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/* lapack/single/sgeqpf.f -- translated by f2c (version 20050501).
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
*/
#ifdef __cplusplus
extern "C" {
#endif
#include "v3p_netlib.h"
/* Table of constant values */
static integer c__1 = 1;
/*< SUBROUTINE SGEQPF( M, N, A, LDA, JPVT, TAU, WORK, INFO ) >*/
/* Subroutine */ int sgeqpf_(integer *m, integer *n, real *a, integer *lda,
integer *jpvt, real *tau, real *work, integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2, i__3;
real r__1, r__2;
/* Builtin functions */
double sqrt(doublereal);
/* Local variables */
integer i__, j, ma, mn;
real aii;
integer pvt;
real temp, temp2;
extern doublereal snrm2_(integer *, real *, integer *);
extern /* Subroutine */ int slarf_(char *, integer *, integer *, real *,
integer *, real *, real *, integer *, real *, ftnlen);
integer itemp;
extern /* Subroutine */ int sswap_(integer *, real *, integer *, real *,
integer *), sgeqr2_(integer *, integer *, real *, integer *, real
*, real *, integer *), sorm2r_(char *, char *, integer *, integer
*, integer *, real *, integer *, real *, real *, integer *, real *
, integer *, ftnlen, ftnlen), xerbla_(char *, integer *, ftnlen),
slarfg_(integer *, real *, real *, integer *, real *);
extern integer isamax_(integer *, real *, integer *);
/* -- LAPACK test routine (version 3.0) -- */
/* Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., */
/* Courant Institute, Argonne National Lab, and Rice University */
/* March 31, 1993 */
/* .. Scalar Arguments .. */
/*< INTEGER INFO, LDA, M, N >*/
/* .. */
/* .. Array Arguments .. */
/*< INTEGER JPVT( * ) >*/
/*< REAL A( LDA, * ), TAU( * ), WORK( * ) >*/
/* .. */
/* Purpose */
/* ======= */
/* This routine is deprecated and has been replaced by routine SGEQP3. */
/* SGEQPF 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) REAL 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) REAL array, dimension (min(M,N)) */
/* The scalar factors of the elementary reflectors. */
/* WORK (workspace) REAL 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. */
/* ===================================================================== */
/* .. Parameters .. */
/*< REAL ZERO, ONE >*/
/*< PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0 ) >*/
/* .. */
/* .. Local Scalars .. */
/*< INTEGER I, ITEMP, J, MA, MN, PVT >*/
/*< REAL AII, TEMP, TEMP2 >*/
/* .. */
/* .. External Subroutines .. */
/*< EXTERNAL SGEQR2, SLARF, SLARFG, SORM2R, SSWAP, XERBLA >*/
/* .. */
/* .. Intrinsic Functions .. */
/*< INTRINSIC ABS, MAX, MIN, SQRT >*/
/* .. */
/* .. External Functions .. */
/*< INTEGER ISAMAX >*/
/*< REAL SNRM2 >*/
/*< EXTERNAL ISAMAX, SNRM2 >*/
/* .. */
/* .. Executable Statements .. */
/* Test the input arguments */
/*< INFO = 0 >*/
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
--jpvt;
--tau;
--work;
/* Function Body */
*info = 0;
/*< IF( M.LT.0 ) THEN >*/
if (*m < 0) {
/*< INFO = -1 >*/
*info = -1;
/*< ELSE IF( N.LT.0 ) THEN >*/
} else if (*n < 0) {
/*< INFO = -2 >*/
*info = -2;
/*< ELSE IF( LDA.LT.MAX( 1, M ) ) THEN >*/
} else if (*lda < max(1,*m)) {
/*< INFO = -4 >*/
*info = -4;
/*< END IF >*/
}
/*< IF( INFO.NE.0 ) THEN >*/
if (*info != 0) {
/*< CALL XERBLA( 'SGEQPF', -INFO ) >*/
i__1 = -(*info);
xerbla_("SGEQPF", &i__1, (ftnlen)6);
/*< RETURN >*/
return 0;
/*< END IF >*/
}
/*< MN = MIN( M, N ) >*/
mn = min(*m,*n);
/* Move initial columns up front */
/*< ITEMP = 1 >*/
itemp = 1;
/*< DO 10 I = 1, N >*/
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
/*< IF( JPVT( I ).NE.0 ) THEN >*/
if (jpvt[i__] != 0) {
/*< IF( I.NE.ITEMP ) THEN >*/
if (i__ != itemp) {
/*< CALL SSWAP( M, A( 1, I ), 1, A( 1, ITEMP ), 1 ) >*/
sswap_(m, &a[i__ * a_dim1 + 1], &c__1, &a[itemp * a_dim1 + 1],
&c__1);
/*< JPVT( I ) = JPVT( ITEMP ) >*/
jpvt[i__] = jpvt[itemp];
/*< JPVT( ITEMP ) = I >*/
jpvt[itemp] = i__;
/*< ELSE >*/
} else {
/*< JPVT( I ) = I >*/
jpvt[i__] = i__;
/*< END IF >*/
}
/*< ITEMP = ITEMP + 1 >*/
++itemp;
/*< ELSE >*/
} else {
/*< JPVT( I ) = I >*/
jpvt[i__] = i__;
/*< END IF >*/
}
/*< 10 CONTINUE >*/
/* L10: */
}
/*< ITEMP = ITEMP - 1 >*/
--itemp;
/* Compute the QR factorization and update remaining columns */
/*< IF( ITEMP.GT.0 ) THEN >*/
if (itemp > 0) {
/*< MA = MIN( ITEMP, M ) >*/
ma = min(itemp,*m);
/*< CALL SGEQR2( M, MA, A, LDA, TAU, WORK, INFO ) >*/
sgeqr2_(m, &ma, &a[a_offset], lda, &tau[1], &work[1], info);
/*< IF( MA.LT.N ) THEN >*/
if (ma < *n) {
/*< >*/
i__1 = *n - ma;
sorm2r_("Left", "Transpose", m, &i__1, &ma, &a[a_offset], lda, &
tau[1], &a[(ma + 1) * a_dim1 + 1], lda, &work[1], info, (
ftnlen)4, (ftnlen)9);
/*< END IF >*/
}
/*< END IF >*/
}
/*< IF( ITEMP.LT.MN ) THEN >*/
if (itemp < mn) {
/* Initialize partial column norms. The first n elements of */
/* work store the exact column norms. */
/*< DO 20 I = ITEMP + 1, N >*/
i__1 = *n;
for (i__ = itemp + 1; i__ <= i__1; ++i__) {
/*< WORK( I ) = SNRM2( M-ITEMP, A( ITEMP+1, I ), 1 ) >*/
i__2 = *m - itemp;
work[i__] = snrm2_(&i__2, &a[itemp + 1 + i__ * a_dim1], &c__1);
/*< WORK( N+I ) = WORK( I ) >*/
work[*n + i__] = work[i__];
/*< 20 CONTINUE >*/
/* L20: */
}
/* Compute factorization */
/*< DO 40 I = ITEMP + 1, MN >*/
i__1 = mn;
for (i__ = itemp + 1; i__ <= i__1; ++i__) {
/* Determine ith pivot column and swap if necessary */
/*< PVT = ( I-1 ) + ISAMAX( N-I+1, WORK( I ), 1 ) >*/
i__2 = *n - i__ + 1;
pvt = i__ - 1 + isamax_(&i__2, &work[i__], &c__1);
/*< IF( PVT.NE.I ) THEN >*/
if (pvt != i__) {
/*< CALL SSWAP( M, A( 1, PVT ), 1, A( 1, I ), 1 ) >*/
sswap_(m, &a[pvt * a_dim1 + 1], &c__1, &a[i__ * a_dim1 + 1], &
c__1);
/*< ITEMP = JPVT( PVT ) >*/
itemp = jpvt[pvt];
/*< JPVT( PVT ) = JPVT( I ) >*/
jpvt[pvt] = jpvt[i__];
/*< JPVT( I ) = ITEMP >*/
jpvt[i__] = itemp;
/*< WORK( PVT ) = WORK( I ) >*/
work[pvt] = work[i__];
/*< WORK( N+PVT ) = WORK( N+I ) >*/
work[*n + pvt] = work[*n + i__];
/*< END IF >*/
}
/* Generate elementary reflector H(i) */
/*< IF( I.LT.M ) THEN >*/
if (i__ < *m) {
/*< CALL SLARFG( M-I+1, A( I, I ), A( I+1, I ), 1, TAU( I ) ) >*/
i__2 = *m - i__ + 1;
slarfg_(&i__2, &a[i__ + i__ * a_dim1], &a[i__ + 1 + i__ *
a_dim1], &c__1, &tau[i__]);
/*< ELSE >*/
} else {
/*< CALL SLARFG( 1, A( M, M ), A( M, M ), 1, TAU( M ) ) >*/
slarfg_(&c__1, &a[*m + *m * a_dim1], &a[*m + *m * a_dim1], &
c__1, &tau[*m]);
/*< END IF >*/
}
/*< IF( I.LT.N ) THEN >*/
if (i__ < *n) {
/* Apply H(i) to A(i:m,i+1:n) from the left */
/*< AII = A( I, I ) >*/
aii = a[i__ + i__ * a_dim1];
/*< A( I, I ) = ONE >*/
a[i__ + i__ * a_dim1] = (float)1.;
/*< >*/
i__2 = *m - i__ + 1;
i__3 = *n - i__;
slarf_("LEFT", &i__2, &i__3, &a[i__ + i__ * a_dim1], &c__1, &
tau[i__], &a[i__ + (i__ + 1) * a_dim1], lda, &work[(*
n << 1) + 1], (ftnlen)4);
/*< A( I, I ) = AII >*/
a[i__ + i__ * a_dim1] = aii;
/*< END IF >*/
}
/* Update partial column norms */
/*< DO 30 J = I + 1, N >*/
i__2 = *n;
for (j = i__ + 1; j <= i__2; ++j) {
/*< IF( WORK( J ).NE.ZERO ) THEN >*/
if (work[j] != (float)0.) {
/*< TEMP = ONE - ( ABS( A( I, J ) ) / WORK( J ) )**2 >*/
/* Computing 2nd power */
r__2 = (r__1 = a[i__ + j * a_dim1], dabs(r__1)) / work[j];
temp = (float)1. - r__2 * r__2;
/*< TEMP = MAX( TEMP, ZERO ) >*/
temp = dmax(temp,(float)0.);
/*< TEMP2 = ONE + 0.05*TEMP*( WORK( J ) / WORK( N+J ) )**2 >*/
/* Computing 2nd power */
r__1 = work[j] / work[*n + j];
temp2 = temp * (float).05 * (r__1 * r__1) + (float)1.;
/*< IF( TEMP2.EQ.ONE ) THEN >*/
if (temp2 == (float)1.) {
/*< IF( M-I.GT.0 ) THEN >*/
if (*m - i__ > 0) {
/*< WORK( J ) = SNRM2( M-I, A( I+1, J ), 1 ) >*/
i__3 = *m - i__;
work[j] = snrm2_(&i__3, &a[i__ + 1 + j * a_dim1],
&c__1);
/*< WORK( N+J ) = WORK( J ) >*/
work[*n + j] = work[j];
/*< ELSE >*/
} else {
/*< WORK( J ) = ZERO >*/
work[j] = (float)0.;
/*< WORK( N+J ) = ZERO >*/
work[*n + j] = (float)0.;
/*< END IF >*/
}
/*< ELSE >*/
} else {
/*< WORK( J ) = WORK( J )*SQRT( TEMP ) >*/
work[j] *= sqrt(temp);
/*< END IF >*/
}
/*< END IF >*/
}
/*< 30 CONTINUE >*/
/* L30: */
}
/*< 40 CONTINUE >*/
/* L40: */
}
/*< END IF >*/
}
/*< RETURN >*/
return 0;
/* End of SGEQPF */
/*< END >*/
} /* sgeqpf_ */
#ifdef __cplusplus
}
#endif
|
