--- rpl/lapack/lapack/dtzrqf.f 2010/04/21 13:45:27 1.2
+++ rpl/lapack/lapack/dtzrqf.f 2023/08/07 08:39:14 1.19
@@ -1,9 +1,144 @@
+*> \brief \b DTZRQF
+*
+* =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+* http://www.netlib.org/lapack/explore-html/
+*
+*> \htmlonly
+*> Download DTZRQF + dependencies
+*>
+*> [TGZ]
+*>
+*> [ZIP]
+*>
+*> [TXT]
+*> \endhtmlonly
+*
+* Definition:
+* ===========
+*
+* SUBROUTINE DTZRQF( M, N, A, LDA, TAU, INFO )
+*
+* .. Scalar Arguments ..
+* INTEGER INFO, LDA, M, N
+* ..
+* .. Array Arguments ..
+* DOUBLE PRECISION A( LDA, * ), TAU( * )
+* ..
+*
+*
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
+*>
+*> This routine is deprecated and has been replaced by routine DTZRZF.
+*>
+*> DTZRQF reduces the M-by-N ( M<=N ) real upper trapezoidal matrix A
+*> to upper triangular form by means of orthogonal transformations.
+*>
+*> The upper trapezoidal matrix A is factored as
+*>
+*> A = ( R 0 ) * Z,
+*>
+*> where Z is an N-by-N orthogonal matrix and R is an M-by-M upper
+*> triangular matrix.
+*> \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 >= M.
+*> \endverbatim
+*>
+*> \param[in,out] A
+*> \verbatim
+*> A is DOUBLE PRECISION array, dimension (LDA,N)
+*> On entry, the leading M-by-N upper trapezoidal part of the
+*> array A must contain the matrix to be factorized.
+*> On exit, the leading M-by-M upper triangular part of A
+*> contains the upper triangular matrix R, and elements M+1 to
+*> N of the first M rows of A, with the array TAU, represent the
+*> orthogonal matrix Z as a product of M elementary reflectors.
+*> \endverbatim
+*>
+*> \param[in] LDA
+*> \verbatim
+*> LDA is INTEGER
+*> The leading dimension of the array A. LDA >= max(1,M).
+*> \endverbatim
+*>
+*> \param[out] TAU
+*> \verbatim
+*> TAU is DOUBLE PRECISION array, dimension (M)
+*> The scalar factors of the elementary reflectors.
+*> \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 doubleOTHERcomputational
+*
+*> \par Further Details:
+* =====================
+*>
+*> \verbatim
+*>
+*> The factorization is obtained by Householder's method. The kth
+*> transformation matrix, Z( k ), which is used to introduce zeros into
+*> the ( m - k + 1 )th row of A, is given in the form
+*>
+*> Z( k ) = ( I 0 ),
+*> ( 0 T( k ) )
+*>
+*> where
+*>
+*> T( k ) = I - tau*u( k )*u( k )**T, u( k ) = ( 1 ),
+*> ( 0 )
+*> ( z( k ) )
+*>
+*> tau is a scalar and z( k ) is an ( n - m ) element vector.
+*> tau and z( k ) are chosen to annihilate the elements of the kth row
+*> of X.
+*>
+*> The scalar tau is returned in the kth element of TAU and the vector
+*> u( k ) in the kth row of A, such that the elements of z( k ) are
+*> in a( k, m + 1 ), ..., a( k, n ). The elements of R are returned in
+*> the upper triangular part of A.
+*>
+*> Z is given by
+*>
+*> Z = Z( 1 ) * Z( 2 ) * ... * Z( m ).
+*> \endverbatim
+*>
+* =====================================================================
SUBROUTINE DTZRQF( M, N, A, LDA, TAU, INFO )
*
-* -- LAPACK 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
@@ -12,77 +147,6 @@
DOUBLE PRECISION A( LDA, * ), TAU( * )
* ..
*
-* Purpose
-* =======
-*
-* This routine is deprecated and has been replaced by routine DTZRZF.
-*
-* DTZRQF reduces the M-by-N ( M<=N ) real upper trapezoidal matrix A
-* to upper triangular form by means of orthogonal transformations.
-*
-* The upper trapezoidal matrix A is factored as
-*
-* A = ( R 0 ) * Z,
-*
-* where Z is an N-by-N orthogonal matrix and R is an M-by-M upper
-* triangular matrix.
-*
-* 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 >= M.
-*
-* A (input/output) DOUBLE PRECISION array, dimension (LDA,N)
-* On entry, the leading M-by-N upper trapezoidal part of the
-* array A must contain the matrix to be factorized.
-* On exit, the leading M-by-M upper triangular part of A
-* contains the upper triangular matrix R, and elements M+1 to
-* N of the first M rows of A, with the array TAU, represent the
-* orthogonal matrix Z as a product of M elementary reflectors.
-*
-* LDA (input) INTEGER
-* The leading dimension of the array A. LDA >= max(1,M).
-*
-* TAU (output) DOUBLE PRECISION array, dimension (M)
-* The scalar factors of the elementary reflectors.
-*
-* INFO (output) INTEGER
-* = 0: successful exit
-* < 0: if INFO = -i, the i-th argument had an illegal value
-*
-* Further Details
-* ===============
-*
-* The factorization is obtained by Householder's method. The kth
-* transformation matrix, Z( k ), which is used to introduce zeros into
-* the ( m - k + 1 )th row of A, is given in the form
-*
-* Z( k ) = ( I 0 ),
-* ( 0 T( k ) )
-*
-* where
-*
-* T( k ) = I - tau*u( k )*u( k )', u( k ) = ( 1 ),
-* ( 0 )
-* ( z( k ) )
-*
-* tau is a scalar and z( k ) is an ( n - m ) element vector.
-* tau and z( k ) are chosen to annihilate the elements of the kth row
-* of X.
-*
-* The scalar tau is returned in the kth element of TAU and the vector
-* u( k ) in the kth row of A, such that the elements of z( k ) are
-* in a( k, m + 1 ), ..., a( k, n ). The elements of R are returned in
-* the upper triangular part of A.
-*
-* Z is given by
-*
-* Z = Z( 1 ) * Z( 2 ) * ... * Z( m ).
-*
* =====================================================================
*
* .. Parameters ..
@@ -96,7 +160,7 @@
INTRINSIC MAX, MIN
* ..
* .. External Subroutines ..
- EXTERNAL DAXPY, DCOPY, DGEMV, DGER, DLARFP, XERBLA
+ EXTERNAL DAXPY, DCOPY, DGEMV, DGER, DLARFG, XERBLA
* ..
* .. Executable Statements ..
*
@@ -130,7 +194,7 @@
* Use a Householder reflection to zero the kth row of A.
* First set up the reflection.
*
- CALL DLARFP( N-M+1, A( K, K ), A( K, M1 ), LDA, TAU( K ) )
+ CALL DLARFG( N-M+1, A( K, K ), A( K, M1 ), LDA, TAU( K ) )
*
IF( ( TAU( K ).NE.ZERO ) .AND. ( K.GT.1 ) ) THEN
*
@@ -149,7 +213,7 @@
$ LDA, A( K, M1 ), LDA, ONE, TAU, 1 )
*
* Now form a( k ) := a( k ) - tau*w
-* and B := B - tau*w*z( k )'.
+* and B := B - tau*w*z( k )**T.
*
CALL DAXPY( K-1, -TAU( K ), TAU, 1, A( 1, K ), 1 )
CALL DGER( K-1, N-M, -TAU( K ), TAU, 1, A( K, M1 ), LDA,