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matrix.cpp
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matrix.cpp
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/*
Copyright © 2022 Alexey A. Shcherbakov. All rights reserved.
This file is part of the SingleParticleScattering project.
This is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 2 of the License, or
(at your option) any later version.
This sortware is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
*/
#include <iostream>
#include <memory.h>
#include "./matrix.h"
#ifdef _OPENMP
#include <omp.h>
#endif
const double nz_ = 1.e-15;
////////////////////////////////////////////////////////////////
// implementation of the class Vector //////////////////////////
////////////////////////////////////////////////////////////////
Vector::Vector(unsigned Mown) {
Nrow = Mown;
Data = new Complex[Nrow];
}
Vector::Vector(const Vector& V) {
Nrow = V.Nrow;
Data = new Complex[Nrow];
memcpy(Data,V.Data,Nrow*sizeof(Complex));
}
Vector::~Vector() {delete[] Data;}
Vector& Vector::operator = (const Vector& M) {
if (Nrow != M.Nrow) {if (Nrow) delete[] Data; Nrow = M.Nrow; Data = new Complex[Nrow];}
memcpy(Data, M.Data, Nrow*sizeof(Complex));
return *this;
}
Vector& Vector::operator += (const Vector& M) {
Complex *D1 = Data;
Complex *D2 = M.Data;
Complex *D1end = Data + Nrow;
if ((*this).Nrow != M.Nrow) {cout<<"Vector operator += : wrong vector length\n"; return *this;}
while (D1 < D1end) *D1++ += *D2++;
return *this;
}
Vector& Vector::operator -= (const Vector& M) {
Complex *D1 = Data;
Complex *D2 = M.Data;
Complex *D1end = Data + Nrow;
if ((*this).Nrow != M.Nrow) {cout<<"Vector operator -= : wrong vector length\n"; return *this;}
while (D1 < D1end) *D1++ -= *D2++;
return *this;
}
Vector Vector::operator * (const Complex tc) {
Vector V(*this);
for (int i=0; i<Nrow; i++) V.Data[i] *= tc;
return V;
}
Complex Vector::operator * (const Vector& B) const {
if (Nrow != B.Nrow) {cout<<"Vector operator * Vector : wrong vector length\n"; return 0.;}
Complex tc = 0.;
#ifdef _OPENMP
{
if (Nrow < 1.e6) {
double ta, taa, tb, tbb, *va, *vb, *vc, *vd;
va = reinterpret_cast <double*>(Data); vb = reinterpret_cast <double*>(B.Data);
vc = reinterpret_cast <double*>(&tc); vd=va+2*Nrow;
while (va<vd) {ta = *va++; taa = *va++; tb = *vb++; tbb = *vb++; *vc += ta*tb+taa*tbb; *(vc+1) += ta*tbb-taa*tb;}
}
else {
double tvr = 0., tvi = 0.;
#pragma omp parallel default(shared) reduction(+:tvr,tvi)
{
int nt = omp_get_thread_num(), np = omp_get_num_threads(), nn = Nrow/np;
double ta, taa, tb, tbb, *va, *vb, *vd;
va = reinterpret_cast<double*>(Data) + 2*nt*nn; vb = reinterpret_cast<double*>(B.Data) + 2*nt*nn;
vd = (nt == np-1) ? (reinterpret_cast<double*>(Data) + 2*Nrow) : va + 2*nn;
while (va<vd) {
ta = *va++; taa = *va++;
tb = *vb++; tbb = *vb++;
tvr += ta*tb + taa*tbb;
tvi += ta*tbb - taa*tb;
}
}
tc = Complex(tvr,tvi);
}
}
#else
{
double ta, taa, tb, tbb, *va, *vb, *vc, *vd;
va = reinterpret_cast <double*>(Data); vb = reinterpret_cast <double*>(B.Data);
vc = reinterpret_cast <double*>(&tc); vd=va+2*Nrow;
while (va<vd) {ta = *va++; taa = *va++; tb = *vb++; tbb = *vb++; *vc += ta*tb+taa*tbb; *(vc+1) += ta*tbb-taa*tb;}
}
#endif
return tc;
}
Vector Vector::operator * (const Matrix& B) {
Vector C(B.Ncol);
if (Nrow != B.Nrow) {cout<<"Vector operator * Matrix : wrong vector length\n"; return C;}
double *va, *vb, *vc, *vaa, *vbb, *vcc, ta, taa, tb, tbb;
va = reinterpret_cast <double*>(Data); vb = reinterpret_cast <double*>(B.Data);
vc = reinterpret_cast <double*>(C.Data); vbb = vb + 2*B.Nrow*B.Ncol;
for (vcc=vc+2*B.Ncol; vc<vcc; vc+=2) {
*vc = *(vc+1) = 0.;
for (vaa=vb; vaa<vbb; vaa += 2*B.Ncol)
{ta = *va++; taa = *va++; tb = *vaa; tbb = *(vaa+1); *vc += ta*tb-taa*tbb; *(vc+1) += ta*tbb+taa*tb;}
va -= 2*Nrow; vb += 2;
}
return C;
}
void Vector::GMResG(const Matrix &M, int kn, int knn, double mmax, bool wr) {
cout.precision(16);
double *va, *vb, tvr, tvi, tv1r, tv1i, tv2r, tv2i;
Vector B(Nrow), BB(Nrow), R(*this);
Vector **V, **W; V = new Vector* [knn+2]; W = new Vector* [knn+2];
int k, kk = 0, i, j;
double tv, *D, max, lmax; D = new double [knn+2];
Complex tc;
for (i=0; i<Nrow; i++) BB.Data[i] = 0.;
lbl2:
k = 0; V[0] = new Vector(Nrow); W[0] = new Vector(Nrow); *V[0] = R; goto lbl3;
do {
tv = 0.; for (i=0; i<Nrow; i++) {tc = W[k]->Data[i]; tv += abs(tc*tc);} D[k] = 1./tv;
tc = 0.; for (i=0; i<Nrow; i++) tc += R.Data[i]*conj(W[k]->Data[i]); tc *= D[k];
for (i=0; i<Nrow; i++) BB.Data[i] += V[k]->Data[i]*tc;
for (i=0; i<Nrow; i++) B.Data[i] = W[k]->Data[i]*tc; R -= B;
max = 0; for (i=0; i<Nrow; i++) {tv = abs(B.Data[i]); if (tv > max) max = tv;}
if (k) {
if (max <= mmax) goto lbl1;
if (((max > lmax)&&(k >= kn))||(k > knn)) {for (i=0; i<=k; i++) {delete W[i]; delete V[i];} goto lbl2;}
}
lmax = max; kk++; k++;
V[k] = new Vector(Nrow); W[k] = new Vector(Nrow);
*V[k] = *W[k-1];
if (wr) cout<<"\tGMResG "<<k<<"\t "<<max<<endl;
lbl3:
*W[k] = (*V[k])*M;
B = *W[k];
for (j=0; j<k; j++) {
va = reinterpret_cast <double*>(W[j]->Data); vb = reinterpret_cast <double*>(B.Data); tvr = tvi = 0.;
for (i=0; i<Nrow; i++)
{tv1r = *va++; tv2r = *vb++; tv1i = *va++; tv2i = *vb++; tvr += tv1r*tv2r + tv1i*tv2i; tvi += tv2i*tv1r - tv2r*tv1i;}
tc = Complex(tvr,tvi); tc *= D[j]; tvr = tc.real(); tvi = tc.imag();
va = reinterpret_cast <double*>(W[j]->Data); vb = reinterpret_cast <double*>(W[k]->Data);
for (i=0; i<Nrow; i++) {tv1r = *va++; tv1i = *va++; *vb++ -= tvr*tv1r - tvi*tv1i; *vb++ -= tvr*tv1i + tvi*tv1r;}
va = reinterpret_cast <double*>(V[j]->Data); vb = reinterpret_cast <double*>(V[k]->Data);
for (i=0; i<Nrow; i++) {tv1r = *va++; tv1i = *va++; *vb++ -= tvr*tv1r - tvi*tv1i; *vb++ -= tvr*tv1i + tvi*tv1r;}
}
} while (1);
lbl1:
for (i=0; i<k; i++) {delete W[i]; delete V[i];}
delete [] V; delete [] W; delete [] D;
cout<<kk<<" GMResG error: "<<max<<endl;
*this = BB;
}
void Vector::GMResG(void *PP, Vector (*mul)(const Vector&, void*), int kn, int knn, double mmax, bool wr) {
cout.precision(16);
double *va, *vb, tvr, tvi, tv1r, tv1i, tv2r, tv2i;
Vector B(Nrow), BB(Nrow), R(*this);
Vector **V, **W; V = new Vector* [knn+2]; W = new Vector* [knn+2];
int k, kk = 0, i, j;
double tv, *D, max, lmax; D = new double [knn+2];
Complex tc;
for (i=0; i<Nrow; i++) BB.Data[i] = 0.;
lbl2:
k = 0; V[0] = new Vector(Nrow); W[0] = new Vector(Nrow); *V[0] = R;
goto lbl3;
do {
tv = 0.; for (i=0; i<Nrow; i++) {tc = W[k]->Data[i]; tv += abs(tc*tc);} D[k] = 1./tv;
tc = 0.; for (i=0; i<Nrow; i++) tc += R.Data[i]*conj(W[k]->Data[i]); tc *= D[k];
for (i=0; i<Nrow; i++) BB.Data[i] += V[k]->Data[i]*tc;
for (i=0; i<Nrow; i++) B.Data[i] = W[k]->Data[i]*tc; R -= B;
max = 0; for (i=0; i<Nrow; i++) {tv = abs(B.Data[i]); if (tv > max) max = tv;}
if (k) {
if (max <= mmax) goto lbl1;
if (((max > lmax)&&(k >= kn))||(k > knn)) {for (i=0; i<=k; i++) {delete W[i]; delete V[i];} goto lbl2;}
}
lmax = max; kk++; k++;
V[k] = new Vector(Nrow); W[k] = new Vector(Nrow);
*V[k] = *W[k-1];
if (wr) cout<<"\tGMResG "<<k<<"\t "<<max<<endl;
lbl3:
*W[k] = mul(*V[k],PP);
B = *W[k];
for (j=0; j<k; j++) {
va = reinterpret_cast <double*>(W[j]->Data); vb = reinterpret_cast <double*>(B.Data); tvr = tvi = 0.;
for (i=0; i<Nrow; i++)
{tv1r = *va++; tv2r = *vb++; tv1i = *va++; tv2i = *vb++; tvr += tv1r*tv2r + tv1i*tv2i; tvi += tv2i*tv1r - tv2r*tv1i;}
tc = Complex(tvr,tvi); tc *= D[j]; tvr = tc.real(); tvi = tc.imag();
va = reinterpret_cast <double*>(W[j]->Data); vb = reinterpret_cast <double*>(W[k]->Data);
for (i=0; i<Nrow; i++) {tv1r = *va++; tv1i = *va++; *vb++ -= tvr*tv1r - tvi*tv1i; *vb++ -= tvr*tv1i + tvi*tv1r;}
va = reinterpret_cast <double*>(V[j]->Data); vb = reinterpret_cast <double*>(V[k]->Data);
for (i=0; i<Nrow; i++) {tv1r = *va++; tv1i = *va++; *vb++ -= tvr*tv1r - tvi*tv1i; *vb++ -= tvr*tv1i + tvi*tv1r;}
}
} while (1);
lbl1:
for (i=0; i<k+1; i++) {delete W[i]; delete V[i];}
delete [] V; delete [] W; delete [] D;
if (wr) cout<<" GMResG error: "<<max<<endl;
*this = BB;
}
void Vector::GMResAG(const Matrix& M, int km, double mmax, bool wr) {
int i, k, kk;
double tv, max, lmax;
double *pv1, *pv2, tvr, tvi, tv1r, tv1i, tv2r, tv2i;
Complex tc, *ss, *cc, *gg, *y, *h1, *h2;
Vector Z(*this), Z0(*this), **V, **H;
lbl2:
V = new Vector* [km+1]; H = new Vector* [km+1];
ss = new Complex [km]; cc = new Complex [km]; gg = new Complex [km+1]; y = new Complex [km];
for (i=0; i<km+1; i++) gg[i] = 0.;
kk = 0; V[0] = new Vector (Nrow);
gg[0] = tv = Z.normF();
if (tv>1.e-10) tv = 1./tv;
for (i=0; i<Nrow; i++) V[0]->Data[i] = tv*Z(i);
do {
V[kk+1] = new Vector(Nrow); H[kk] = new Vector(kk+2);
*V[kk+1] = (*V[kk])*M;
for (k=0; k<kk+1; k++) {
H[kk]->Data[k] = tc = (*V[k])*(*V[kk+1]); tvr = tc.real(); tvi = tc.imag();
pv1 = reinterpret_cast<double*>(V[kk+1]->Data); pv2 = reinterpret_cast<double*>(V[k]->Data);
for (i=0; i<Nrow; i++) {tv1r = *pv2++; tv1i = *pv2++; *pv1++ -= (tvr*tv1r - tvi*tv1i); *pv1++ -= (tvr*tv1i + tvi*tv1r);}
//for (i=0; i<Nrow; i++) V[kk+1]->Data[i] -= tc*V[k]->Data[i];
}
tv = (*V[kk+1]).normF();
H[kk]->Data[kk+1] = tv;
if ( fabs(tv)>1.e-10 ) {tv = 1./tv; for (i=0; i<Nrow; i++) V[kk+1]->Data[i] *= tv;}
h1 = h2 = H[kk]->Data; h2++;
for (k=0; k<kk; k++, h1++, h2++) {
*h1 = cc[k]*(tc = *h1) + ss[k]* *h2;
*h2 = -conj(ss[k])*tc + cc[k]* *h2;
}
h1 = h2 = H[kk]->Data + kk; h2++;
if (abs(*h2) < 1.e-10) {ss[kk] = 0.; cc[kk] = 1.;}
else if (abs(*h1) < 1.e-10) {ss[kk] = conj(*h2)/abs(*h2); cc[kk] = 0.;}
else {
tv = 1./sqrt( std::norm(*h1) + std::norm(*h2) );
cc[kk] = tv*abs(*h1); ss[kk] = tv*conj(*h2)*(*h1)/abs(*h1);
}
*h1 = cc[kk]*(tc = *h1) + ss[kk]* *h2;
*h2 = -conj(ss[kk])*tc + cc[kk]* *h2;
gg[kk+1] = -gg[kk]*conj(ss[kk]); gg[kk] *= cc[kk];
max = abs(gg[kk+1]);
if (wr) cout<<"GMResAG "<<kk<<"\t "<<tv<<endl;
//if ( (kk) && ((kk==knn-1) || ((max > lmax) && (kk > kn))) ) {kk++; goto lbl1;}
//else {lmax = max; kk++;}
++kk;
} while ((max > mmax) && (kk < km));
lbl1:
for (k=kk-1; k>=0; k--) {y[k] = gg[k]; for (i=kk-1; i>k; i--) y[k] -= y[i]*H[i]->Data[k]; y[k] /= H[k]->Data[k];}
for (i=0; i<Nrow; i++) Z.Data[i] = 0.;
for (k=0; k<kk; k++) {
tvr = y[k].real(); tvi = y[k].imag();
pv1 = reinterpret_cast<double*>(Z.Data); pv2 = reinterpret_cast<double*>(V[k]->Data);
for (i=0; i<Nrow; i++) {
tv2r = *pv2++; tv2i = *pv2++;
*pv1++ += tvr*tv2r - tvi*tv2i; *pv1++ += tvr*tv2i + tvi*tv2r;
}
}
for (k=0; k<kk; k++) {delete V[k]; delete H[k];} delete V[kk];
delete [] V; delete [] H;
delete [] ss; delete [] cc; delete [] gg; delete [] y;
if (max > mmax) {Z = (Z0 = Z0 - Z*M); goto lbl2;}
cout<<" GMResAG resudial: "<<max<<endl;
*this = Z;
}
void Vector::GMResAG(void *PP, Vector (*mul)(const Vector&, void*), int km, double mmax, bool wr) {
int i, k, kk; long sd = 1;
double tv, max, lmax;
double *pv1, *pv2, tvr, tvi, tv1r, tv1i, tv2r, tv2i, res1, res2;
Complex tc, *ss, *cc, *gg, *y, *h1, *h2;
Vector Z(*this), Z0(*this), **V, **H, X1(*this), X2(*this);
cout.precision(10);
lbl2:
V = new Vector* [km+1]; H = new Vector* [km];
ss = new Complex [km]; cc = new Complex [km]; gg = new Complex [km+1]; y = new Complex [km];
for (i=0; i<km+1; i++) gg[i] = 0.;
kk = 0; V[0] = new Vector (Nrow);
gg[0] = res2 = tv = Z.normF();
if (tv>1.e-10) tv = 1./tv;
for (i=0; i<Nrow; i++) V[0]->Data[i] = tv*Z(i);
do {
V[kk+1] = new Vector(Nrow); H[kk] = new Vector(kk+2);
*V[kk+1] = mul(*V[kk],PP);
//cout<<V[kk+1]->normF(); cin.get();
for (k=0; k<kk+1; k++) {
H[kk]->Data[k] = tc = (*V[k])*(*V[kk+1]); tvr = tc.real(); tvi = tc.imag();
pv1 = reinterpret_cast<double*>(V[kk+1]->Data); pv2 = reinterpret_cast<double*>(V[k]->Data);
for (i=0; i<Nrow; i++) {
tv1r = *pv2++; tv1i = *pv2++;
*pv1++ -= (tvr*tv1r - tvi*tv1i);
*pv1++ -= (tvr*tv1i + tvi*tv1r);
} //for (i=0; i<Nrow; i++) V[kk+1]->Data[i] -= tc*V[k]->Data[i];
}
tv = V[kk+1]->normF();
H[kk]->Data[kk+1] = tv;
if (fabs(tv) > 1.e-14) {tv = 1./tv; for (i=0; i<Nrow; i++) V[kk+1]->Data[i] *= tv;}
//else {cout<<"gmres error\n"; cin.get(); return;}
h1 = h2 = H[kk]->Data; h2++;
for (k=0; k<kk; k++, h1++, h2++) {
*h1 = cc[k]*(tc = *h1) + ss[k]* *h2;
*h2 = -conj(ss[k])*tc + cc[k]* *h2;
}
h1 = h2 = H[kk]->Data + kk; h2++;
if (abs(*h2) < 1.e-10) {ss[kk] = 0.; cc[kk] = 1.;}
else if (abs(*h1) < 1.e-10) {ss[kk] = conj(*h2)/abs(*h2); cc[kk] = 0.;}
else {
tv = 1./sqrt( std::norm(*h1) + std::norm(*h2) );
cc[kk] = tv*abs(*h1); ss[kk] = tv*conj(*h2)*(*h1)/abs(*h1);
}
*h1 = cc[kk]*(tc = *h1) + ss[kk]* *h2;
*h2 = -conj(ss[kk])*tc + cc[kk]* *h2;
gg[kk+1] = -gg[kk]*conj(ss[kk]); gg[kk] *= cc[kk];
/**/
// calculate intermediate solution
if (1) {
X1 = X2;
for (k=kk; k>=0; k--) {y[k] = gg[k]; for (i=kk; i>k; i--) y[k] -= y[i]*H[i]->Data[k]; y[k] /= H[k]->Data[k];}
for (i=0; i<Nrow; i++) X2.Data[i] = 0.;
if (kk > 0) for (k=0; k<kk+1; k++) {for (i=0; i<Nrow; i++) X2.Data[i] += y[k]*V[k]->Data[i];}
}
/**/
max = abs(gg[kk+1]); res1 = res2; res2 = max;
//if (wr) cout<<"\tgmres iteration "<<kk<<" residual: "<<max<<endl; //cin.get();
if (wr) cout<<"\tgmres iteration "<<kk<<" residual: "<<max<<" solution: "<<X2.cmp(X1)/X2.normF()<<endl; //cin.get();
} while ((max > mmax) && (fabs(res2/res1-1.) > 1.e-10) && (++kk < km));
lbl1:
if ((max > mmax) && (kk == km)) kk--;
for (k=kk; k>=0; k--) {y[k] = gg[k]; for (i=kk; i>k; i--) y[k] -= y[i]*H[i]->Data[k]; y[k] /= H[k]->Data[k];}
for (i=0; i<Nrow; i++) Z.Data[i] = 0.;
if (kk > 0) for (k=0; k<kk+1; k++) {
//if (wr) {cout<<" gmres out: "<<k<<" "<<y[k]<<" "<<V[k]->Data[8]<<" "<<V[k]->Data[24]<<endl;}
tvr = y[k].real(); tvi = y[k].imag();
pv1 = reinterpret_cast<double*>(Z.Data); pv2 = reinterpret_cast<double*>(V[k]->Data);
for (i=0; i<Nrow; i++) {
tv2r = *pv2++; tv2i = *pv2++;
*pv1++ += tvr*tv2r - tvi*tv2i; *pv1++ += tvr*tv2i + tvi*tv2r;
}// for (i=0; i<Nrow; i++) Z.Data[i] += y[k]*V[k]->Data[i];
}
else Z = *V[0];
for (k=0; k<kk+1; k++) {delete V[k]; delete H[k];} delete V[kk+1]; delete [] V; delete [] H;
delete [] ss; delete [] cc; delete [] gg; delete [] y;
//if (max > mmax) {Z = mul(Z,PP); Z = (Z0 = Z0 - Z); goto lbl2;}
cout<<" gmres resudial: "<<max<<" "<<kk<<endl;
*this = Z;
}
void Vector::GMResM(void *PP, Vector (*mul)(const Vector&, void*), const Vector &X0, int km, double mmax, bool wr) {
int i, k, kk;
double tv, max, lmax;
double *pv1, *pv2, tvr, tvi, tv1r, tv1i, tv2r, tv2i;
Complex tc, *ss, *cc, *gg, *y, *h1, *h2;
Vector Z(Nrow), X(X0), B(*this), **V, **H;
cout.precision(10);
do {
Z = B - mul(X,PP);
V = new Vector* [km+1]; H = new Vector* [km];
ss = new Complex [km]; cc = new Complex [km]; gg = new Complex [km+1]; y = new Complex [km];
for (i=0; i<km+1; i++) gg[i] = 0.;
kk = 0; V[0] = new Vector (Nrow);
gg[0] = tv = Z.normF();
if (tv > 1.e-14) tv = 1./tv;
for (i=0; i<Nrow; i++) V[0]->Data[i] = tv*Z(i);
do {
V[kk+1] = new Vector(Nrow); H[kk] = new Vector(kk+2);
*V[kk+1] = mul(*V[kk],PP);
for (k=0; k<kk+1; k++) {
H[kk]->Data[k] = tc = (*V[k])*(*V[kk+1]);
for (i=0; i<Nrow; i++) V[kk+1]->Data[i] -= tc*V[k]->Data[i];
}
H[kk]->Data[kk+1] = tv = (*V[kk+1]).normF();
if (fabs(tv) > 1.e-14) {tv = 1./tv; for (i=0; i<Nrow; i++) V[kk+1]->Data[i] *= tv;}
h1 = h2 = H[kk]->Data; h2++;
for (k=0; k<kk; k++, h1++, h2++) {
*h1 = cc[k]*(tc = *h1) + ss[k]* *h2;
*h2 = -conj(ss[k])*tc + cc[k]* *h2;
}
//h1 = h2 = H[kk]->Data + kk; h2++;
if (abs(*h2) < 1.e-14) {ss[kk] = 0.; cc[kk] = 1.;}
else if (abs(*h1) < 1.e-14) {ss[kk] = conj(*h2)/abs(*h2); cc[kk] = 0.;}
else {
tv = 1./sqrt( std::norm(*h1) + std::norm(*h2) );
cc[kk] = tv*abs(*h1); ss[kk] = tv*conj(*h2)*(*h1)/abs(*h1);
}
*h1 = cc[kk]*(tc = *h1) + ss[kk]* *h2;
*h2 = -conj(ss[kk])*tc + cc[kk]* *h2;
gg[kk+1] = -gg[kk]*conj(ss[kk]); gg[kk] *= cc[kk];
max = abs(gg[kk+1]);
if (wr) cout<<"\tGMResAG "<<kk<<"\t "<<max<<endl;
} while ((max > mmax) && (++kk < km));
for (k=kk-1; k>=0; k--) {y[k] = gg[k]; for (i=kk-1; i>k; i--) y[k] -= y[i]*H[i]->Data[k]; y[k] /= H[k]->Data[k];}
// retrieve solution
memset(X.Data,0,Nrow*sizeof(Complex));
for (k=0; k<kk; k++) X += y[k]* *V[k];
for (k=0; k<kk; k++) {delete V[k]; delete H[k];} delete V[kk]; delete [] V; delete [] H;
delete [] ss; delete [] cc; delete [] gg; delete [] y;
cin.get();
} while (max > mmax);
cout<<" GMResAG resudial: "<<max<<" "<<kk<<endl;
*this = X;
}
void Vector::GMResAH(const Matrix& M, int kn, int knn, double mmax, bool wr) {
int i, k, kk;
double tv, *nv;
Complex tc, *ss, *cc, *gg, *y, *h1, *h2;
Vector Z(*this), **V, **H;
nv = new double [knn+1];
ss = new Complex [knn]; cc = new Complex [knn];
gg = new Complex [knn+1]; y = new Complex [knn];
V = new Vector * [knn+1]; H = new Vector * [knn+1];
for (i=0; i<knn+1; i++) gg[i] = 0.;
V[0] = new Vector(Nrow);
*V[0] = Z; if (abs(Z(0))>1.e-10) V[0]->Data[0] += Z.normF()*Z(0)/abs(Z(0));
tc = (*V[0])*(*V[0]); nv[0] = 1./tc.real(); tc = (*V[0])*Z; tc *= 2.*nv[0];
for (i=0; i<Nrow; i++) Z.Data[i] -= tc*V[0]->Data[i];
gg[0] = Z(0);
tc = -2.*conj(V[0]->Data[0])*nv[0];
for (i=0; i<Nrow; i++) Z.Data[i] = tc*V[0]->Data[i]; Z.Data[0] += 1.;
Z = Z*M;
tc = (*V[0])*Z; tc *= 2.*nv[0];
for (i=0; i<Nrow; i++) Z.Data[i] -= tc*V[0]->Data[i];
kk = 0;
do {
V[kk+1] = new Vector(Nrow);
for (i=0; i<kk+1; i++) V[kk+1]->Data[i] = 0.;
for (i=kk+1; i<Nrow; i++) V[kk+1]->Data[i] = Z(i);
if ( abs(Z(kk+1))>1.e-10 ) V[kk+1]->Data[kk+1] += Z.normF(kk+1)*Z(kk+1)/abs(Z(kk+1));
tc = (*V[kk+1])*(*V[kk+1]); nv[kk+1] = 1./tc.real(); tc = (*V[kk+1])*Z; tc *= 2.*nv[kk+1];
for (i=0; i<Nrow; i++) Z.Data[i] -= tc*V[kk+1]->Data[i];
H[kk] = new Vector(kk+2);
for (i=0; i<kk+2; i++) {H[kk]->Data[i] = Z(i);}// cout<<" H "<<i<<" "<<Z(i)<<endl;}
tc = -2.*conj(V[kk+1]->Data[kk+1])*nv[kk+1];
for (i=0; i<Nrow; i++) Z.Data[i] = tc*V[kk+1]->Data[i]; Z.Data[kk+1] += 1.;
for (k=kk; k>=0; k--) {tc = (*V[k])*Z; tc *= 2.*nv[k]; for (i=0; i<Nrow; i++) Z.Data[i] -= tc*V[k]->Data[i];}
Z = Z*M;
for (k=0; k<kk+2; k++) {tc = (*V[k])*Z; tc *= 2.*nv[k]; for (i=0; i<Nrow; i++) Z.Data[i] -= tc*V[k]->Data[i];}
h1 = h2 = H[kk]->Data; h2++;
for (k=0; k<kk; k++, h1++, h2++) {
*h1 = cc[k]*(tc = *h1) + ss[k]* *h2;
*h2 = -conj(ss[k])*tc + cc[k]* *h2;
}
h1 = h2 = H[kk]->Data + kk; h2++;
if ( abs(*h2)<1.e-10 ) {ss[kk] = 0.; cc[kk] = 1.;}
else if ( abs(*h1)<1.e-10 ) {ss[kk] = conj(*h2)/abs(*h2); cc[kk] = 0.;}
else {
tv = 1./sqrt( std::norm(*h1) + std::norm(*h2) );
cc[kk] = tv*abs(*h1); ss[kk] = tv*conj(*h2)*(*h1)/abs(*h1);
}
*h1 = cc[kk]*(tc = *h1) + ss[kk]* *h2;
*h2 = -conj(ss[kk])*tc + cc[kk]* *h2;
gg[kk+1] = -gg[kk]*conj(ss[kk]); gg[kk] *= cc[kk];
tv = abs(gg[kk+1]);
if (wr) cout<<"\tGMResAH "<<kk<<"\t "<<tv<<endl;
kk++;
} while ( (kk < knn) && (tv > mmax) );
lbl1:
cout<<" GMResAH resudial: "<<abs(gg[kk+1])<<endl;
for (k=kk-1; k>=0; k--) {
y[k] = gg[k];
for (i=kk-1; i>k; i--) y[k] -= y[i]*H[i]->Data[k];
y[k] /= H[k]->Data[k];
}
for (i=0; i<Nrow; i++) Z.Data[i] = 0.;
for (k=kk-1; k>=0; k--) {
Z.Data[k] += y[k];
tc = (*V[k])*Z; tc *= 2.*nv[k]; for (i=0; i<Nrow; i++) Z.Data[i] -= tc*V[k]->Data[i];
}
delete [] nv;
delete [] ss; delete [] cc;
delete [] gg; delete [] y;
for (k=0; k<kk; k++) {delete V[k]; delete H[k];} delete V[kk]; delete [] V; delete [] H;
*this = Z;
}
void Vector::GMResAH(void *PP, Vector (*mul)(const Vector&, void*), int kn, int knn, double mmax, bool wr) {
int i, k, kk;
double tv, *nv;
double *pv1, *pv2, tvr, tvi, tv1r, tv1i;
Complex tc, *tcl, *ss, *cc, *gg, *y, *h1, *h2;
Vector Z(*this), **V, **H;
nv = new double [knn+1];
ss = new Complex [knn]; cc = new Complex [knn];
gg = new Complex [knn+1]; y = new Complex [knn];
V = new Vector * [knn+1]; H = new Vector * [knn+1];
for (i=0; i<knn+1; i++) gg[i] = 0.;
V[0] = new Vector(Z);
if (abs(Z(0))>1.e-10) V[0]->Data[0] += Z.normF()*Z(0)/abs(Z(0));
else V[0]->Data[0] += Z.normF();
tc = (*V[0])*(*V[0]); nv[0] = 1./tc.real(); tc = (*V[0])*Z; tc *= 2.*nv[0];
for (i=0; i<Nrow; i++) Z.Data[i] -= tc*V[0]->Data[i];
gg[0] = Z(0);
tc = -2.*conj(V[0]->Data[0])*nv[0];
for (i=0; i<Nrow; i++) Z.Data[i] = tc*V[0]->Data[i]; Z.Data[0] += 1.;
Z = mul(Z,PP);
tc = (*V[0])*Z; tc *= 2.*nv[0];
for (i=0; i<Nrow; i++) Z.Data[i] -= tc*V[0]->Data[i];
kk = 0;
do {
V[kk+1] = new Vector(Nrow);
for (i=0; i<kk+1; i++) V[kk+1]->Data[i] = 0.;
for (i=kk+1; i<Nrow; i++) V[kk+1]->Data[i] = Z(i);
if ( abs(Z(kk+1))>1.e-10 ) V[kk+1]->Data[kk+1] += Z.normF(kk+1)*Z(kk+1)/abs(Z(kk+1));
else V[kk+1]->Data[kk+1] += Z.normF(kk+1);
tc = (*V[kk+1])*(*V[kk+1]); nv[kk+1] = 1./tc.real(); tc = (*V[kk+1])*Z; tc *= 2.*nv[kk+1];
pv1 = reinterpret_cast<double*>(Z.Data); pv2 = reinterpret_cast<double*>(V[kk+1]->Data); tvr = tc.real(); tvi = tc.imag();
for (i=0; i<Nrow; i++) {tv1r = *pv2++; tv1i = *pv2++; *pv1++ -= tvr*tv1r - tvi*tv1i; *pv1++ -= tvr*tv1i + tvi*tv1r;}
//for (i=0; i<Nrow; i++) Z.Data[i] -= tc*V[kk+1]->Data[i];
H[kk] = new Vector(kk+2);
for (i=0; i<kk+2; i++) {H[kk]->Data[i] = Z(i);}
tc = -2.*conj(V[kk+1]->Data[kk+1])*nv[kk+1];
pv1 = reinterpret_cast<double*>(Z.Data); pv2 = reinterpret_cast<double*>(V[kk+1]->Data); tvr = tc.real(); tvi = tc.imag();
for (i=0; i<Nrow; i++) {tv1r = *pv2++; tv1i = *pv2++; *pv1++ = tvr*tv1r - tvi*tv1i; *pv1++ = tvr*tv1i + tvi*tv1r;}
//for (i=0; i<Nrow; i++) Z.Data[i] = tc*V[kk+1]->Data[i];
Z.Data[kk+1] += 1.;
for (k=kk; k>=0; k--) {
tc = (*V[k])*Z; tc *= 2.*nv[k];
pv1 = reinterpret_cast<double*>(Z.Data); pv2 = reinterpret_cast<double*>(V[k]->Data); tvr = tc.real(); tvi = tc.imag();
for (i=0; i<Nrow; i++) {tv1r = *pv2++; tv1i = *pv2++; *pv1++ -= tvr*tv1r - tvi*tv1i; *pv1++ -= tvr*tv1i + tvi*tv1r;}
//for (i=0; i<Nrow; i++) Z.Data[i] -= tc*V[k]->Data[i];
}
Z = mul(Z,PP);
for (k=0; k<kk+2; k++) {
tc = (*V[k])*Z; tc *= 2.*nv[k];
pv1 = reinterpret_cast<double*>(Z.Data); pv2 = reinterpret_cast<double*>(V[k]->Data); tvr = tc.real(); tvi = tc.imag();
for (i=0; i<Nrow; i++) {tv1r = *pv2++; tv1i = *pv2++; *pv1++ -= tvr*tv1r - tvi*tv1i; *pv1++ -= tvr*tv1i + tvi*tv1r;}
//for (i=0; i<Nrow; i++) Z.Data[i] -= tc*V[k]->Data[i];
}
h1 = h2 = H[kk]->Data; h2++;
for (k=0; k<kk; k++, h1++, h2++) {
*h1 = cc[k]*(tc = *h1) + ss[k]* *h2;
*h2 = -conj(ss[k])*tc + cc[k]* *h2;
}
h1 = h2 = H[kk]->Data + kk; h2++;
if ( abs(*h2)<1.e-10 ) {ss[kk] = 0.; cc[kk] = 1.;}
else if ( abs(*h1)<1.e-10 ) {ss[kk] = conj(*h2)/abs(*h2); cc[kk] = 0.;}
else {
tv = 1./sqrt( std::norm(*h1) + std::norm(*h2) );
cc[kk] = tv*abs(*h1); ss[kk] = tv*conj(*h2)*(*h1)/abs(*h1);
}
*h1 = cc[kk]*(tc = *h1) + ss[kk]* *h2;
*h2 = -conj(ss[kk])*tc + cc[kk]* *h2;
gg[kk+1] = -gg[kk]*conj(ss[kk]); gg[kk] *= cc[kk];
tv = abs(gg[kk+1]);
if (wr) cout<<"\tGMResAH "<<kk<<"\t "<<tv<<endl;
kk++;
} while ( (kk < knn) && (tv > mmax) );
lbl1:
cout<<" GMResAH resudial: "<<abs(gg[kk+1])<<endl;
for (k=kk-1; k>=0; k--) {
y[k] = gg[k];
for (i=kk-1; i>k; i--) y[k] -= y[i]*H[i]->Data[k];
y[k] /= H[k]->Data[k];
}
for (i=0; i<Nrow; i++) Z.Data[i] = 0.;
for (k=kk-1; k>=0; k--) {
Z.Data[k] += y[k]; tc = (*V[k])*Z; tc *= 2.*nv[k];
pv1 = reinterpret_cast<double*>(Z.Data); pv2 = reinterpret_cast<double*>(V[k]->Data); tvr = tc.real(); tvi = tc.imag();
for (i=0; i<Nrow; i++) {tv1r = *pv2++; tv1i = *pv2++; *pv1++ -= tvr*tv1r - tvi*tv1i; *pv1++ -= tvr*tv1i + tvi*tv1r;}
// for (i=0; i<Nrow; i++) Z.Data[i] -= tc*V[k]->Data[i];
}
delete [] nv;
delete [] ss; delete [] cc;
delete [] gg; delete [] y;
for (k=0; k<kk; k++) {delete V[k]; delete H[k];} delete V[kk]; delete [] V; delete [] H;
*this = Z;
}
void Vector::CG(const Matrix &M, int kn, double mmax, bool wr) {
int k = 0; double tv; Complex tc, tcc;
Vector R(*this), P(*this), PP(*this);
memset(Data,0,Nrow*sizeof(Complex));
do {
PP = P*M; tc = (tcc = (R*R))/(PP*P);
*this += tc*P; R -= tc*PP; tv = abs(tc)*P.normF();
P = R + ((R*R)/tcc)*P;
if (wr) cout << "CG " << k << " " << tv << endl;
} while ((tv > mmax)&&(++k < kn));
cout << " CG " << k << " " << tv << endl;
}
void Vector::BiCG(const Matrix &M, int kn, double mmax, bool wr) {
int k = 0; double tv; Complex tc, tcc; Matrix MT(M); MT = M.mconj();
Vector R1(*this), R2(*this), P1(*this), P2(*this), PP(*this);
memset(Data,0,Nrow*sizeof(Complex));
do {
PP = P1*M; tc = (tcc = (R1*R2))/(PP*P2); R1 -= tc*PP;
*this += tc*P1; tv = abs(tc)*P1.normF();
PP = P2*MT; R2 -= tc*PP;
tc = (R1*R2)/tcc; P1 = R1 + tc*P1; P2 = R2 + tc*P2;
if (wr) cout << "BiCG " << k << " " << tv << endl;
} while ((tv > mmax)&&(++k < kn));
cout << " BiCG " << k << " " << tv << endl;
}
void Vector::BiCGs(const Matrix &M, int kn, double mmax, bool wr) {
int k = 0; double tv; Complex ta, tw, tc; Matrix MT(M); MT = M.mconj();
Vector R(*this), RR(*this), P(*this), SS(*this), PP(*this);
memset(Data,0,Nrow*sizeof(Complex));
tc = R*RR;
do {
PP = P*M; ta = tc/(PP*RR); *this += ta*P; tv = abs(ta)*P.normF();
R -= ta*PP; SS = R*M; tw = (SS*R)/(SS*SS); *this += tw*R; tv += abs(tw)*R.normF();
R -= tw*SS; ta /= tw*tc; ta *= (tc = (R*RR));
P = R + ta*(P - tw*PP);
if (wr) cout << "BiCGs " << k << " " << tv << endl;
} while ((tv > mmax)&&(++k < kn));
cout << " BiCGs " << k << " " << tv << endl;
}
void Vector::BiCGs(void *par, Vector (*mul)(const Vector&, void*), int kn, double mmax, bool wr) {
/**
int k = 0; double tv; Complex ta, tw, tc;
Vector R(*this), RR(*this), P(*this), SS(*this), PP(*this);
memset(Data,0,Nrow*sizeof(Complex));
tc = R*RR;
do {
PP = mul(P,par); //PP = P*M;
ta = tc/(PP*RR); *this += ta*P; tv = abs(ta)*P.normF();
R -= ta*PP;
SS = mul(R,par); //SS = R*M;
tw = (SS*R)/(SS*SS); *this += tw*R; tv += abs(tw)*R.normF();
R -= tw*SS; ta /= tw*tc; ta *= (tc = (R*RR));
P = R + ta*(P - tw*PP);
if (wr) cout << "BiCGs " << k << " " << tv << endl;
} while ((tv > mmax)&&(++k < kn));
cout << " BiCGs " << k << " " << tv << endl;
/**/
int k = 0; double tv; Complex ta, tw, tt, trh1, trh2, tb;
Vector VP(*this), VR(*this), VRR(*this), VS(*this), VT(*this), VV(*this);
memset(Data,0,Nrow*sizeof(Complex));
memset(VV.Data,0,Nrow*sizeof(Complex));
memset(VP.Data,0,Nrow*sizeof(Complex));
trh1 = ta = tw = 1.;
do {
trh2 = VRR*VR;
tb = trh2/trh1*ta/tw;
VP = VR + tb*(VP - tw*VV);
VV = mul(VP,par);
ta = trh2/(VRR*VV);
VS = VR - ta*VV;
VT = mul(VS,par);
tw = tt = 0.; for (int i=0; i<Nrow; ++i) {tw += VT(i)*VS(i); tt += VT(i)*VT(i);} tw /= tt;
*this = *this + tw*VS + ta*VP;
VR = VS - tw*VT;
trh1 = trh2; tv = VR.normF();
if (wr) cout << "BiCGs " << k << " " << tv << endl;
} while ((tv > mmax)&&(++k < kn));
}
void Vector::BiCGs(void *par, Vector (*mul)(const Vector&, void*), const Vector &V0, int kn, double mmax, bool wr) {
int k = 0; double tv; Complex ta, tw, tt, trh1, trh2, tb;
Vector VP(*this), VR(*this), VRR(*this), VS(*this), VT(*this), VV(*this);
memset(Data,0,Nrow*sizeof(Complex));
memset(VV.Data,0,Nrow*sizeof(Complex));
memset(VP.Data,0,Nrow*sizeof(Complex));
//cout<<Nrow<<" "<<V0.Nrow<<endl; cin.get();
VRR = VR = VR - mul(V0,par);
trh1 = ta = tw = 1.;
do {
trh2 = VRR*VR;
tb = trh2/trh1*ta/tw;
VP = VR + tb*(VP - tw*VV);
VV = mul(VP,par);
ta = trh2/(VRR*VV);
VS = VR - ta*VV;
VT = mul(VS,par);
tw = tt = 0.; for (int i=0; i<Nrow; ++i) {tw += VT(i)*VS(i); tt += VT(i)*VT(i);} tw /= tt;
*this = *this + tw*VS + ta*VP;
VR = VS - tw*VT;
trh1 = trh2; tv = VR.normF();
if (wr) cout << "BiCGs " << k << " " << tv << endl;
} while ((tv > mmax)&&(++k < kn));
}
Vector Vector::calc_LSa(const Matrix &M) {
if ((Nrow != M.Ncol) || (M.Ncol < M.Nrow)) return *this; // exception
if (M.Ncol == M.Nrow) return *this/M;
int i, j, N = M.Nrow;
Matrix D(N);
Vector V(N);
for (i=0; i<N; i++) for (j=0; j<N; j++) {}
return V;
}
Vector& Vector::operator /= (const Matrix& A) {
if (A.Ncol != A.Nrow) {cout<<"Vector operator /= : matrix is not square\n"; return *this;}
if (A.Nrow != Nrow) {cout<<"Vector operator /= : wrong matrix dimension\n"; return *this;}
int i, ii;
Matrix AA(Nrow);
for (i=0; i<Nrow; i++) for (ii=0; ii<Nrow; ii++) AA.Data[i*Nrow+ii] = A.Data[ii*Nrow+i];
*this %= AA; return *this;
}
Vector& Vector::operator %= (const Matrix& A) {
if (A.Ncol != A.Nrow) {cout<<"Vector operator %= : matrix is not square\n"; return *this;}
if (A.Nrow != Nrow) {cout<<"Vector operator %= : wrong matrix dimension\n"; return *this;}
double MaxMod, NewMod;
const double NearZero = 1.e-15;
Matrix R(A);
int i, ii, j, jj, t = 2*Nrow;
double *vva, *vvb, *vvc, *vv, va, vb, vc, vd, tv;
Complex *a = R.Data, *b = Data, *aa, *bb, *aaa = R.Data + Nrow*Nrow - 1, ra;
for(i=0; i<Nrow-1; i++,a+=Nrow+1,b++) {
MaxMod = abs(*a); j = i; vva = reinterpret_cast <double*>(a+Nrow);
for (ii=i+1; ii<Nrow; ii++,vva+=2*Nrow) {
va = *vva; vb = *(vva+1); NewMod = sqrt(va*va+vb*vb);
if (MaxMod < NewMod) {MaxMod = NewMod; j = ii;}
}
if (MaxMod <= NearZero) {cout<<"Vector operator %= : matrix is zero\n"; return *this;}
jj = 2*(Nrow-i);
if (j > i) {
vva = reinterpret_cast <double*>(a); vvc = reinterpret_cast <double*>(a+(j-i)*Nrow); vv = vvc+jj;
while(vvc < vv) {tv = *vva; *vva++ = *vvc; *vvc++ = tv;}
vva = reinterpret_cast <double*>(b); vvc = reinterpret_cast <double*>(b+(j-i));
tv = *vva; *vva++ = *vvc; *vvc++ = tv; tv = *vva; *vva++ = *vvc; *vvc++ = tv;
}
jj -= 2;
//ra = -1./(*a);
va = a->real(); vb = a->imag(); tv = va*va+vb*vb; ra = Complex(-va/tv,vb/tv);
for (aa=a+Nrow,bb=b+1; aa<aaa; aa+=Nrow,bb++) {
va = ra.real(); vb = ra.imag();
tv = aa->real(); vd = aa->imag(); vc = va*tv-vb*vd; vd = va*vd+vb*tv;
vva = reinterpret_cast <double*>(a+1); vvc = reinterpret_cast <double*>(aa+1); vv = vvc+jj;
while(vvc < vv) {va = *vva++; vb = *vva++; *vvc++ += va*vc-vb*vd; *vvc++ += va*vd+vb*vc;}
vva = reinterpret_cast <double*>(b); vvc = reinterpret_cast <double*>(bb);
va = *vva++; vb = *vva; *vvc++ += va*vc-vb*vd; *vvc += va*vd+vb*vc;
}
}
for (i=Nrow-1; i>=0; i--,a-=Nrow+1,b--) {
//ra = 1./(*a); vc = ra.real(); vd = ra.imag();
va = a->real(); vb = a->imag(); tv = va*va+vb*vb; vc = va/tv; vd = -vb/tv;
vvc = reinterpret_cast <double*>(b);
va = *vvc; vb = *(vvc+1); *vvc++ = va*vc-vb*vd; *vvc = va*vd+vb*vc;
vvb = reinterpret_cast <double*>(R.Data+i);
for (bb=Data; bb<b; vvb+=2*Nrow,bb++) {
vc = *vvb; vd = *(vvb+1);
vva = reinterpret_cast <double*>(b); vvc = reinterpret_cast <double*>(bb);
va = *vva++; vb = *vva; *vvc++ -= va*vc-vb*vd; *vvc -= va*vd+vb*vc;
}
}
return *this;
}
double Vector::normF(int nn) const {
if ( nn >= Nrow ) return 0.;
double tv = 0., tvr, tvi, *pv;
pv = reinterpret_cast<double*>(this->Data) + 2*nn;
for (int i=nn; i<Nrow; i++) {tvr = *pv++; tvi = *pv++; tv += tvr*tvr + tvi*tvi;}
return sqrt(tv);
}
double Vector::cmp(const Vector &V) {
if (Nrow != V.Nrow) return -1.;
double tv = 0., tvv;
for (int i=0; i<Nrow; i++) if (tv < (tvv = abs(V.Data[i] - Data[i]))) tv = tvv;
return tv;
}
double Vector::cmpa(const Vector &V) {
if (Nrow != V.Nrow) return -1.;
double tv = 0., tvv;
for (int i=0; i<Nrow; i++) if (tv < (tvv = fabs(abs(V.Data[i]) - abs(Data[i])))) tv = tvv;
return tv;
}
void qsort(Complex *A, int iLo, int iHi) {
int Lo, Hi; double Mid; Complex tc;
Lo = iLo; Hi = iHi; Mid = A[(Lo+Hi)/2].real();
do {
while (A[Lo].real() < Mid) Lo++; while (A[Hi].real() > Mid) Hi--;
if (Lo <= Hi) {tc = A[Lo]; A[Lo++] = A[Hi]; A[Hi--] = tc;}
} while (Lo <= Hi);
if (Hi > iLo) qsort(A,iLo,Hi); if (Lo < iHi) qsort(A,Lo,iHi);
}
void qsort(Complex *A, Matrix &ME, int iLo, int iHi) {
int i, Lo, Hi; double Mid; Complex tc;
Lo = iLo; Hi = iHi; Mid = A[(Lo+Hi)/2].real();
do {
while (A[Lo].real() < Mid) Lo++; while (A[Hi].real() > Mid) Hi--;
if (Lo <= Hi) {
tc = A[Lo]; A[Lo] = A[Hi]; A[Hi] = tc;
for (i=0; i<ME.Nrow; ++i) {tc = ME(i,Lo); ME.Data[i*ME.Nrow+Lo] = ME(i,Hi); ME.Data[i*ME.Nrow+Hi] = tc;}
Lo++; Hi--;
}
} while (Lo <= Hi);
if (Hi > iLo) qsort(A,ME,iLo,Hi); if (Lo < iHi) qsort(A,ME,Lo,iHi);
}
void Vector::qsort() {
int Lo, Hi; double Mid; Complex tc;
Lo = 0; Hi = Nrow-1; Mid = Data[(Lo+Hi)/2].real();
do {
while (Data[Lo].real() < Mid) Lo++; while (Data[Hi].real() > Mid) Hi--;
if (Lo <= Hi) {tc = Data[Lo]; Data[Lo++] = Data[Hi]; Data[Hi--] = tc;}
} while (Lo <= Hi);
if (Hi > 0) ::qsort(Data,0,Hi); if (Lo < Nrow-1) ::qsort(Data,Lo,Nrow-1);
}
void Vector::qsorta() {
int Lo, Hi; double Mid; Complex tc;
Lo = 0; Hi = Nrow-1; Mid = abs(Data[(Lo+Hi)/2]);
do {
while (abs(Data[Lo]) < Mid) Lo++; while (abs(Data[Hi]) > Mid) Hi--;
if (Lo <= Hi) {tc = Data[Lo]; Data[Lo++] = Data[Hi]; Data[Hi--] = tc;}
} while (Lo <= Hi);
if (Hi > 0) ::qsort(Data,0,Hi); if (Lo < Nrow-1) ::qsort(Data,Lo,Nrow-1);
}
void Vector::qsort(Matrix &ME) {
int i, Lo, Hi; double Mid; Complex tc;
Lo = 0; Hi = Nrow-1; Mid = Data[(Lo+Hi)/2].real();
do {
while (Data[Lo].real() < Mid) Lo++; while (Data[Hi].real() > Mid) Hi--;
if (Lo <= Hi) {
tc = Data[Lo]; Data[Lo] = Data[Hi]; Data[Hi] = tc;
for (i=0; i<Nrow; ++i) {tc = ME(i,Lo); ME.Data[i*Nrow+Lo] = ME(i,Hi); ME.Data[i*Nrow+Hi] = tc;}
Lo++; Hi--;
}
} while (Lo <= Hi);
if (Hi > 0) ::qsort(Data,ME,0,Hi); if (Lo < Nrow-1) ::qsort(Data,ME,Lo,Nrow-1);
}
Complex Vector::poly(Complex x) {
Complex s;
int i;
if (abs(x) < 1) {s = x; for (i=Nrow-1; i>0; i--) {s += Data[i]; s *= x;} s += Data[0];}
else {s = Data[0]/x; for (i=1; i<Nrow; i++) {s += Data[i]; s /= x;} s += 1;}
return s;
}
Vector Vector::pcoeff() {
int i, j;
Vector A(Nrow), B(Nrow);
for (j=1; j<Nrow; j++) A.Data[j] = 0.; A.Data[0] = 1.;
for (i=0; i<Nrow; i++) {
B.Data[0] = 0; for (j=1; j<Nrow; j++) B.Data[j] = A.Data[j-1];
for (j=0; j<=i; j++) B.Data[j] -= A.Data[j]*Data[i];
for (j=0; j<Nrow; j++) A.Data[j] = B.Data[j];
}
return A;
}
Vector Vector::roots() {
Vector D(Nrow);
if (Nrow == 1) {D.Data[0] = -Data[0]; return D;}
int i, j;
Matrix M(Nrow);
for (i=0; i<Nrow; i++) for (j=0; j<Nrow; j++) M.Data[i*Nrow+j] = 0.;
for (i=0; i<Nrow; i++) M.Data[i] = -Data[Nrow-1-i]; for (i=1; i<Nrow; i++) M.Data[i*Nrow+i-1] = 1.;
D = M.diag(0); D.qsort();
return D;
}
///////////////////////////////////////////////////////////////////////
// implementations of the class Matrix ////////////////////////////////
///////////////////////////////////////////////////////////////////////
Matrix::Matrix(unsigned Mown, unsigned Mext) {
Nrow = Mown;
Ncol = (Mext) ? Mext : Mown;
Data = new Complex[Nrow*Ncol];
}
Matrix::Matrix(const Matrix& M) {
Nrow = M.Nrow; Ncol = M.Ncol;
Data = new Complex[Nrow*Ncol];
memcpy(Data, M.Data, Nrow*Ncol*sizeof(Complex));
}
Matrix::~Matrix() {delete [] Data;}
double Matrix::normF(int n1) const {
double tv = 0.;
//for (int i=n1; i<Nrow*Ncol; i++) tv += abs(Data[i]*Data[i]);
if (n1 > -1) for (int i=0; i<n1; i++) tv += abs(Data[i]*Data[i]);
else for (int i=0; i<Nrow*Ncol; i++) tv += abs(Data[i]*Data[i]);
return sqrt(tv);//
}
double Matrix::cmp(const Matrix &M) {
if ((Nrow != M.Nrow) || (Ncol != M.Ncol)) return -1.;
double tv = 0., tvv;
for (int i=0; i<Nrow*Ncol; i++) if (tv < (tvv = abs(M.Data[i] - Data[i]))) tv = tvv;
return tv;
}
double Matrix::cmpa(const Matrix &M) {
if ((Nrow != M.Nrow) || (Ncol != M.Ncol)) return -1.;
double tv = 0., tvv;
for (int i=0; i<Nrow*Ncol; i++) if (tv < (tvv = fabs(abs(M.Data[i]) - abs(Data[i])))) tv = tvv;
return tv;
}
void Matrix::print(const int pres) const {
cout.precision(pres);
for (int i=0; i<Nrow; ++i) {
for (int ii=0; ii<Ncol; ++ii) cout << Data[i*Ncol+ii] << " ";
cout << endl;
}
}
void Matrix::eye(void) {
int N = (Nrow < Ncol) ? Nrow : Ncol;
memset(Data,0,Nrow*Ncol*sizeof(Complex));
for (int i=0; i<N; ++i) Data[i*Ncol+i] = 1.;
}
Matrix& Matrix::operator = (const Matrix& M) {
if ((Nrow != M.Nrow)||(Ncol != M.Ncol))
{if (Nrow*Ncol) delete[] Data; Nrow = M.Nrow; Ncol = M.Ncol; Data = new Complex[Nrow*Ncol];}
memcpy(Data, M.Data, Nrow*Ncol*sizeof(Complex));
return *this;
}
Matrix Matrix::transp() const {
int i, j; Matrix M(Ncol,Nrow);
for (i=0; i<Nrow; i++) for (j=0; j<Ncol; j++) M.Data[j*Nrow+i] = Data[i*Ncol+j];
return M;
}
Matrix Matrix::mconj() const {
int i, j; Matrix M(Ncol,Nrow);
for (i=0; i<Nrow; i++) for (j=0; j<Ncol; j++) M.Data[j*Nrow+i] = conj(Data[i*Ncol+j]);
return M;
}