bool qr(const mat &A, mat &Q, mat &R, bmat &P)
{
int info;
int m = A.rows();
int n = A.cols();
int lwork = n;
int k = std::min(m, n);
vec tau(k);
vec work(lwork);
ivec jpvt(n);
jpvt.zeros();
R = A;
// perform workspace query for optimum lwork value
int lwork_tmp = -1;
dgeqp3_(&m, &n, R._data(), &m, jpvt._data(), tau._data(), work._data(),
&lwork_tmp, &info);
if (info == 0) {
lwork = static_cast<int>(work(0));
work.set_size(lwork, false);
}
dgeqp3_(&m, &n, R._data(), &m, jpvt._data(), tau._data(), work._data(),
&lwork, &info);
Q = R;
Q.set_size(m, m, true);
// construct permutation matrix
P = zeros_b(n, n);
for (int j = 0; j < n; j++)
P(jpvt(j) - 1, j) = 1;
// construct R
for (int i = 0; i < m; i++)
for (int j = 0; j < std::min(i, n); j++)
R(i, j) = 0;
// perform workspace query for optimum lwork value
lwork_tmp = -1;
dorgqr_(&m, &m, &k, Q._data(), &m, tau._data(), work._data(), &lwork_tmp,
&info);
if (info == 0) {
lwork = static_cast<int>(work(0));
work.set_size(lwork, false);
}
dorgqr_(&m, &m, &k, Q._data(), &m, tau._data(), work._data(), &lwork,
&info);
return (info == 0);
}
void Stiefel::ObtainPerp(Variable *x) const
{
const double *xM = x->ObtainReadData();
SharedSpace *SharedSpacePerp = new SharedSpace(2, n, n - p);
double *Perp = SharedSpacePerp->ObtainWriteEntireData();
for (integer i = 0; i < n * (n - p); i++)
Perp[i] = genrand_gaussian();
double *temp = new double[p * (n - p)];
char *transn = const_cast<char *> ("n"), *transt = const_cast<char *> ("t");
double one = 1, zero = 0, neg_one = -1;
integer P = p, N = n, NmP = n - p;
// temp = X^T * Perp
dgemm_(transt, transn, &P, &NmP, &N, &one, const_cast<double *> (xM), &N, Perp, &N, &zero, temp, &P);
// Perp = Perp - X * temp
dgemm_(transn, transn, &N, &NmP, &P, &neg_one, const_cast<double *> (xM), &N, temp, &P, &one, Perp, &N);
delete[] temp;
integer *jpvt = new integer[NmP];
integer lwork = 2 * NmP + (1 + NmP) * INITIALBLOCKSIZE, info;
double *tau = new double[NmP + lwork];
double *work = tau + NmP;
for (integer i = 0; i < NmP; i++)
jpvt[i] = 0;
dgeqp3_(&N, &NmP, Perp, &N, jpvt, tau, work, &lwork, &info);
if (info < 0)
Rcpp::Rcout << "Error in qr decomposition!" << std::endl;
dorgqr_(&N, &NmP, &NmP, Perp, &N, tau, work, &lwork, &info);
if (info < 0)
Rcpp::Rcout << "Error in forming Q matrix!" << std::endl;
delete[] jpvt;
delete[] tau;
x->AddToTempData("Perp", SharedSpacePerp);
};
void Stiefel::ObtainExtrHHR(Variable *x, Vector *intretax, Vector *result) const
{
if (!x->TempDataExist("HHR"))
{
const double *xM = x->ObtainReadData();
SharedSpace *HouseHolderResult = new SharedSpace(2, x->Getsize()[0], x->Getsize()[1]);
double *ptrHHR = HouseHolderResult->ObtainWriteEntireData();
SharedSpace *HHRTau = new SharedSpace(1, x->Getsize()[1]);
double *tau = HHRTau->ObtainWriteEntireData();
integer N = x->Getsize()[0], P = x->Getsize()[1], Length = N * P, inc = 1;
double one = 1, zero = 0;
dcopy_(&Length, const_cast<double *> (xM), &inc, ptrHHR, &inc);
integer *jpvt = new integer[P];
integer info;
integer lwork = -1;
double lworkopt;
for (integer i = 0; i < P; i++)
jpvt[i] = i + 1;
dgeqp3_(&N, &P, ptrHHR, &N, jpvt, tau, &lworkopt, &lwork, &info);
lwork = static_cast<integer> (lworkopt);
double *work = new double[lwork];
dgeqp3_(&N, &P, ptrHHR, &N, jpvt, tau, work, &lwork, &info);
x->AddToTempData("HHR", HouseHolderResult);
x->AddToTempData("HHRTau", HHRTau);
if (info < 0)
Rcpp::Rcout << "Error in qr decomposition!" << std::endl;
for (integer i = 0; i < P; i++)
{
if (jpvt[i] != (i + 1))
Rcpp::Rcout << "Error in qf retraction!" << std::endl;
}
delete[] jpvt;
delete[] work;
}
const double *xM = x->ObtainReadData();
const SharedSpace *HHR = x->ObtainReadTempData("HHR");
const SharedSpace *HHRTau = x->ObtainReadTempData("HHRTau");
const double *ptrHHR = HHR->ObtainReadData();
const double *ptrHHRTau = HHRTau->ObtainReadData();
const double *intretaxTV = intretax->ObtainReadData();
double *resultTV = result->ObtainWriteEntireData();
char *transn = const_cast<char *> ("n"), *sidel = const_cast<char *> ("l");
integer N = x->Getsize()[0], P = x->Getsize()[1], inc = 1, Length = N * P;
integer info;
double r2 = sqrt(2.0);
integer idx = 0;
for (integer i = 0; i < p; i++)
{
resultTV[i + i * n] = 0;
for (integer j = i + 1; j < p; j++)
{
resultTV[j + i * n] = intretaxTV[idx] / r2;
resultTV[i + j * n] = -resultTV[j + i * n];
idx++;
}
}
for (integer i = 0; i < p; i++)
{
for (integer j = p; j < n; j++)
{
resultTV[j + i * n] = intretaxTV[idx];
idx++;
}
}
double sign;
for (integer i = 0; i < p; i++)
{
sign = (ptrHHR[i + n * i] >= 0) ? 1 : -1;
dscal_(&P, &sign, resultTV + i, &N);
}
integer lwork = -1;
double lworkopt;
dormqr_(sidel, transn, &N, &P, &P, const_cast<double *> (ptrHHR), &N, const_cast<double *> (ptrHHRTau), resultTV, &N, &lworkopt, &lwork, &info);
lwork = static_cast<integer> (lworkopt);
double *work = new double[lwork];
dormqr_(sidel, transn, &N, &P, &P, const_cast<double *> (ptrHHR), &N, const_cast<double *> (ptrHHRTau), resultTV, &N, work, &lwork, &info);
delete[] work;
};
void Stiefel::qfRetraction(Variable *x, Vector *etax, Variable *result) const
{
//x->Print("x in qf:");//---
const double *U = x->ObtainReadData();
const double *V;
Vector *exetax = nullptr;
if (IsIntrApproach)
{
exetax = EMPTYEXTR->ConstructEmpty();
ObtainExtr(x, etax, exetax);
V = exetax->ObtainReadData();
//exetax->Print("exetax:");//---
}
else
{
V = etax->ObtainReadData();
}
double *resultM = result->ObtainWriteEntireData();
SharedSpace *HouseHolderResult = new SharedSpace(2, x->Getsize()[0], x->Getsize()[1]);
double *ptrHHR = HouseHolderResult->ObtainWriteEntireData();
SharedSpace *HHRTau = new SharedSpace(1, x->Getsize()[1]);
double *tau = HHRTau->ObtainWriteEntireData();
integer N = x->Getsize()[0], P = x->Getsize()[1], Length = N * P, inc = 1;
double one = 1, zero = 0;
dcopy_(&Length, const_cast<double *> (V), &inc, ptrHHR, &inc);
daxpy_(&Length, &one, const_cast<double *> (U), &inc, ptrHHR, &inc);
integer *jpvt = new integer[P];
integer info;
integer lwork = -1;
double lworkopt;
for (integer i = 0; i < P; i++)
jpvt[i] = i + 1;
dgeqp3_(&N, &P, ptrHHR, &N, jpvt, tau, &lworkopt, &lwork, &info);
lwork = static_cast<integer> (lworkopt);
double *work = new double[lwork];
dgeqp3_(&N, &P, ptrHHR, &N, jpvt, tau, work, &lwork, &info);
if (info < 0)
Rcpp::Rcout << "Error in qr decomposition!" << std::endl;
for (integer i = 0; i < P; i++)
{
if (jpvt[i] != (i + 1))
Rcpp::Rcout << "Error in qf retraction!" << std::endl;
}
double *signs = new double[P];
for (integer i = 0; i < P; i++)
signs[i] = (ptrHHR[i + i * N] >= 0) ? 1 : -1;
dcopy_(&Length, ptrHHR, &inc, resultM, &inc);
dorgqr_(&N, &P, &P, resultM, &N, tau, work, &lwork, &info);
if (info < 0)
Rcpp::Rcout << "Error in forming Q matrix!" << std::endl;
for (integer i = 0; i < P; i++)
dscal_(&N, signs + i, resultM + i * N, &inc);
result->AddToTempData("HHR", HouseHolderResult);
result->AddToTempData("HHRTau", HHRTau);
delete[] jpvt;
delete[] work;
delete[] signs;
if (exetax != nullptr)
delete exetax;
//result->Print("result in qf:");//---
};
GURLS_EXPORT void geqp3( int *m, int *n, double *A, int *lda, int *jpvt, double *tau, double *work, int *lwork, int *info)
{
dgeqp3_(m, n, A, lda, jpvt, tau, work, lwork, info);
}
bool CLinkMatrix::build(const CMatrix< C_FLOAT64 > & matrix)
{
bool success = true;
CMatrix< C_FLOAT64 > M(matrix);
C_INT NumCols = (C_INT) M.numCols();
C_INT NumRows = (C_INT) M.numRows();
C_INT LDA = std::max<C_INT>(1, NumCols);
CVector< C_INT > JPVT(NumRows);
JPVT = 0;
C_INT32 Dim = std::min(NumCols, NumRows);
if (Dim == 0)
{
C_INT32 i;
mRowPivots.resize(NumRows);
for (i = 0; i < NumRows; i++)
mRowPivots[i] = i;
resize(NumRows, 0);
return success;
}
CVector< C_FLOAT64 > TAU(Dim);
CVector< C_FLOAT64 > WORK(1);
C_INT LWORK = -1;
C_INT INFO;
// QR factorization of the stoichiometry matrix
/*
* -- LAPACK routine (version 3.0) --
* Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
* Courant Institute, Argonne National Lab, and Rice University
* June 30, 1999
*
* Purpose
* =======
*
* DGEQP3 computes a QR factorization with column pivoting of a
* matrix A: A*P = Q*R using Level 3 BLAS.
*
* Arguments
* =========
*
* M (input) INTEGER
* The number of rows of the matrix A. M >= 0.
*
* N (input) INTEGER
* The number of columns of the matrix A. N >= 0.
*
* A (input/output) DOUBLE PRECISION array, dimension (LDA,N)
* On entry, the M-by-N matrix A.
* On exit, the upper triangle of the array contains the
* min(M,N)-by-N upper trapezoidal matrix R; the elements below
* the diagonal, together with the array TAU, represent the
* orthogonal matrix Q as a product of min(M,N) elementary
* reflectors.
*
* LDA (input) INTEGER
* The leading dimension of the array A. LDA >= max(1,M).
*
* JPVT (input/output) INTEGER array, dimension (N)
* On entry, if JPVT(J).ne.0, the J-th column of A is permuted
* to the front of A*P (a leading column); if JPVT(J)=0,
* the J-th column of A is a free column.
* On exit, if JPVT(J)=K, then the J-th column of A*P was the
* the K-th column of A.
*
* TAU (output) DOUBLE PRECISION array, dimension (min(M,N))
* The scalar factors of the elementary reflectors.
*
* WORK (workspace/output) DOUBLE PRECISION array, dimension (LWORK)
* On exit, if INFO=0, WORK(1) returns the optimal LWORK.
*
* LWORK (input) INTEGER
* The dimension of the array WORK. LWORK >= 3*N+1.
* For optimal performance LWORK >= 2*N+(N+1)*NB, where NB
* is the optimal blocksize.
*
* If LWORK = -1, then a workspace query is assumed; the routine
* only calculates the optimal size of the WORK array, returns
* this value as the first entry of the WORK array, and no error
* message related to LWORK is issued by XERBLA.
*
* INFO (output) INTEGER
* = 0: successful exit.
* < 0: if INFO = -i, the i-th argument had an illegal value.
*
* Further Details
* ===============
*
* The matrix Q is represented as a product of elementary reflectors
*
* Q = H(1) H(2) . . . H(k), where k = min(m,n).
*
* Each H(i) has the form
*
* H(i) = I - tau * v * v'
*
* where tau is a real/complex scalar, and v is a real/complex vector
* with v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in
* A(i+1:m,i), and tau in TAU(i).
*
* Based on contributions by
* G. Quintana-Orti, Depto. de Informatica, Universidad Jaime I, Spain
* X. Sun, Computer Science Dept., Duke University, USA
*
*/
dgeqp3_(&NumCols, &NumRows, M.array(), &LDA,
JPVT.array(), TAU.array(), WORK.array(), &LWORK, &INFO);
if (INFO < 0) fatalError();
LWORK = (C_INT) WORK[0];
WORK.resize(LWORK);
dgeqp3_(&NumCols, &NumRows, M.array(), &LDA,
JPVT.array(), TAU.array(), WORK.array(), &LWORK, &INFO);
if (INFO < 0) fatalError();
C_INT32 i;
mRowPivots.resize(NumRows);
for (i = 0; i < NumRows; i++)
mRowPivots[i] = JPVT[i] - 1;
C_INT independent = 0;
while (independent < Dim &&
fabs(M(independent, independent)) > 100.0 * std::numeric_limits< C_FLOAT64 >::epsilon()) independent++;
mIndependent = independent;
// Resize mL
resize(NumRows - independent, independent);
if (NumRows == independent || independent == 0)
{
return success;
}
/* to take care of differences between fortran's and c's memory access,
we need to take the transpose, i.e.,the upper triangular */
char cL = 'U';
char cU = 'N'; /* values in the diagonal of R */
// Calculate Row Echelon form of R.
// First invert R_1,1
/* int dtrtri_(char *uplo,
* char *diag,
* integer *n,
* doublereal * A,
* integer *lda,
* integer *info);
* -- LAPACK routine (version 3.0) --
* Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
* Courant Institute, Argonne National Lab, and Rice University
* March 31, 1993
*
* Purpose
* =======
*
* DTRTRI computes the inverse of a real upper or lower triangular
* matrix A.
*
* This is the Level 3 BLAS version of the algorithm.
*
* Arguments
* =========
*
* uplo (input) CHARACTER*1
* = 'U': A is upper triangular;
* = 'L': A is lower triangular.
*
* diag (input) CHARACTER*1
* = 'N': A is non-unit triangular;
* = 'U': A is unit triangular.
*
* n (input) INTEGER
* The order of the matrix A. n >= 0.
*
* A (input/output) DOUBLE PRECISION array, dimension (lda,n)
* On entry, the triangular matrix A. If uplo = 'U', the
* leading n-by-n upper triangular part of the array A contains
* the upper triangular matrix, and the strictly lower
* triangular part of A is not referenced. If uplo = 'L', the
* leading n-by-n lower triangular part of the array A contains
* the lower triangular matrix, and the strictly upper
* triangular part of A is not referenced. If diag = 'U', the
* diagonal elements of A are also not referenced and are
* assumed to be 1.
* On exit, the (triangular) inverse of the original matrix, in
* the same storage format.
*
* lda (input) INTEGER
* The leading dimension of the array A. lda >= 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, A(i,i) is exactly zero. The triangular
* matrix is singular and its inverse can not be computed.
*/
dtrtri_(&cL, &cU, &independent, M.array(), &LDA, &INFO);
if (INFO < 0) fatalError();
C_INT32 j, k;
// Compute Link_0 = inverse(R_1,1) * R_1,2
// :TODO: Use dgemm
C_FLOAT64 * pTmp1 = array();
C_FLOAT64 * pTmp2;
C_FLOAT64 * pTmp3;
for (j = 0; j < NumRows - independent; j++)
for (i = 0; i < independent; i++, pTmp1++)
{
pTmp2 = &M(j + independent, i);
pTmp3 = &M(i, i);
// assert(&mL(j, i) == pTmp3);
*pTmp1 = 0.0;
for (k = i; k < independent; k++, pTmp2++, pTmp3 += NumCols)
{
// assert(&M(j + independent, k) == pTmp2);
// assert(&M(k, i) == pTmp3);
*pTmp1 += *pTmp3 * *pTmp2;
}
if (fabs(*pTmp1) < 100.0 * std::numeric_limits< C_FLOAT64 >::epsilon()) *pTmp1 = 0.0;
}
// We need to convert the pivot vector into a swap vector.
mPivotInverse.resize(mRowPivots.size());
size_t * pCurrentIndex = mPivotInverse.array();
size_t * pEnd = pCurrentIndex + mRowPivots.size();
for (size_t i = 0; pCurrentIndex != pEnd; ++pCurrentIndex, ++i)
{
*pCurrentIndex = i;
}
CVector< size_t > CurrentColumn(mPivotInverse);
size_t * pCurrentColumn = CurrentColumn.array();
mSwapVector.resize(mRowPivots.size());
C_INT * pJPVT = mSwapVector.array();
pCurrentIndex = mPivotInverse.array();
const size_t * pPivot = mRowPivots.array();
for (; pCurrentIndex != pEnd; ++pPivot, ++pJPVT, ++pCurrentIndex, ++pCurrentColumn)
{
// Swap Index
size_t * pToIndex = & mPivotInverse[*pPivot];
size_t * pFromIndex = & mPivotInverse[*pCurrentColumn];
// Swap Column
size_t * pToColumn = & CurrentColumn[*pToIndex];
size_t * pFromColumn = pCurrentColumn;
// Swap
*pJPVT = *pToIndex + 1;
size_t tmp = *pFromIndex;
*pFromIndex = *pToIndex;
*pToIndex = tmp;
tmp = *pFromColumn;
*pFromColumn = *pToColumn;
*pToColumn = tmp;
}
return success;
}
__cminpack_attr__
void __cminpack_func__(qrfac)(int m, int n, real *a, int
lda, int pivot, int *ipvt, int lipvt, real *rdiag,
real *acnorm, real *wa)
{
#ifdef USE_LAPACK
int i, j, k;
double t;
double* tau = wa;
const int ltau = m > n ? n : m;
int lwork = -1;
int info = 0;
double* work;
if (pivot) {
assert( lipvt >= n );
/* set all columns free */
memset(ipvt, 0, sizeof(int)*n);
}
/* query optimal size of work */
lwork = -1;
if (pivot) {
dgeqp3_(&m,&n,a,&lda,ipvt,tau,tau,&lwork,&info);
lwork = (int)tau[0];
assert( lwork >= 3*n+1 );
} else {
dgeqrf_(&m,&n,a,&lda,tau,tau,&lwork,&info);
lwork = (int)tau[0];
assert( lwork >= 1 && lwork >= n );
}
assert( info == 0 );
/* alloc work area */
work = (double *)malloc(sizeof(double)*lwork);
assert(work != NULL);
/* set acnorm first (from the doc of qrfac, acnorm may point to the same area as rdiag) */
if (acnorm != rdiag) {
for (j = 0; j < n; ++j) {
acnorm[j] = __cminpack_enorm__(m, &a[j * lda]);
}
}
/* QR decomposition */
if (pivot) {
dgeqp3_(&m,&n,a,&lda,ipvt,tau,work,&lwork,&info);
} else {
dgeqrf_(&m,&n,a,&lda,tau,work,&lwork,&info);
}
assert(info == 0);
/* set rdiag, before the diagonal is replaced */
memset(rdiag, 0, sizeof(double)*n);
for(i=0 ; i<n ; ++i) {
rdiag[i] = a[i*lda+i];
}
/* modify lower trinagular part to look like qrfac's output */
for(i=0 ; i<ltau ; ++i) {
k = i*lda+i;
t = tau[i];
a[k] = t;
for(j=i+1 ; j<m ; j++) {
k++;
a[k] *= t;
}
}
free(work);
#else /* !USE_LAPACK */
/* Initialized data */
#define p05 .05
/* System generated locals */
real d1;
/* Local variables */
int i, j, k, jp1;
real sum;
real temp;
int minmn;
real epsmch;
real ajnorm;
/* ********** */
/* subroutine qrfac */
/* this subroutine uses householder transformations with column */
/* pivoting (optional) to compute a qr factorization of the */
/* m by n matrix a. that is, qrfac determines an orthogonal */
/* matrix q, a permutation matrix p, and an upper trapezoidal */
/* matrix r with diagonal elements of nonincreasing magnitude, */
/* such that a*p = q*r. the householder transformation for */
/* column k, k = 1,2,...,min(m,n), is of the form */
/* t */
/* i - (1/u(k))*u*u */
/* where u has zeros in the first k-1 positions. the form of */
/* this transformation and the method of pivoting first */
/* appeared in the corresponding linpack subroutine. */
/* the subroutine statement is */
/* subroutine qrfac(m,n,a,lda,pivot,ipvt,lipvt,rdiag,acnorm,wa) */
/* where */
/* m is a positive integer input variable set to the number */
/* of rows of a. */
/* n is a positive integer input variable set to the number */
/* of columns of a. */
/* a is an m by n array. on input a contains the matrix for */
/* which the qr factorization is to be computed. on output */
/* the strict upper trapezoidal part of a contains the strict */
/* upper trapezoidal part of r, and the lower trapezoidal */
/* part of a contains a factored form of q (the non-trivial */
/* elements of the u vectors described above). */
/* lda is a positive integer input variable not less than m */
/* which specifies the leading dimension of the array a. */
/* pivot is a logical input variable. if pivot is set true, */
/* then column pivoting is enforced. if pivot is set false, */
/* then no column pivoting is done. */
/* ipvt is an integer output array of length lipvt. ipvt */
/* defines the permutation matrix p such that a*p = q*r. */
/* column j of p is column ipvt(j) of the identity matrix. */
/* if pivot is false, ipvt is not referenced. */
/* lipvt is a positive integer input variable. if pivot is false, */
/* then lipvt may be as small as 1. if pivot is true, then */
/* lipvt must be at least n. */
/* rdiag is an output array of length n which contains the */
/* diagonal elements of r. */
/* acnorm is an output array of length n which contains the */
/* norms of the corresponding columns of the input matrix a. */
/* if this information is not needed, then acnorm can coincide */
/* with rdiag. */
/* wa is a work array of length n. if pivot is false, then wa */
/* can coincide with rdiag. */
/* subprograms called */
/* minpack-supplied ... dpmpar,enorm */
/* fortran-supplied ... dmax1,dsqrt,min0 */
/* argonne national laboratory. minpack project. march 1980. */
/* burton s. garbow, kenneth e. hillstrom, jorge j. more */
/* ********** */
(void)lipvt;
/* epsmch is the machine precision. */
epsmch = __cminpack_func__(dpmpar)(1);
/* compute the initial column norms and initialize several arrays. */
for (j = 0; j < n; ++j) {
acnorm[j] = __cminpack_enorm__(m, &a[j * lda + 0]);
rdiag[j] = acnorm[j];
wa[j] = rdiag[j];
if (pivot) {
ipvt[j] = j+1;
}
}
/* reduce a to r with householder transformations. */
minmn = min(m,n);
for (j = 0; j < minmn; ++j) {
if (pivot) {
/* bring the column of largest norm into the pivot position. */
int kmax = j;
for (k = j; k < n; ++k) {
if (rdiag[k] > rdiag[kmax]) {
kmax = k;
}
}
if (kmax != j) {
for (i = 0; i < m; ++i) {
temp = a[i + j * lda];
a[i + j * lda] = a[i + kmax * lda];
a[i + kmax * lda] = temp;
}
rdiag[kmax] = rdiag[j];
wa[kmax] = wa[j];
k = ipvt[j];
ipvt[j] = ipvt[kmax];
ipvt[kmax] = k;
}
}
/* compute the householder transformation to reduce the */
/* j-th column of a to a multiple of the j-th unit vector. */
ajnorm = __cminpack_enorm__(m - (j+1) + 1, &a[j + j * lda]);
if (ajnorm != 0.) {
if (a[j + j * lda] < 0.) {
ajnorm = -ajnorm;
}
for (i = j; i < m; ++i) {
a[i + j * lda] /= ajnorm;
}
a[j + j * lda] += 1.;
/* apply the transformation to the remaining columns */
/* and update the norms. */
jp1 = j + 1;
if (n > jp1) {
for (k = jp1; k < n; ++k) {
sum = 0.;
for (i = j; i < m; ++i) {
sum += a[i + j * lda] * a[i + k * lda];
}
temp = sum / a[j + j * lda];
for (i = j; i < m; ++i) {
a[i + k * lda] -= temp * a[i + j * lda];
}
if (pivot && rdiag[k] != 0.) {
temp = a[j + k * lda] / rdiag[k];
/* Computing MAX */
d1 = 1. - temp * temp;
rdiag[k] *= sqrt((max((real)0.,d1)));
/* Computing 2nd power */
d1 = rdiag[k] / wa[k];
if (p05 * (d1 * d1) <= epsmch) {
rdiag[k] = __cminpack_enorm__(m - (j+1), &a[jp1 + k * lda]);
wa[k] = rdiag[k];
}
}
}
}
}
rdiag[j] = -ajnorm;
}
/* last card of subroutine qrfac. */
#endif /* !USE_LAPACK */
} /* qrfac_ */
/* Subroutine */ int dgelsy_(integer *m, integer *n, integer *nrhs,
doublereal *a, integer *lda, doublereal *b, integer *ldb, integer *
jpvt, doublereal *rcond, integer *rank, doublereal *work, integer *
lwork, integer *info)
{
/* -- LAPACK driver routine (version 3.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
June 30, 1999
Purpose
=======
DGELSY computes the minimum-norm solution to a real linear least
squares problem:
minimize || A * X - B ||
using a complete orthogonal factorization of A. A is an M-by-N
matrix which may be rank-deficient.
Several right hand side vectors b and solution vectors x can be
handled in a single call; they are stored as the columns of the
M-by-NRHS right hand side matrix B and the N-by-NRHS solution
matrix X.
The routine first computes a QR factorization with column pivoting:
A * P = Q * [ R11 R12 ]
[ 0 R22 ]
with R11 defined as the largest leading submatrix whose estimated
condition number is less than 1/RCOND. The order of R11, RANK,
is the effective rank of A.
Then, R22 is considered to be negligible, and R12 is annihilated
by orthogonal transformations from the right, arriving at the
complete orthogonal factorization:
A * P = Q * [ T11 0 ] * Z
[ 0 0 ]
The minimum-norm solution is then
X = P * Z' [ inv(T11)*Q1'*B ]
[ 0 ]
where Q1 consists of the first RANK columns of Q.
This routine is basically identical to the original xGELSX except
three differences:
o The call to the subroutine xGEQPF has been substituted by the
the call to the subroutine xGEQP3. This subroutine is a Blas-3
version of the QR factorization with column pivoting.
o Matrix B (the right hand side) is updated with Blas-3.
o The permutation of matrix B (the right hand side) is faster and
more simple.
Arguments
=========
M (input) INTEGER
The number of rows of the matrix A. M >= 0.
N (input) INTEGER
The number of columns of the matrix A. N >= 0.
NRHS (input) INTEGER
The number of right hand sides, i.e., the number of
columns of matrices B and X. NRHS >= 0.
A (input/output) DOUBLE PRECISION array, dimension (LDA,N)
On entry, the M-by-N matrix A.
On exit, A has been overwritten by details of its
complete orthogonal factorization.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,M).
B (input/output) DOUBLE PRECISION array, dimension (LDB,NRHS)
On entry, the M-by-NRHS right hand side matrix B.
On exit, the N-by-NRHS solution matrix X.
LDB (input) INTEGER
The leading dimension of the array B. LDB >= max(1,M,N).
JPVT (input/output) INTEGER array, dimension (N)
On entry, if JPVT(i) .ne. 0, the i-th column of A is permuted
to the front of AP, otherwise column i is a free column.
On exit, if JPVT(i) = k, then the i-th column of AP
was the k-th column of A.
RCOND (input) DOUBLE PRECISION
RCOND is used to determine the effective rank of A, which
is defined as the order of the largest leading triangular
submatrix R11 in the QR factorization with pivoting of A,
whose estimated condition number < 1/RCOND.
RANK (output) INTEGER
The effective rank of A, i.e., the order of the submatrix
R11. This is the same as the order of the submatrix T11
in the complete orthogonal factorization of A.
WORK (workspace/output) DOUBLE PRECISION array, dimension (LWORK)
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORK (input) INTEGER
The dimension of the array WORK.
The unblocked strategy requires that:
LWORK >= MAX( MN+3*N+1, 2*MN+NRHS ),
where MN = min( M, N ).
The block algorithm requires that:
LWORK >= MAX( MN+2*N+NB*(N+1), 2*MN+NB*NRHS ),
where NB is an upper bound on the blocksize returned
by ILAENV for the routines DGEQP3, DTZRZF, STZRQF, DORMQR,
and DORMRZ.
If LWORK = -1, then a workspace query is assumed; the routine
only calculates the optimal size of the WORK array, returns
this value as the first entry of the WORK array, and no error
message related to LWORK is issued by XERBLA.
INFO (output) INTEGER
= 0: successful exit
< 0: If INFO = -i, the i-th argument had an illegal value.
Further Details
===============
Based on contributions by
A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA
E. Quintana-Orti, Depto. de Informatica, Universidad Jaime I, Spain
G. Quintana-Orti, Depto. de Informatica, Universidad Jaime I, Spain
=====================================================================
Parameter adjustments */
/* Table of constant values */
static integer c__1 = 1;
static integer c_n1 = -1;
static integer c__0 = 0;
static doublereal c_b31 = 0.;
static integer c__2 = 2;
static doublereal c_b54 = 1.;
/* System generated locals */
integer a_dim1, a_offset, b_dim1, b_offset, i__1, i__2;
doublereal d__1, d__2;
/* Local variables */
static doublereal anrm, bnrm, smin, smax;
static integer i__, j, iascl, ibscl;
extern /* Subroutine */ int dcopy_(integer *, doublereal *, integer *,
doublereal *, integer *);
static integer ismin, ismax;
static doublereal c1, c2;
extern /* Subroutine */ int dtrsm_(char *, char *, char *, char *,
integer *, integer *, doublereal *, doublereal *, integer *,
doublereal *, integer *), dlaic1_(
integer *, integer *, doublereal *, doublereal *, doublereal *,
doublereal *, doublereal *, doublereal *, doublereal *);
static doublereal wsize, s1, s2;
extern /* Subroutine */ int dgeqp3_(integer *, integer *, doublereal *,
integer *, integer *, doublereal *, doublereal *, integer *,
integer *), dlabad_(doublereal *, doublereal *);
static integer nb;
extern doublereal dlamch_(char *), dlange_(char *, integer *,
integer *, doublereal *, integer *, doublereal *);
static integer mn;
extern /* Subroutine */ int dlascl_(char *, integer *, integer *,
doublereal *, doublereal *, integer *, integer *, doublereal *,
integer *, integer *), dlaset_(char *, integer *, integer
*, doublereal *, doublereal *, doublereal *, integer *),
xerbla_(char *, integer *);
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *, ftnlen, ftnlen);
static doublereal bignum;
static integer nb1, nb2, nb3, nb4;
extern /* Subroutine */ int dormqr_(char *, char *, integer *, integer *,
integer *, doublereal *, integer *, doublereal *, doublereal *,
integer *, doublereal *, integer *, integer *);
static doublereal sminpr, smaxpr, smlnum;
extern /* Subroutine */ int dormrz_(char *, char *, integer *, integer *,
integer *, integer *, doublereal *, integer *, doublereal *,
doublereal *, integer *, doublereal *, integer *, integer *);
static integer lwkopt;
static logical lquery;
extern /* Subroutine */ int dtzrzf_(integer *, integer *, doublereal *,
integer *, doublereal *, doublereal *, integer *, integer *);
#define a_ref(a_1,a_2) a[(a_2)*a_dim1 + a_1]
#define b_ref(a_1,a_2) b[(a_2)*b_dim1 + a_1]
a_dim1 = *lda;
a_offset = 1 + a_dim1 * 1;
a -= a_offset;
b_dim1 = *ldb;
b_offset = 1 + b_dim1 * 1;
b -= b_offset;
--jpvt;
--work;
/* Function Body */
mn = min(*m,*n);
ismin = mn + 1;
ismax = (mn << 1) + 1;
/* Test the input arguments. */
*info = 0;
nb1 = ilaenv_(&c__1, "DGEQRF", " ", m, n, &c_n1, &c_n1, (ftnlen)6, (
ftnlen)1);
nb2 = ilaenv_(&c__1, "DGERQF", " ", m, n, &c_n1, &c_n1, (ftnlen)6, (
ftnlen)1);
nb3 = ilaenv_(&c__1, "DORMQR", " ", m, n, nrhs, &c_n1, (ftnlen)6, (ftnlen)
1);
nb4 = ilaenv_(&c__1, "DORMRQ", " ", m, n, nrhs, &c_n1, (ftnlen)6, (ftnlen)
1);
/* Computing MAX */
i__1 = max(nb1,nb2), i__1 = max(i__1,nb3);
nb = max(i__1,nb4);
/* Computing MAX */
i__1 = 1, i__2 = mn + (*n << 1) + nb * (*n + 1), i__1 = max(i__1,i__2),
i__2 = (mn << 1) + nb * *nrhs;
lwkopt = max(i__1,i__2);
work[1] = (doublereal) lwkopt;
lquery = *lwork == -1;
if (*m < 0) {
*info = -1;
} else if (*n < 0) {
*info = -2;
} else if (*nrhs < 0) {
*info = -3;
} else if (*lda < max(1,*m)) {
*info = -5;
} else /* if(complicated condition) */ {
/* Computing MAX */
i__1 = max(1,*m);
if (*ldb < max(i__1,*n)) {
*info = -7;
} else /* if(complicated condition) */ {
/* Computing MAX */
i__1 = 1, i__2 = mn + *n * 3 + 1, i__1 = max(i__1,i__2), i__2 = (
mn << 1) + *nrhs;
if (*lwork < max(i__1,i__2) && ! lquery) {
*info = -12;
}
}
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("DGELSY", &i__1);
return 0;
} else if (lquery) {
return 0;
}
/* Quick return if possible
Computing MIN */
i__1 = min(*m,*n);
if (min(i__1,*nrhs) == 0) {
*rank = 0;
return 0;
}
/* Get machine parameters */
smlnum = dlamch_("S") / dlamch_("P");
bignum = 1. / smlnum;
dlabad_(&smlnum, &bignum);
/* Scale A, B if max entries outside range [SMLNUM,BIGNUM] */
anrm = dlange_("M", m, n, &a[a_offset], lda, &work[1]);
iascl = 0;
if (anrm > 0. && anrm < smlnum) {
/* Scale matrix norm up to SMLNUM */
dlascl_("G", &c__0, &c__0, &anrm, &smlnum, m, n, &a[a_offset], lda,
info);
iascl = 1;
} else if (anrm > bignum) {
/* Scale matrix norm down to BIGNUM */
dlascl_("G", &c__0, &c__0, &anrm, &bignum, m, n, &a[a_offset], lda,
info);
iascl = 2;
} else if (anrm == 0.) {
/* Matrix all zero. Return zero solution. */
i__1 = max(*m,*n);
dlaset_("F", &i__1, nrhs, &c_b31, &c_b31, &b[b_offset], ldb);
*rank = 0;
goto L70;
}
bnrm = dlange_("M", m, nrhs, &b[b_offset], ldb, &work[1]);
ibscl = 0;
if (bnrm > 0. && bnrm < smlnum) {
/* Scale matrix norm up to SMLNUM */
dlascl_("G", &c__0, &c__0, &bnrm, &smlnum, m, nrhs, &b[b_offset], ldb,
info);
ibscl = 1;
} else if (bnrm > bignum) {
/* Scale matrix norm down to BIGNUM */
dlascl_("G", &c__0, &c__0, &bnrm, &bignum, m, nrhs, &b[b_offset], ldb,
info);
ibscl = 2;
}
/* Compute QR factorization with column pivoting of A:
A * P = Q * R */
i__1 = *lwork - mn;
dgeqp3_(m, n, &a[a_offset], lda, &jpvt[1], &work[1], &work[mn + 1], &i__1,
info);
wsize = mn + work[mn + 1];
/* workspace: MN+2*N+NB*(N+1).
Details of Householder rotations stored in WORK(1:MN).
Determine RANK using incremental condition estimation */
work[ismin] = 1.;
work[ismax] = 1.;
smax = (d__1 = a_ref(1, 1), abs(d__1));
smin = smax;
if ((d__1 = a_ref(1, 1), abs(d__1)) == 0.) {
*rank = 0;
i__1 = max(*m,*n);
dlaset_("F", &i__1, nrhs, &c_b31, &c_b31, &b[b_offset], ldb);
goto L70;
} else {
*rank = 1;
}
L10:
if (*rank < mn) {
i__ = *rank + 1;
dlaic1_(&c__2, rank, &work[ismin], &smin, &a_ref(1, i__), &a_ref(i__,
i__), &sminpr, &s1, &c1);
dlaic1_(&c__1, rank, &work[ismax], &smax, &a_ref(1, i__), &a_ref(i__,
i__), &smaxpr, &s2, &c2);
if (smaxpr * *rcond <= sminpr) {
i__1 = *rank;
for (i__ = 1; i__ <= i__1; ++i__) {
work[ismin + i__ - 1] = s1 * work[ismin + i__ - 1];
work[ismax + i__ - 1] = s2 * work[ismax + i__ - 1];
/* L20: */
}
work[ismin + *rank] = c1;
work[ismax + *rank] = c2;
smin = sminpr;
smax = smaxpr;
++(*rank);
goto L10;
}
}
/* workspace: 3*MN.
Logically partition R = [ R11 R12 ]
[ 0 R22 ]
where R11 = R(1:RANK,1:RANK)
[R11,R12] = [ T11, 0 ] * Y */
if (*rank < *n) {
i__1 = *lwork - (mn << 1);
dtzrzf_(rank, n, &a[a_offset], lda, &work[mn + 1], &work[(mn << 1) +
1], &i__1, info);
}
/* workspace: 2*MN.
Details of Householder rotations stored in WORK(MN+1:2*MN)
B(1:M,1:NRHS) := Q' * B(1:M,1:NRHS) */
i__1 = *lwork - (mn << 1);
dormqr_("Left", "Transpose", m, nrhs, &mn, &a[a_offset], lda, &work[1], &
b[b_offset], ldb, &work[(mn << 1) + 1], &i__1, info);
/* Computing MAX */
d__1 = wsize, d__2 = (mn << 1) + work[(mn << 1) + 1];
wsize = max(d__1,d__2);
/* workspace: 2*MN+NB*NRHS.
B(1:RANK,1:NRHS) := inv(T11) * B(1:RANK,1:NRHS) */
dtrsm_("Left", "Upper", "No transpose", "Non-unit", rank, nrhs, &c_b54, &
a[a_offset], lda, &b[b_offset], ldb);
i__1 = *nrhs;
for (j = 1; j <= i__1; ++j) {
i__2 = *n;
for (i__ = *rank + 1; i__ <= i__2; ++i__) {
b_ref(i__, j) = 0.;
/* L30: */
}
/* L40: */
}
/* B(1:N,1:NRHS) := Y' * B(1:N,1:NRHS) */
if (*rank < *n) {
i__1 = *n - *rank;
i__2 = *lwork - (mn << 1);
dormrz_("Left", "Transpose", n, nrhs, rank, &i__1, &a[a_offset], lda,
&work[mn + 1], &b[b_offset], ldb, &work[(mn << 1) + 1], &i__2,
info);
}
/* workspace: 2*MN+NRHS.
B(1:N,1:NRHS) := P * B(1:N,1:NRHS) */
i__1 = *nrhs;
for (j = 1; j <= i__1; ++j) {
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
work[jpvt[i__]] = b_ref(i__, j);
/* L50: */
}
dcopy_(n, &work[1], &c__1, &b_ref(1, j), &c__1);
/* L60: */
}
/* workspace: N.
Undo scaling */
if (iascl == 1) {
dlascl_("G", &c__0, &c__0, &anrm, &smlnum, n, nrhs, &b[b_offset], ldb,
info);
dlascl_("U", &c__0, &c__0, &smlnum, &anrm, rank, rank, &a[a_offset],
lda, info);
} else if (iascl == 2) {
dlascl_("G", &c__0, &c__0, &anrm, &bignum, n, nrhs, &b[b_offset], ldb,
info);
dlascl_("U", &c__0, &c__0, &bignum, &anrm, rank, rank, &a[a_offset],
lda, info);
}
if (ibscl == 1) {
dlascl_("G", &c__0, &c__0, &smlnum, &bnrm, n, nrhs, &b[b_offset], ldb,
info);
} else if (ibscl == 2) {
dlascl_("G", &c__0, &c__0, &bignum, &bnrm, n, nrhs, &b[b_offset], ldb,
info);
}
L70:
work[1] = (doublereal) lwkopt;
return 0;
/* End of DGELSY */
} /* dgelsy_ */
/* Subroutine */ int dchkq3_(logical *dotype, integer *nm, integer *mval,
integer *nn, integer *nval, integer *nnb, integer *nbval, integer *
nxval, doublereal *thresh, doublereal *a, doublereal *copya,
doublereal *s, doublereal *copys, doublereal *tau, doublereal *work,
integer *iwork, integer *nout)
{
/* Initialized data */
static integer iseedy[4] = { 1988,1989,1990,1991 };
/* Format strings */
static char fmt_9999[] = "(1x,a,\002 M =\002,i5,\002, N =\002,i5,\002, N"
"B =\002,i4,\002, type \002,i2,\002, test \002,i2,\002, ratio "
"=\002,g12.5)";
/* System generated locals */
integer i__1, i__2, i__3, i__4, i__5;
doublereal d__1;
/* Builtin functions */
/* Subroutine */ int s_copy(char *, char *, ftnlen, ftnlen);
integer s_wsfe(cilist *), do_fio(integer *, char *, ftnlen), e_wsfe(void);
/* Local variables */
integer i__, k, m, n, nb, im, in, lw, nx, lda, inb;
doublereal eps;
integer mode, info;
char path[3];
integer ilow, nrun;
extern /* Subroutine */ int alahd_(integer *, char *);
integer ihigh, nfail, iseed[4], imode;
extern doublereal dqpt01_(integer *, integer *, integer *, doublereal *,
doublereal *, integer *, doublereal *, integer *, doublereal *,
integer *), dqrt11_(integer *, integer *, doublereal *, integer *,
doublereal *, doublereal *, integer *), dqrt12_(integer *,
integer *, doublereal *, integer *, doublereal *, doublereal *,
integer *);
integer mnmin;
extern /* Subroutine */ int icopy_(integer *, integer *, integer *,
integer *, integer *);
integer istep, nerrs, lwork;
extern /* Subroutine */ int dgeqp3_(integer *, integer *, doublereal *,
integer *, integer *, doublereal *, doublereal *, integer *,
integer *);
extern doublereal dlamch_(char *);
extern /* Subroutine */ int dlaord_(char *, integer *, doublereal *,
integer *), dlacpy_(char *, integer *, integer *,
doublereal *, integer *, doublereal *, integer *),
dlaset_(char *, integer *, integer *, doublereal *, doublereal *,
doublereal *, integer *), alasum_(char *, integer *,
integer *, integer *, integer *), dlatms_(integer *,
integer *, char *, integer *, char *, doublereal *, integer *,
doublereal *, doublereal *, integer *, integer *, char *,
doublereal *, integer *, doublereal *, integer *), xlaenv_(integer *, integer *);
doublereal result[3];
/* Fortran I/O blocks */
static cilist io___28 = { 0, 0, 0, fmt_9999, 0 };
/* -- LAPACK test routine (version 3.1.1) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* January 2007 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* DCHKQ3 tests DGEQP3. */
/* Arguments */
/* ========= */
/* DOTYPE (input) LOGICAL array, dimension (NTYPES) */
/* The matrix types to be used for testing. Matrices of type j */
/* (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) = */
/* .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used. */
/* NM (input) INTEGER */
/* The number of values of M contained in the vector MVAL. */
/* MVAL (input) INTEGER array, dimension (NM) */
/* The values of the matrix row dimension M. */
/* NN (input) INTEGER */
/* The number of values of N contained in the vector NVAL. */
/* NVAL (input) INTEGER array, dimension (NN) */
/* The values of the matrix column dimension N. */
/* NNB (input) INTEGER */
/* The number of values of NB and NX contained in the */
/* vectors NBVAL and NXVAL. The blocking parameters are used */
/* in pairs (NB,NX). */
/* NBVAL (input) INTEGER array, dimension (NNB) */
/* The values of the blocksize NB. */
/* NXVAL (input) INTEGER array, dimension (NNB) */
/* The values of the crossover point NX. */
/* THRESH (input) DOUBLE PRECISION */
/* The threshold value for the test ratios. A result is */
/* included in the output file if RESULT >= THRESH. To have */
/* every test ratio printed, use THRESH = 0. */
/* A (workspace) DOUBLE PRECISION array, dimension (MMAX*NMAX) */
/* where MMAX is the maximum value of M in MVAL and NMAX is the */
/* maximum value of N in NVAL. */
/* COPYA (workspace) DOUBLE PRECISION array, dimension (MMAX*NMAX) */
/* S (workspace) DOUBLE PRECISION array, dimension */
/* (min(MMAX,NMAX)) */
/* COPYS (workspace) DOUBLE PRECISION array, dimension */
/* (min(MMAX,NMAX)) */
/* TAU (workspace) DOUBLE PRECISION array, dimension (MMAX) */
/* WORK (workspace) DOUBLE PRECISION array, dimension */
/* (MMAX*NMAX + 4*NMAX + MMAX) */
/* IWORK (workspace) INTEGER array, dimension (2*NMAX) */
/* NOUT (input) INTEGER */
/* The unit number for output. */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. Local Arrays .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Scalars in Common .. */
/* .. */
/* .. Common blocks .. */
/* .. */
/* .. Data statements .. */
/* Parameter adjustments */
--iwork;
--work;
--tau;
--copys;
--s;
--copya;
--a;
--nxval;
--nbval;
--nval;
--mval;
--dotype;
/* Function Body */
/* .. */
/* .. Executable Statements .. */
/* Initialize constants and the random number seed. */
s_copy(path, "Double precision", (ftnlen)1, (ftnlen)16);
s_copy(path + 1, "Q3", (ftnlen)2, (ftnlen)2);
nrun = 0;
nfail = 0;
nerrs = 0;
for (i__ = 1; i__ <= 4; ++i__) {
iseed[i__ - 1] = iseedy[i__ - 1];
/* L10: */
}
eps = dlamch_("Epsilon");
infoc_1.infot = 0;
i__1 = *nm;
for (im = 1; im <= i__1; ++im) {
/* Do for each value of M in MVAL. */
m = mval[im];
lda = max(1,m);
i__2 = *nn;
for (in = 1; in <= i__2; ++in) {
/* Do for each value of N in NVAL. */
n = nval[in];
mnmin = min(m,n);
/* Computing MAX */
i__3 = 1, i__4 = m * max(m,n) + (mnmin << 2) + max(m,n), i__3 =
max(i__3,i__4), i__4 = m * n + (mnmin << 1) + (n << 2);
lwork = max(i__3,i__4);
for (imode = 1; imode <= 6; ++imode) {
if (! dotype[imode]) {
goto L70;
}
/* Do for each type of matrix */
/* 1: zero matrix */
/* 2: one small singular value */
/* 3: geometric distribution of singular values */
/* 4: first n/2 columns fixed */
/* 5: last n/2 columns fixed */
/* 6: every second column fixed */
mode = imode;
if (imode > 3) {
mode = 1;
}
/* Generate test matrix of size m by n using */
/* singular value distribution indicated by `mode'. */
i__3 = n;
for (i__ = 1; i__ <= i__3; ++i__) {
iwork[i__] = 0;
/* L20: */
}
if (imode == 1) {
dlaset_("Full", &m, &n, &c_b11, &c_b11, ©a[1], &lda);
i__3 = mnmin;
for (i__ = 1; i__ <= i__3; ++i__) {
copys[i__] = 0.;
/* L30: */
}
} else {
d__1 = 1. / eps;
dlatms_(&m, &n, "Uniform", iseed, "Nonsymm", ©s[1], &
mode, &d__1, &c_b16, &m, &n, "No packing", ©a[
1], &lda, &work[1], &info);
if (imode >= 4) {
if (imode == 4) {
ilow = 1;
istep = 1;
/* Computing MAX */
i__3 = 1, i__4 = n / 2;
ihigh = max(i__3,i__4);
} else if (imode == 5) {
/* Computing MAX */
i__3 = 1, i__4 = n / 2;
ilow = max(i__3,i__4);
istep = 1;
ihigh = n;
} else if (imode == 6) {
ilow = 1;
istep = 2;
ihigh = n;
}
i__3 = ihigh;
i__4 = istep;
for (i__ = ilow; i__4 < 0 ? i__ >= i__3 : i__ <= i__3;
i__ += i__4) {
iwork[i__] = 1;
/* L40: */
}
}
dlaord_("Decreasing", &mnmin, ©s[1], &c__1);
}
i__4 = *nnb;
for (inb = 1; inb <= i__4; ++inb) {
/* Do for each pair of values (NB,NX) in NBVAL and NXVAL. */
nb = nbval[inb];
xlaenv_(&c__1, &nb);
nx = nxval[inb];
xlaenv_(&c__3, &nx);
/* Get a working copy of COPYA into A and a copy of */
/* vector IWORK. */
dlacpy_("All", &m, &n, ©a[1], &lda, &a[1], &lda);
icopy_(&n, &iwork[1], &c__1, &iwork[n + 1], &c__1);
/* Compute the QR factorization with pivoting of A */
/* Computing MAX */
i__3 = 1, i__5 = (n << 1) + nb * (n + 1);
lw = max(i__3,i__5);
/* Compute the QP3 factorization of A */
s_copy(srnamc_1.srnamt, "DGEQP3", (ftnlen)32, (ftnlen)6);
dgeqp3_(&m, &n, &a[1], &lda, &iwork[n + 1], &tau[1], &
work[1], &lw, &info);
/* Compute norm(svd(a) - svd(r)) */
result[0] = dqrt12_(&m, &n, &a[1], &lda, ©s[1], &work[
1], &lwork);
/* Compute norm( A*P - Q*R ) */
result[1] = dqpt01_(&m, &n, &mnmin, ©a[1], &a[1], &
lda, &tau[1], &iwork[n + 1], &work[1], &lwork);
/* Compute Q'*Q */
result[2] = dqrt11_(&m, &mnmin, &a[1], &lda, &tau[1], &
work[1], &lwork);
/* Print information about the tests that did not pass */
/* the threshold. */
for (k = 1; k <= 3; ++k) {
if (result[k - 1] >= *thresh) {
if (nfail == 0 && nerrs == 0) {
alahd_(nout, path);
}
io___28.ciunit = *nout;
s_wsfe(&io___28);
do_fio(&c__1, "DGEQP3", (ftnlen)6);
do_fio(&c__1, (char *)&m, (ftnlen)sizeof(integer))
;
do_fio(&c__1, (char *)&n, (ftnlen)sizeof(integer))
;
do_fio(&c__1, (char *)&nb, (ftnlen)sizeof(integer)
);
do_fio(&c__1, (char *)&imode, (ftnlen)sizeof(
integer));
do_fio(&c__1, (char *)&k, (ftnlen)sizeof(integer))
;
do_fio(&c__1, (char *)&result[k - 1], (ftnlen)
sizeof(doublereal));
e_wsfe();
++nfail;
}
/* L50: */
}
nrun += 3;
/* L60: */
}
L70:
;
}
/* L80: */
}
/* L90: */
}
/* Print a summary of the results. */
alasum_(path, nout, &nfail, &nrun, &nerrs);
/* End of DCHKQ3 */
return 0;
} /* dchkq3_ */
