--- rpl/lapack/lapack/dggbak.f 2010/08/13 21:03:46 1.6
+++ rpl/lapack/lapack/dggbak.f 2023/08/07 08:38:50 1.18
@@ -1,10 +1,153 @@
+*> \brief \b DGGBAK
+*
+* =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+* http://www.netlib.org/lapack/explore-html/
+*
+*> \htmlonly
+*> Download DGGBAK + dependencies
+*>
+*> [TGZ]
+*>
+*> [ZIP]
+*>
+*> [TXT]
+*> \endhtmlonly
+*
+* Definition:
+* ===========
+*
+* SUBROUTINE DGGBAK( JOB, SIDE, N, ILO, IHI, LSCALE, RSCALE, M, V,
+* LDV, INFO )
+*
+* .. Scalar Arguments ..
+* CHARACTER JOB, SIDE
+* INTEGER IHI, ILO, INFO, LDV, M, N
+* ..
+* .. Array Arguments ..
+* DOUBLE PRECISION LSCALE( * ), RSCALE( * ), V( LDV, * )
+* ..
+*
+*
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
+*>
+*> DGGBAK forms the right or left eigenvectors of a real generalized
+*> eigenvalue problem A*x = lambda*B*x, by backward transformation on
+*> the computed eigenvectors of the balanced pair of matrices output by
+*> DGGBAL.
+*> \endverbatim
+*
+* Arguments:
+* ==========
+*
+*> \param[in] JOB
+*> \verbatim
+*> JOB is CHARACTER*1
+*> Specifies the type of backward transformation required:
+*> = 'N': do nothing, return immediately;
+*> = 'P': do backward transformation for permutation only;
+*> = 'S': do backward transformation for scaling only;
+*> = 'B': do backward transformations for both permutation and
+*> scaling.
+*> JOB must be the same as the argument JOB supplied to DGGBAL.
+*> \endverbatim
+*>
+*> \param[in] SIDE
+*> \verbatim
+*> SIDE is CHARACTER*1
+*> = 'R': V contains right eigenvectors;
+*> = 'L': V contains left eigenvectors.
+*> \endverbatim
+*>
+*> \param[in] N
+*> \verbatim
+*> N is INTEGER
+*> The number of rows of the matrix V. N >= 0.
+*> \endverbatim
+*>
+*> \param[in] ILO
+*> \verbatim
+*> ILO is INTEGER
+*> \endverbatim
+*>
+*> \param[in] IHI
+*> \verbatim
+*> IHI is INTEGER
+*> The integers ILO and IHI determined by DGGBAL.
+*> 1 <= ILO <= IHI <= N, if N > 0; ILO=1 and IHI=0, if N=0.
+*> \endverbatim
+*>
+*> \param[in] LSCALE
+*> \verbatim
+*> LSCALE is DOUBLE PRECISION array, dimension (N)
+*> Details of the permutations and/or scaling factors applied
+*> to the left side of A and B, as returned by DGGBAL.
+*> \endverbatim
+*>
+*> \param[in] RSCALE
+*> \verbatim
+*> RSCALE is DOUBLE PRECISION array, dimension (N)
+*> Details of the permutations and/or scaling factors applied
+*> to the right side of A and B, as returned by DGGBAL.
+*> \endverbatim
+*>
+*> \param[in] M
+*> \verbatim
+*> M is INTEGER
+*> The number of columns of the matrix V. M >= 0.
+*> \endverbatim
+*>
+*> \param[in,out] V
+*> \verbatim
+*> V is DOUBLE PRECISION array, dimension (LDV,M)
+*> On entry, the matrix of right or left eigenvectors to be
+*> transformed, as returned by DTGEVC.
+*> On exit, V is overwritten by the transformed eigenvectors.
+*> \endverbatim
+*>
+*> \param[in] LDV
+*> \verbatim
+*> LDV is INTEGER
+*> The leading dimension of the matrix V. LDV >= max(1,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 doubleGBcomputational
+*
+*> \par Further Details:
+* =====================
+*>
+*> \verbatim
+*>
+*> See R.C. Ward, Balancing the generalized eigenvalue problem,
+*> SIAM J. Sci. Stat. Comp. 2 (1981), 141-152.
+*> \endverbatim
+*>
+* =====================================================================
SUBROUTINE DGGBAK( JOB, SIDE, N, ILO, IHI, LSCALE, RSCALE, M, V,
$ LDV, 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 ..
CHARACTER JOB, SIDE
@@ -14,67 +157,6 @@
DOUBLE PRECISION LSCALE( * ), RSCALE( * ), V( LDV, * )
* ..
*
-* Purpose
-* =======
-*
-* DGGBAK forms the right or left eigenvectors of a real generalized
-* eigenvalue problem A*x = lambda*B*x, by backward transformation on
-* the computed eigenvectors of the balanced pair of matrices output by
-* DGGBAL.
-*
-* Arguments
-* =========
-*
-* JOB (input) CHARACTER*1
-* Specifies the type of backward transformation required:
-* = 'N': do nothing, return immediately;
-* = 'P': do backward transformation for permutation only;
-* = 'S': do backward transformation for scaling only;
-* = 'B': do backward transformations for both permutation and
-* scaling.
-* JOB must be the same as the argument JOB supplied to DGGBAL.
-*
-* SIDE (input) CHARACTER*1
-* = 'R': V contains right eigenvectors;
-* = 'L': V contains left eigenvectors.
-*
-* N (input) INTEGER
-* The number of rows of the matrix V. N >= 0.
-*
-* ILO (input) INTEGER
-* IHI (input) INTEGER
-* The integers ILO and IHI determined by DGGBAL.
-* 1 <= ILO <= IHI <= N, if N > 0; ILO=1 and IHI=0, if N=0.
-*
-* LSCALE (input) DOUBLE PRECISION array, dimension (N)
-* Details of the permutations and/or scaling factors applied
-* to the left side of A and B, as returned by DGGBAL.
-*
-* RSCALE (input) DOUBLE PRECISION array, dimension (N)
-* Details of the permutations and/or scaling factors applied
-* to the right side of A and B, as returned by DGGBAL.
-*
-* M (input) INTEGER
-* The number of columns of the matrix V. M >= 0.
-*
-* V (input/output) DOUBLE PRECISION array, dimension (LDV,M)
-* On entry, the matrix of right or left eigenvectors to be
-* transformed, as returned by DTGEVC.
-* On exit, V is overwritten by the transformed eigenvectors.
-*
-* LDV (input) INTEGER
-* The leading dimension of the matrix V. LDV >= max(1,N).
-*
-* INFO (output) INTEGER
-* = 0: successful exit.
-* < 0: if INFO = -i, the i-th argument had an illegal value.
-*
-* Further Details
-* ===============
-*
-* See R.C. Ward, Balancing the generalized eigenvalue problem,
-* SIAM J. Sci. Stat. Comp. 2 (1981), 141-152.
-*
* =====================================================================
*
* .. Local Scalars ..
@@ -89,7 +171,7 @@
EXTERNAL DSCAL, DSWAP, XERBLA
* ..
* .. Intrinsic Functions ..
- INTRINSIC MAX
+ INTRINSIC MAX, INT
* ..
* .. Executable Statements ..
*
@@ -170,7 +252,7 @@
$ GO TO 50
*
DO 40 I = ILO - 1, 1, -1
- K = RSCALE( I )
+ K = INT(RSCALE( I ))
IF( K.EQ.I )
$ GO TO 40
CALL DSWAP( M, V( I, 1 ), LDV, V( K, 1 ), LDV )
@@ -180,7 +262,7 @@
IF( IHI.EQ.N )
$ GO TO 70
DO 60 I = IHI + 1, N
- K = RSCALE( I )
+ K = INT(RSCALE( I ))
IF( K.EQ.I )
$ GO TO 60
CALL DSWAP( M, V( I, 1 ), LDV, V( K, 1 ), LDV )
@@ -194,7 +276,7 @@
IF( ILO.EQ.1 )
$ GO TO 90
DO 80 I = ILO - 1, 1, -1
- K = LSCALE( I )
+ K = INT(LSCALE( I ))
IF( K.EQ.I )
$ GO TO 80
CALL DSWAP( M, V( I, 1 ), LDV, V( K, 1 ), LDV )
@@ -204,7 +286,7 @@
IF( IHI.EQ.N )
$ GO TO 110
DO 100 I = IHI + 1, N
- K = LSCALE( I )
+ K = INT(LSCALE( I ))
IF( K.EQ.I )
$ GO TO 100
CALL DSWAP( M, V( I, 1 ), LDV, V( K, 1 ), LDV )