--- rpl/lapack/lapack/dlaqps.f 2010/04/21 13:45:18 1.2
+++ rpl/lapack/lapack/dlaqps.f 2023/08/07 08:38:55 1.21
@@ -1,10 +1,183 @@
+*> \brief \b DLAQPS computes a step of QR factorization with column pivoting of a real m-by-n matrix A by using BLAS level 3.
+*
+* =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+* http://www.netlib.org/lapack/explore-html/
+*
+*> \htmlonly
+*> Download DLAQPS + dependencies
+*>
+*> [TGZ]
+*>
+*> [ZIP]
+*>
+*> [TXT]
+*> \endhtmlonly
+*
+* Definition:
+* ===========
+*
+* SUBROUTINE DLAQPS( M, N, OFFSET, NB, KB, A, LDA, JPVT, TAU, VN1,
+* VN2, AUXV, F, LDF )
+*
+* .. Scalar Arguments ..
+* INTEGER KB, LDA, LDF, M, N, NB, OFFSET
+* ..
+* .. Array Arguments ..
+* INTEGER JPVT( * )
+* DOUBLE PRECISION A( LDA, * ), AUXV( * ), F( LDF, * ), TAU( * ),
+* $ VN1( * ), VN2( * )
+* ..
+*
+*
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
+*>
+*> DLAQPS computes a step of QR factorization with column pivoting
+*> of a real M-by-N matrix A by using Blas-3. It tries to factorize
+*> NB columns from A starting from the row OFFSET+1, and updates all
+*> of the matrix with Blas-3 xGEMM.
+*>
+*> In some cases, due to catastrophic cancellations, it cannot
+*> factorize NB columns. Hence, the actual number of factorized
+*> columns is returned in KB.
+*>
+*> Block A(1:OFFSET,1:N) is accordingly pivoted, but not factorized.
+*> \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] OFFSET
+*> \verbatim
+*> OFFSET is INTEGER
+*> The number of rows of A that have been factorized in
+*> previous steps.
+*> \endverbatim
+*>
+*> \param[in] NB
+*> \verbatim
+*> NB is INTEGER
+*> The number of columns to factorize.
+*> \endverbatim
+*>
+*> \param[out] KB
+*> \verbatim
+*> KB is INTEGER
+*> The number of columns actually factorized.
+*> \endverbatim
+*>
+*> \param[in,out] A
+*> \verbatim
+*> A is DOUBLE PRECISION array, dimension (LDA,N)
+*> On entry, the M-by-N matrix A.
+*> On exit, block A(OFFSET+1:M,1:KB) is the triangular
+*> factor obtained and block A(1:OFFSET,1:N) has been
+*> accordingly pivoted, but no factorized.
+*> The rest of the matrix, block A(OFFSET+1:M,KB+1:N) has
+*> been updated.
+*> \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)
+*> JPVT(I) = K <==> Column K of the full matrix A has been
+*> permuted into position I in AP.
+*> \endverbatim
+*>
+*> \param[out] TAU
+*> \verbatim
+*> TAU is DOUBLE PRECISION array, dimension (KB)
+*> The scalar factors of the elementary reflectors.
+*> \endverbatim
+*>
+*> \param[in,out] VN1
+*> \verbatim
+*> VN1 is DOUBLE PRECISION array, dimension (N)
+*> The vector with the partial column norms.
+*> \endverbatim
+*>
+*> \param[in,out] VN2
+*> \verbatim
+*> VN2 is DOUBLE PRECISION array, dimension (N)
+*> The vector with the exact column norms.
+*> \endverbatim
+*>
+*> \param[in,out] AUXV
+*> \verbatim
+*> AUXV is DOUBLE PRECISION array, dimension (NB)
+*> Auxiliary vector.
+*> \endverbatim
+*>
+*> \param[in,out] F
+*> \verbatim
+*> F is DOUBLE PRECISION array, dimension (LDF,NB)
+*> Matrix F**T = L*Y**T*A.
+*> \endverbatim
+*>
+*> \param[in] LDF
+*> \verbatim
+*> LDF is INTEGER
+*> The leading dimension of the array F. LDF >= max(1,N).
+*> \endverbatim
+*
+* Authors:
+* ========
+*
+*> \author Univ. of Tennessee
+*> \author Univ. of California Berkeley
+*> \author Univ. of Colorado Denver
+*> \author NAG Ltd.
+*
+*> \ingroup doubleOTHERauxiliary
+*
+*> \par Contributors:
+* ==================
+*>
+*> G. Quintana-Orti, Depto. de Informatica, Universidad Jaime I, Spain
+*> X. Sun, Computer Science Dept., Duke University, USA
+*> \n
+*> Partial column norm updating strategy modified on April 2011
+*> Z. Drmac and Z. Bujanovic, Dept. of Mathematics,
+*> University of Zagreb, Croatia.
+*
+*> \par References:
+* ================
+*>
+*> LAPACK Working Note 176
+*
+*> \htmlonly
+*> [PDF]
+*> \endhtmlonly
+*
+* =====================================================================
SUBROUTINE DLAQPS( M, N, OFFSET, NB, KB, A, LDA, JPVT, TAU, VN1,
$ VN2, AUXV, F, LDF )
*
-* -- LAPACK auxiliary routine (version 3.2) --
+* -- LAPACK auxiliary 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 KB, LDA, LDF, M, N, NB, OFFSET
@@ -15,84 +188,6 @@
$ VN1( * ), VN2( * )
* ..
*
-* Purpose
-* =======
-*
-* DLAQPS computes a step of QR factorization with column pivoting
-* of a real M-by-N matrix A by using Blas-3. It tries to factorize
-* NB columns from A starting from the row OFFSET+1, and updates all
-* of the matrix with Blas-3 xGEMM.
-*
-* In some cases, due to catastrophic cancellations, it cannot
-* factorize NB columns. Hence, the actual number of factorized
-* columns is returned in KB.
-*
-* Block A(1:OFFSET,1:N) is accordingly pivoted, but not factorized.
-*
-* 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
-*
-* OFFSET (input) INTEGER
-* The number of rows of A that have been factorized in
-* previous steps.
-*
-* NB (input) INTEGER
-* The number of columns to factorize.
-*
-* KB (output) INTEGER
-* The number of columns actually factorized.
-*
-* A (input/output) DOUBLE PRECISION array, dimension (LDA,N)
-* On entry, the M-by-N matrix A.
-* On exit, block A(OFFSET+1:M,1:KB) is the triangular
-* factor obtained and block A(1:OFFSET,1:N) has been
-* accordingly pivoted, but no factorized.
-* The rest of the matrix, block A(OFFSET+1:M,KB+1:N) has
-* been updated.
-*
-* LDA (input) INTEGER
-* The leading dimension of the array A. LDA >= max(1,M).
-*
-* JPVT (input/output) INTEGER array, dimension (N)
-* JPVT(I) = K <==> Column K of the full matrix A has been
-* permuted into position I in AP.
-*
-* TAU (output) DOUBLE PRECISION array, dimension (KB)
-* The scalar factors of the elementary reflectors.
-*
-* VN1 (input/output) DOUBLE PRECISION array, dimension (N)
-* The vector with the partial column norms.
-*
-* VN2 (input/output) DOUBLE PRECISION array, dimension (N)
-* The vector with the exact column norms.
-*
-* AUXV (input/output) DOUBLE PRECISION array, dimension (NB)
-* Auxiliar vector.
-*
-* F (input/output) DOUBLE PRECISION array, dimension (LDF,NB)
-* Matrix F' = L*Y'*A.
-*
-* LDF (input) INTEGER
-* The leading dimension of the array F. LDF >= max(1,N).
-*
-* Further Details
-* ===============
-*
-* Based on contributions by
-* G. Quintana-Orti, Depto. de Informatica, Universidad Jaime I, Spain
-* X. Sun, Computer Science Dept., Duke University, USA
-*
-* 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 ..
@@ -104,7 +199,7 @@
DOUBLE PRECISION AKK, TEMP, TEMP2, TOL3Z
* ..
* .. External Subroutines ..
- EXTERNAL DGEMM, DGEMV, DLARFP, DSWAP
+ EXTERNAL DGEMM, DGEMV, DLARFG, DSWAP
* ..
* .. Intrinsic Functions ..
INTRINSIC ABS, DBLE, MAX, MIN, NINT, SQRT
@@ -142,7 +237,7 @@
END IF
*
* Apply previous Householder reflectors to column K:
-* A(RK:M,K) := A(RK:M,K) - A(RK:M,1:K-1)*F(K,1:K-1)'.
+* A(RK:M,K) := A(RK:M,K) - A(RK:M,1:K-1)*F(K,1:K-1)**T.
*
IF( K.GT.1 ) THEN
CALL DGEMV( 'No transpose', M-RK+1, K-1, -ONE, A( RK, 1 ),
@@ -152,9 +247,9 @@
* Generate elementary reflector H(k).
*
IF( RK.LT.M ) THEN
- CALL DLARFP( M-RK+1, A( RK, K ), A( RK+1, K ), 1, TAU( K ) )
+ CALL DLARFG( M-RK+1, A( RK, K ), A( RK+1, K ), 1, TAU( K ) )
ELSE
- CALL DLARFP( 1, A( RK, K ), A( RK, K ), 1, TAU( K ) )
+ CALL DLARFG( 1, A( RK, K ), A( RK, K ), 1, TAU( K ) )
END IF
*
AKK = A( RK, K )
@@ -162,7 +257,7 @@
*
* Compute Kth column of F:
*
-* Compute F(K+1:N,K) := tau(K)*A(RK:M,K+1:N)'*A(RK:M,K).
+* Compute F(K+1:N,K) := tau(K)*A(RK:M,K+1:N)**T*A(RK:M,K).
*
IF( K.LT.N ) THEN
CALL DGEMV( 'Transpose', M-RK+1, N-K, TAU( K ),
@@ -177,7 +272,7 @@
20 CONTINUE
*
* Incremental updating of F:
-* F(1:N,K) := F(1:N,K) - tau(K)*F(1:N,1:K-1)*A(RK:M,1:K-1)'
+* F(1:N,K) := F(1:N,K) - tau(K)*F(1:N,1:K-1)*A(RK:M,1:K-1)**T
* *A(RK:M,K).
*
IF( K.GT.1 ) THEN
@@ -189,7 +284,7 @@
END IF
*
* Update the current row of A:
-* A(RK,K+1:N) := A(RK,K+1:N) - A(RK,1:K)*F(K+1:N,1:K)'.
+* A(RK,K+1:N) := A(RK,K+1:N) - A(RK,1:K)*F(K+1:N,1:K)**T.
*
IF( K.LT.N ) THEN
CALL DGEMV( 'No transpose', N-K, K, -ONE, F( K+1, 1 ), LDF,
@@ -229,7 +324,7 @@
*
* Apply the block reflector to the rest of the matrix:
* A(OFFSET+KB+1:M,KB+1:N) := A(OFFSET+KB+1:M,KB+1:N) -
-* A(OFFSET+KB+1:M,1:KB)*F(KB+1:N,1:KB)'.
+* A(OFFSET+KB+1:M,1:KB)*F(KB+1:N,1:KB)**T.
*
IF( KB.LT.MIN( N, M-OFFSET ) ) THEN
CALL DGEMM( 'No transpose', 'Transpose', M-RK, N-KB, KB, -ONE,
@@ -244,9 +339,9 @@
ITEMP = NINT( VN2( LSTICC ) )
VN1( LSTICC ) = DNRM2( M-RK, A( RK+1, LSTICC ), 1 )
*
-* NOTE: The computation of VN1( LSTICC ) relies on the fact that
+* NOTE: The computation of VN1( LSTICC ) relies on the fact that
* SNRM2 does not fail on vectors with norm below the value of
-* SQRT(DLAMCH('S'))
+* SQRT(DLAMCH('S'))
*
VN2( LSTICC ) = VN1( LSTICC )
LSTICC = ITEMP