--- rpl/lapack/lapack/dggbal.f 2010/12/21 13:53:26 1.8
+++ rpl/lapack/lapack/dggbal.f 2011/11/21 20:42:52 1.9
@@ -1,10 +1,186 @@
+*> \brief \b DGGBAL
+*
+* =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+* http://www.netlib.org/lapack/explore-html/
+*
+*> \htmlonly
+*> Download DGGBAL + dependencies
+*>
+*> [TGZ]
+*>
+*> [ZIP]
+*>
+*> [TXT]
+*> \endhtmlonly
+*
+* Definition:
+* ===========
+*
+* SUBROUTINE DGGBAL( JOB, N, A, LDA, B, LDB, ILO, IHI, LSCALE,
+* RSCALE, WORK, INFO )
+*
+* .. Scalar Arguments ..
+* CHARACTER JOB
+* INTEGER IHI, ILO, INFO, LDA, LDB, N
+* ..
+* .. Array Arguments ..
+* DOUBLE PRECISION A( LDA, * ), B( LDB, * ), LSCALE( * ),
+* $ RSCALE( * ), WORK( * )
+* ..
+*
+*
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
+*>
+*> DGGBAL balances a pair of general real matrices (A,B). This
+*> involves, first, permuting A and B by similarity transformations to
+*> isolate eigenvalues in the first 1 to ILO$-$1 and last IHI+1 to N
+*> elements on the diagonal; and second, applying a diagonal similarity
+*> transformation to rows and columns ILO to IHI to make the rows
+*> and columns as close in norm as possible. Both steps are optional.
+*>
+*> Balancing may reduce the 1-norm of the matrices, and improve the
+*> accuracy of the computed eigenvalues and/or eigenvectors in the
+*> generalized eigenvalue problem A*x = lambda*B*x.
+*> \endverbatim
+*
+* Arguments:
+* ==========
+*
+*> \param[in] JOB
+*> \verbatim
+*> JOB is CHARACTER*1
+*> Specifies the operations to be performed on A and B:
+*> = 'N': none: simply set ILO = 1, IHI = N, LSCALE(I) = 1.0
+*> and RSCALE(I) = 1.0 for i = 1,...,N.
+*> = 'P': permute only;
+*> = 'S': scale only;
+*> = 'B': both permute and scale.
+*> \endverbatim
+*>
+*> \param[in] N
+*> \verbatim
+*> N is INTEGER
+*> The order of the matrices A and B. N >= 0.
+*> \endverbatim
+*>
+*> \param[in,out] A
+*> \verbatim
+*> A is DOUBLE PRECISION array, dimension (LDA,N)
+*> On entry, the input matrix A.
+*> On exit, A is overwritten by the balanced matrix.
+*> If JOB = 'N', A is not referenced.
+*> \endverbatim
+*>
+*> \param[in] LDA
+*> \verbatim
+*> LDA is INTEGER
+*> The leading dimension of the array A. LDA >= max(1,N).
+*> \endverbatim
+*>
+*> \param[in,out] B
+*> \verbatim
+*> B is DOUBLE PRECISION array, dimension (LDB,N)
+*> On entry, the input matrix B.
+*> On exit, B is overwritten by the balanced matrix.
+*> If JOB = 'N', B is not referenced.
+*> \endverbatim
+*>
+*> \param[in] LDB
+*> \verbatim
+*> LDB is INTEGER
+*> The leading dimension of the array B. LDB >= max(1,N).
+*> \endverbatim
+*>
+*> \param[out] ILO
+*> \verbatim
+*> ILO is INTEGER
+*> \endverbatim
+*>
+*> \param[out] IHI
+*> \verbatim
+*> IHI is INTEGER
+*> ILO and IHI are set to integers such that on exit
+*> A(i,j) = 0 and B(i,j) = 0 if i > j and
+*> j = 1,...,ILO-1 or i = IHI+1,...,N.
+*> If JOB = 'N' or 'S', ILO = 1 and IHI = N.
+*> \endverbatim
+*>
+*> \param[out] LSCALE
+*> \verbatim
+*> LSCALE is DOUBLE PRECISION array, dimension (N)
+*> Details of the permutations and scaling factors applied
+*> to the left side of A and B. If P(j) is the index of the
+*> row interchanged with row j, and D(j)
+*> is the scaling factor applied to row j, then
+*> LSCALE(j) = P(j) for J = 1,...,ILO-1
+*> = D(j) for J = ILO,...,IHI
+*> = P(j) for J = IHI+1,...,N.
+*> The order in which the interchanges are made is N to IHI+1,
+*> then 1 to ILO-1.
+*> \endverbatim
+*>
+*> \param[out] RSCALE
+*> \verbatim
+*> RSCALE is DOUBLE PRECISION array, dimension (N)
+*> Details of the permutations and scaling factors applied
+*> to the right side of A and B. If P(j) is the index of the
+*> column interchanged with column j, and D(j)
+*> is the scaling factor applied to column j, then
+*> LSCALE(j) = P(j) for J = 1,...,ILO-1
+*> = D(j) for J = ILO,...,IHI
+*> = P(j) for J = IHI+1,...,N.
+*> The order in which the interchanges are made is N to IHI+1,
+*> then 1 to ILO-1.
+*> \endverbatim
+*>
+*> \param[out] WORK
+*> \verbatim
+*> WORK is DOUBLE PRECISION array, dimension (lwork)
+*> lwork must be at least max(1,6*N) when JOB = 'S' or 'B', and
+*> at least 1 when JOB = 'N' or 'P'.
+*> \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 November 2011
+*
+*> \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 DGGBAL( JOB, N, A, LDA, B, LDB, ILO, IHI, LSCALE,
$ RSCALE, WORK, INFO )
*
-* -- LAPACK routine (version 3.2.2) --
+* -- LAPACK computational routine (version 3.4.0) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
-* June 2010
+* November 2011
*
* .. Scalar Arguments ..
CHARACTER JOB
@@ -15,93 +191,6 @@
$ RSCALE( * ), WORK( * )
* ..
*
-* Purpose
-* =======
-*
-* DGGBAL balances a pair of general real matrices (A,B). This
-* involves, first, permuting A and B by similarity transformations to
-* isolate eigenvalues in the first 1 to ILO$-$1 and last IHI+1 to N
-* elements on the diagonal; and second, applying a diagonal similarity
-* transformation to rows and columns ILO to IHI to make the rows
-* and columns as close in norm as possible. Both steps are optional.
-*
-* Balancing may reduce the 1-norm of the matrices, and improve the
-* accuracy of the computed eigenvalues and/or eigenvectors in the
-* generalized eigenvalue problem A*x = lambda*B*x.
-*
-* Arguments
-* =========
-*
-* JOB (input) CHARACTER*1
-* Specifies the operations to be performed on A and B:
-* = 'N': none: simply set ILO = 1, IHI = N, LSCALE(I) = 1.0
-* and RSCALE(I) = 1.0 for i = 1,...,N.
-* = 'P': permute only;
-* = 'S': scale only;
-* = 'B': both permute and scale.
-*
-* N (input) INTEGER
-* The order of the matrices A and B. N >= 0.
-*
-* A (input/output) DOUBLE PRECISION array, dimension (LDA,N)
-* On entry, the input matrix A.
-* On exit, A is overwritten by the balanced matrix.
-* If JOB = 'N', A is not referenced.
-*
-* LDA (input) INTEGER
-* The leading dimension of the array A. LDA >= max(1,N).
-*
-* B (input/output) DOUBLE PRECISION array, dimension (LDB,N)
-* On entry, the input matrix B.
-* On exit, B is overwritten by the balanced matrix.
-* If JOB = 'N', B is not referenced.
-*
-* LDB (input) INTEGER
-* The leading dimension of the array B. LDB >= max(1,N).
-*
-* ILO (output) INTEGER
-* IHI (output) INTEGER
-* ILO and IHI are set to integers such that on exit
-* A(i,j) = 0 and B(i,j) = 0 if i > j and
-* j = 1,...,ILO-1 or i = IHI+1,...,N.
-* If JOB = 'N' or 'S', ILO = 1 and IHI = N.
-*
-* LSCALE (output) DOUBLE PRECISION array, dimension (N)
-* Details of the permutations and scaling factors applied
-* to the left side of A and B. If P(j) is the index of the
-* row interchanged with row j, and D(j)
-* is the scaling factor applied to row j, then
-* LSCALE(j) = P(j) for J = 1,...,ILO-1
-* = D(j) for J = ILO,...,IHI
-* = P(j) for J = IHI+1,...,N.
-* The order in which the interchanges are made is N to IHI+1,
-* then 1 to ILO-1.
-*
-* RSCALE (output) DOUBLE PRECISION array, dimension (N)
-* Details of the permutations and scaling factors applied
-* to the right side of A and B. If P(j) is the index of the
-* column interchanged with column j, and D(j)
-* is the scaling factor applied to column j, then
-* LSCALE(j) = P(j) for J = 1,...,ILO-1
-* = D(j) for J = ILO,...,IHI
-* = P(j) for J = IHI+1,...,N.
-* The order in which the interchanges are made is N to IHI+1,
-* then 1 to ILO-1.
-*
-* WORK (workspace) DOUBLE PRECISION array, dimension (lwork)
-* lwork must be at least max(1,6*N) when JOB = 'S' or 'B', and
-* at least 1 when JOB = 'N' or 'P'.
-*
-* 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.
-*
* =====================================================================
*
* .. Parameters ..