate_hky_p_matrices(freqs, kappa, blens, rs);') - else: - model_block.append('pmats = calculate_hky_p_matrices(freqs, kappa, blens);') - elif params.model == 'JC69': - transformed_data_declarations.append('vector[4] freqs = rep_vector(0.25,4);') - functions_block.append(JC69(params.categories, params.invariant)) - if params.invariant or params.categories > 1: - model_block.append('pmats = calculate_jc69_p_matrices(blens, rs);') - else: - model_block.append('pmats = calculate_jc69_p_matrices(blens);') - else: - raise ValueError('Supports JC69, HKY and GTR only.') - - # Tree likelihood - model_block.append(likelihood(params.categories > 1 or params.invariant, params.clock is not None)) - - if params.clock is not None: - model_block.append(jacobian(params.heterochronous)) - - script = '' - - if len(functions_block) > 0: - script += 'functions{' + '\n'.join(functions_block) + '\n}\n\n' - - script += 'data{\n' + '\t' + '\n\t'.join(data_block) + '\n}\n\n' - - if len(transformed_data_declarations) != 0: - script += 'transformed data{\n' - script += '\t' + '\n\t'.join(transformed_data_declarations) + '\n\n' - script += '\t' + '\n\t'.join(transformed_data_block) + '\n}\n\n' - - script += 'parameters{\n' + '\t' + '\n\t'.join(parameters_block) + '\n}\n\n' - - if len(transformed_parameters_declarations) != 0: - script += 'transformed parameters{\n' - script += '\t' + '\n\t'.join(transformed_parameters_declarations) + '\n\n' - script += '\t' + '\n\t'.join(transformed_parameters_block) + '\n}\n\n' - - script += 'model{\n' - script += '\t' + '\n\t'.join(model_block_declarations) + '\n\n' - script += '\t' + '\n\t'.join(model_priors) + '\n\n' - script += '\t' + '\n\t'.join(model_block) + '\n}\n\n' - - return script + functions_block.append(skygrid_coalescent(params.heterochronous)) + functions_block.append(GMRF()) + + data_block.append('int G; // number of grid interval') + data_block.append('vector[G] grid;') + + parameters_block.append('vector[G] thetas; // log space') + parameters_block.append('real tau;') + + if params.heterochronous: + model_priors.append('heights ~ skygrid_coalescent(thetas, map, grid, lowers);') + else: + model_priors.append('heights ~ skygrid_coalescent(thetas, map, grid);') + model_priors.append('thetas ~ gmrf(tau);') + model_priors.append('tau ~ gamma(0.001, 0.001);') + else: + parameters_block.append('vector [bcount] blens; // branch lengths') + model_priors.append('blens ~ exponential(10);') + + # Substitution model + if params.model == 'GTR': + data_block.append('vector[4] frequencies_alpha; // parameters of the prior on frequencies') + data_block.append('vector[6] rates_alpha; // parameters of the prior on rates') + + parameters_block.append('simplex[6] rates;') + parameters_block.append('simplex[4] freqs;') + + model_priors.append('rates ~ dirichlet(rates_alpha);') + model_priors.append('freqs ~ dirichlet(frequencies_alpha);') + + functions_block.append(GTR(params.categories, params.invariant)) + if params.invariant or params.categories > 1: + model_block.append('pmats = calculate_gtr_p_matrices(freqs, rates, blens, rs);') + else: + model_block.append('pmats = calculate_gtr_p_matrices(freqs, rates, blens);') + elif params.model == 'HKY': + data_block.append('vector[4] frequencies_alpha; // parameters of the prior on frequencies') + + parameters_block.append('real kappa;') + parameters_block.append('simplex[4] freqs;') + + model_priors.append('kappa ~ lognormal(1.0,1.25);') + model_priors.append('freqs ~ dirichlet(frequencies_alpha);') + + functions_block.append(HKY(params.categories, params.invariant)) + if params.invariant or params.categories > 1: + model_block.append('pmats = calculate_hky_p_matrices(freqs, kappa, blens, rs);') + else: + model_block.append('pmats = calculate_hky_p_matrices(freqs, kappa, blens);') + elif params.model == 'JC69': + transformed_data_declarations.append('vector[4] freqs = rep_vector(0.25,4);') + functions_block.append(JC69(params.categories, params.invariant)) + if params.invariant or params.categories > 1: + model_block.append('pmats = calculate_jc69_p_matrices(blens, rs);') + else: + model_block.append('pmats = calculate_jc69_p_matrices(blens);') + else: + raise ValueError('Supports JC69, HKY and GTR only.') + + # Tree likelihood + model_block.append(likelihood(params.categories > 1 or params.invariant, params.clock is not None)) + + if params.clock is not None: + model_block.append(jacobian(params.heterochronous)) + + script = '' + + if len(functions_block) > 0: + script += 'functions{' + '\n'.join(functions_block) + '\n}\n\n' + + script += 'data{\n' + '\t' + '\n\t'.join(data_block) + '\n}\n\n' + + if len(transformed_data_declarations) != 0: + script += 'transformed data{\n' + script += '\t' + '\n\t'.join(transformed_data_declarations) + '\n\n' + script += '\t' + '\n\t'.join(transformed_data_block) + '\n}\n\n' + + script += 'parameters{\n' + '\t' + '\n\t'.join(parameters_block) + '\n}\n\n' + + if len(transformed_parameters_declarations) != 0: + script += 'transformed parameters{\n' + script += '\t' + '\n\t'.join(transformed_parameters_declarations) + '\n\n' + script += '\t' + '\n\t'.join(transformed_parameters_block) + '\n}\n\n' + + script += 'model{\n' + script += '\t' + '\n\t'.join(model_block_declarations) + '\n\n' + script += '\t' + '\n\t'.join(model_priors) + '\n\n' + script += '\t' + '\n\t'.join(model_block) + '\n}\n\n' + + return script From 6e0690b5d5374db5d19ca48d6a846eb46c529b19 Mon Sep 17 00:00:00 2001 From: Luiz Max Carvalho Date: Sat, 5 Oct 2019 11:25:35 -0300 Subject: [PATCH 13/14] fixing bug; more investigation needed --- phylostan/generate_script.py | 19 ++++++++++--------- 1 file changed, 10 insertions(+), 9 deletions(-) diff --git a/phylostan/generate_script.py b/phylostan/generate_script.py index 266ec11..ec9e5ab 100755 --- a/phylostan/generate_script.py +++ b/phylostan/generate_script.py @@ -157,16 +157,17 @@ def integrated_constant_coalescent(heterochronous=False): real finish; real interval; + for( i in 1:nodeCount ){{ - // internal node: transform - if(map[i, 1] > S){{ - times[map[i, 1]] = heights[map[i, 1]-S]; - childCounts[map[i, 1]] = 2; - }} - else{{ - times[map[i, 1]] = lowers[map[i, 1]]; - childCounts[map[i, 1]] = 0; - }} + // internal node: transform + if(map[i,1] > S){{ + times[map[i,1]] = heights[map[i,1]-S]; + childCounts[map[i,1]] = 2; + }} + else{{ + times[map[i,1]] = {1}; + childCounts[map[i,1]] = 0; + }} }} // calculate intervals From 8edecd51ab29501ca09f778e95660f77e9cbd33a Mon Sep 17 00:00:00 2001 From: Luiz Max Carvalho Date: Sat, 16 Nov 2019 10:32:48 -0300 Subject: [PATCH 14/14] new integrated density --- phylostan/generate_script.py | 18 ++++++++++-------- 1 file changed, 10 insertions(+), 8 deletions(-) diff --git a/phylostan/generate_script.py b/phylostan/generate_script.py index ec9e5ab..6281415 100755 --- a/phylostan/generate_script.py +++ b/phylostan/generate_script.py @@ -135,13 +135,15 @@ def constant_coalescent(heterochronous=False): def integrated_constant_coalescent(heterochronous=False): integrated_constant_coalescent_str = """ - real integrated_density(real t, real kappa, real u){{ - real z = kappa*t; - real w = square(z + u); - real lnum = log(2*w*log(u + z) + 3*square(z) + 4*u*z - w*(2*log(z) + 3)); - real ldenom = log(2) + log(w); - return(log(2) + log(kappa) + lnum - ldenom -log(u)); - }} + real integrated_density(real t, real s, real u){{ + real ch = (square(s) -s)/2; + real lc1 = log(2) + log(ch) -log(u); + real c2 = ch*t; + real Fu = log(u + c2) + (4*c2*u + 3*square(c2))/(2*square(u + c2)); + real Fzero = log(c2) + 3.0/2; + real ans = lc1 + log(Fu-Fzero); + return(ans); + }} real integrated_constant_coalescent_log(real[] heights, real U, int[,] map{0}){{ int S = size(heights) + 1; // number of leaves from the number of internal nodes int nodeCount = size(heights) + S; @@ -182,7 +184,7 @@ def integrated_constant_coalescent(heterochronous=False): interval = finish - start; if(interval != 0.0 && childCounts[indices[i]] != 0 ){{ - logP += integrated_density(interval, lineageCount*(lineageCount-1.0)/2.0, U); + logP += integrated_density(interval, lineageCount, U); }} // sampling event if (childCounts[indices[i]] == 0) {{