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sdpa_linear.cpp
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sdpa_linear.cpp
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/* -------------------------------------------------------------
This file is a component of SDPA
Copyright (C) 2004-2012 SDPA Project
This program 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 program 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.
You should have received a copy of the GNU General Public License
along with this program; if not, write to the Free Software
Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
------------------------------------------------------------- */
#include "sdpa_linear.h"
#include "sdpa_dataset.h"
#include "sdpa_dpotrf.h"
#include "sdpa_algebra.h"
namespace sdpa {
double Lal::getMinEigen(DenseMatrix& lMat,
DenseMatrix& xMat,
DenseMatrix& Q,
Vector& out, Vector& b, Vector& r,
Vector& q, Vector& qold,
Vector& w, Vector& tmp,
Vector& diagVec, Vector& diagVec2,
Vector& workVec)
{
double alpha,beta,value;
double min = 1.0e+51, min_old = 1.0e+52;
double error = 1.0e+10;
int nDim = xMat.nRow;
int k = 0, kk = 0;
diagVec.initialize(1.0e+50);
diagVec2.setZero();
q.setZero();
r.initialize(1.0);
beta = sqrt((double)nDim); // norm of "r"
// nakata 2004/12/12
while (k<nDim
&& k<sqrt((double)nDim)+10
&& beta > 1.0e-16
&& ( k<20 ||
fabs(min-min_old) > (1.0e-5)*fabs(min)+(1.0e-8)
// && (fabs(min-min_old) > (1.0e-3)*fabs(min)+(1.0e-6)
|| fabs(error*beta) > (1.0e-2)*fabs(min)+(1.0e-6) )
) {
// rMessage("k = " << k);
qold.copyFrom(q);
value = 1.0/beta;
Lal::let(q,'=',r,'*',&value);
// w = (lMat^T)*q
w.copyFrom(q);
dtrmv_fc ((char *)"Lower",(char *)"Transpose",
(char *)"NotUnit",&nDim,
lMat.de_ele,&nDim,w.ele,&IONE,
strlen("Lower"), strlen("Transpose"),strlen("NotUnit"));
Lal::let(tmp,'=',xMat,'*',w);
w.copyFrom(tmp);
dtrmv_fc ((char *)"Lower",(char *)"NoTranspose",
(char *)"NotUnit",&nDim,
lMat.de_ele,&nDim,w.ele,&IONE,
strlen("Lower"), strlen("NoTranspose"),strlen("NotUnit"));
// w = lMat*xMat*(lMat^T)*q
// rMessage("w = ");
// w.display();
Lal::let(alpha,'=',q,'.',w);
diagVec.ele[k] = alpha;
Lal::let(r,'=',w,'-',q,&alpha);
Lal::let(r,'=',r,'-',qold,&beta);
// rMessage("r = ");
// r.display();
if ( kk>=sqrt((double)k) || k==nDim-1 || k>sqrt((double)nDim+9) ) {
kk = 0;
out.copyFrom(diagVec);
b.copyFrom(diagVec2);
out.ele[nDim-1] = diagVec.ele[k];
b.ele[nDim-1] = 0.0;
// rMessage("out = ");
// out.display();
// rMessage("b = ");
// b.display();
int info;
int kp1 = k+1;
dsteqr_fc ((char *)"I_withEigenvalues",&kp1,out.ele,b.ele,
Q.de_ele, &Q.nRow, workVec.ele, &info,
strlen("I_withEigenvalues"));
if (info < 0) {
rError(" rLanczos :: bad argument " << -info
<< " Q.nRow = " << Q.nRow
<< ": nDim = " << nDim
<< ": kp1 = " << kp1);
} else if (info > 0) {
rMessage(" rLanczos :: cannot converge " << info);
break;
}
// rMessage("out = ");
// out.display();
// rMessage("Q = ");
// Q.display();
min_old = min;
#if 0
min = 1.0e+50;
error = 1.0e+10;
for (int i=0; i<k+1; ++i) {
if (min>out.ele[i]){
min = out.ele[i];
error = Q.de_ele[k+Q.nCol*i];
}
}
#else
// out have eigen values with ascending order.
min = out.ele[0];
error = Q.de_ele[k];
#endif
} // end of 'if ( kk>=sqrt(k) ...)'
// printf("\n");
Lal::let(value,'=',r,'.',r);
beta = sqrt(value);
diagVec2.ele[k] = beta;
++k;
++kk;
} // end of while
// rMessage("k = " << k);
return min - fabs(error*beta);
}
double Lal::getMinEigenValue(DenseMatrix& aMat,
Vector& eigenVec,
Vector& workVec)
{
// aMat is rewritten.
// aMat must be symmetric.
// eigenVec is the space of eigen values
// and needs memory of length aMat.nRow
// workVec is temporary space and needs
// 3*aMat.nRow-1 length memory.
int N = aMat.nRow;
int LWORK, info;
switch (aMat.type) {
case DenseMatrix::DENSE:
LWORK = 3*N-1;
// "N" means that we need not eigen vectors
// "L" means that we refer only lower triangular.
dsyev_fc((char *)"NonVectors",(char *)"Lower",&N,aMat.de_ele,&N,
eigenVec.ele,workVec.ele,&LWORK,&info,
strlen("NonVectors"), strlen("Lower"));
if (info!=0) {
if (info < 0) {
rMessage("getMinEigenValue:: info is mistaken " << info);
} else {
rMessage("getMinEigenValue:: cannot decomposition");
}
exit(0);
return 0.0;
}
return eigenVec.ele[0];
// Eigen values are sorted by ascending order.
break;
case DenseMatrix::COMPLETION:
rError("DenseMatrix:: no support for COMPLETION");
break;
}
return 0.0;
}
double Lal::getOneNorm(Vector& b)
{
double ret = 0.0;
int nDim = b.nDim;
for (int k=0; k<nDim; ++k) {
ret = max(ret,fabs(b.ele[k]));
}
return ret;
}
double Lal::getOneNorm(SparseMatrix& C)
{
double ret = 0.0;
if (C.type == SparseMatrix::SPARSE) {
int size = C.NonZeroCount;
if (C.DataStruct == SparseMatrix::DSarrays) {
for (int i=0; i<size; ++i) {
ret = max(ret,fabs(C.sp_ele[i]));
}
}
else {
for (int i=0; i<size; ++i) {
ret = max(ret,fabs(C.DataS[i].vEle));
}
}
} else if (C.type == SparseMatrix::DENSE) {
int size = C.nRow * C.nCol;
for (int i=0; i<size; ++i) {
ret = max(ret,fabs(C.de_ele[i]));
}
}
return ret;
}
double Lal::getOneNorm(SparseLinearSpace& C)
{
double ret = 0.0;
int SDP_sp_nBlock = C.SDP_sp_nBlock;
int SOCP_sp_nBlock = C.SOCP_sp_nBlock;
int LP_sp_nBlock = C.LP_sp_nBlock;
for (int l=0; l<SDP_sp_nBlock; ++l) {
ret = max(ret,getOneNorm(C.SDP_sp_block[l]));
}
for (int l=0; l<SOCP_sp_nBlock; ++l) {
rError("io:: current version does not support SOCP");
}
for (int l=0; l<LP_sp_nBlock; ++l) {
ret = max(ret, fabs(C.LP_sp_block[l]));
}
return ret;
}
double Lal::getTwoNorm(Vector& b)
{
double ret = 0.0;
let(ret,'=',b,'.',b);
return ret;
}
double Lal::getTwoNorm(DenseMatrix& X)
{
double ret = 0.0;
let(ret,'=',X,'.',X);
return ret;
}
double Lal::getTwoNorm(DenseLinearSpace& X)
{
double ret = 0.0;
int SDP_nBlock = X.SDP_nBlock;
int SOCP_nBlock = X.SOCP_nBlock;
int LP_nBlock = X.LP_nBlock;
for (int l=0; l<SDP_nBlock; ++l) {
ret += getTwoNorm(X.SDP_block[l]);
}
for (int l=0; l<SOCP_nBlock; ++l) {
rError("io:: current version does not support SOCP");
}
for (int l=0; l<LP_nBlock; ++l) {
ret += X.LP_block[l] * X.LP_block[l];
}
return ret;
}
bool Lal::getInnerProduct(double& ret, Vector& aVec, Vector& bVec)
{
int N = aVec.nDim;
if (N != bVec.nDim) {
rError("getInnerProduct:: different memory size");
}
ret = ddot_fc(&N,aVec.ele,&IONE,bVec.ele,&IONE);
return SDPA_SUCCESS;
}
bool Lal::getInnerProduct(double& ret,
BlockVector& aVec, BlockVector& bVec)
{
if (aVec.nBlock != bVec.nBlock) {
rError("getInnerProduct:: different memory size");
}
bool total_judge = SDPA_SUCCESS;
ret = 0.0;
double tmp_ret;
for (int l=0; l<aVec.nBlock; ++l) {
bool judge = getInnerProduct(tmp_ret,aVec.ele[l],bVec.ele[l]);
ret += tmp_ret;
if (judge == SDPA_FAILURE) {
total_judge = SDPA_FAILURE;
}
}
return total_judge;
}
bool Lal::getInnerProduct(double& ret,
DenseMatrix& aMat, DenseMatrix& bMat)
{
if (aMat.nRow!=bMat.nRow || aMat.nCol!=bMat.nCol) {
rError("getInnerProduct:: different memory size");
}
int length;
switch (aMat.type) {
case DenseMatrix::DENSE:
length = aMat.nRow*aMat.nCol;
ret = ddot_fc(&length,aMat.de_ele,&IONE,bMat.de_ele,&IONE);
break;
case DenseMatrix::COMPLETION:
rError("DenseMatrix:: no support for COMPLETION");
break;
}
return SDPA_SUCCESS;
}
bool Lal::getInnerProduct(double& ret,
SparseMatrix& aMat, DenseMatrix& bMat)
{
if (aMat.nRow!=bMat.nRow || aMat.nCol!=bMat.nCol) {
rError("getInnerProduct:: different memory size");
}
int length;
int amari,shou;
switch(aMat.type) {
case SparseMatrix::SPARSE:
// Attension: in SPARSE case, only half elements
// are stored. And bMat must be DENSE case.
ret = 0.0;
// rMessage("aMat.NonZeroCount == " << aMat.NonZeroCount);
#if 0
for (int index=0; index<aMat.NonZeroCount; ++index) {
#if DATA_CAPSULE
int i = aMat.DataS[index].vRow;
int j = aMat.DataS[index].vCol;
double value = aMat.DataS[index].vEle;
#else
int i = aMat.row_index [index];
int j = aMat.column_index[index];
double value = aMat.sp_ele [index];
#endif
// rMessage("i=" << i << " j=" << j);
if (i==j) {
ret+= value*bMat.de_ele[i+bMat.nRow*j];
} else {
ret+= value*(bMat.de_ele[i+bMat.nRow*j]
+ bMat.de_ele[j+bMat.nRow*i]);
}
}
#else
amari = aMat.NonZeroCount % 4;
shou = aMat.NonZeroCount / 4;
for (int index=0; index<amari; ++index) {
#if DATA_CAPSULE
int i = aMat.DataS[index].vRow;
int j = aMat.DataS[index].vCol;
double value = aMat.DataS[index].vEle;
#else
int i = aMat.row_index [index];
int j = aMat.column_index[index];
double value = aMat.sp_ele [index];
#endif
// rMessage("i=" << i << " j=" << j);
if (i==j) {
ret+= value*bMat.de_ele[i+bMat.nRow*j];
} else {
ret+= value*(bMat.de_ele[i+bMat.nRow*j]
+ bMat.de_ele[j+bMat.nRow*i]);
}
}
for (int index=amari,counter = 0;
counter < shou ; ++counter, index+=4) {
#if DATA_CAPSULE
int i1 = aMat.DataS[index].vRow;
int j1 = aMat.DataS[index].vCol;
double value1 = aMat.DataS[index].vEle;
#else
int i1 = aMat.row_index [index];
int j1 = aMat.column_index[index];
double value1 = aMat.sp_ele [index];
#endif
double ret1 = 0.0;
// rMessage("i=" << i << " j=" << j);
if (i1==j1) {
ret1 = value1*bMat.de_ele[i1+bMat.nRow*j1];
} else {
ret1 = value1*(bMat.de_ele[i1+bMat.nRow*j1]
+ bMat.de_ele[j1+bMat.nRow*i1]);
}
#if DATA_CAPSULE
int i2 = aMat.DataS[index+1].vRow;
int j2 = aMat.DataS[index+1].vCol;
double value2 = aMat.DataS[index+1].vEle;
#else
int i2 = aMat.row_index [index+1];
int j2 = aMat.column_index[index+1];
double value2 = aMat.sp_ele [index+1];
#endif
double ret2 = 0.0;
// rMessage("i=" << i << " j=" << j);
if (i2==j2) {
ret2 = value2*bMat.de_ele[i2+bMat.nRow*j2];
} else {
ret2 = value2*(bMat.de_ele[i2+bMat.nRow*j2]
+ bMat.de_ele[j2+bMat.nRow*i2]);
}
#if DATA_CAPSULE
int i3 = aMat.DataS[index+2].vRow;
int j3 = aMat.DataS[index+2].vCol;
double value3 = aMat.DataS[index+2].vEle;
#else
int i3 = aMat.row_index [index+2];
int j3 = aMat.column_index[index+2];
double value3 = aMat.sp_ele [index+2];
#endif
double ret3 = 0.0;
// rMessage("i=" << i << " j=" << j);
if (i3==j3) {
ret3 = value3*bMat.de_ele[i3+bMat.nRow*j3];
} else {
ret3 = value3*(bMat.de_ele[i3+bMat.nRow*j3]
+ bMat.de_ele[j3+bMat.nRow*i3]);
}
#if DATA_CAPSULE
int i4 = aMat.DataS[index+3].vRow;
int j4 = aMat.DataS[index+3].vCol;
double value4 = aMat.DataS[index+3].vEle;
#else
int i4 = aMat.row_index [index+3];
int j4 = aMat.column_index[index+3];
double value4 = aMat.sp_ele [index+3];
#endif
double ret4 = 0.0;
// rMessage("i=" << i << " j=" << j);
if (i4==j4) {
ret4 = value4*bMat.de_ele[i4+bMat.nRow*j4];
} else {
ret4 = value4*(bMat.de_ele[i4+bMat.nRow*j4]
+ bMat.de_ele[j4+bMat.nRow*i4]);
}
// ret += ret1;
// ret += ret2;
// ret += ret3;
// ret += ret4;
ret += (ret1+ret2+ret3+ret4);
}
#endif
break;
case SparseMatrix::DENSE:
length = aMat.nRow*aMat.nCol;
ret = ddot_fc(&length,aMat.de_ele,&IONE,bMat.de_ele,&IONE);
break;
}
return SDPA_SUCCESS;
}
bool Lal::getCholesky(DenseMatrix& retMat,DenseMatrix& aMat)
{
if (retMat.nRow!=aMat.nRow || retMat.nCol!=aMat.nCol
|| retMat.type!=aMat.type) {
rError("getCholesky:: different memory size");
}
int length,info,shou,amari;
switch (retMat.type) {
case DenseMatrix::DENSE:
length = retMat.nRow * retMat.nCol;
dcopy_fc(&length,aMat.de_ele,&IONE,retMat.de_ele,&IONE);
#if 1
dpotrf_fc((char *)"Lower",&retMat.nRow,retMat.de_ele,
&retMat.nRow,&info,strlen("Lower"));
#else
info = choleskyFactorWithAdjust(retMat);
#endif
if (info!=0) {
rMessage("cannot cholesky decomposition");
rMessage("Could you try with smaller gammaStar?");
return SDPA_FAILURE;
}
// Make matrix as lower triangular matrix
#if 0
for (int j=0; j<retMat.nCol; ++j) {
for (int i=0; i<j; ++i) {
retMat.de_ele[i+retMat.nCol*j] = 0.0;
}
}
#else
for (int j=0; j<retMat.nCol; ++j) {
shou = j/4;
amari = j%4;
for (int i=0; i<amari; ++i) {
retMat.de_ele[i+retMat.nCol*j] = 0.0;
}
for (int i=amari,count=0; count < shou; ++count, i+=4) {
retMat.de_ele[i+retMat.nCol*j] = 0.0;
retMat.de_ele[i+1+retMat.nCol*j] = 0.0;
retMat.de_ele[i+2+retMat.nCol*j] = 0.0;
retMat.de_ele[i+3+retMat.nCol*j] = 0.0;
}
}
#endif
break;
case DenseMatrix::COMPLETION:
rError("DenseMatrix:: no support for COMPLETION");
break;
}
return SDPA_SUCCESS;
}
// nakata 2004/12/01
// modified 2008/05/20 "aMat.sp_ele[indexA1] = 0.0;"
// aMat = L L^T
bool Lal::getCholesky(SparseMatrix& aMat, int* diagonalIndex)
{
int nDIM = aMat.nRow;
int indexA1,indexA2,indexB2;
int i,k1,k2,k3;
// double tmp,tmp2;
// int tmp3;
if (aMat.type != SparseMatrix::SPARSE){
rError("Lal::getCholesky aMat is not sparse format");
}
for (i=0 ; i<nDIM ; ++i) {
indexA1 = diagonalIndex[i];
indexA2 = diagonalIndex[i+1];
if (aMat.sp_ele[indexA1]<0.0) {
// printf("aMat(sparse) is not positive definite\n");
aMat.sp_ele[indexA1] = 0.0;
} else {
// inverse diagonal
aMat.sp_ele[indexA1] = 1.0 / sqrt(aMat.sp_ele[indexA1]);
}
for (k1= indexA1+1 ; k1<indexA2 ; ++k1) {
aMat.sp_ele[k1] *= aMat.sp_ele[indexA1];
}
for (k1=indexA1+1 ; k1<indexA2 ; ++k1) {
const double tmp = aMat.sp_ele[k1];
k3 = diagonalIndex[aMat.column_index[k1]];
indexB2 = diagonalIndex[aMat.column_index[k1]+1];
for (k2=k1 ; k2<indexA2 ; ++k2) {
const double tmp2 = aMat.sp_ele[k2];
const double tmp4 = tmp*tmp2;
const int tmp3 = aMat.column_index[k2];
for (; k3<indexB2 ; ++k3) {
if (aMat.column_index[k3] == tmp3){
aMat.sp_ele[k3] -= tmp4;
k3++;
break;
}
}
}
}
}
return true;
}
bool Lal::getInvLowTriangularMatrix(DenseMatrix& retMat,
DenseMatrix& aMat)
{
// Make inverse with refference only to lower triangular.
if (retMat.nRow!=aMat.nRow || retMat.nCol!=aMat.nCol
|| retMat.type!=aMat.type) {
rError("getCholesky:: different memory size");
}
switch (retMat.type) {
case DenseMatrix::DENSE:
retMat.setIdentity();
dtrsm_fc((char *)"Left",(char *)"Lower",
(char *)"NoTraspose",(char *)"NonUnitDiagonal",
&aMat.nRow, &aMat.nCol, &DONE, aMat.de_ele,
&aMat.nRow, retMat.de_ele, &retMat.nRow,
strlen("Left"),strlen("Lower"),
strlen("NoTraspose"),strlen("NonUnitDiagonal"));
break;
case DenseMatrix::COMPLETION:
rError("DenseMatrix:: no support for COMPLETION");
break;
}
return SDPA_SUCCESS;
}
bool Lal::getSymmetrize(DenseMatrix& aMat)
{
switch (aMat.type) {
case DenseMatrix::DENSE:
if (aMat.nRow != aMat.nCol) {
rError("getSymmetrize:: different memory size");
}
for (int index = 0; index<aMat.nRow-1; ++index) {
int index1 = index+index*aMat.nRow + 1;
int index2 = index+(index+1)*aMat.nRow;
int length = aMat.nRow - 1 - index;
// aMat.de_ele[index1] += aMat.de_ele[index2]
daxpy_fc(&length,&DONE,&aMat.de_ele[index2],&aMat.nRow,
&aMat.de_ele[index1],&IONE);
// aMat.de_ele[index1] /= 2.0
double half = 0.5;
dscal_fc(&length,&half,&aMat.de_ele[index1],&IONE);
// aMat.de_ele[index2] = aMat.de_ele[index1]
dcopy_fc(&length,&aMat.de_ele[index1],&IONE,
&aMat.de_ele[index2],&aMat.nRow);
}
break;
case DenseMatrix::COMPLETION:
rError("no support for COMPLETION");
break;
}
return SDPA_SUCCESS;
}
bool Lal::getTranspose(DenseMatrix& retMat,
DenseMatrix& aMat)
{
if (aMat.nRow != aMat.nCol) {
rError("getTranspose:: different memory size");
// Of course, a non-symmetric matrix has
// its transposed matrix,
// but in this algorithm we have to make
// transposed matrix only when symmetric matrix.
}
retMat.copyFrom(aMat);
switch (aMat.type) {
case DenseMatrix::DENSE:
#if 0
for (int i=0; i<aMat.nRow; ++i) {
for (int j=0; j<=i; ++j) {
int index1 = i+aMat.nCol*j;
int index2 = j+aMat.nCol*i;
retMat.de_ele[index1] = aMat.de_ele[index2];
retMat.de_ele[index2] = aMat.de_ele[index1];
}
}
#else
for (int i=0; i<aMat.nRow; ++i) {
int shou = (i+1)/4;
int amari = (i+1)%4;
for (int j=0; j<amari; ++j) {
int index1 = i+aMat.nCol*j;
int index2 = j+aMat.nCol*i;
retMat.de_ele[index1] = aMat.de_ele[index2];
retMat.de_ele[index2] = aMat.de_ele[index1];
}
for (int j=amari,counter =0 ; counter < shou;
++counter, j+=4) {
int index1 = i+aMat.nCol*j;
int index_1 = j+aMat.nCol*i;
retMat.de_ele[index1] = aMat.de_ele[index_1];
retMat.de_ele[index_1] = aMat.de_ele[index1];
int index2 = i+aMat.nCol*(j+1);
int index_2 = (j+1)+aMat.nCol*i;
retMat.de_ele[index2] = aMat.de_ele[index_2];
retMat.de_ele[index_2] = aMat.de_ele[index2];
int index3 = i+aMat.nCol*(j+2);
int index_3 = (j+2)+aMat.nCol*i;
retMat.de_ele[index3] = aMat.de_ele[index_3];
retMat.de_ele[index_3] = aMat.de_ele[index3];
int index4 = i+aMat.nCol*(j+3);
int index_4 = (j+3)+aMat.nCol*i;
retMat.de_ele[index4] = aMat.de_ele[index_4];
retMat.de_ele[index_4] = aMat.de_ele[index4];
}
}
#endif
break;
case DenseMatrix::COMPLETION:
rError("no support for COMPLETION");
break;
}
return SDPA_SUCCESS;
}
int Lal::rdpotf2_(char*uplo, int *n, double *a, int *lda, int *info)
{
int nRow = *lda;
for (int j = 0; j <*n; ++j) {
double ajj = a[j +nRow*j]
- ddot_fc(&j, &a[j], lda, &a[j], lda);
// Here is point.(start)
if (ajj <= (float)-1.0e-6) {
a[j + j * nRow] = ajj;
*info = j+1;
return 0;
}
if (ajj <= (float)1.0e-14) {
ajj = 1e100;
a[j + j * nRow] = ajj;
} else {
ajj = sqrt(ajj);
a[j + j * nRow] = ajj;
}
// Here is point.(end)
if (j < *n-1) {
int i = *n-1 - j;
dgemv_fc((char *)(char *)"No transpose",
&i, &j, &DMONE, &a[j + 1],
lda, &a[j], lda, &DONE,
&a[(j + 1)+nRow*j], &IONE, strlen("No transpose"));
double d1 = 1.0 / ajj;
dscal_fc(&i, &d1, &a[(j + 1)+nRow*j], &IONE);
}
}
return 0;
}
int Lal::rdpotrf_(char *uplo, int *n, double *a, int *lda, int *info)
{
// This funciton makes Cholesky factorization
// in only case Lower Triangular.
// That is, A will be L*L**T, not U**T*U.
int nRow = *lda;
*info = 0;
int nb = ilaenv_fc(&IONE, (char *)"DPOTRF", (char *)"L", n,
&IMONE,&IONE, &IMONE,
strlen("DPOTRF"), strlen("L"));
if (nb <= 1 || nb >= *n) {
// Here is point.
rdpotf2_(uplo, n, a, lda, info);
} else {
for (int j = 0; j < *n; j += nb) {
int jb = min(nb,*n- j);
dsyrk_fc((char *)"Lower", (char *)"No transpose", &jb,
&j, &DMONE, &a[j], lda,
&DONE, &a[j+nRow*j], lda,
strlen("Lower"), strlen("No transpose"));
// Here is point.
rdpotf2_((char *)"Lower", &jb, &a[j+nRow*j], lda, info);
if (*info != 0) {
*info = *info + j - 1;
return 0;
}
if (j + jb <= *n-1) {
int i = *n - j - jb;
dgemm_fc((char *)"No transpose", (char *)"Transpose", &i, &jb,
&j, &DMONE, &a[j + jb], lda, &a[j], lda,
&DONE, &a[(j + jb)+nRow*j], lda,
strlen("No transpose"), strlen("Transpose"));
dtrsm_fc((char *)"Right", (char *)"Lower",
(char *)"Transpose", (char *)"Non-unit",
&i, &jb, &DONE, &a[j+nRow*j], lda,
&a[(j + jb)+nRow*j], lda,
strlen("Right"), strlen("Lower"),
strlen("Transpose"), strlen("Non-unit"));
}
}
}
return 0;
}
bool Lal::choleskyFactorWithAdjust(DenseMatrix& aMat)
{
int info=0;
#if 1
// aMat.display();
TimeStart(START1);
info = rATL_dpotrfL(aMat.nRow, aMat.de_ele,aMat.nRow);
TimeEnd(END1);
// rMessage("Schur colesky ::" << TimeCal(START1,END1));
// aMat.display();
#elif 1
dpotrf_fc("Lower",&aMat.nRow,aMat.de_ele,&aMat.nRow,
&info,strlen("Lower"));
#else
rdpotrf_("Lower",&aMat.nRow,aMat.de_ele,&aMat.nRow,&info);
#endif
if (info < 0) {
rMessage("cholesky argument is wrong " << -info);
} else if (info > 0) {
rMessage("cholesky miss condition :: not positive definite"
<< " :: info = " << info);
rMessage("There are some possibilities.");
rMessage("1. SDPA terminates due to inaccuracy of numerical error");
rMessage("2. The input problem may not have (any) interior-points");
rMessage("3. Input matrices are linearly dependent");
return SDPA_FAILURE;
}
return SDPA_SUCCESS;
#if 0
double ZERO_DETECT = 1.0e-3;
double NONZERO = 1.0e-7;
// no idea version
// if Cholesky factorization failed, then exit soon.
int info = 1; // info == 0 means success
int start = 0;
while (start<aMat.nRow) {
int N = aMat.nRow - start;
dpotf2_("Lower",&N,&aMat.de_ele[start+start*aMat.nRow],
&aMat.nRow,&info);
if (info <=0) {
// rMessage("Cholesky is very nice");
break;
}
start += (info-1); // next target
double wrong = aMat.de_ele[start+start*aMat.nRow];
if (wrong < -ZERO_DETECT) {
rMessage("cholesky adjust position " << start);
rMessage("cannot cholesky decomposition"
" with adjust " << wrong);
return SDPA_FAILURE;
}
aMat.de_ele[start+start*aMat.nRow] = NONZERO;
if (start<aMat.nRow-1) {
// improve the right down element of 0
for (int j=1; j<=aMat.nRow-1-start; ++j) {
double& migi = aMat.de_ele[start+(start+j)*aMat.nRow];
double& shita = aMat.de_ele[(start+j)+start*aMat.nRow];
double& mishi = aMat.de_ele[(start+j)+(start+j)*aMat.nRow];
// rMessage(" mishi = " << mishi);
if (mishi < NONZERO) {
// rMessage(" mishi < NONZERO ");
mishi = NONZERO;
migi = NONZERO * 0.1;
shita = NONZERO * 0.1;
} else if (migi*shita > NONZERO*mishi) {
// rMessage(" migi*migi > NONZERO*mishi ");
migi = sqrt(NONZERO*mishi) * 0.99;
shita = sqrt(NONZERO*mishi) * 0.99;
}
}
}
rMessage("cholesky adjust position " << start);
}
if (info < 0) {
rError("argument is something wrong " << info);
}
return SDPA_SUCCESS;
#endif
}
bool Lal::solveSystems(Vector& xVec,
DenseMatrix& aMat, Vector& bVec)
{
// aMat must have done Cholesky factorized.
if (aMat.nCol!=xVec.nDim || aMat.nRow!=bVec.nDim
|| aMat.nRow!=aMat.nCol) {
rError("solveSystems:: different memory size");
}
if (aMat.type!=DenseMatrix::DENSE) {
rError("solveSystems:: matrix type must be DENSE");
}
xVec.copyFrom(bVec);
dtrsv_fc((char *)"Lower", (char *)"NoTranspose", (char *)"NonUnit",
&aMat.nRow, aMat.de_ele, &aMat.nCol, xVec.ele,&IONE,
strlen("Lower"), strlen("NoTranspose"), strlen("NonUnit"));
dtrsv_fc((char *)"Lower", (char *)"Transpose", (char *)"NonUnit",
&aMat.nRow, aMat.de_ele, &aMat.nCol, xVec.ele,&IONE,
strlen("Lower"), strlen("Transpose"), strlen("NonUnit"));
return SDPA_SUCCESS;
}
// nakata 2004/12/01
bool Lal::solveSystems(Vector& xVec,
SparseMatrix& aMat, Vector& bVec)
{
#define TUNEUP 0
#if TUNEUP
if (aMat.nCol!=xVec.nDim || aMat.nRow!=bVec.nDim
|| aMat.nRow!=aMat.nCol) {
printf("A.row:%d A.col:%d x.row:%d b.row:%d\n",
aMat.nCol,aMat.nRow,xVec.nDim ,bVec.nDim);
rError("solveSystems(sparse):: different memory size");
}
int length;
int amari,shou,counter;
switch(aMat.type) {
case SparseMatrix::SPARSE:
#endif
// Attension: in SPARSE case, only half elements
// are stored. And bMat must be DENSE case.
// rMessage("aMat.NonZeroCount == " << aMat.NonZeroCount);
xVec.copyFrom(bVec);
#if TUNEUP
shou = aMat.NonZeroCount / 4;
amari = aMat.NonZeroCount % 4;
int i,j;
double value;
for (int index=0; index<amari; ++index) {
#if DATA_CAPSULE
int i = aMat.DataS[index].vRow;
int j = aMat.DataS[index].vCol;
double value = aMat.DataS[index].vEle;
#else
int i = aMat.row_index [index];
int j = aMat.column_index[index];
double value = aMat.sp_ele [index];
#endif
// rMessage("i=" << i << " j=" << j);
if (i==j) {
xVec.ele[i] *= value;
} else {
xVec.ele[j] -= value * xVec.ele[i];
}
}
for (int index=amari, counter=0; counter<shou; ++counter, index+=4) {
#if DATA_CAPSULE
i = aMat.DataS[index].vRow;
j = aMat.DataS[index].vCol;
value = aMat.DataS[index].vEle;
#else
i = aMat.row_index [index];
j = aMat.column_index[index];
value = aMat.sp_ele [index];
#endif
if (i==j) {
xVec.ele[i] *= value;
} else {
xVec.ele[j] -= value * xVec.ele[i];
}
#if DATA_CAPSULE
i = aMat.DataS[index+1].vRow;
j = aMat.DataS[index+1].vCol;
value = aMat.DataS[index+1].vEle;
#else
i = aMat.row_index [index+1];
j = aMat.column_index[index+1];
value = aMat.sp_ele [index+1];
#endif
if (i==j) {
xVec.ele[i] *= value;
} else {
xVec.ele[j] -= value * xVec.ele[i];
}
#if DATA_CAPSULE
i = aMat.DataS[index+2].vRow;
j = aMat.DataS[index+2].vCol;
value = aMat.DataS[index+2].vEle;
#else
i = aMat.row_index [index+2];
j = aMat.column_index[index+2];
value = aMat.sp_ele [index+2];
#endif
if (i==j) {
xVec.ele[i] *= value;
} else {
xVec.ele[j] -= value * xVec.ele[i];
}
#if DATA_CAPSULE
i = aMat.DataS[index+3].vRow;
j = aMat.DataS[index+3].vCol;
value = aMat.DataS[index+3].vEle;
#else
i = aMat.row_index [index+3];
j = aMat.column_index[index+3];
value = aMat.sp_ele [index+3];
#endif
if (i==j) {
xVec.ele[i] *= value;
} else {
xVec.ele[j] -= value * xVec.ele[i];
}
}
for (int index=aMat.NonZeroCount - 1;
index >= aMat.NonZeroCount - amari; --index) {
#if DATA_CAPSULE
i = aMat.DataS[index].vRow;
j = aMat.DataS[index].vCol;
value = aMat.DataS[index].vEle;
#else
i = aMat.row_index [index];
j = aMat.column_index[index];
value = aMat.sp_ele [index];
#endif
// rMessage("i=" << i << " j=" << j);
if (i==j) {
xVec.ele[i] *= value;
} else {
xVec.ele[j] -= value * xVec.ele[i];
}
}
for (int index=aMat.NonZeroCount - amari - 1,counter=0 ;
counter<shou ; ++counter,index-=4) {
#if DATA_CAPSULE
i = aMat.DataS[index].vRow;
j = aMat.DataS[index].vCol;
value = aMat.DataS[index].vEle;
#else
i = aMat.row_index [index];
j = aMat.column_index[index];