/* Subroutine */ int dgeqpf_(integer *m, integer *n, doublereal *a, integer *
lda, integer *jpvt, doublereal *tau, doublereal *work, integer *info)
{
/* -- LAPACK test routine (version 2.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
March 31, 1993
Purpose
=======
DGEQPF computes a QR factorization with column pivoting of a
real M-by-N matrix A: A*P = Q*R.
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 triangular 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(i) .ne. 0, the i-th column of A is permuted
to the front of A*P (a leading column); if JPVT(i) = 0,
the i-th column of A is a free column.
On exit, if JPVT(i) = k, then the i-th column of A*P
was the k-th column of A.
TAU (output) DOUBLE PRECISION array, dimension (min(M,N))
The scalar factors of the elementary reflectors.
WORK (workspace) DOUBLE PRECISION array, dimension (3*N)
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(n)
Each H(i) has the form
H = I - tau * v * v'
where tau is a real scalar, and v is a real 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).
The matrix P is represented in jpvt as follows: If
jpvt(j) = i
then the jth column of P is the ith canonical unit vector.
=====================================================================
Test the input arguments
Parameter adjustments
Function Body */
/* Table of constant values */
static integer c__1 = 1;
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2, i__3;
doublereal d__1, d__2;
/* Builtin functions */
double sqrt(doublereal);
/* Local variables */
static doublereal temp;
extern doublereal dnrm2_(integer *, doublereal *, integer *);
static doublereal temp2;
static integer i, j;
extern /* Subroutine */ int dlarf_(char *, integer *, integer *,
doublereal *, integer *, doublereal *, doublereal *, integer *,
doublereal *);
static integer itemp;
extern /* Subroutine */ int dswap_(integer *, doublereal *, integer *,
doublereal *, integer *), dgeqr2_(integer *, integer *,
doublereal *, integer *, doublereal *, doublereal *, integer *),
dorm2r_(char *, char *, integer *, integer *, integer *,
doublereal *, integer *, doublereal *, doublereal *, integer *,
doublereal *, integer *);
static integer ma, mn;
extern /* Subroutine */ int dlarfg_(integer *, doublereal *, doublereal *,
integer *, doublereal *);
extern integer idamax_(integer *, doublereal *, integer *);
extern /* Subroutine */ int xerbla_(char *, integer *);
static doublereal aii;
static integer pvt;
#define JPVT(I) jpvt[(I)-1]
#define TAU(I) tau[(I)-1]
#define WORK(I) work[(I)-1]
#define A(I,J) a[(I)-1 + ((J)-1)* ( *lda)]
*info = 0;
if (*m < 0) {
*info = -1;
} else if (*n < 0) {
*info = -2;
} else if (*lda < max(1,*m)) {
*info = -4;
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("DGEQPF", &i__1);
return 0;
}
mn = min(*m,*n);
/* Move initial columns up front */
itemp = 1;
i__1 = *n;
for (i = 1; i <= *n; ++i) {
if (JPVT(i) != 0) {
if (i != itemp) {
dswap_(m, &A(1,i), &c__1, &A(1,itemp), &
c__1);
JPVT(i) = JPVT(itemp);
JPVT(itemp) = i;
} else {
JPVT(i) = i;
}
++itemp;
} else {
JPVT(i) = i;
}
/* L10: */
}
--itemp;
/* Compute the QR factorization and update remaining columns */
if (itemp > 0) {
ma = min(itemp,*m);
dgeqr2_(m, &ma, &A(1,1), lda, &TAU(1), &WORK(1), info);
if (ma < *n) {
i__1 = *n - ma;
dorm2r_("Left", "Transpose", m, &i__1, &ma, &A(1,1), lda, &
TAU(1), &A(1,ma+1), lda, &WORK(1), info);
}
}
if (itemp < mn) {
/* Initialize partial column norms. The first n elements of
work store the exact column norms. */
i__1 = *n;
for (i = itemp + 1; i <= *n; ++i) {
i__2 = *m - itemp;
WORK(i) = dnrm2_(&i__2, &A(itemp+1,i), &c__1);
WORK(*n + i) = WORK(i);
/* L20: */
}
/* Compute factorization */
i__1 = mn;
for (i = itemp + 1; i <= mn; ++i) {
/* Determine ith pivot column and swap if necessary */
i__2 = *n - i + 1;
pvt = i - 1 + idamax_(&i__2, &WORK(i), &c__1);
if (pvt != i) {
dswap_(m, &A(1,pvt), &c__1, &A(1,i), &
c__1);
itemp = JPVT(pvt);
JPVT(pvt) = JPVT(i);
JPVT(i) = itemp;
WORK(pvt) = WORK(i);
WORK(*n + pvt) = WORK(*n + i);
}
/* Generate elementary reflector H(i) */
if (i < *m) {
i__2 = *m - i + 1;
dlarfg_(&i__2, &A(i,i), &A(i+1,i), &
c__1, &TAU(i));
} else {
dlarfg_(&c__1, &A(*m,*m), &A(*m,*m), &
c__1, &TAU(*m));
}
if (i < *n) {
/* Apply H(i) to A(i:m,i+1:n) from the left */
aii = A(i,i);
A(i,i) = 1.;
i__2 = *m - i + 1;
i__3 = *n - i;
dlarf_("LEFT", &i__2, &i__3, &A(i,i), &c__1, &TAU(
i), &A(i,i+1), lda, &WORK((*n << 1) +
1));
A(i,i) = aii;
}
/* Update partial column norms */
i__2 = *n;
for (j = i + 1; j <= *n; ++j) {
if (WORK(j) != 0.) {
/* Computing 2nd power */
d__2 = (d__1 = A(i,j), abs(d__1)) / WORK(j);
temp = 1. - d__2 * d__2;
temp = max(temp,0.);
/* Computing 2nd power */
d__1 = WORK(j) / WORK(*n + j);
temp2 = temp * .05 * (d__1 * d__1) + 1.;
if (temp2 == 1.) {
if (*m - i > 0) {
i__3 = *m - i;
WORK(j) = dnrm2_(&i__3, &A(i+1,j), &
c__1);
WORK(*n + j) = WORK(j);
} else {
WORK(j) = 0.;
WORK(*n + j) = 0.;
}
} else {
WORK(j) *= sqrt(temp);
}
}
/* L30: */
}
/* L40: */
}
}
return 0;
/* End of DGEQPF */
} /* dgeqpf_ */
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;
}
/* Subroutine */ int dgelsx_(integer *m, integer *n, integer *nrhs,
doublereal *a, integer *lda, doublereal *b, integer *ldb, integer *
jpvt, doublereal *rcond, integer *rank, doublereal *work, integer *
info)
{
/* -- LAPACK driver routine (version 2.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
March 31, 1993
Purpose
=======
DGELSX 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.
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.
If m >= n and RANK = n, the residual sum-of-squares for
the solution in the i-th column is given by the sum of
squares of elements N+1:M in that column.
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 an
initial column, otherwise it is a free column. Before
the QR factorization of A, all initial columns are
permuted to the leading positions; only the remaining
free columns are moved as a result of column pivoting
during the factorization.
On exit, if JPVT(i) = k, then the i-th column of A*P
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) DOUBLE PRECISION array, dimension
(max( min(M,N)+3*N, 2*min(M,N)+NRHS )),
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
=====================================================================
Parameter adjustments
Function Body */
/* Table of constant values */
static integer c__0 = 0;
static doublereal c_b13 = 0.;
static integer c__2 = 2;
static integer c__1 = 1;
static doublereal c_b36 = 1.;
/* System generated locals */
integer a_dim1, a_offset, b_dim1, b_offset, i__1, i__2;
doublereal d__1;
/* Local variables */
static doublereal anrm, bnrm, smin, smax;
static integer i, j, k, iascl, ibscl, 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 s1, s2, t1, t2;
extern /* Subroutine */ int dorm2r_(char *, char *, integer *, integer *,
integer *, doublereal *, integer *, doublereal *, doublereal *,
integer *, doublereal *, integer *), dlabad_(
doublereal *, doublereal *);
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 *), dgeqpf_(integer *, integer *,
doublereal *, integer *, integer *, doublereal *, doublereal *,
integer *), dlaset_(char *, integer *, integer *, doublereal *,
doublereal *, doublereal *, integer *), xerbla_(char *,
integer *);
static doublereal bignum;
extern /* Subroutine */ int dlatzm_(char *, integer *, integer *,
doublereal *, integer *, doublereal *, doublereal *, doublereal *,
integer *, doublereal *);
static doublereal sminpr, smaxpr, smlnum;
extern /* Subroutine */ int dtzrqf_(integer *, integer *, doublereal *,
integer *, doublereal *, integer *);
#define JPVT(I) jpvt[(I)-1]
#define WORK(I) work[(I)-1]
#define A(I,J) a[(I)-1 + ((J)-1)* ( *lda)]
#define B(I,J) b[(I)-1 + ((J)-1)* ( *ldb)]
mn = min(*m,*n);
ismin = mn + 1;
ismax = (mn << 1) + 1;
/* Test the input arguments. */
*info = 0;
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;
}
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("DGELSX", &i__1);
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 elements outside range [SMLNUM,BIGNUM] */
anrm = dlange_("M", m, n, &A(1,1), 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(1,1), 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(1,1), lda,
info);
iascl = 2;
} else if (anrm == 0.) {
/* VISMatrix all zero. Return zero solution. */
i__1 = max(*m,*n);
dlaset_("F", &i__1, nrhs, &c_b13, &c_b13, &B(1,1), ldb);
*rank = 0;
goto L100;
}
bnrm = dlange_("M", m, nrhs, &B(1,1), 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(1,1), 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(1,1), ldb,
info);
ibscl = 2;
}
/* Compute QR factorization with column pivoting of A:
A * P = Q * R */
dgeqpf_(m, n, &A(1,1), lda, &JPVT(1), &WORK(1), &WORK(mn + 1), info);
/* workspace 3*N. 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(1,1), abs(d__1));
smin = smax;
if ((d__1 = A(1,1), abs(d__1)) == 0.) {
*rank = 0;
i__1 = max(*m,*n);
dlaset_("F", &i__1, nrhs, &c_b13, &c_b13, &B(1,1), ldb);
goto L100;
} else {
*rank = 1;
}
L10:
if (*rank < mn) {
i = *rank + 1;
dlaic1_(&c__2, rank, &WORK(ismin), &smin, &A(1,i), &A(i,i), &sminpr, &s1, &c1);
dlaic1_(&c__1, rank, &WORK(ismax), &smax, &A(1,i), &A(i,i), &smaxpr, &s2, &c2);
if (smaxpr * *rcond <= sminpr) {
i__1 = *rank;
for (i = 1; i <= *rank; ++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;
}
}
/* Logically partition R = [ R11 R12 ]
[ 0 R22 ]
where R11 = R(1:RANK,1:RANK)
[R11,R12] = [ T11, 0 ] * Y */
if (*rank < *n) {
dtzrqf_(rank, n, &A(1,1), lda, &WORK(mn + 1), info);
}
/* Details of Householder rotations stored in WORK(MN+1:2*MN)
B(1:M,1:NRHS) := Q' * B(1:M,1:NRHS) */
dorm2r_("Left", "Transpose", m, nrhs, &mn, &A(1,1), lda, &WORK(1), &
B(1,1), ldb, &WORK((mn << 1) + 1), info);
/* workspace NRHS
B(1:RANK,1:NRHS) := inv(T11) * B(1:RANK,1:NRHS) */
dtrsm_("Left", "Upper", "No transpose", "Non-unit", rank, nrhs, &c_b36, &
A(1,1), lda, &B(1,1), ldb);
i__1 = *n;
for (i = *rank + 1; i <= *n; ++i) {
i__2 = *nrhs;
for (j = 1; j <= *nrhs; ++j) {
B(i,j) = 0.;
/* L30: */
}
/* L40: */
}
/* B(1:N,1:NRHS) := Y' * B(1:N,1:NRHS) */
if (*rank < *n) {
i__1 = *rank;
for (i = 1; i <= *rank; ++i) {
i__2 = *n - *rank + 1;
dlatzm_("Left", &i__2, nrhs, &A(i,*rank+1), lda, &
WORK(mn + i), &B(i,1), &B(*rank+1,1), ldb,
&WORK((mn << 1) + 1));
/* L50: */
}
}
/* workspace NRHS
B(1:N,1:NRHS) := P * B(1:N,1:NRHS) */
i__1 = *nrhs;
for (j = 1; j <= *nrhs; ++j) {
i__2 = *n;
for (i = 1; i <= *n; ++i) {
WORK((mn << 1) + i) = 1.;
/* L60: */
}
i__2 = *n;
for (i = 1; i <= *n; ++i) {
if (WORK((mn << 1) + i) == 1.) {
if (JPVT(i) != i) {
k = i;
t1 = B(k,j);
t2 = B(JPVT(k),j);
L70:
B(JPVT(k),j) = t1;
WORK((mn << 1) + k) = 0.;
t1 = t2;
k = JPVT(k);
t2 = B(JPVT(k),j);
if (JPVT(k) != i) {
goto L70;
}
B(i,j) = t1;
WORK((mn << 1) + k) = 0.;
}
}
/* L80: */
}
/* L90: */
}
/* Undo scaling */
if (iascl == 1) {
dlascl_("G", &c__0, &c__0, &anrm, &smlnum, n, nrhs, &B(1,1), ldb,
info);
dlascl_("U", &c__0, &c__0, &smlnum, &anrm, rank, rank, &A(1,1),
lda, info);
} else if (iascl == 2) {
dlascl_("G", &c__0, &c__0, &anrm, &bignum, n, nrhs, &B(1,1), ldb,
info);
dlascl_("U", &c__0, &c__0, &bignum, &anrm, rank, rank, &A(1,1),
lda, info);
}
if (ibscl == 1) {
dlascl_("G", &c__0, &c__0, &smlnum, &bnrm, n, nrhs, &B(1,1), ldb,
info);
} else if (ibscl == 2) {
dlascl_("G", &c__0, &c__0, &bignum, &bnrm, n, nrhs, &B(1,1), ldb,
info);
}
L100:
return 0;
/* End of DGELSX */
} /* dgelsx_ */