--- rpl/lapack/lapack/zgbequb.f 2010/12/21 13:53:42 1.4
+++ rpl/lapack/lapack/zgbequb.f 2011/11/21 20:43:08 1.5
@@ -1,16 +1,171 @@
+*> \brief \b ZGBEQUB
+*
+* =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+* http://www.netlib.org/lapack/explore-html/
+*
+*> \htmlonly
+*> Download ZGBEQUB + dependencies
+*>
+*> [TGZ]
+*>
+*> [ZIP]
+*>
+*> [TXT]
+*> \endhtmlonly
+*
+* Definition:
+* ===========
+*
+* SUBROUTINE ZGBEQUB( M, N, KL, KU, AB, LDAB, R, C, ROWCND, COLCND,
+* AMAX, INFO )
+*
+* .. Scalar Arguments ..
+* INTEGER INFO, KL, KU, LDAB, M, N
+* DOUBLE PRECISION AMAX, COLCND, ROWCND
+* ..
+* .. Array Arguments ..
+* DOUBLE PRECISION C( * ), R( * )
+* COMPLEX*16 AB( LDAB, * )
+* ..
+*
+*
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
+*>
+*> ZGBEQUB computes row and column scalings intended to equilibrate an
+*> M-by-N matrix A and reduce its condition number. R returns the row
+*> scale factors and C the column scale factors, chosen to try to make
+*> the largest element in each row and column of the matrix B with
+*> elements B(i,j)=R(i)*A(i,j)*C(j) have an absolute value of at most
+*> the radix.
+*>
+*> R(i) and C(j) are restricted to be a power of the radix between
+*> SMLNUM = smallest safe number and BIGNUM = largest safe number. Use
+*> of these scaling factors is not guaranteed to reduce the condition
+*> number of A but works well in practice.
+*>
+*> This routine differs from ZGEEQU by restricting the scaling factors
+*> to a power of the radix. Baring over- and underflow, scaling by
+*> these factors introduces no additional rounding errors. However, the
+*> scaled entries' magnitured are no longer approximately 1 but lie
+*> between sqrt(radix) and 1/sqrt(radix).
+*> \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 >= 0.
+*> \endverbatim
+*>
+*> \param[in] KL
+*> \verbatim
+*> KL is INTEGER
+*> The number of subdiagonals within the band of A. KL >= 0.
+*> \endverbatim
+*>
+*> \param[in] KU
+*> \verbatim
+*> KU is INTEGER
+*> The number of superdiagonals within the band of A. KU >= 0.
+*> \endverbatim
+*>
+*> \param[in] AB
+*> \verbatim
+*> AB is DOUBLE PRECISION array, dimension (LDAB,N)
+*> On entry, the matrix A in band storage, in rows 1 to KL+KU+1.
+*> The j-th column of A is stored in the j-th column of the
+*> array AB as follows:
+*> AB(KU+1+i-j,j) = A(i,j) for max(1,j-KU)<=i<=min(N,j+kl)
+*> \endverbatim
+*>
+*> \param[in] LDAB
+*> \verbatim
+*> LDAB is INTEGER
+*> The leading dimension of the array A. LDAB >= max(1,M).
+*> \endverbatim
+*>
+*> \param[out] R
+*> \verbatim
+*> R is DOUBLE PRECISION array, dimension (M)
+*> If INFO = 0 or INFO > M, R contains the row scale factors
+*> for A.
+*> \endverbatim
+*>
+*> \param[out] C
+*> \verbatim
+*> C is DOUBLE PRECISION array, dimension (N)
+*> If INFO = 0, C contains the column scale factors for A.
+*> \endverbatim
+*>
+*> \param[out] ROWCND
+*> \verbatim
+*> ROWCND is DOUBLE PRECISION
+*> If INFO = 0 or INFO > M, ROWCND contains the ratio of the
+*> smallest R(i) to the largest R(i). If ROWCND >= 0.1 and
+*> AMAX is neither too large nor too small, it is not worth
+*> scaling by R.
+*> \endverbatim
+*>
+*> \param[out] COLCND
+*> \verbatim
+*> COLCND is DOUBLE PRECISION
+*> If INFO = 0, COLCND contains the ratio of the smallest
+*> C(i) to the largest C(i). If COLCND >= 0.1, it is not
+*> worth scaling by C.
+*> \endverbatim
+*>
+*> \param[out] AMAX
+*> \verbatim
+*> AMAX is DOUBLE PRECISION
+*> Absolute value of largest matrix element. If AMAX is very
+*> close to overflow or very close to underflow, the matrix
+*> should be scaled.
+*> \endverbatim
+*>
+*> \param[out] INFO
+*> \verbatim
+*> INFO is INTEGER
+*> = 0: successful exit
+*> < 0: if INFO = -i, the i-th argument had an illegal value
+*> > 0: if INFO = i, and i is
+*> <= M: the i-th row of A is exactly zero
+*> > M: the (i-M)-th column of A is exactly zero
+*> \endverbatim
+*
+* Authors:
+* ========
+*
+*> \author Univ. of Tennessee
+*> \author Univ. of California Berkeley
+*> \author Univ. of Colorado Denver
+*> \author NAG Ltd.
+*
+*> \date November 2011
+*
+*> \ingroup complex16GBcomputational
+*
+* =====================================================================
SUBROUTINE ZGBEQUB( M, N, KL, KU, AB, LDAB, R, C, ROWCND, COLCND,
$ AMAX, INFO )
*
-* -- LAPACK routine (version 3.2) --
-* -- Contributed by James Demmel, Deaglan Halligan, Yozo Hida and --
-* -- Jason Riedy of Univ. of California Berkeley. --
-* -- November 2008 --
-*
-* -- LAPACK is a software package provided by Univ. of Tennessee, --
-* -- Univ. of California Berkeley and NAG Ltd. --
+* -- 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..--
+* November 2011
*
- IMPLICIT NONE
-* ..
* .. Scalar Arguments ..
INTEGER INFO, KL, KU, LDAB, M, N
DOUBLE PRECISION AMAX, COLCND, ROWCND
@@ -20,81 +175,6 @@
COMPLEX*16 AB( LDAB, * )
* ..
*
-* Purpose
-* =======
-*
-* ZGBEQUB computes row and column scalings intended to equilibrate an
-* M-by-N matrix A and reduce its condition number. R returns the row
-* scale factors and C the column scale factors, chosen to try to make
-* the largest element in each row and column of the matrix B with
-* elements B(i,j)=R(i)*A(i,j)*C(j) have an absolute value of at most
-* the radix.
-*
-* R(i) and C(j) are restricted to be a power of the radix between
-* SMLNUM = smallest safe number and BIGNUM = largest safe number. Use
-* of these scaling factors is not guaranteed to reduce the condition
-* number of A but works well in practice.
-*
-* This routine differs from ZGEEQU by restricting the scaling factors
-* to a power of the radix. Baring over- and underflow, scaling by
-* these factors introduces no additional rounding errors. However, the
-* scaled entries' magnitured are no longer approximately 1 but lie
-* between sqrt(radix) and 1/sqrt(radix).
-*
-* 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 >= 0.
-*
-* KL (input) INTEGER
-* The number of subdiagonals within the band of A. KL >= 0.
-*
-* KU (input) INTEGER
-* The number of superdiagonals within the band of A. KU >= 0.
-*
-* AB (input) DOUBLE PRECISION array, dimension (LDAB,N)
-* On entry, the matrix A in band storage, in rows 1 to KL+KU+1.
-* The j-th column of A is stored in the j-th column of the
-* array AB as follows:
-* AB(KU+1+i-j,j) = A(i,j) for max(1,j-KU)<=i<=min(N,j+kl)
-*
-* LDAB (input) INTEGER
-* The leading dimension of the array A. LDAB >= max(1,M).
-*
-* R (output) DOUBLE PRECISION array, dimension (M)
-* If INFO = 0 or INFO > M, R contains the row scale factors
-* for A.
-*
-* C (output) DOUBLE PRECISION array, dimension (N)
-* If INFO = 0, C contains the column scale factors for A.
-*
-* ROWCND (output) DOUBLE PRECISION
-* If INFO = 0 or INFO > M, ROWCND contains the ratio of the
-* smallest R(i) to the largest R(i). If ROWCND >= 0.1 and
-* AMAX is neither too large nor too small, it is not worth
-* scaling by R.
-*
-* COLCND (output) DOUBLE PRECISION
-* If INFO = 0, COLCND contains the ratio of the smallest
-* C(i) to the largest C(i). If COLCND >= 0.1, it is not
-* worth scaling by C.
-*
-* AMAX (output) DOUBLE PRECISION
-* Absolute value of largest matrix element. If AMAX is very
-* close to overflow or very close to underflow, the matrix
-* should be scaled.
-*
-* INFO (output) INTEGER
-* = 0: successful exit
-* < 0: if INFO = -i, the i-th argument had an illegal value
-* > 0: if INFO = i, and i is
-* <= M: the i-th row of A is exactly zero
-* > M: the (i-M)-th column of A is exactly zero
-*
* =====================================================================
*
* .. Parameters ..