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/* dgeqp3.f -- translated by f2c (version 20061008).
You must link the resulting object file with libf2c:
on Microsoft Windows system, link with libf2c.lib;
on Linux or Unix systems, link with .../path/to/libf2c.a -lm
or, if you install libf2c.a in a standard place, with -lf2c -lm
-- in that order, at the end of the command line, as in
cc *.o -lf2c -lm
Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
http://www.netlib.org/f2c/libf2c.zip
*/
#include "f2c.h"
#include "blaswrap.h"
/* Table of constant values */
static integer c__1 = 1;
static integer c_n1 = -1;
static integer c__3 = 3;
static integer c__2 = 2;
/* Subroutine */ int dgeqp3_(integer *m, integer *n, doublereal *a, integer *
lda, integer *jpvt, doublereal *tau, doublereal *work, integer *lwork,
integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2, i__3;
/* Local variables */
integer j, jb, na, nb, sm, sn, nx, fjb, iws, nfxd;
extern doublereal dnrm2_(integer *, doublereal *, integer *);
integer nbmin, minmn;
extern /* Subroutine */ int dswap_(integer *, doublereal *, integer *,
doublereal *, integer *);
integer minws;
extern /* Subroutine */ int dlaqp2_(integer *, integer *, integer *,
doublereal *, integer *, integer *, doublereal *, doublereal *,
doublereal *, doublereal *), dgeqrf_(integer *, integer *,
doublereal *, integer *, doublereal *, doublereal *, integer *,
integer *), xerbla_(char *, integer *);
extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *);
extern /* Subroutine */ int dlaqps_(integer *, integer *, integer *,
integer *, integer *, doublereal *, integer *, integer *,
doublereal *, doublereal *, doublereal *, doublereal *,
doublereal *, integer *);
integer topbmn, sminmn;
extern /* Subroutine */ int dormqr_(char *, char *, integer *, integer *,
integer *, doublereal *, integer *, doublereal *, doublereal *,
integer *, doublereal *, integer *, integer *);
integer lwkopt;
logical lquery;
/* -- LAPACK routine (version 3.2) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* 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 (MAX(1,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 */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Test input arguments */
/* ==================== */
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
--jpvt;
--tau;
--work;
/* Function Body */
*info = 0;
lquery = *lwork == -1;
if (*m < 0) {
*info = -1;
} else if (*n < 0) {
*info = -2;
} else if (*lda < max(1,*m)) {
*info = -4;
}
if (*info == 0) {
minmn = min(*m,*n);
if (minmn == 0) {
iws = 1;
lwkopt = 1;
} else {
iws = *n * 3 + 1;
nb = ilaenv_(&c__1, "DGEQRF", " ", m, n, &c_n1, &c_n1);
lwkopt = (*n << 1) + (*n + 1) * nb;
}
work[1] = (doublereal) lwkopt;
if (*lwork < iws && ! lquery) {
*info = -8;
}
}
if (*info != 0) {
i__1 = -(*info);
xerbla_("DGEQP3", &i__1);
return 0;
} else if (lquery) {
return 0;
}
/* Quick return if possible. */
if (minmn == 0) {
return 0;
}
/* Move initial columns up front. */
nfxd = 1;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
if (jpvt[j] != 0) {
if (j != nfxd) {
dswap_(m, &a[j * a_dim1 + 1], &c__1, &a[nfxd * a_dim1 + 1], &
c__1);
jpvt[j] = jpvt[nfxd];
jpvt[nfxd] = j;
} else {
jpvt[j] = j;
}
++nfxd;
} else {
jpvt[j] = j;
}
/* L10: */
}
--nfxd;
/* Factorize fixed columns */
/* ======================= */
/* Compute the QR factorization of fixed columns and update */
/* remaining columns. */
if (nfxd > 0) {
na = min(*m,nfxd);
/* CC CALL DGEQR2( M, NA, A, LDA, TAU, WORK, INFO ) */
dgeqrf_(m, &na, &a[a_offset], lda, &tau[1], &work[1], lwork, info);
/* Computing MAX */
i__1 = iws, i__2 = (integer) work[1];
iws = max(i__1,i__2);
if (na < *n) {
/* CC CALL DORM2R( 'Left', 'Transpose', M, N-NA, NA, A, LDA, */
/* CC $ TAU, A( 1, NA+1 ), LDA, WORK, INFO ) */
i__1 = *n - na;
dormqr_("Left", "Transpose", m, &i__1, &na, &a[a_offset], lda, &
tau[1], &a[(na + 1) * a_dim1 + 1], lda, &work[1], lwork,
info);
/* Computing MAX */
i__1 = iws, i__2 = (integer) work[1];
iws = max(i__1,i__2);
}
}
/* Factorize free columns */
/* ====================== */
if (nfxd < minmn) {
sm = *m - nfxd;
sn = *n - nfxd;
sminmn = minmn - nfxd;
/* Determine the block size. */
nb = ilaenv_(&c__1, "DGEQRF", " ", &sm, &sn, &c_n1, &c_n1);
nbmin = 2;
nx = 0;
if (nb > 1 && nb < sminmn) {
/* Determine when to cross over from blocked to unblocked code. */
/* Computing MAX */
i__1 = 0, i__2 = ilaenv_(&c__3, "DGEQRF", " ", &sm, &sn, &c_n1, &
c_n1);
nx = max(i__1,i__2);
if (nx < sminmn) {
/* Determine if workspace is large enough for blocked code. */
minws = (sn << 1) + (sn + 1) * nb;
iws = max(iws,minws);
if (*lwork < minws) {
/* Not enough workspace to use optimal NB: Reduce NB and */
/* determine the minimum value of NB. */
nb = (*lwork - (sn << 1)) / (sn + 1);
/* Computing MAX */
i__1 = 2, i__2 = ilaenv_(&c__2, "DGEQRF", " ", &sm, &sn, &
c_n1, &c_n1);
nbmin = max(i__1,i__2);
}
}
}
/* Initialize partial column norms. The first N elements of work */
/* store the exact column norms. */
i__1 = *n;
for (j = nfxd + 1; j <= i__1; ++j) {
work[j] = dnrm2_(&sm, &a[nfxd + 1 + j * a_dim1], &c__1);
work[*n + j] = work[j];
/* L20: */
}
if (nb >= nbmin && nb < sminmn && nx < sminmn) {
/* Use blocked code initially. */
j = nfxd + 1;
/* Compute factorization: while loop. */
topbmn = minmn - nx;
L30:
if (j <= topbmn) {
/* Computing MIN */
i__1 = nb, i__2 = topbmn - j + 1;
jb = min(i__1,i__2);
/* Factorize JB columns among columns J:N. */
i__1 = *n - j + 1;
i__2 = j - 1;
i__3 = *n - j + 1;
dlaqps_(m, &i__1, &i__2, &jb, &fjb, &a[j * a_dim1 + 1], lda, &
jpvt[j], &tau[j], &work[j], &work[*n + j], &work[(*n
<< 1) + 1], &work[(*n << 1) + jb + 1], &i__3);
j += fjb;
goto L30;
}
} else {
j = nfxd + 1;
}
/* Use unblocked code to factor the last or only block. */
if (j <= minmn) {
i__1 = *n - j + 1;
i__2 = j - 1;
dlaqp2_(m, &i__1, &i__2, &a[j * a_dim1 + 1], lda, &jpvt[j], &tau[
j], &work[j], &work[*n + j], &work[(*n << 1) + 1]);
}
}
work[1] = (doublereal) iws;
return 0;
/* End of DGEQP3 */
} /* dgeqp3_ */
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