--- rpl/lapack/lapack/dla_gbrpvgrw.f 2010/12/21 13:53:28 1.4 +++ rpl/lapack/lapack/dla_gbrpvgrw.f 2011/11/21 20:42:53 1.5 @@ -1,16 +1,127 @@ +*> \brief \b DLA_GBRPVGRW +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +*> \htmlonly +*> Download DLA_GBRPVGRW + dependencies +*> +*> [TGZ] +*> +*> [ZIP] +*> +*> [TXT] +*> \endhtmlonly +* +* Definition: +* =========== +* +* DOUBLE PRECISION FUNCTION DLA_GBRPVGRW( N, KL, KU, NCOLS, AB, +* LDAB, AFB, LDAFB ) +* +* .. Scalar Arguments .. +* INTEGER N, KL, KU, NCOLS, LDAB, LDAFB +* .. +* .. Array Arguments .. +* DOUBLE PRECISION AB( LDAB, * ), AFB( LDAFB, * ) +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> DLA_GBRPVGRW computes the reciprocal pivot growth factor +*> norm(A)/norm(U). The "max absolute element" norm is used. If this is +*> much less than 1, the stability of the LU factorization of the +*> (equilibrated) matrix A could be poor. This also means that the +*> solution X, estimated condition numbers, and error bounds could be +*> unreliable. +*> \endverbatim +* +* Arguments: +* ========== +* +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> The number of linear equations, i.e., the order 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] NCOLS +*> \verbatim +*> NCOLS is INTEGER +*> The number of columns of the matrix A. NCOLS >= 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 AB. LDAB >= KL+KU+1. +*> \endverbatim +*> +*> \param[in] AFB +*> \verbatim +*> AFB is DOUBLE PRECISION array, dimension (LDAFB,N) +*> Details of the LU factorization of the band matrix A, as +*> computed by DGBTRF. U is stored as an upper triangular +*> band matrix with KL+KU superdiagonals in rows 1 to KL+KU+1, +*> and the multipliers used during the factorization are stored +*> in rows KL+KU+2 to 2*KL+KU+1. +*> \endverbatim +*> +*> \param[in] LDAFB +*> \verbatim +*> LDAFB is INTEGER +*> The leading dimension of the array AFB. LDAFB >= 2*KL+KU+1. +*> \endverbatim +* +* Authors: +* ======== +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup doubleGBcomputational +* +* ===================================================================== DOUBLE PRECISION FUNCTION DLA_GBRPVGRW( N, KL, KU, NCOLS, AB, $ LDAB, AFB, LDAFB ) * -* -- LAPACK routine (version 3.2.2) -- -* -- Contributed by James Demmel, Deaglan Halligan, Yozo Hida and -- -* -- Jason Riedy of Univ. of California Berkeley. -- -* -- June 2010 -- -* -* -- 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 N, KL, KU, NCOLS, LDAB, LDAFB * .. @@ -18,51 +129,6 @@ DOUBLE PRECISION AB( LDAB, * ), AFB( LDAFB, * ) * .. * -* Purpose -* ======= -* -* DLA_GBRPVGRW computes the reciprocal pivot growth factor -* norm(A)/norm(U). The "max absolute element" norm is used. If this is -* much less than 1, the stability of the LU factorization of the -* (equilibrated) matrix A could be poor. This also means that the -* solution X, estimated condition numbers, and error bounds could be -* unreliable. -* -* Arguments -* ========= -* -* N (input) INTEGER -* The number of linear equations, i.e., the order 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. -* -* NCOLS (input) INTEGER -* The number of columns of the matrix A. NCOLS >= 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 AB. LDAB >= KL+KU+1. -* -* AFB (input) DOUBLE PRECISION array, dimension (LDAFB,N) -* Details of the LU factorization of the band matrix A, as -* computed by DGBTRF. U is stored as an upper triangular -* band matrix with KL+KU superdiagonals in rows 1 to KL+KU+1, -* and the multipliers used during the factorization are stored -* in rows KL+KU+2 to 2*KL+KU+1. -* -* LDAFB (input) INTEGER -* The leading dimension of the array AFB. LDAFB >= 2*KL+KU+1. -* * ===================================================================== * * .. Local Scalars ..