--- rpl/lapack/lapack/dorgbr.f 2010/12/21 13:53:34 1.7
+++ rpl/lapack/lapack/dorgbr.f 2017/06/17 11:06:29 1.17
@@ -1,9 +1,166 @@
+*> \brief \b DORGBR
+*
+* =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+* http://www.netlib.org/lapack/explore-html/
+*
+*> \htmlonly
+*> Download DORGBR + dependencies
+*>
+*> [TGZ]
+*>
+*> [ZIP]
+*>
+*> [TXT]
+*> \endhtmlonly
+*
+* Definition:
+* ===========
+*
+* SUBROUTINE DORGBR( VECT, M, N, K, A, LDA, TAU, WORK, LWORK, INFO )
+*
+* .. Scalar Arguments ..
+* CHARACTER VECT
+* INTEGER INFO, K, LDA, LWORK, M, N
+* ..
+* .. Array Arguments ..
+* DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * )
+* ..
+*
+*
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
+*>
+*> DORGBR generates one of the real orthogonal matrices Q or P**T
+*> determined by DGEBRD when reducing a real matrix A to bidiagonal
+*> form: A = Q * B * P**T. Q and P**T are defined as products of
+*> elementary reflectors H(i) or G(i) respectively.
+*>
+*> If VECT = 'Q', A is assumed to have been an M-by-K matrix, and Q
+*> is of order M:
+*> if m >= k, Q = H(1) H(2) . . . H(k) and DORGBR returns the first n
+*> columns of Q, where m >= n >= k;
+*> if m < k, Q = H(1) H(2) . . . H(m-1) and DORGBR returns Q as an
+*> M-by-M matrix.
+*>
+*> If VECT = 'P', A is assumed to have been a K-by-N matrix, and P**T
+*> is of order N:
+*> if k < n, P**T = G(k) . . . G(2) G(1) and DORGBR returns the first m
+*> rows of P**T, where n >= m >= k;
+*> if k >= n, P**T = G(n-1) . . . G(2) G(1) and DORGBR returns P**T as
+*> an N-by-N matrix.
+*> \endverbatim
+*
+* Arguments:
+* ==========
+*
+*> \param[in] VECT
+*> \verbatim
+*> VECT is CHARACTER*1
+*> Specifies whether the matrix Q or the matrix P**T is
+*> required, as defined in the transformation applied by DGEBRD:
+*> = 'Q': generate Q;
+*> = 'P': generate P**T.
+*> \endverbatim
+*>
+*> \param[in] M
+*> \verbatim
+*> M is INTEGER
+*> The number of rows of the matrix Q or P**T to be returned.
+*> M >= 0.
+*> \endverbatim
+*>
+*> \param[in] N
+*> \verbatim
+*> N is INTEGER
+*> The number of columns of the matrix Q or P**T to be returned.
+*> N >= 0.
+*> If VECT = 'Q', M >= N >= min(M,K);
+*> if VECT = 'P', N >= M >= min(N,K).
+*> \endverbatim
+*>
+*> \param[in] K
+*> \verbatim
+*> K is INTEGER
+*> If VECT = 'Q', the number of columns in the original M-by-K
+*> matrix reduced by DGEBRD.
+*> If VECT = 'P', the number of rows in the original K-by-N
+*> matrix reduced by DGEBRD.
+*> K >= 0.
+*> \endverbatim
+*>
+*> \param[in,out] A
+*> \verbatim
+*> A is DOUBLE PRECISION array, dimension (LDA,N)
+*> On entry, the vectors which define the elementary reflectors,
+*> as returned by DGEBRD.
+*> On exit, the M-by-N matrix Q or P**T.
+*> \endverbatim
+*>
+*> \param[in] LDA
+*> \verbatim
+*> LDA is INTEGER
+*> The leading dimension of the array A. LDA >= max(1,M).
+*> \endverbatim
+*>
+*> \param[in] TAU
+*> \verbatim
+*> TAU is DOUBLE PRECISION array, dimension
+*> (min(M,K)) if VECT = 'Q'
+*> (min(N,K)) if VECT = 'P'
+*> TAU(i) must contain the scalar factor of the elementary
+*> reflector H(i) or G(i), which determines Q or P**T, as
+*> returned by DGEBRD in its array argument TAUQ or TAUP.
+*> \endverbatim
+*>
+*> \param[out] WORK
+*> \verbatim
+*> WORK is DOUBLE PRECISION 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,min(M,N)).
+*> For optimum performance LWORK >= min(M,N)*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 doubleGBcomputational
+*
+* =====================================================================
SUBROUTINE DORGBR( VECT, M, N, K, 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 ..
CHARACTER VECT
@@ -13,86 +170,6 @@
DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * )
* ..
*
-* Purpose
-* =======
-*
-* DORGBR generates one of the real orthogonal matrices Q or P**T
-* determined by DGEBRD when reducing a real matrix A to bidiagonal
-* form: A = Q * B * P**T. Q and P**T are defined as products of
-* elementary reflectors H(i) or G(i) respectively.
-*
-* If VECT = 'Q', A is assumed to have been an M-by-K matrix, and Q
-* is of order M:
-* if m >= k, Q = H(1) H(2) . . . H(k) and DORGBR returns the first n
-* columns of Q, where m >= n >= k;
-* if m < k, Q = H(1) H(2) . . . H(m-1) and DORGBR returns Q as an
-* M-by-M matrix.
-*
-* If VECT = 'P', A is assumed to have been a K-by-N matrix, and P**T
-* is of order N:
-* if k < n, P**T = G(k) . . . G(2) G(1) and DORGBR returns the first m
-* rows of P**T, where n >= m >= k;
-* if k >= n, P**T = G(n-1) . . . G(2) G(1) and DORGBR returns P**T as
-* an N-by-N matrix.
-*
-* Arguments
-* =========
-*
-* VECT (input) CHARACTER*1
-* Specifies whether the matrix Q or the matrix P**T is
-* required, as defined in the transformation applied by DGEBRD:
-* = 'Q': generate Q;
-* = 'P': generate P**T.
-*
-* M (input) INTEGER
-* The number of rows of the matrix Q or P**T to be returned.
-* M >= 0.
-*
-* N (input) INTEGER
-* The number of columns of the matrix Q or P**T to be returned.
-* N >= 0.
-* If VECT = 'Q', M >= N >= min(M,K);
-* if VECT = 'P', N >= M >= min(N,K).
-*
-* K (input) INTEGER
-* If VECT = 'Q', the number of columns in the original M-by-K
-* matrix reduced by DGEBRD.
-* If VECT = 'P', the number of rows in the original K-by-N
-* matrix reduced by DGEBRD.
-* K >= 0.
-*
-* A (input/output) DOUBLE PRECISION array, dimension (LDA,N)
-* On entry, the vectors which define the elementary reflectors,
-* as returned by DGEBRD.
-* On exit, the M-by-N matrix Q or P**T.
-*
-* LDA (input) INTEGER
-* The leading dimension of the array A. LDA >= max(1,M).
-*
-* TAU (input) DOUBLE PRECISION array, dimension
-* (min(M,K)) if VECT = 'Q'
-* (min(N,K)) if VECT = 'P'
-* TAU(i) must contain the scalar factor of the elementary
-* reflector H(i) or G(i), which determines Q or P**T, as
-* returned by DGEBRD in its array argument TAUQ or TAUP.
-*
-* WORK (workspace/output) DOUBLE PRECISION 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,min(M,N)).
-* For optimum performance LWORK >= min(M,N)*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
-*
* =====================================================================
*
* .. Parameters ..
@@ -101,12 +178,11 @@
* ..
* .. Local Scalars ..
LOGICAL LQUERY, WANTQ
- INTEGER I, IINFO, J, LWKOPT, MN, NB
+ INTEGER I, IINFO, J, LWKOPT, MN
* ..
* .. External Functions ..
LOGICAL LSAME
- INTEGER ILAENV
- EXTERNAL LSAME, ILAENV
+ EXTERNAL LSAME
* ..
* .. External Subroutines ..
EXTERNAL DORGLQ, DORGQR, XERBLA
@@ -139,19 +215,35 @@
END IF
*
IF( INFO.EQ.0 ) THEN
+ WORK( 1 ) = 1
IF( WANTQ ) THEN
- NB = ILAENV( 1, 'DORGQR', ' ', M, N, K, -1 )
+ IF( M.GE.K ) THEN
+ CALL DORGQR( M, N, K, A, LDA, TAU, WORK, -1, IINFO )
+ ELSE
+ IF( M.GT.1 ) THEN
+ CALL DORGQR( M-1, M-1, M-1, A( 2, 2 ), LDA, TAU, WORK,
+ $ -1, IINFO )
+ END IF
+ END IF
ELSE
- NB = ILAENV( 1, 'DORGLQ', ' ', M, N, K, -1 )
+ IF( K.LT.N ) THEN
+ CALL DORGLQ( M, N, K, A, LDA, TAU, WORK, -1, IINFO )
+ ELSE
+ IF( N.GT.1 ) THEN
+ CALL DORGLQ( N-1, N-1, N-1, A( 2, 2 ), LDA, TAU, WORK,
+ $ -1, IINFO )
+ END IF
+ END IF
END IF
- LWKOPT = MAX( 1, MN )*NB
- WORK( 1 ) = LWKOPT
+ LWKOPT = WORK( 1 )
+ LWKOPT = MAX (LWKOPT, MN)
END IF
*
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'DORGBR', -INFO )
RETURN
ELSE IF( LQUERY ) THEN
+ WORK( 1 ) = LWKOPT
RETURN
END IF
*
@@ -201,7 +293,7 @@
END IF
ELSE
*
-* Form P', determined by a call to DGEBRD to reduce a k-by-n
+* Form P**T, determined by a call to DGEBRD to reduce a k-by-n
* matrix
*
IF( K.LT.N ) THEN
@@ -215,7 +307,7 @@
* If k >= n, assume m = n
*
* Shift the vectors which define the elementary reflectors one
-* row downward, and set the first row and column of P' to
+* row downward, and set the first row and column of P**T to
* those of the unit matrix
*
A( 1, 1 ) = ONE
@@ -230,7 +322,7 @@
60 CONTINUE
IF( N.GT.1 ) THEN
*
-* Form P'(2:n,2:n)
+* Form P**T(2:n,2:n)
*
CALL DORGLQ( N-1, N-1, N-1, A( 2, 2 ), LDA, TAU, WORK,
$ LWORK, IINFO )