dla_gbrpvgrw (3p)

Name

dla_gbrpvgrw - compute the reciprocal pivot growth factor norm(A)/norm(U) for a general banded matrix

Synopsis

DOUBLE PRECISION FUNCTION DLA_GBRPVGRW(N, KL, KU, NCOLS, AB, LDAB, AFB,
LDAFB)


INTEGER N, KL, KU, NCOLS, LDAB, LDAFB

DOUBLE PRECISION AB(LDAB,*), AFB(LDAFB,*)


DOUBLE  PRECISION  FUNCTION DLA_GBRPVGRW_64(N, KL, KU, NCOLS, AB, LDAB,
AFB, LDAFB)


INTEGER*8 N, KL, KU, NCOLS, LDAB, LDAFB

DOUBLE PRECISION AB(LDAB,*), AFB(LDAFB,*)


F95 INTERFACE
REAL(8) FUNCTION LA_GBRPVGRW(N, KL, KU, NCOLS, AB, LDAB, AFB, LDAFB)


INTEGER :: N, KL, KU, NCOLS, LDAB, LDAFB

REAL(8), DIMENSION(:,:) :: AB, AFB


REAL(8) FUNCTION LA_GBRPVGRW_64(N, KL, KU, NCOLS, AB, LDAB, AFB, LDAFB)


INTEGER(8) :: N, KL, KU, NCOLS, LDAB, LDAFB

REAL(8), DIMENSION(:,:) :: AB, AFB


C INTERFACE
#include <sunperf.h>

double  dla_gbrpvgrw (int n, int kl, int ku, int ncols, double *ab, int
ldab, double *afb, int ldafb);

double dla_gbrpvgrw_64 (long n, long kl, long ku,  long  ncols,  double
*ab, long ldab, double *afb, long ldafb);

Description

Oracle Solaris Studio Performance Library                     dla_gbrpvgrw(3P)



NAME
       dla_gbrpvgrw   -   compute   the   reciprocal   pivot   growth   factor
       norm(A)/norm(U) for a general banded matrix


SYNOPSIS
       DOUBLE PRECISION FUNCTION DLA_GBRPVGRW(N, KL, KU, NCOLS, AB, LDAB, AFB,
                 LDAFB)


       INTEGER N, KL, KU, NCOLS, LDAB, LDAFB

       DOUBLE PRECISION AB(LDAB,*), AFB(LDAFB,*)


       DOUBLE  PRECISION  FUNCTION DLA_GBRPVGRW_64(N, KL, KU, NCOLS, AB, LDAB,
                 AFB, LDAFB)


       INTEGER*8 N, KL, KU, NCOLS, LDAB, LDAFB

       DOUBLE PRECISION AB(LDAB,*), AFB(LDAFB,*)


   F95 INTERFACE
       REAL(8) FUNCTION LA_GBRPVGRW(N, KL, KU, NCOLS, AB, LDAB, AFB, LDAFB)


       INTEGER :: N, KL, KU, NCOLS, LDAB, LDAFB

       REAL(8), DIMENSION(:,:) :: AB, AFB


       REAL(8) FUNCTION LA_GBRPVGRW_64(N, KL, KU, NCOLS, AB, LDAB, AFB, LDAFB)


       INTEGER(8) :: N, KL, KU, NCOLS, LDAB, LDAFB

       REAL(8), DIMENSION(:,:) :: AB, AFB


   C INTERFACE
       #include <sunperf.h>

       double  dla_gbrpvgrw (int n, int kl, int ku, int ncols, double *ab, int
                 ldab, double *afb, int ldafb);

       double dla_gbrpvgrw_64 (long n, long kl, long ku,  long  ncols,  double
                 *ab, long ldab, double *afb, long 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 (equili-
       brated) matrix A could be poor. This also means that  the  solution  X,
       estimated condition numbers, and error bounds could be unreliable.


ARGUMENTS
       N (input)
                 N is INTEGER
                 The number of linear equations, i.e., the order of the matrix
                 A. N >= 0.


       KL (input)
                 KL is INTEGER
                 The number of subdiagonals within the band of A. KL >= 0.


       KU (input)
                 KU is INTEGER
                 The number of superdiagonals within the band of A. KU >= 0.


       NCOLS (input)
                 NCOLS is INTEGER
                 The number of columns of the matrix A. NCOLS >= 0.


       AB (input)
                 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)


       LDAB (input)
                 LDAB is INTEGER
                 The leading dimension of the array AB.
                 LDAB >= KL+KU+1.


       AFB (input)
                 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 multipli-
                 ers used during the factorization are stored in rows  KL+KU+2
                 to 2*KL+KU+1.


       LDAFB (input)
                 LDAFB is INTEGER
                 The leading dimension of the array AFB.
                 LDAFB >= 2*KL+KU+1.




                                  7 Nov 2015                  dla_gbrpvgrw(3P)