void solveSingleScatterers(LSMSSystemParameters &lsms, LocalTypeInfo &local,
std::vector<Matrix<Real> > &vr, Complex energy,
std::vector<NonRelativisticSingleScattererSolution> &solution,int iie)
{
// ========================== SINGLE SCATTERER STUFF
Complex prel=std::sqrt(energy*(1.0+energy*c2inv));
Complex pnrel=std::sqrt(energy);
for(int i=0; i<local.num_local; i++)
solution[i].init(lsms,local.atom[i],&local.tmatStore(iie*local.blkSizeTmatStore,i));
if(lsms.nrelv>0) prel=pnrel;
if(local.atom.size()>solution.size()) solution.resize(local.atom.size());
// this is not ready for multithreading yet
// else: pragma omp parallel for
// if(lsms.global.iprint>=0) printf("calculate single scatterer solutions.\n");
for(int i=0; i<local.atom.size(); i++)
{
// if(lsms.global.iprint>=1) printf("calc single scatterer %d.%d\n",comm.rank,i);
//printf("calc single scatterer atom no. = %d\n",i);
calculateSingleScattererSolution(lsms,local.atom[i],vr[i],energy,prel,pnrel,solution[i]);
// calculate pmat_m (needed for tr_pxtau)
int kkrsz=local.atom[i].kkrsz;
int kkrszsqr=kkrsz*kkrsz;
int info;
int ipvt[kkrsz];
if(lsms.n_spin_cant==2 && lsms.nrel_rel==0)
{
local.atom[i].pmat_m[iie].resize(kkrsz,kkrsz);
Complex *pmat = new Complex[kkrszsqr];
Complex *wbig = new Complex[kkrszsqr];
Complex *pmat_m_ptr=&local.atom[i].pmat_m[iie](0,0);
cblas_zcopy(kkrszsqr,&solution[i].tmat_l(0,0,0),1,pmat,1);
cblas_zcopy(kkrszsqr,&solution[i].tmat_l(0,0,1),1,pmat_m_ptr,1);
zgetrf_(&kkrsz,&kkrsz,pmat_m_ptr,&kkrsz,ipvt,&info);
zgetri_(&kkrsz,pmat_m_ptr,&kkrsz,ipvt,wbig,&kkrszsqr,&info);
// -------------------------------------------------------------
zgetrf_(&kkrsz,&kkrsz,pmat,&kkrsz,ipvt,&info);
zgetri_(&kkrsz,pmat,&kkrsz,ipvt,wbig,&kkrszsqr,&info);
for(int j=0; j<kkrszsqr; j++) pmat_m_ptr[j]-=pmat[j];
delete [] wbig;
delete [] pmat;
}
}
// ========= END SINGLE SCATTERER STUFF ======================
}
DLLEXPORT int z_lu_factor(int m, doublecomplex a[], int ipiv[])
{
int info = 0;
zgetrf_(&m,&m,a,&m,ipiv,&info);
for(int i = 0; i < m; ++i ){
ipiv[i] -= 1;
}
return info;
}
DLLEXPORT MKL_INT z_lu_factor(MKL_INT m, MKL_Complex16 a[], MKL_INT ipiv[])
{
MKL_INT info = 0;
zgetrf_(&m,&m,a,&m,ipiv,&info);
for(MKL_INT i = 0; i < m; ++i ){
ipiv[i] -= 1;
}
return info;
}
void QuasiNewton<dcomplex>::symmNonHerDiag(int NTrial, ostream &output){
char JOBVL = 'N';
char JOBVR = 'V';
int TwoNTrial = 2*NTrial;
int *IPIV = new int[TwoNTrial];
int INFO;
ComplexCMMap SSuper(this->SSuperMem, TwoNTrial,TwoNTrial);
ComplexCMMap ASuper(this->ASuperMem, TwoNTrial,TwoNTrial);
ComplexCMMap SCPY(this->SCPYMem, TwoNTrial,TwoNTrial);
ComplexCMMap NHrProd(this->NHrProdMem,TwoNTrial,TwoNTrial);
SCPY = SSuper; // Copy of original matrix to use for re-orthogonalization
// Invert the metric (maybe not needed?)
zgetrf_(&TwoNTrial,&TwoNTrial,this->SSuperMem,&TwoNTrial,IPIV,&INFO);
zgetri_(&TwoNTrial,this->SSuperMem,&TwoNTrial,IPIV,this->WORK,&this->LWORK,
&INFO);
delete [] IPIV;
NHrProd = SSuper * ASuper;
// cout << "PROD" << endl << NHrProd << endl;
zgeev_(&JOBVL,&JOBVR,&TwoNTrial,NHrProd.data(),&TwoNTrial,this->ERMem,
this->SSuperMem,&TwoNTrial,this->SSuperMem,&TwoNTrial,
this->WORK,&this->LWORK,this->RWORK,&INFO);
// Sort eigensystem using Bubble Sort
ComplexVecMap E(this->ERMem,TwoNTrial);
ComplexCMMap VR(this->SSuperMem,TwoNTrial,TwoNTrial);
// cout << endl << ER << endl;
this->eigSrt(VR,E);
// cout << endl << ER << endl;
// Grab the "positive paired" roots (throw away other element of the pair)
this->ERMem += NTrial;
new (&E ) ComplexVecMap(this->ERMem,NTrial);
new (&SSuper) ComplexCMMap(this->SSuperMem+2*NTrial*NTrial,2*NTrial,NTrial);
RealVecMap ER(this->RealEMem,NTrial);
ER = E.real();
/*
* Re-orthogonalize the eigenvectors with respect to the metric S(R)
* because DSYGV orthogonalzies the vectors with respect to E(R)
* because we solve the opposite problem.
*
* Gramm-Schmidt
*/
this->metBiOrth(SSuper,SCPY);
// Separate the eigenvectors into gerade and ungerade parts
ComplexCMMap XTSigmaR(this->XTSigmaRMem,NTrial,NTrial);
ComplexCMMap XTSigmaL(this->XTSigmaLMem,NTrial,NTrial);
XTSigmaR = SSuper.block(0, 0,NTrial,NTrial);
XTSigmaL = SSuper.block(NTrial,0,NTrial,NTrial);
// CErr();
}
// Interface to lapack routine zgetrf
// mm: nrow of A
// nn: ncol of A
void lapack_zgetrf(int mm, int nn, dcmplx *AA, int *ipiv)
{
int lda, info;
lda = (1 > mm) ? 1 : mm;
zgetrf_(&mm, &nn, AA, &lda, ipiv, &info);
check(info == 0, "Failed zgetrf, info = %d", info);
return;
error:
abort();
}
DLLEXPORT int z_lu_inverse(int n, doublecomplex a[], doublecomplex work[], int lwork)
{
int* ipiv = new int[n];
int info = 0;
zgetrf_(&n,&n,a,&n,ipiv,&info);
if (info != 0){
delete[] ipiv;
return info;
}
zgetri_(&n,a,&n,ipiv,work,&lwork,&info);
delete[] ipiv;
return info;
}
DLLEXPORT MKL_INT z_lu_inverse(MKL_INT n, MKL_Complex16 a[], MKL_Complex16 work[], MKL_INT lwork)
{
MKL_INT* ipiv = new MKL_INT[n];
MKL_INT info = 0;
zgetrf_(&n,&n,a,&n,ipiv,&info);
if (info != 0){
delete[] ipiv;
return info;
}
zgetri_(&n,a,&n,ipiv,work,&lwork,&info);
delete[] ipiv;
return info;
}
bool inv(const cmat &X, cmat &Y)
{
// it_assert1(X.rows() == X.cols(), "inv: matrix is not square");
int m = X.rows(), info, lwork;
lwork = m; // may be choosen better
ivec p(m);
Y = X;
cvec work(lwork);
zgetrf_(&m, &m, Y._data(), &m, p._data(), &info); // LU-factorization
if (info!=0)
return false;
zgetri_(&m, Y._data(), &m, p._data(), work._data(), &lwork, &info);
return (info==0);
}
matrix LU(const matrix& A)
{ static StopWatch watch("LU(matrix)");
watch.start();
// Perform LU decomposition
int N = A.nRows();
myassert(N > 0);
myassert(N == A.nCols());
matrix LU(A); //destructible copy
int ldA = A.nRows(); //leading dimension
std::vector<int> iPivot(N); //pivot info
int info; //error code in return
//LU decomposition (in place):
zgetrf_(&N, &N, LU.data(), &ldA, iPivot.data(), &info);
if(info<0) { logPrintf("Argument# %d to LAPACK LU decomposition routine ZGETRF is invalid.\n", -info); stackTraceExit(1); }
watch.stop();
return LU;
}
//! build and factorize "complex" matrix
//! \param alpha : we add alpha*I to the real part of the Jacobian.
//! \param beta : we add alpha*I to the imaginary part of the Jacobian.
//! \param Jac the jacobian.
inline void decomc(double alpha,double beta,const MatrixReal& Jac)
{
for(int j=1;j<=n;j++)
#include "Ivdep.hpp"
for(int i=1;i<=n;i++)
E2R.set(i,j,-Jac(i,j));
#include "Ivdep.hpp"
for(int i=1;i<=n;i++)
{
E2R.Re(i,i)+=alpha;
E2R.Im(i,i)=beta;
}
int nn=n,info;
zgetrf_(&nn,&nn,&E2R,&nn,&(ipivc[0]),&info);
if(info!=0)
throw OdesException("odes::Matrices::decomc zgetrf,info=",info);
}
void zinverma ( doubleComplex* in, doubleComplex* out, int leadDimIn )
{
int info = 0 ;
int* vectPivot = (int*) malloc ( sizeof(int) * (unsigned int)( leadDimIn) );
doubleComplex* work = (doubleComplex*) malloc ( sizeof(doubleComplex) * (unsigned int) (leadDimIn*leadDimIn) );
int i = 0 ;
for ( i = 0 ; i < leadDimIn*leadDimIn ; i ++)
{
out[i] = in[i] ;
}
zgetrf_ ( &leadDimIn, &leadDimIn, out, &leadDimIn, vectPivot, &info );
zgetri_ ( &leadDimIn, out, &leadDimIn , vectPivot, work , &leadDimIn , &info );
free(vectPivot);
free(work);
}
int
mad_cmat_det (const cnum_t x[], cnum_t *r, ssz_t n)
{
CHKX;
const int nn=n;
int info=0, ipiv[n];
mad_alloc_tmp(cnum_t, a, n*n);
mad_cvec_copy(x, a, n*n);
zgetrf_(&nn, &nn, a, &nn, ipiv, &info);
if (info < 0) error("invalid input argument");
int perm = 0;
cnum_t det = 1;
for (int i=0, j=0; i < n; i++, j+=n+1)
det *= a[j], perm += ipiv[i] != i+1;
mad_free_tmp(a);
*r = perm & 1 ? -det : det;
return info;
}
DLLEXPORT MKL_INT z_lu_solve(MKL_INT n, MKL_INT nrhs, MKL_Complex16 a[], MKL_Complex16 b[])
{
MKL_Complex16* clone = new MKL_Complex16[n*n];
std::memcpy(clone, a, n*n*sizeof(MKL_Complex16));
MKL_INT* ipiv = new MKL_INT[n];
MKL_INT info = 0;
zgetrf_(&n, &n, clone, &n, ipiv, &info);
if (info != 0){
delete[] ipiv;
delete[] clone;
return info;
}
char trans ='N';
zgetrs_(&trans, &n, &nrhs, clone, &n, ipiv, b, &n, &info);
delete[] ipiv;
delete[] clone;
return info;
}
DLLEXPORT int z_lu_solve(int n, int nrhs, doublecomplex a[], doublecomplex b[])
{
doublecomplex* clone = new doublecomplex[n*n];
memcpy(clone, a, n*n*sizeof(doublecomplex));
int* ipiv = new int[n];
int info = 0;
zgetrf_(&n, &n, clone, &n, ipiv, &info);
if (info != 0){
delete[] ipiv;
delete[] clone;
return info;
}
char trans ='N';
zgetrs_(&trans, &n, &nrhs, clone, &n, ipiv, b, &n, &info);
delete[] ipiv;
delete[] clone;
return info;
}
matrix inv(const matrix& A)
{ static StopWatch watch("inv(matrix)");
watch.start();
int N = A.nRows();
myassert(N > 0);
myassert(N == A.nCols());
matrix invA(A); //destructible copy
int ldA = A.nRows(); //leading dimension
std::vector<int> iPivot(N); //pivot info
int info; //error code in return
//LU decomposition (in place):
zgetrf_(&N, &N, invA.data(), &ldA, iPivot.data(), &info);
if(info<0) { logPrintf("Argument# %d to LAPACK LU decomposition routine ZGETRF is invalid.\n", -info); stackTraceExit(1); }
if(info>0) { logPrintf("LAPACK LU decomposition routine ZGETRF found input matrix to be singular at the %d'th step.\n", info); stackTraceExit(1); }
//Compute inverse in place:
int lWork = (64+1)*N;
std::vector<complex> work(lWork);
zgetri_(&N, invA.data(), &ldA, iPivot.data(), work.data(), &lWork, &info);
if(info<0) { logPrintf("Argument# %d to LAPACK matrix inversion routine ZGETRI is invalid.\n", -info); stackTraceExit(1); }
if(info>0) { logPrintf("LAPACK matrix inversion routine ZGETRI found input matrix to be singular at the %d'th step.\n", info); stackTraceExit(1); }
watch.stop();
return invA;
}
/**
* <p>Same as {@link dlm_invert_gel} but for complex input</p>
*
*/
INT16 dlm_invert_gelC(COMPLEX64* A, INT32 nXA, COMPLEX64* lpnDet) {
integer n = (integer) nXA;
integer c__1 = 1;
integer c_n1 = -1;
integer info = 0;
integer* ipiv = dlp_calloc(n, sizeof(integer));
void* work = NULL;
char opts[1] = { ' ' };
extern integer ilaenv_(integer*,char*,char*,integer*,integer*,integer*,integer*,ftnlen,ftnlen);
#ifdef __MAX_TYPE_32BIT
extern int cgetrf_(integer*,integer*,complex*,integer*,integer*,integer*);
extern int cgetri_(integer*,complex*,integer*,integer*,complex*,integer*,integer*);
char name[8] = { 'C', 'G', 'E', 'T', 'R', 'I' };
integer lwork = n * ilaenv_(&c__1, name, opts, &n, &c_n1, &c_n1, &c_n1, (ftnlen)6, (ftnlen)1);
work = dlp_calloc(lwork, sizeof(complex));
if(!ipiv || !work) return ERR_MEM;
cgetrf_(&n,&n,(complex*)A,&n,ipiv,&info);
if(lpnDet != NULL) *lpnDet = (info > 0) ? CMPLX(0.0) : dlm_get_det_trfC(A, nXA, ipiv);
cgetri_(&n,(complex*)A,&n,ipiv,work,&lwork,&info);
#else
extern int zgetrf_(integer*,integer*,doublecomplex*,integer*,integer*,integer*);
extern int zgetri_(integer*,doublecomplex*,integer*,integer*,doublecomplex*,integer*,integer*);
char name[8] = { 'Z', 'G', 'E', 'T', 'R', 'I' };
integer lwork = n * ilaenv_(&c__1, name, opts, &n, &c_n1, &c_n1, &c_n1, (ftnlen) 6, (ftnlen) 1);
work = dlp_calloc(lwork, sizeof(doublecomplex));
if (!ipiv || !work) return ERR_MEM;
zgetrf_(&n, &n, (doublecomplex*) A, &n, ipiv, &info);
if (lpnDet != NULL) *lpnDet = (info > 0) ? CMPLX(0.0) : dlm_get_det_trfC(A, nXA, ipiv);
zgetri_(&n, (doublecomplex*) A, &n, ipiv, work, &lwork, &info);
#endif
dlp_free(work);
dlp_free(ipiv);
return (info == 0) ? O_K : NOT_EXEC;
}
/* Subroutine */ int zgesv_(integer *n, integer *nrhs, doublecomplex *a,
integer *lda, integer *ipiv, doublecomplex *b, integer *ldb, integer *
info)
{
/* System generated locals */
integer a_dim1, a_offset, b_dim1, b_offset, i__1;
/* Local variables */
extern /* Subroutine */ int xerbla_(char *, integer *), zgetrf_(
integer *, integer *, doublecomplex *, integer *, integer *,
integer *), zgetrs_(char *, integer *, integer *, doublecomplex *,
integer *, integer *, doublecomplex *, integer *, integer *);
/* -- LAPACK driver routine (version 3.1) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* ZGESV computes the solution to a complex system of linear equations */
/* A * X = B, */
/* where A is an N-by-N matrix and X and B are N-by-NRHS matrices. */
/* The LU decomposition with partial pivoting and row interchanges is */
/* used to factor A as */
/* A = P * L * U, */
/* where P is a permutation matrix, L is unit lower triangular, and U is */
/* upper triangular. The factored form of A is then used to solve the */
/* system of equations A * X = B. */
/* Arguments */
/* ========= */
/* N (input) INTEGER */
/* The number of linear equations, i.e., the order of the */
/* matrix A. N >= 0. */
/* NRHS (input) INTEGER */
/* The number of right hand sides, i.e., the number of columns */
/* of the matrix B. NRHS >= 0. */
/* A (input/output) COMPLEX*16 array, dimension (LDA,N) */
/* On entry, the N-by-N coefficient matrix A. */
/* On exit, the factors L and U from the factorization */
/* A = P*L*U; the unit diagonal elements of L are not stored. */
/* LDA (input) INTEGER */
/* The leading dimension of the array A. LDA >= max(1,N). */
/* IPIV (output) INTEGER array, dimension (N) */
/* The pivot indices that define the permutation matrix P; */
/* row i of the matrix was interchanged with row IPIV(i). */
/* B (input/output) COMPLEX*16 array, dimension (LDB,NRHS) */
/* On entry, the N-by-NRHS matrix of right hand side matrix B. */
/* On exit, if INFO = 0, the N-by-NRHS solution matrix X. */
/* LDB (input) INTEGER */
/* The leading dimension of the array B. LDB >= max(1,N). */
/* INFO (output) INTEGER */
/* = 0: successful exit */
/* < 0: if INFO = -i, the i-th argument had an illegal value */
/* > 0: if INFO = i, U(i,i) is exactly zero. The factorization */
/* has been completed, but the factor U is exactly */
/* singular, so the solution could not be computed. */
/* ===================================================================== */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Test the input parameters. */
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
--ipiv;
b_dim1 = *ldb;
b_offset = 1 + b_dim1;
b -= b_offset;
/* Function Body */
*info = 0;
if (*n < 0) {
*info = -1;
} else if (*nrhs < 0) {
*info = -2;
} else if (*lda < max(1,*n)) {
*info = -4;
} else if (*ldb < max(1,*n)) {
*info = -7;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("ZGESV ", &i__1);
return 0;
}
/* Compute the LU factorization of A. */
zgetrf_(n, n, &a[a_offset], lda, &ipiv[1], info);
if (*info == 0) {
/* Solve the system A*X = B, overwriting B with X. */
zgetrs_("No transpose", n, nrhs, &a[a_offset], lda, &ipiv[1], &b[
b_offset], ldb, info);
}
return 0;
/* End of ZGESV */
} /* zgesv_ */
/* Main program */
int main() {
/* Locals */
int n = N, info,i,j;
int iter = 1;
/* Local arrays */
static complex A2[N][N];
static complex B2[N][N];
static complex A[N][N];
static complex U[N][N];
static complex b[N];
srand (1337);
static int ipiv[N];
int max = 0;
int min = 0;
int mu = 3;
int ml = 3;
int md = ml+mu+1;
complex sumA = 0;
complex sumU = 0;
complex ratio = 0;
//Initialize random band matrix
for (i=0;i<n;i++){
for (j=0; j<n; j++){
A2[i][j]=0;
B2[i][j]=0;
U[i][j]=0;
}
}
for (j=0;j<n;j++){
max = 0 > j-mu ? 0 : j-mu ;
min = n < j+ml+1 ? n : j+ml+1 ;
for(i=max;i<min;i++){
A2[i][j] = ((1 - ( 20.0 * rand() / ( RAND_MAX + 1.0 ) )),(1 - ( 20.0 * rand() / ( RAND_MAX + 1.0 ))));
}
}
for (i=0;i<n;i++){
for (j=0;j<n;j++){
A[i][j]=A2[i][j];
}
}
for (i=0;i<n;i++){
U[i][i]=1;
}
/// B2(ML+MU+1+i-j,j) = A(i,j) for max(1,j-MU)<=i<=min(N,j+ML)
for (j=0;j<n;j++){
max = (0 < j-mu) ? j-mu : 0 ;
min = (n < j+ml+1) ? n : j+ml+1 ;
for(i=max;i<min;i++){
B2[j][md+i-j-1]= A[j][i];
}
}
printf( "Matrix A\n" );
for( i = 0; i < n; i++ ) {
for( j = 0; j < n; j++ ) printf( " (%6.2f ,%6.2f) ", A[j][i] );
printf( "\n" );
}
printf( "Compressed A\n" );
for( i = 0; i < n; i++ ) {
for( j = 0; j < n; j++ ) printf( " (%6.2f, %6.2f)", B2[j][i] );
printf( "\n" );
}
printf( "Enter General Factor\n" );
for (i=0;i<iter;i++){
// printf( "Enter General Factor\n" );
zgetrf_(&n, &n, A2, &n, ipiv, &info);
// printf( "%d",info );
// printf( "Enter Inversion\n" );
zgetri_( &n, A2, &n, ipiv, b, &n, &info );
// printf( "%d",info );
// printf( "Exit inversion\n" );
}
printf( "\nExit inversion\n" );
printf( "Entering Banded Solve\n" );
for (i=0;i<iter;i++){
zgbsv_( &n, &ml, &mu, &n, B2, &n, ipiv, U, &n, &info );
// printf( "%d",info );
}
printf( "Exited Banded Solve\n" );
for (i=0;i<N;i++){
for (j=0;j<N;j++){
sumA = A2[j][i]+sumA;
sumU = U[j][i]+sumU;
}
}
ratio = sumA/sumU;
printf( "Accuracy - %f\n",ratio );
printf( "%d\n",info );
printf( "Inversed A\n" );
for( i = 0; i < n; i++ ) {
for( j = 0; j < n; j++ ) printf( " (%6.8f, %6.2f)", A2[j][i] );
printf( "\n" );
}
printf( "Inversed A (solve)\n" );
for( i = 0; i < n; i++ ) {
for( j = 0; j < n; j++ ) printf( " (%6.8f, %6.2f)", U[j][i] );
printf( "\n" );
}
exit( 0 );
}
/* Subroutine */ int zerrge_(char *path, integer *nunit)
{
/* System generated locals */
integer i__1;
doublereal d__1, d__2;
doublecomplex z__1;
/* Builtin functions */
integer s_wsle(cilist *), e_wsle(void);
/* Subroutine */ int s_copy(char *, char *, ftnlen, ftnlen);
/* Local variables */
doublecomplex a[16] /* was [4][4] */, b[4];
integer i__, j;
doublereal r__[4];
doublecomplex w[8], x[4];
char c2[2];
doublereal r1[4], r2[4];
doublecomplex af[16] /* was [4][4] */;
integer ip[4], info;
doublereal anrm, ccond, rcond;
extern /* Subroutine */ int zgbtf2_(integer *, integer *, integer *,
integer *, doublecomplex *, integer *, integer *, integer *),
zgetf2_(integer *, integer *, doublecomplex *, integer *, integer
*, integer *), alaesm_(char *, logical *, integer *);
extern logical lsamen_(integer *, char *, char *);
extern /* Subroutine */ int zgbcon_(char *, integer *, integer *, integer
*, doublecomplex *, integer *, integer *, doublereal *,
doublereal *, doublecomplex *, doublereal *, integer *),
chkxer_(char *, integer *, integer *, logical *, logical *), zgecon_(char *, integer *, doublecomplex *, integer *,
doublereal *, doublereal *, doublecomplex *, doublereal *,
integer *), zgbequ_(integer *, integer *, integer *,
integer *, doublecomplex *, integer *, doublereal *, doublereal *,
doublereal *, doublereal *, doublereal *, integer *), zgbrfs_(
char *, integer *, integer *, integer *, integer *, doublecomplex
*, integer *, doublecomplex *, integer *, integer *,
doublecomplex *, integer *, doublecomplex *, integer *,
doublereal *, doublereal *, doublecomplex *, doublereal *,
integer *), zgbtrf_(integer *, integer *, integer *,
integer *, doublecomplex *, integer *, integer *, integer *),
zgeequ_(integer *, integer *, doublecomplex *, integer *,
doublereal *, doublereal *, doublereal *, doublereal *,
doublereal *, integer *), zgerfs_(char *, integer *, integer *,
doublecomplex *, integer *, doublecomplex *, integer *, integer *,
doublecomplex *, integer *, doublecomplex *, integer *,
doublereal *, doublereal *, doublecomplex *, doublereal *,
integer *), zgetrf_(integer *, integer *, doublecomplex *,
integer *, integer *, integer *), zgetri_(integer *,
doublecomplex *, integer *, integer *, doublecomplex *, integer *,
integer *), zgbtrs_(char *, integer *, integer *, integer *,
integer *, doublecomplex *, integer *, integer *, doublecomplex *,
integer *, integer *), zgetrs_(char *, integer *,
integer *, doublecomplex *, integer *, integer *, doublecomplex *,
integer *, integer *);
/* Fortran I/O blocks */
static cilist io___1 = { 0, 0, 0, 0, 0 };
/* -- LAPACK test routine (version 3.1) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* ZERRGE tests the error exits for the COMPLEX*16 routines */
/* for general matrices. */
/* Arguments */
/* ========= */
/* PATH (input) CHARACTER*3 */
/* The LAPACK path name for the routines to be tested. */
/* NUNIT (input) INTEGER */
/* The unit number for output. */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. Local Arrays .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Scalars in Common .. */
/* .. */
/* .. Common blocks .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
infoc_1.nout = *nunit;
io___1.ciunit = infoc_1.nout;
s_wsle(&io___1);
e_wsle();
s_copy(c2, path + 1, (ftnlen)2, (ftnlen)2);
/* Set the variables to innocuous values. */
for (j = 1; j <= 4; ++j) {
for (i__ = 1; i__ <= 4; ++i__) {
i__1 = i__ + (j << 2) - 5;
d__1 = 1. / (doublereal) (i__ + j);
d__2 = -1. / (doublereal) (i__ + j);
z__1.r = d__1, z__1.i = d__2;
a[i__1].r = z__1.r, a[i__1].i = z__1.i;
i__1 = i__ + (j << 2) - 5;
d__1 = 1. / (doublereal) (i__ + j);
d__2 = -1. / (doublereal) (i__ + j);
z__1.r = d__1, z__1.i = d__2;
af[i__1].r = z__1.r, af[i__1].i = z__1.i;
/* L10: */
}
i__1 = j - 1;
b[i__1].r = 0., b[i__1].i = 0.;
r1[j - 1] = 0.;
r2[j - 1] = 0.;
i__1 = j - 1;
w[i__1].r = 0., w[i__1].i = 0.;
i__1 = j - 1;
x[i__1].r = 0., x[i__1].i = 0.;
ip[j - 1] = j;
/* L20: */
}
infoc_1.ok = TRUE_;
/* Test error exits of the routines that use the LU decomposition */
/* of a general matrix. */
if (lsamen_(&c__2, c2, "GE")) {
/* ZGETRF */
s_copy(srnamc_1.srnamt, "ZGETRF", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
zgetrf_(&c_n1, &c__0, a, &c__1, ip, &info);
chkxer_("ZGETRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
zgetrf_(&c__0, &c_n1, a, &c__1, ip, &info);
chkxer_("ZGETRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
zgetrf_(&c__2, &c__1, a, &c__1, ip, &info);
chkxer_("ZGETRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* ZGETF2 */
s_copy(srnamc_1.srnamt, "ZGETF2", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
zgetf2_(&c_n1, &c__0, a, &c__1, ip, &info);
chkxer_("ZGETF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
zgetf2_(&c__0, &c_n1, a, &c__1, ip, &info);
chkxer_("ZGETF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
zgetf2_(&c__2, &c__1, a, &c__1, ip, &info);
chkxer_("ZGETF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* ZGETRI */
s_copy(srnamc_1.srnamt, "ZGETRI", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
zgetri_(&c_n1, a, &c__1, ip, w, &c__1, &info);
chkxer_("ZGETRI", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
zgetri_(&c__2, a, &c__1, ip, w, &c__2, &info);
chkxer_("ZGETRI", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 6;
zgetri_(&c__2, a, &c__2, ip, w, &c__1, &info);
chkxer_("ZGETRI", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* ZGETRS */
s_copy(srnamc_1.srnamt, "ZGETRS", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
zgetrs_("/", &c__0, &c__0, a, &c__1, ip, b, &c__1, &info);
chkxer_("ZGETRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
zgetrs_("N", &c_n1, &c__0, a, &c__1, ip, b, &c__1, &info);
chkxer_("ZGETRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
zgetrs_("N", &c__0, &c_n1, a, &c__1, ip, b, &c__1, &info);
chkxer_("ZGETRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
zgetrs_("N", &c__2, &c__1, a, &c__1, ip, b, &c__2, &info);
chkxer_("ZGETRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 8;
zgetrs_("N", &c__2, &c__1, a, &c__2, ip, b, &c__1, &info);
chkxer_("ZGETRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* ZGERFS */
s_copy(srnamc_1.srnamt, "ZGERFS", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
zgerfs_("/", &c__0, &c__0, a, &c__1, af, &c__1, ip, b, &c__1, x, &
c__1, r1, r2, w, r__, &info);
chkxer_("ZGERFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
zgerfs_("N", &c_n1, &c__0, a, &c__1, af, &c__1, ip, b, &c__1, x, &
c__1, r1, r2, w, r__, &info);
chkxer_("ZGERFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
zgerfs_("N", &c__0, &c_n1, a, &c__1, af, &c__1, ip, b, &c__1, x, &
c__1, r1, r2, w, r__, &info);
chkxer_("ZGERFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
zgerfs_("N", &c__2, &c__1, a, &c__1, af, &c__2, ip, b, &c__2, x, &
c__2, r1, r2, w, r__, &info);
chkxer_("ZGERFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 7;
zgerfs_("N", &c__2, &c__1, a, &c__2, af, &c__1, ip, b, &c__2, x, &
c__2, r1, r2, w, r__, &info);
chkxer_("ZGERFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 10;
zgerfs_("N", &c__2, &c__1, a, &c__2, af, &c__2, ip, b, &c__1, x, &
c__2, r1, r2, w, r__, &info);
chkxer_("ZGERFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 12;
zgerfs_("N", &c__2, &c__1, a, &c__2, af, &c__2, ip, b, &c__2, x, &
c__1, r1, r2, w, r__, &info);
chkxer_("ZGERFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* ZGECON */
s_copy(srnamc_1.srnamt, "ZGECON", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
zgecon_("/", &c__0, a, &c__1, &anrm, &rcond, w, r__, &info)
;
chkxer_("ZGECON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
zgecon_("1", &c_n1, a, &c__1, &anrm, &rcond, w, r__, &info)
;
chkxer_("ZGECON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
zgecon_("1", &c__2, a, &c__1, &anrm, &rcond, w, r__, &info)
;
chkxer_("ZGECON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* ZGEEQU */
s_copy(srnamc_1.srnamt, "ZGEEQU", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
zgeequ_(&c_n1, &c__0, a, &c__1, r1, r2, &rcond, &ccond, &anrm, &info);
chkxer_("ZGEEQU", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
zgeequ_(&c__0, &c_n1, a, &c__1, r1, r2, &rcond, &ccond, &anrm, &info);
chkxer_("ZGEEQU", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
zgeequ_(&c__2, &c__2, a, &c__1, r1, r2, &rcond, &ccond, &anrm, &info);
chkxer_("ZGEEQU", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* Test error exits of the routines that use the LU decomposition */
/* of a general band matrix. */
} else if (lsamen_(&c__2, c2, "GB")) {
/* ZGBTRF */
s_copy(srnamc_1.srnamt, "ZGBTRF", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
zgbtrf_(&c_n1, &c__0, &c__0, &c__0, a, &c__1, ip, &info);
chkxer_("ZGBTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
zgbtrf_(&c__0, &c_n1, &c__0, &c__0, a, &c__1, ip, &info);
chkxer_("ZGBTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
zgbtrf_(&c__1, &c__1, &c_n1, &c__0, a, &c__1, ip, &info);
chkxer_("ZGBTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
zgbtrf_(&c__1, &c__1, &c__0, &c_n1, a, &c__1, ip, &info);
chkxer_("ZGBTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 6;
zgbtrf_(&c__2, &c__2, &c__1, &c__1, a, &c__3, ip, &info);
chkxer_("ZGBTRF", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* ZGBTF2 */
s_copy(srnamc_1.srnamt, "ZGBTF2", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
zgbtf2_(&c_n1, &c__0, &c__0, &c__0, a, &c__1, ip, &info);
chkxer_("ZGBTF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
zgbtf2_(&c__0, &c_n1, &c__0, &c__0, a, &c__1, ip, &info);
chkxer_("ZGBTF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
zgbtf2_(&c__1, &c__1, &c_n1, &c__0, a, &c__1, ip, &info);
chkxer_("ZGBTF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
zgbtf2_(&c__1, &c__1, &c__0, &c_n1, a, &c__1, ip, &info);
chkxer_("ZGBTF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 6;
zgbtf2_(&c__2, &c__2, &c__1, &c__1, a, &c__3, ip, &info);
chkxer_("ZGBTF2", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* ZGBTRS */
s_copy(srnamc_1.srnamt, "ZGBTRS", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
zgbtrs_("/", &c__0, &c__0, &c__0, &c__1, a, &c__1, ip, b, &c__1, &
info);
chkxer_("ZGBTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
zgbtrs_("N", &c_n1, &c__0, &c__0, &c__1, a, &c__1, ip, b, &c__1, &
info);
chkxer_("ZGBTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
zgbtrs_("N", &c__1, &c_n1, &c__0, &c__1, a, &c__1, ip, b, &c__1, &
info);
chkxer_("ZGBTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
zgbtrs_("N", &c__1, &c__0, &c_n1, &c__1, a, &c__1, ip, b, &c__1, &
info);
chkxer_("ZGBTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
zgbtrs_("N", &c__1, &c__0, &c__0, &c_n1, a, &c__1, ip, b, &c__1, &
info);
chkxer_("ZGBTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 7;
zgbtrs_("N", &c__2, &c__1, &c__1, &c__1, a, &c__3, ip, b, &c__2, &
info);
chkxer_("ZGBTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 10;
zgbtrs_("N", &c__2, &c__0, &c__0, &c__1, a, &c__1, ip, b, &c__1, &
info);
chkxer_("ZGBTRS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* ZGBRFS */
s_copy(srnamc_1.srnamt, "ZGBRFS", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
zgbrfs_("/", &c__0, &c__0, &c__0, &c__0, a, &c__1, af, &c__1, ip, b, &
c__1, x, &c__1, r1, r2, w, r__, &info);
chkxer_("ZGBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
zgbrfs_("N", &c_n1, &c__0, &c__0, &c__0, a, &c__1, af, &c__1, ip, b, &
c__1, x, &c__1, r1, r2, w, r__, &info);
chkxer_("ZGBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
zgbrfs_("N", &c__1, &c_n1, &c__0, &c__0, a, &c__1, af, &c__1, ip, b, &
c__1, x, &c__1, r1, r2, w, r__, &info);
chkxer_("ZGBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
zgbrfs_("N", &c__1, &c__0, &c_n1, &c__0, a, &c__1, af, &c__1, ip, b, &
c__1, x, &c__1, r1, r2, w, r__, &info);
chkxer_("ZGBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 5;
zgbrfs_("N", &c__1, &c__0, &c__0, &c_n1, a, &c__1, af, &c__1, ip, b, &
c__1, x, &c__1, r1, r2, w, r__, &info);
chkxer_("ZGBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 7;
zgbrfs_("N", &c__2, &c__1, &c__1, &c__1, a, &c__2, af, &c__4, ip, b, &
c__2, x, &c__2, r1, r2, w, r__, &info);
chkxer_("ZGBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 9;
zgbrfs_("N", &c__2, &c__1, &c__1, &c__1, a, &c__3, af, &c__3, ip, b, &
c__2, x, &c__2, r1, r2, w, r__, &info);
chkxer_("ZGBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 12;
zgbrfs_("N", &c__2, &c__0, &c__0, &c__1, a, &c__1, af, &c__1, ip, b, &
c__1, x, &c__2, r1, r2, w, r__, &info);
chkxer_("ZGBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 14;
zgbrfs_("N", &c__2, &c__0, &c__0, &c__1, a, &c__1, af, &c__1, ip, b, &
c__2, x, &c__1, r1, r2, w, r__, &info);
chkxer_("ZGBRFS", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* ZGBCON */
s_copy(srnamc_1.srnamt, "ZGBCON", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
zgbcon_("/", &c__0, &c__0, &c__0, a, &c__1, ip, &anrm, &rcond, w, r__,
&info);
chkxer_("ZGBCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
zgbcon_("1", &c_n1, &c__0, &c__0, a, &c__1, ip, &anrm, &rcond, w, r__,
&info);
chkxer_("ZGBCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
zgbcon_("1", &c__1, &c_n1, &c__0, a, &c__1, ip, &anrm, &rcond, w, r__,
&info);
chkxer_("ZGBCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
zgbcon_("1", &c__1, &c__0, &c_n1, a, &c__1, ip, &anrm, &rcond, w, r__,
&info);
chkxer_("ZGBCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 6;
zgbcon_("1", &c__2, &c__1, &c__1, a, &c__3, ip, &anrm, &rcond, w, r__,
&info);
chkxer_("ZGBCON", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
/* ZGBEQU */
s_copy(srnamc_1.srnamt, "ZGBEQU", (ftnlen)6, (ftnlen)6);
infoc_1.infot = 1;
zgbequ_(&c_n1, &c__0, &c__0, &c__0, a, &c__1, r1, r2, &rcond, &ccond,
&anrm, &info);
chkxer_("ZGBEQU", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 2;
zgbequ_(&c__0, &c_n1, &c__0, &c__0, a, &c__1, r1, r2, &rcond, &ccond,
&anrm, &info);
chkxer_("ZGBEQU", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 3;
zgbequ_(&c__1, &c__1, &c_n1, &c__0, a, &c__1, r1, r2, &rcond, &ccond,
&anrm, &info);
chkxer_("ZGBEQU", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 4;
zgbequ_(&c__1, &c__1, &c__0, &c_n1, a, &c__1, r1, r2, &rcond, &ccond,
&anrm, &info);
chkxer_("ZGBEQU", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
infoc_1.infot = 6;
zgbequ_(&c__2, &c__2, &c__1, &c__1, a, &c__2, r1, r2, &rcond, &ccond,
&anrm, &info);
chkxer_("ZGBEQU", &infoc_1.infot, &infoc_1.nout, &infoc_1.lerr, &
infoc_1.ok);
}
/* Print a summary line. */
alaesm_(path, &infoc_1.ok, &infoc_1.nout);
return 0;
/* End of ZERRGE */
} /* zerrge_ */
/* Subroutine */ int zgesvxx_(char *fact, char *trans, integer *n, integer *
nrhs, doublecomplex *a, integer *lda, doublecomplex *af, integer *
ldaf, integer *ipiv, char *equed, doublereal *r__, doublereal *c__,
doublecomplex *b, integer *ldb, doublecomplex *x, integer *ldx,
doublereal *rcond, doublereal *rpvgrw, doublereal *berr, integer *
n_err_bnds__, doublereal *err_bnds_norm__, doublereal *
err_bnds_comp__, integer *nparams, doublereal *params, doublecomplex *
work, doublereal *rwork, integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, af_dim1, af_offset, b_dim1, b_offset, x_dim1,
x_offset, err_bnds_norm_dim1, err_bnds_norm_offset,
err_bnds_comp_dim1, err_bnds_comp_offset, i__1;
doublereal d__1, d__2;
/* Local variables */
integer j;
extern doublereal zla_rpvgrw__(integer *, integer *, doublecomplex *,
integer *, doublecomplex *, integer *);
doublereal amax;
extern logical lsame_(char *, char *);
doublereal rcmin, rcmax;
logical equil;
extern doublereal dlamch_(char *);
doublereal colcnd;
logical nofact;
extern /* Subroutine */ int xerbla_(char *, integer *);
doublereal bignum;
extern /* Subroutine */ int zlaqge_(integer *, integer *, doublecomplex *,
integer *, doublereal *, doublereal *, doublereal *, doublereal *
, doublereal *, char *);
integer infequ;
logical colequ;
doublereal rowcnd;
logical notran;
extern /* Subroutine */ int zgetrf_(integer *, integer *, doublecomplex *,
integer *, integer *, integer *), zlacpy_(char *, integer *,
integer *, doublecomplex *, integer *, doublecomplex *, integer *);
doublereal smlnum;
extern /* Subroutine */ int zgetrs_(char *, integer *, integer *,
doublecomplex *, integer *, integer *, doublecomplex *, integer *,
integer *);
logical rowequ;
extern /* Subroutine */ int zlascl2_(integer *, integer *, doublereal *,
doublecomplex *, integer *), zgeequb_(integer *, integer *,
doublecomplex *, integer *, doublereal *, doublereal *,
doublereal *, doublereal *, doublereal *, integer *), zgerfsx_(
char *, char *, integer *, integer *, doublecomplex *, integer *,
doublecomplex *, integer *, integer *, doublereal *, doublereal *,
doublecomplex *, integer *, doublecomplex *, integer *,
doublereal *, doublereal *, integer *, doublereal *, doublereal *,
integer *, doublereal *, doublecomplex *, doublereal *, integer *
);
/* -- LAPACK driver routine (version 3.2) -- */
/* -- Contributed by James Demmel, Deaglan Halligan, Yozo Hida and -- */
/* -- Jason Riedy of Univ. of California Berkeley. -- */
/* -- November 2008 -- */
/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
/* -- Univ. of California Berkeley and NAG Ltd. -- */
/* .. */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* ZGESVXX uses the LU factorization to compute the solution to a */
/* complex*16 system of linear equations A * X = B, where A is an */
/* N-by-N matrix and X and B are N-by-NRHS matrices. */
/* If requested, both normwise and maximum componentwise error bounds */
/* are returned. ZGESVXX will return a solution with a tiny */
/* guaranteed error (O(eps) where eps is the working machine */
/* precision) unless the matrix is very ill-conditioned, in which */
/* case a warning is returned. Relevant condition numbers also are */
/* calculated and returned. */
/* ZGESVXX accepts user-provided factorizations and equilibration */
/* factors; see the definitions of the FACT and EQUED options. */
/* Solving with refinement and using a factorization from a previous */
/* ZGESVXX call will also produce a solution with either O(eps) */
/* errors or warnings, but we cannot make that claim for general */
/* user-provided factorizations and equilibration factors if they */
/* differ from what ZGESVXX would itself produce. */
/* Description */
/* =========== */
/* The following steps are performed: */
/* 1. If FACT = 'E', double precision scaling factors are computed to equilibrate */
/* the system: */
/* TRANS = 'N': diag(R)*A*diag(C) *inv(diag(C))*X = diag(R)*B */
/* TRANS = 'T': (diag(R)*A*diag(C))**T *inv(diag(R))*X = diag(C)*B */
/* TRANS = 'C': (diag(R)*A*diag(C))**H *inv(diag(R))*X = diag(C)*B */
/* Whether or not the system will be equilibrated depends on the */
/* scaling of the matrix A, but if equilibration is used, A is */
/* overwritten by diag(R)*A*diag(C) and B by diag(R)*B (if TRANS='N') */
/* or diag(C)*B (if TRANS = 'T' or 'C'). */
/* 2. If FACT = 'N' or 'E', the LU decomposition is used to factor */
/* the matrix A (after equilibration if FACT = 'E') as */
/* A = P * L * U, */
/* where P is a permutation matrix, L is a unit lower triangular */
/* matrix, and U is upper triangular. */
/* 3. If some U(i,i)=0, so that U is exactly singular, then the */
/* routine returns with INFO = i. Otherwise, the factored form of A */
/* is used to estimate the condition number of the matrix A (see */
/* argument RCOND). If the reciprocal of the condition number is less */
/* than machine precision, the routine still goes on to solve for X */
/* and compute error bounds as described below. */
/* 4. The system of equations is solved for X using the factored form */
/* of A. */
/* 5. By default (unless PARAMS(LA_LINRX_ITREF_I) is set to zero), */
/* the routine will use iterative refinement to try to get a small */
/* error and error bounds. Refinement calculates the residual to at */
/* least twice the working precision. */
/* 6. If equilibration was used, the matrix X is premultiplied by */
/* diag(C) (if TRANS = 'N') or diag(R) (if TRANS = 'T' or 'C') so */
/* that it solves the original system before equilibration. */
/* Arguments */
/* ========= */
/* Some optional parameters are bundled in the PARAMS array. These */
/* settings determine how refinement is performed, but often the */
/* defaults are acceptable. If the defaults are acceptable, users */
/* can pass NPARAMS = 0 which prevents the source code from accessing */
/* the PARAMS argument. */
/* FACT (input) CHARACTER*1 */
/* Specifies whether or not the factored form of the matrix A is */
/* supplied on entry, and if not, whether the matrix A should be */
/* equilibrated before it is factored. */
/* = 'F': On entry, AF and IPIV contain the factored form of A. */
/* If EQUED is not 'N', the matrix A has been */
/* equilibrated with scaling factors given by R and C. */
/* A, AF, and IPIV are not modified. */
/* = 'N': The matrix A will be copied to AF and factored. */
/* = 'E': The matrix A will be equilibrated if necessary, then */
/* copied to AF and factored. */
/* TRANS (input) CHARACTER*1 */
/* Specifies the form of the system of equations: */
/* = 'N': A * X = B (No transpose) */
/* = 'T': A**T * X = B (Transpose) */
/* = 'C': A**H * X = B (Conjugate Transpose) */
/* N (input) INTEGER */
/* The number of linear equations, i.e., the order of the */
/* matrix A. N >= 0. */
/* NRHS (input) INTEGER */
/* The number of right hand sides, i.e., the number of columns */
/* of the matrices B and X. NRHS >= 0. */
/* A (input/output) COMPLEX*16 array, dimension (LDA,N) */
/* On entry, the N-by-N matrix A. If FACT = 'F' and EQUED is */
/* not 'N', then A must have been equilibrated by the scaling */
/* factors in R and/or C. A is not modified if FACT = 'F' or */
/* 'N', or if FACT = 'E' and EQUED = 'N' on exit. */
/* On exit, if EQUED .ne. 'N', A is scaled as follows: */
/* EQUED = 'R': A := diag(R) * A */
/* EQUED = 'C': A := A * diag(C) */
/* EQUED = 'B': A := diag(R) * A * diag(C). */
/* LDA (input) INTEGER */
/* The leading dimension of the array A. LDA >= max(1,N). */
/* AF (input or output) COMPLEX*16 array, dimension (LDAF,N) */
/* If FACT = 'F', then AF is an input argument and on entry */
/* contains the factors L and U from the factorization */
/* A = P*L*U as computed by ZGETRF. If EQUED .ne. 'N', then */
/* AF is the factored form of the equilibrated matrix A. */
/* If FACT = 'N', then AF is an output argument and on exit */
/* returns the factors L and U from the factorization A = P*L*U */
/* of the original matrix A. */
/* If FACT = 'E', then AF is an output argument and on exit */
/* returns the factors L and U from the factorization A = P*L*U */
/* of the equilibrated matrix A (see the description of A for */
/* the form of the equilibrated matrix). */
/* LDAF (input) INTEGER */
/* The leading dimension of the array AF. LDAF >= max(1,N). */
/* IPIV (input or output) INTEGER array, dimension (N) */
/* If FACT = 'F', then IPIV is an input argument and on entry */
/* contains the pivot indices from the factorization A = P*L*U */
/* as computed by ZGETRF; row i of the matrix was interchanged */
/* with row IPIV(i). */
/* If FACT = 'N', then IPIV is an output argument and on exit */
/* contains the pivot indices from the factorization A = P*L*U */
/* of the original matrix A. */
/* If FACT = 'E', then IPIV is an output argument and on exit */
/* contains the pivot indices from the factorization A = P*L*U */
/* of the equilibrated matrix A. */
/* EQUED (input or output) CHARACTER*1 */
/* Specifies the form of equilibration that was done. */
/* = 'N': No equilibration (always true if FACT = 'N'). */
/* = 'R': Row equilibration, i.e., A has been premultiplied by */
/* diag(R). */
/* = 'C': Column equilibration, i.e., A has been postmultiplied */
/* by diag(C). */
/* = 'B': Both row and column equilibration, i.e., A has been */
/* replaced by diag(R) * A * diag(C). */
/* EQUED is an input argument if FACT = 'F'; otherwise, it is an */
/* output argument. */
/* R (input or output) DOUBLE PRECISION array, dimension (N) */
/* The row scale factors for A. If EQUED = 'R' or 'B', A is */
/* multiplied on the left by diag(R); if EQUED = 'N' or 'C', R */
/* is not accessed. R is an input argument if FACT = 'F'; */
/* otherwise, R is an output argument. If FACT = 'F' and */
/* EQUED = 'R' or 'B', each element of R must be positive. */
/* If R is output, each element of R is a power of the radix. */
/* If R is input, each element of R should be a power of the radix */
/* to ensure a reliable solution and error estimates. Scaling by */
/* powers of the radix does not cause rounding errors unless the */
/* result underflows or overflows. Rounding errors during scaling */
/* lead to refining with a matrix that is not equivalent to the */
/* input matrix, producing error estimates that may not be */
/* reliable. */
/* C (input or output) DOUBLE PRECISION array, dimension (N) */
/* The column scale factors for A. If EQUED = 'C' or 'B', A is */
/* multiplied on the right by diag(C); if EQUED = 'N' or 'R', C */
/* is not accessed. C is an input argument if FACT = 'F'; */
/* otherwise, C is an output argument. If FACT = 'F' and */
/* EQUED = 'C' or 'B', each element of C must be positive. */
/* If C is output, each element of C is a power of the radix. */
/* If C is input, each element of C should be a power of the radix */
/* to ensure a reliable solution and error estimates. Scaling by */
/* powers of the radix does not cause rounding errors unless the */
/* result underflows or overflows. Rounding errors during scaling */
/* lead to refining with a matrix that is not equivalent to the */
/* input matrix, producing error estimates that may not be */
/* reliable. */
/* B (input/output) COMPLEX*16 array, dimension (LDB,NRHS) */
/* On entry, the N-by-NRHS right hand side matrix B. */
/* On exit, */
/* if EQUED = 'N', B is not modified; */
/* if TRANS = 'N' and EQUED = 'R' or 'B', B is overwritten by */
/* diag(R)*B; */
/* if TRANS = 'T' or 'C' and EQUED = 'C' or 'B', B is */
/* overwritten by diag(C)*B. */
/* LDB (input) INTEGER */
/* The leading dimension of the array B. LDB >= max(1,N). */
/* X (output) COMPLEX*16 array, dimension (LDX,NRHS) */
/* If INFO = 0, the N-by-NRHS solution matrix X to the original */
/* system of equations. Note that A and B are modified on exit */
/* if EQUED .ne. 'N', and the solution to the equilibrated system is */
/* inv(diag(C))*X if TRANS = 'N' and EQUED = 'C' or 'B', or */
/* inv(diag(R))*X if TRANS = 'T' or 'C' and EQUED = 'R' or 'B'. */
/* LDX (input) INTEGER */
/* The leading dimension of the array X. LDX >= max(1,N). */
/* RCOND (output) DOUBLE PRECISION */
/* Reciprocal scaled condition number. This is an estimate of the */
/* reciprocal Skeel condition number of the matrix A after */
/* equilibration (if done). If this is less than the machine */
/* precision (in particular, if it is zero), the matrix is singular */
/* to working precision. Note that the error may still be small even */
/* if this number is very small and the matrix appears ill- */
/* conditioned. */
/* RPVGRW (output) DOUBLE PRECISION */
/* Reciprocal pivot growth. On exit, this contains the reciprocal */
/* pivot growth factor norm(A)/norm(U). The "max absolute element" */
/* norm is used. If this is much less than 1, then the stability of */
/* the LU factorization of the (equilibrated) matrix A could be poor. */
/* This also means that the solution X, estimated condition numbers, */
/* and error bounds could be unreliable. If factorization fails with */
/* 0<INFO<=N, then this contains the reciprocal pivot growth factor */
/* for the leading INFO columns of A. In ZGESVX, this quantity is */
/* returned in WORK(1). */
/* BERR (output) DOUBLE PRECISION array, dimension (NRHS) */
/* Componentwise relative backward error. This is the */
/* componentwise relative backward error of each solution vector X(j) */
/* (i.e., the smallest relative change in any element of A or B that */
/* makes X(j) an exact solution). */
/* N_ERR_BNDS (input) INTEGER */
/* Number of error bounds to return for each right hand side */
/* and each type (normwise or componentwise). See ERR_BNDS_NORM and */
/* ERR_BNDS_COMP below. */
/* ERR_BNDS_NORM (output) DOUBLE PRECISION array, dimension (NRHS, N_ERR_BNDS) */
/* For each right-hand side, this array contains information about */
/* various error bounds and condition numbers corresponding to the */
/* normwise relative error, which is defined as follows: */
/* Normwise relative error in the ith solution vector: */
/* max_j (abs(XTRUE(j,i) - X(j,i))) */
/* ------------------------------ */
/* max_j abs(X(j,i)) */
/* The array is indexed by the type of error information as described */
/* below. There currently are up to three pieces of information */
/* returned. */
/* The first index in ERR_BNDS_NORM(i,:) corresponds to the ith */
/* right-hand side. */
/* The second index in ERR_BNDS_NORM(:,err) contains the following */
/* three fields: */
/* err = 1 "Trust/don't trust" boolean. Trust the answer if the */
/* reciprocal condition number is less than the threshold */
/* sqrt(n) * dlamch('Epsilon'). */
/* err = 2 "Guaranteed" error bound: The estimated forward error, */
/* almost certainly within a factor of 10 of the true error */
/* so long as the next entry is greater than the threshold */
/* sqrt(n) * dlamch('Epsilon'). This error bound should only */
/* be trusted if the previous boolean is true. */
/* err = 3 Reciprocal condition number: Estimated normwise */
/* reciprocal condition number. Compared with the threshold */
/* sqrt(n) * dlamch('Epsilon') to determine if the error */
/* estimate is "guaranteed". These reciprocal condition */
/* numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some */
/* appropriately scaled matrix Z. */
/* Let Z = S*A, where S scales each row by a power of the */
/* radix so all absolute row sums of Z are approximately 1. */
/* See Lapack Working Note 165 for further details and extra */
/* cautions. */
/* ERR_BNDS_COMP (output) DOUBLE PRECISION array, dimension (NRHS, N_ERR_BNDS) */
/* For each right-hand side, this array contains information about */
/* various error bounds and condition numbers corresponding to the */
/* componentwise relative error, which is defined as follows: */
/* Componentwise relative error in the ith solution vector: */
/* abs(XTRUE(j,i) - X(j,i)) */
/* max_j ---------------------- */
/* abs(X(j,i)) */
/* The array is indexed by the right-hand side i (on which the */
/* componentwise relative error depends), and the type of error */
/* information as described below. There currently are up to three */
/* pieces of information returned for each right-hand side. If */
/* componentwise accuracy is not requested (PARAMS(3) = 0.0), then */
/* ERR_BNDS_COMP is not accessed. If N_ERR_BNDS .LT. 3, then at most */
/* the first (:,N_ERR_BNDS) entries are returned. */
/* The first index in ERR_BNDS_COMP(i,:) corresponds to the ith */
/* right-hand side. */
/* The second index in ERR_BNDS_COMP(:,err) contains the following */
/* three fields: */
/* err = 1 "Trust/don't trust" boolean. Trust the answer if the */
/* reciprocal condition number is less than the threshold */
/* sqrt(n) * dlamch('Epsilon'). */
/* err = 2 "Guaranteed" error bound: The estimated forward error, */
/* almost certainly within a factor of 10 of the true error */
/* so long as the next entry is greater than the threshold */
/* sqrt(n) * dlamch('Epsilon'). This error bound should only */
/* be trusted if the previous boolean is true. */
/* err = 3 Reciprocal condition number: Estimated componentwise */
/* reciprocal condition number. Compared with the threshold */
/* sqrt(n) * dlamch('Epsilon') to determine if the error */
/* estimate is "guaranteed". These reciprocal condition */
/* numbers are 1 / (norm(Z^{-1},inf) * norm(Z,inf)) for some */
/* appropriately scaled matrix Z. */
/* Let Z = S*(A*diag(x)), where x is the solution for the */
/* current right-hand side and S scales each row of */
/* A*diag(x) by a power of the radix so all absolute row */
/* sums of Z are approximately 1. */
/* See Lapack Working Note 165 for further details and extra */
/* cautions. */
/* NPARAMS (input) INTEGER */
/* Specifies the number of parameters set in PARAMS. If .LE. 0, the */
/* PARAMS array is never referenced and default values are used. */
/* PARAMS (input / output) DOUBLE PRECISION array, dimension NPARAMS */
/* Specifies algorithm parameters. If an entry is .LT. 0.0, then */
/* that entry will be filled with default value used for that */
/* parameter. Only positions up to NPARAMS are accessed; defaults */
/* are used for higher-numbered parameters. */
/* PARAMS(LA_LINRX_ITREF_I = 1) : Whether to perform iterative */
/* refinement or not. */
/* Default: 1.0D+0 */
/* = 0.0 : No refinement is performed, and no error bounds are */
/* computed. */
/* = 1.0 : Use the extra-precise refinement algorithm. */
/* (other values are reserved for future use) */
/* PARAMS(LA_LINRX_ITHRESH_I = 2) : Maximum number of residual */
/* computations allowed for refinement. */
/* Default: 10 */
/* Aggressive: Set to 100 to permit convergence using approximate */
/* factorizations or factorizations other than LU. If */
/* the factorization uses a technique other than */
/* Gaussian elimination, the guarantees in */
/* err_bnds_norm and err_bnds_comp may no longer be */
/* trustworthy. */
/* PARAMS(LA_LINRX_CWISE_I = 3) : Flag determining if the code */
/* will attempt to find a solution with small componentwise */
/* relative error in the double-precision algorithm. Positive */
/* is true, 0.0 is false. */
/* Default: 1.0 (attempt componentwise convergence) */
/* WORK (workspace) COMPLEX*16 array, dimension (2*N) */
/* RWORK (workspace) DOUBLE PRECISION array, dimension (3*N) */
/* INFO (output) INTEGER */
/* = 0: Successful exit. The solution to every right-hand side is */
/* guaranteed. */
/* < 0: If INFO = -i, the i-th argument had an illegal value */
/* > 0 and <= N: U(INFO,INFO) is exactly zero. The factorization */
/* has been completed, but the factor U is exactly singular, so */
/* the solution and error bounds could not be computed. RCOND = 0 */
/* is returned. */
/* = N+J: The solution corresponding to the Jth right-hand side is */
/* not guaranteed. The solutions corresponding to other right- */
/* hand sides K with K > J may not be guaranteed as well, but */
/* only the first such right-hand side is reported. If a small */
/* componentwise error is not requested (PARAMS(3) = 0.0) then */
/* the Jth right-hand side is the first with a normwise error */
/* bound that is not guaranteed (the smallest J such */
/* that ERR_BNDS_NORM(J,1) = 0.0). By default (PARAMS(3) = 1.0) */
/* the Jth right-hand side is the first with either a normwise or */
/* componentwise error bound that is not guaranteed (the smallest */
/* J such that either ERR_BNDS_NORM(J,1) = 0.0 or */
/* ERR_BNDS_COMP(J,1) = 0.0). See the definition of */
/* ERR_BNDS_NORM(:,1) and ERR_BNDS_COMP(:,1). To get information */
/* about all of the right-hand sides check ERR_BNDS_NORM or */
/* ERR_BNDS_COMP. */
/* ================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Parameter adjustments */
err_bnds_comp_dim1 = *nrhs;
err_bnds_comp_offset = 1 + err_bnds_comp_dim1;
err_bnds_comp__ -= err_bnds_comp_offset;
err_bnds_norm_dim1 = *nrhs;
err_bnds_norm_offset = 1 + err_bnds_norm_dim1;
err_bnds_norm__ -= err_bnds_norm_offset;
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
af_dim1 = *ldaf;
af_offset = 1 + af_dim1;
af -= af_offset;
--ipiv;
--r__;
--c__;
b_dim1 = *ldb;
b_offset = 1 + b_dim1;
b -= b_offset;
x_dim1 = *ldx;
x_offset = 1 + x_dim1;
x -= x_offset;
--berr;
--params;
--work;
--rwork;
/* Function Body */
*info = 0;
nofact = lsame_(fact, "N");
equil = lsame_(fact, "E");
notran = lsame_(trans, "N");
smlnum = dlamch_("Safe minimum");
bignum = 1. / smlnum;
if (nofact || equil) {
*(unsigned char *)equed = 'N';
rowequ = FALSE_;
colequ = FALSE_;
} else {
rowequ = lsame_(equed, "R") || lsame_(equed,
"B");
colequ = lsame_(equed, "C") || lsame_(equed,
"B");
}
/* Default is failure. If an input parameter is wrong or */
/* factorization fails, make everything look horrible. Only the */
/* pivot growth is set here, the rest is initialized in ZGERFSX. */
*rpvgrw = 0.;
/* Test the input parameters. PARAMS is not tested until ZGERFSX. */
if (! nofact && ! equil && ! lsame_(fact, "F")) {
*info = -1;
} else if (! notran && ! lsame_(trans, "T") && !
lsame_(trans, "C")) {
*info = -2;
} else if (*n < 0) {
*info = -3;
} else if (*nrhs < 0) {
*info = -4;
} else if (*lda < max(1,*n)) {
*info = -6;
} else if (*ldaf < max(1,*n)) {
*info = -8;
} else if (lsame_(fact, "F") && ! (rowequ || colequ
|| lsame_(equed, "N"))) {
*info = -10;
} else {
if (rowequ) {
rcmin = bignum;
rcmax = 0.;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
/* Computing MIN */
d__1 = rcmin, d__2 = r__[j];
rcmin = min(d__1,d__2);
/* Computing MAX */
d__1 = rcmax, d__2 = r__[j];
rcmax = max(d__1,d__2);
/* L10: */
}
if (rcmin <= 0.) {
*info = -11;
} else if (*n > 0) {
rowcnd = max(rcmin,smlnum) / min(rcmax,bignum);
} else {
rowcnd = 1.;
}
}
if (colequ && *info == 0) {
rcmin = bignum;
rcmax = 0.;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
/* Computing MIN */
d__1 = rcmin, d__2 = c__[j];
rcmin = min(d__1,d__2);
/* Computing MAX */
d__1 = rcmax, d__2 = c__[j];
rcmax = max(d__1,d__2);
/* L20: */
}
if (rcmin <= 0.) {
*info = -12;
} else if (*n > 0) {
colcnd = max(rcmin,smlnum) / min(rcmax,bignum);
} else {
colcnd = 1.;
}
}
if (*info == 0) {
if (*ldb < max(1,*n)) {
*info = -14;
} else if (*ldx < max(1,*n)) {
*info = -16;
}
}
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("ZGESVXX", &i__1);
return 0;
}
if (equil) {
/* Compute row and column scalings to equilibrate the matrix A. */
zgeequb_(n, n, &a[a_offset], lda, &r__[1], &c__[1], &rowcnd, &colcnd,
&amax, &infequ);
if (infequ == 0) {
/* Equilibrate the matrix. */
zlaqge_(n, n, &a[a_offset], lda, &r__[1], &c__[1], &rowcnd, &
colcnd, &amax, equed);
rowequ = lsame_(equed, "R") || lsame_(equed,
"B");
colequ = lsame_(equed, "C") || lsame_(equed,
"B");
}
/* If the scaling factors are not applied, set them to 1.0. */
if (! rowequ) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
r__[j] = 1.;
}
}
if (! colequ) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
c__[j] = 1.;
}
}
}
/* Scale the right-hand side. */
if (notran) {
if (rowequ) {
zlascl2_(n, nrhs, &r__[1], &b[b_offset], ldb);
}
} else {
if (colequ) {
zlascl2_(n, nrhs, &c__[1], &b[b_offset], ldb);
}
}
if (nofact || equil) {
/* Compute the LU factorization of A. */
zlacpy_("Full", n, n, &a[a_offset], lda, &af[af_offset], ldaf);
zgetrf_(n, n, &af[af_offset], ldaf, &ipiv[1], info);
/* Return if INFO is non-zero. */
if (*info > 0) {
/* Pivot in column INFO is exactly 0 */
/* Compute the reciprocal pivot growth factor of the */
/* leading rank-deficient INFO columns of A. */
*rpvgrw = zla_rpvgrw__(n, info, &a[a_offset], lda, &af[af_offset],
ldaf);
return 0;
}
}
/* Compute the reciprocal pivot growth factor RPVGRW. */
*rpvgrw = zla_rpvgrw__(n, n, &a[a_offset], lda, &af[af_offset], ldaf);
/* Compute the solution matrix X. */
zlacpy_("Full", n, nrhs, &b[b_offset], ldb, &x[x_offset], ldx);
zgetrs_(trans, n, nrhs, &af[af_offset], ldaf, &ipiv[1], &x[x_offset], ldx,
info);
/* Use iterative refinement to improve the computed solution and */
/* compute error bounds and backward error estimates for it. */
zgerfsx_(trans, equed, n, nrhs, &a[a_offset], lda, &af[af_offset], ldaf, &
ipiv[1], &r__[1], &c__[1], &b[b_offset], ldb, &x[x_offset], ldx,
rcond, &berr[1], n_err_bnds__, &err_bnds_norm__[
err_bnds_norm_offset], &err_bnds_comp__[err_bnds_comp_offset],
nparams, ¶ms[1], &work[1], &rwork[1], info);
/* Scale solutions. */
if (colequ && notran) {
zlascl2_(n, nrhs, &c__[1], &x[x_offset], ldx);
} else if (rowequ && ! notran) {
zlascl2_(n, nrhs, &r__[1], &x[x_offset], ldx);
}
return 0;
/* End of ZGESVXX */
} /* zgesvxx_ */
