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svd.cpp
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svd.cpp
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/**
* @file svd.cpp
* @author Melih Altun @2015
**/
#include "svd.h"
/*Singular Value Decomposition
Parameters: (outputs) 1st eigen vector set, diagonal singular values, 2nd eigenvector set, (inputs) input matrix, row count, col count */
void svd(float UU[], float S[], float VV[], float X[], int N, int M)
{
int i, j;
bool transposed = false;
float *V = VV, *U = UU;
if (N < M) { //transpose if rows are less than columns
int tmp = N;
float *Xnew;
Xnew = new float[M*N];
transpose(Xnew, X, N, M);
N = M;
M = tmp;
copy_matrix(X, Xnew, N, M);
V = UU;
U = VV;
transposed = true;
delete[] Xnew;
}
float *Xtr, *Xtr_X, *D, *V0, *U0;
Xtr_X = new float[M*M];
Xtr = new float[N*M];
D = new float[M];
U0 = new float[N];
V0 = new float[M];
transpose(Xtr, X, N, M); //X'
multiply_matrices(Xtr_X, Xtr, X, M, N, M); //X'*X
eig_symetric(V, D, Xtr_X, M, 0); //[V,D]=eig(X'*X)
for (i = 0; i < M; i++) {
if (D[i] >= 0)
D[i] = sqrt(D[i]);
else
D[i] = sqrt(-D[i]); // Something is wrong if X'*X produces negative eigenvalues.
}
vector_to_diagonal(S, D, M);
for (i = 0; i < M; i++) {
for (j = 0; j < M; j++)
V0[j] = V[lin_index(j, i, M)];
multiply_matrix_with_vector(U0, X, V0, N, M);
for (j = 0; j < N; j++)
U[lin_index(j, i, M)] = U0[j] / D[i];
}
if (transposed)
{
float *Xnew;
Xnew = new float[M*N];
transpose(Xnew, X, N, M);
copy_matrix(X, Xnew, M, N);
delete[] Xnew;
}
delete[] Xtr;
Xtr = NULL;
delete[] Xtr_X;
Xtr_X = NULL;
delete[] D;
D = NULL;
delete[] V0;
V0 = NULL;
delete[] U0;
U0 = NULL;
}
/* Computes Pseudo Inverse of a matrix using SVD
Parameters: (output) inverted matrix, (inputs) matrix, row count, col count*/
void psInv(float Y[], float X[], int N, int M)
{
int i;
float *U, *V, *S, *Sinv, *Utr, *V_Sinv;
bool transposed = false;
if (N < M) { //transpose if rows are less than columns
int tmp = N;
float* Xnew;
Xnew = new float[M * N];
transpose(Xnew, X, N, M);
N = M;
M = tmp;
copy_matrix(X, Xnew, N, M);
transposed = true;
delete[] Xnew;
}
S = new float[M*M];
Sinv = new float[M*M];
U = new float[N*M];
V = new float[M*M];
Utr = new float[N*M];
V_Sinv = new float[M*M];
svd(U, S, V, X, N, M);
memset(Sinv, 0, M*M*sizeof(float));
for (i = 0; i < M; i++)
Sinv[lin_index(i, i, M)] = 1 / S[lin_index(i, i, M)];
multiply_square_matrices(V_Sinv, V, Sinv, M);
transpose(Utr, U, N, M);
multiply_matrices(Y, V_Sinv, Utr, M, M, N);
if (transposed) {
float* Xnew;
Xnew = new float[M * N];
transpose(Xnew, X, N, M);
copy_matrix(X, Xnew, N, M);
transpose(Xnew, Y, M, N );
copy_matrix(Y, Xnew, M, N);
delete[] Xnew;
}
delete[] S;
S = NULL;
delete[] Sinv;
Sinv = NULL;
delete[] U;
U = NULL;
delete[] V;
V = NULL;
delete[] Utr;
Utr = NULL;
delete[] V_Sinv;
V_Sinv = NULL;
}