sla_gbrpvgrw (3p)

Name

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

Synopsis

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


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

REAL AB(LDAB,*), AFB(LDAFB,*)


REAL FUNCTION SLA_GBRPVGRW_64(N, KL, KU, NCOLS, AB, LDAB, AFB, LDAFB)


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

REAL AB(LDAB,*), AFB(LDAFB,*)


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


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

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


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


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

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


C INTERFACE
#include <sunperf.h>

float sla_gbrpvgrw (int n, int kl, int ku, int ncols,  float  *ab,  int
ldab, float *afb, int ldafb);

float sla_gbrpvgrw_64 (long n, long kl, long ku, long ncols, float *ab,
long ldab, float *afb, long ldafb);

Description

Oracle Solaris Studio Performance Library                     sla_gbrpvgrw(3P)



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


SYNOPSIS
       REAL FUNCTION SLA_GBRPVGRW(N, KL, KU, NCOLS, AB, LDAB, AFB, LDAFB)


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

       REAL AB(LDAB,*), AFB(LDAFB,*)


       REAL FUNCTION SLA_GBRPVGRW_64(N, KL, KU, NCOLS, AB, LDAB, AFB, LDAFB)


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

       REAL AB(LDAB,*), AFB(LDAFB,*)


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


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

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


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


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

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


   C INTERFACE
       #include <sunperf.h>

       float sla_gbrpvgrw (int n, int kl, int ku, int ncols,  float  *ab,  int
                 ldab, float *afb, int ldafb);

       float sla_gbrpvgrw_64 (long n, long kl, long ku, long ncols, float *ab,
                 long ldab, float *afb, long ldafb);


PURPOSE
       sla_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 REAL 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 REAL array, dimension (LDAFB,N)
                 Details of the LU factorization of the band matrix A, as com-
                 puted by SGBTRF.  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)
                 LDAFB is INTEGER
                 The leading dimension of the array AFB.
                 LDAFB >= 2*KL+KU+1.




                                  7 Nov 2015                  sla_gbrpvgrw(3P)