zla_gbrpvgrw (3p)

Name

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

Synopsis

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


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

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


DOUBLE  PRECISION  FUNCTION ZLA_GBRPVGRW_64(N, KL, KU, NCOLS, AB, LDAB,
AFB, LDAFB)


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

DOUBLE COMPLEX 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

COMPLEX(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

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


C INTERFACE
#include <sunperf.h>

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

double zla_gbrpvgrw_64 (long n, long kl, long ku, long  ncols,  double-
complex *ab, long ldab, doublecomplex *afb, long ldafb);

SH  PURPOSE zla_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 num-
bers, and error bounds could be unreliable.

Description

Oracle Solaris Studio Performance Library                     zla_gbrpvgrw(3P)



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


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


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

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


       DOUBLE  PRECISION  FUNCTION ZLA_GBRPVGRW_64(N, KL, KU, NCOLS, AB, LDAB,
                 AFB, LDAFB)


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

       DOUBLE COMPLEX 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

       COMPLEX(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

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


   C INTERFACE
       #include <sunperf.h>

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

       double zla_gbrpvgrw_64 (long n, long kl, long ku, long  ncols,  double-
                 complex *ab, long ldab, doublecomplex *afb, long ldafb);

                 SH  PURPOSE zla_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 num-
                 bers, 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 COMPLEX*16 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 COMPLEX*16 array, dimension (LDAFB,N)
                 Details of the LU factorization of the band matrix A, as com-
                 puted by ZGBTRF. 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                  zla_gbrpvgrw(3P)