--- rpl/lapack/lapack/ztzrzf.f 2010/08/06 15:29:03 1.3
+++ rpl/lapack/lapack/ztzrzf.f 2017/06/17 10:54:32 1.16
@@ -1,9 +1,160 @@
+*> \brief \b ZTZRZF
+*
+* =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+* http://www.netlib.org/lapack/explore-html/
+*
+*> \htmlonly
+*> Download ZTZRZF + dependencies
+*>
+*> [TGZ]
+*>
+*> [ZIP]
+*>
+*> [TXT]
+*> \endhtmlonly
+*
+* Definition:
+* ===========
+*
+* SUBROUTINE ZTZRZF( M, N, A, LDA, TAU, WORK, LWORK, INFO )
+*
+* .. Scalar Arguments ..
+* INTEGER INFO, LDA, LWORK, M, N
+* ..
+* .. Array Arguments ..
+* COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * )
+* ..
+*
+*
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
+*>
+*> ZTZRZF reduces the M-by-N ( M<=N ) complex upper trapezoidal matrix A
+*> to upper triangular form by means of unitary transformations.
+*>
+*> The upper trapezoidal matrix A is factored as
+*>
+*> A = ( R 0 ) * Z,
+*>
+*> where Z is an N-by-N unitary 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 COMPLEX*16 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
+*> unitary 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 COMPLEX*16 array, dimension (M)
+*> The scalar factors of the elementary reflectors.
+*> \endverbatim
+*>
+*> \param[out] WORK
+*> \verbatim
+*> WORK is COMPLEX*16 array, dimension (MAX(1,LWORK))
+*> On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
+*> \endverbatim
+*>
+*> \param[in] LWORK
+*> \verbatim
+*> LWORK is INTEGER
+*> The dimension of the array WORK. LWORK >= max(1,M).
+*> For optimum performance LWORK >= M*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.
+*> \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.
+*
+*> \date April 2012
+*
+*> \ingroup complex16OTHERcomputational
+*
+*> \par Contributors:
+* ==================
+*>
+*> A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA
+*
+*> \par Further Details:
+* =====================
+*>
+*> \verbatim
+*>
+*> The N-by-N matrix Z can be computed by
+*>
+*> Z = Z(1)*Z(2)* ... *Z(M)
+*>
+*> where each N-by-N Z(k) is given by
+*>
+*> Z(k) = I - tau(k)*v(k)*v(k)**H
+*>
+*> with v(k) is the kth row vector of the M-by-N matrix
+*>
+*> V = ( I A(:,M+1:N) )
+*>
+*> I is the M-by-M identity matrix, A(:,M+1:N)
+*> is the output stored in A on exit from DTZRZF,
+*> and tau(k) is the kth element of the array TAU.
+*>
+*> \endverbatim
+*>
+* =====================================================================
SUBROUTINE ZTZRZF( M, N, A, LDA, TAU, WORK, LWORK, INFO )
*
-* -- LAPACK routine (version 3.2) --
+* -- LAPACK computational routine (version 3.7.0) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
-* November 2006
+* April 2012
*
* .. Scalar Arguments ..
INTEGER INFO, LDA, LWORK, M, N
@@ -12,91 +163,6 @@
COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
-*
-* ZTZRZF reduces the M-by-N ( M<=N ) complex upper trapezoidal matrix A
-* to upper triangular form by means of unitary transformations.
-*
-* The upper trapezoidal matrix A is factored as
-*
-* A = ( R 0 ) * Z,
-*
-* where Z is an N-by-N unitary 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) COMPLEX*16 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
-* unitary 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) COMPLEX*16 array, dimension (M)
-* The scalar factors of the elementary reflectors.
-*
-* WORK (workspace/output) COMPLEX*16 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 >= max(1,M).
-* For optimum performance LWORK >= M*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
-* ===============
-*
-* Based on contributions by
-* A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA
-*
-* 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 ..
@@ -105,8 +171,8 @@
* ..
* .. Local Scalars ..
LOGICAL LQUERY
- INTEGER I, IB, IWS, KI, KK, LDWORK, LWKOPT, M1, MU, NB,
- $ NBMIN, NX
+ INTEGER I, IB, IWS, KI, KK, LDWORK, LWKMIN, LWKOPT,
+ $ M1, MU, NB, NBMIN, NX
* ..
* .. External Subroutines ..
EXTERNAL XERBLA, ZLARZB, ZLARZT, ZLATRZ
@@ -135,16 +201,18 @@
IF( INFO.EQ.0 ) THEN
IF( M.EQ.0 .OR. M.EQ.N ) THEN
LWKOPT = 1
+ LWKMIN = 1
ELSE
*
* Determine the block size.
*
NB = ILAENV( 1, 'ZGERQF', ' ', M, N, -1, -1 )
LWKOPT = M*NB
+ LWKMIN = MAX( 1, M )
END IF
WORK( 1 ) = LWKOPT
*
- IF( LWORK.LT.MAX( 1, M ) .AND. .NOT.LQUERY ) THEN
+ IF( LWORK.LT.LWKMIN .AND. .NOT.LQUERY ) THEN
INFO = -7
END IF
END IF