--- rpl/lapack/lapack/dgbequ.f 2010/12/21 13:53:24 1.7 +++ rpl/lapack/lapack/dgbequ.f 2011/11/21 20:42:49 1.8 @@ -1,10 +1,162 @@ +*> \brief \b DGBEQU +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +*> \htmlonly +*> Download DGBEQU + dependencies +*> +*> [TGZ] +*> +*> [ZIP] +*> +*> [TXT] +*> \endhtmlonly +* +* Definition: +* =========== +* +* SUBROUTINE DGBEQU( 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 AB( LDAB, * ), C( * ), R( * ) +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> DGBEQU computes row and column scalings intended to equilibrate an +*> M-by-N band 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 absolute value 1. +*> +*> R(i) and C(j) are restricted to be 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. +*> \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) +*> The band matrix A, stored 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(m,j+kl). +*> \endverbatim +*> +*> \param[in] LDAB +*> \verbatim +*> LDAB is INTEGER +*> The leading dimension of the array AB. LDAB >= KL+KU+1. +*> \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 doubleGBcomputational +* +* ===================================================================== SUBROUTINE DGBEQU( M, N, KL, KU, AB, LDAB, R, C, ROWCND, COLCND, $ AMAX, INFO ) * -* -- LAPACK routine (version 3.2) -- +* -- 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..-- -* November 2006 +* November 2011 * * .. Scalar Arguments .. INTEGER INFO, KL, KU, LDAB, M, N @@ -14,74 +166,6 @@ DOUBLE PRECISION AB( LDAB, * ), C( * ), R( * ) * .. * -* Purpose -* ======= -* -* DGBEQU computes row and column scalings intended to equilibrate an -* M-by-N band 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 absolute value 1. -* -* R(i) and C(j) are restricted to be 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. -* -* 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) -* The band matrix A, stored 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(m,j+kl). -* -* LDAB (input) INTEGER -* The leading dimension of the array AB. LDAB >= KL+KU+1. -* -* 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 ..