--- rpl/lapack/lapack/dgeqpf.f 2010/01/26 15:22:46 1.1.1.1
+++ rpl/lapack/lapack/dgeqpf.f 2023/08/07 08:38:49 1.19
@@ -1,9 +1,148 @@
+*> \brief \b DGEQPF
+*
+* =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+* http://www.netlib.org/lapack/explore-html/
+*
+*> \htmlonly
+*> Download DGEQPF + dependencies
+*>
+*> [TGZ]
+*>
+*> [ZIP]
+*>
+*> [TXT]
+*> \endhtmlonly
+*
+* Definition:
+* ===========
+*
+* SUBROUTINE DGEQPF( M, N, A, LDA, JPVT, TAU, WORK, INFO )
+*
+* .. Scalar Arguments ..
+* INTEGER INFO, LDA, M, N
+* ..
+* .. Array Arguments ..
+* INTEGER JPVT( * )
+* DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * )
+* ..
+*
+*
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
+*>
+*> This routine is deprecated and has been replaced by routine DGEQP3.
+*>
+*> DGEQPF computes a QR factorization with column pivoting of a
+*> real M-by-N matrix A: A*P = Q*R.
+*> \endverbatim
+*
+* Arguments:
+* ==========
+*
+*> \param[in] M
+*> \verbatim
+*> M is INTEGER
+*> The number of rows of the matrix A. M >= 0.
+*> \endverbatim
+*>
+*> \param[in] N
+*> \verbatim
+*> N is INTEGER
+*> The number of columns of the matrix A. N >= 0
+*> \endverbatim
+*>
+*> \param[in,out] A
+*> \verbatim
+*> A is 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.
+*> \endverbatim
+*>
+*> \param[in] LDA
+*> \verbatim
+*> LDA is INTEGER
+*> The leading dimension of the array A. LDA >= max(1,M).
+*> \endverbatim
+*>
+*> \param[in,out] JPVT
+*> \verbatim
+*> JPVT is 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.
+*> \endverbatim
+*>
+*> \param[out] TAU
+*> \verbatim
+*> TAU is DOUBLE PRECISION array, dimension (min(M,N))
+*> The scalar factors of the elementary reflectors.
+*> \endverbatim
+*>
+*> \param[out] WORK
+*> \verbatim
+*> WORK is DOUBLE PRECISION array, dimension (3*N)
+*> \endverbatim
+*>
+*> \param[out] INFO
+*> \verbatim
+*> INFO is INTEGER
+*> = 0: successful exit
+*> < 0: if INFO = -i, the i-th argument had an illegal value
+*> \endverbatim
+*
+* Authors:
+* ========
+*
+*> \author Univ. of Tennessee
+*> \author Univ. of California Berkeley
+*> \author Univ. of Colorado Denver
+*> \author NAG Ltd.
+*
+*> \ingroup doubleGEcomputational
+*
+*> \par Further Details:
+* =====================
+*>
+*> \verbatim
+*>
+*> 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**T
+*>
+*> 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.
+*>
+*> Partial column norm updating strategy modified by
+*> Z. Drmac and Z. Bujanovic, Dept. of Mathematics,
+*> University of Zagreb, Croatia.
+*> -- April 2011 --
+*> For more details see LAPACK Working Note 176.
+*> \endverbatim
+*>
+* =====================================================================
SUBROUTINE DGEQPF( M, N, A, LDA, JPVT, TAU, WORK, INFO )
*
-* -- LAPACK deprecated driver routine (version 3.2) --
+* -- LAPACK computational routine --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
-* November 2006
*
* .. Scalar Arguments ..
INTEGER INFO, LDA, M, N
@@ -13,74 +152,6 @@
DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
-*
-* This routine is deprecated and has been replaced by routine DGEQP3.
-*
-* 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.
-*
-* Partial column norm updating strategy modified by
-* Z. Drmac and Z. Bujanovic, Dept. of Mathematics,
-* University of Zagreb, Croatia.
-* June 2006.
-* For more details see LAPACK Working Note 176.
-*
* =====================================================================
*
* .. Parameters ..
@@ -92,7 +163,7 @@
DOUBLE PRECISION AII, TEMP, TEMP2, TOL3Z
* ..
* .. External Subroutines ..
- EXTERNAL DGEQR2, DLARF, DLARFP, DORM2R, DSWAP, XERBLA
+ EXTERNAL DGEQR2, DLARF, DLARFG, DORM2R, DSWAP, XERBLA
* ..
* .. Intrinsic Functions ..
INTRINSIC ABS, MAX, MIN, SQRT
@@ -182,9 +253,9 @@
* Generate elementary reflector H(i)
*
IF( I.LT.M ) THEN
- CALL DLARFP( M-I+1, A( I, I ), A( I+1, I ), 1, TAU( I ) )
+ CALL DLARFG( M-I+1, A( I, I ), A( I+1, I ), 1, TAU( I ) )
ELSE
- CALL DLARFP( 1, A( M, M ), A( M, M ), 1, TAU( M ) )
+ CALL DLARFG( 1, A( M, M ), A( M, M ), 1, TAU( M ) )
END IF
*
IF( I.LT.N ) THEN
@@ -205,11 +276,11 @@
*
* NOTE: The following 4 lines follow from the analysis in
* Lapack Working Note 176.
-*
+*
TEMP = ABS( A( I, J ) ) / WORK( J )
TEMP = MAX( ZERO, ( ONE+TEMP )*( ONE-TEMP ) )
TEMP2 = TEMP*( WORK( J ) / WORK( N+J ) )**2
- IF( TEMP2 .LE. TOL3Z ) THEN
+ IF( TEMP2 .LE. TOL3Z ) THEN
IF( M-I.GT.0 ) THEN
WORK( J ) = DNRM2( M-I, A( I+1, J ), 1 )
WORK( N+J ) = WORK( J )