cla_gbrpvgrw - compute the reciprocal pivot growth factor norm(A)/norm(U) for a general banded matrix
REAL FUNCTION CLA_GBRPVGRW(N, KL, KU, NCOLS, AB, LDAB, AFB, LDAFB) INTEGER N, KL, KU, NCOLS, LDAB, LDAFB COMPLEX AB(LDAB,*), AFB(LDAFB,*) REAL FUNCTION CLA_GBRPVGRW_64(N, KL, KU, NCOLS, AB, LDAB, AFB, LDAFB) INTEGER*8 N, KL, KU, NCOLS, LDAB, LDAFB COMPLEX AB(LDAB,*), AFB(LDAFB,*) F95 INTERFACE REAL FUNCTION LA_GBRPVGRW(N, KL, KU, NCOLS, AB, LDAB, AFB, LDAFB) INTEGER :: N, KL, KU, NCOLS, LDAB, LDAFB COMPLEX, DIMENSION(:,:) :: AB, AFB REAL FUNCTION LA_GBRPVGRW_64(N, KL, KU, NCOLS, AB, LDAB, AFB, LDAFB) INTEGER(8) :: N, KL, KU, NCOLS, LDAB, LDAFB COMPLEX, DIMENSION(:,:) :: AB, AFB C INTERFACE #include <sunperf.h> float cla_gbrpvgrw (int n, int kl, int ku, int ncols, floatcomplex *ab, int ldab, floatcomplex *afb, int ldafb); float cla_gbrpvgrw_64 (long n, long kl, long ku, long ncols, floatcom- plex *ab, long ldab, floatcomplex *afb, long ldafb);
Oracle Solaris Studio Performance Library cla_gbrpvgrw(3P) NAME cla_gbrpvgrw - compute the reciprocal pivot growth factor norm(A)/norm(U) for a general banded matrix SYNOPSIS REAL FUNCTION CLA_GBRPVGRW(N, KL, KU, NCOLS, AB, LDAB, AFB, LDAFB) INTEGER N, KL, KU, NCOLS, LDAB, LDAFB COMPLEX AB(LDAB,*), AFB(LDAFB,*) REAL FUNCTION CLA_GBRPVGRW_64(N, KL, KU, NCOLS, AB, LDAB, AFB, LDAFB) INTEGER*8 N, KL, KU, NCOLS, LDAB, LDAFB COMPLEX AB(LDAB,*), AFB(LDAFB,*) F95 INTERFACE REAL FUNCTION LA_GBRPVGRW(N, KL, KU, NCOLS, AB, LDAB, AFB, LDAFB) INTEGER :: N, KL, KU, NCOLS, LDAB, LDAFB COMPLEX, DIMENSION(:,:) :: AB, AFB REAL FUNCTION LA_GBRPVGRW_64(N, KL, KU, NCOLS, AB, LDAB, AFB, LDAFB) INTEGER(8) :: N, KL, KU, NCOLS, LDAB, LDAFB COMPLEX, DIMENSION(:,:) :: AB, AFB C INTERFACE #include <sunperf.h> float cla_gbrpvgrw (int n, int kl, int ku, int ncols, floatcomplex *ab, int ldab, floatcomplex *afb, int ldafb); float cla_gbrpvgrw_64 (long n, long kl, long ku, long ncols, floatcom- plex *ab, long ldab, floatcomplex *afb, long ldafb); PURPOSE cla_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 COMPLEX 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 array, dimension (LDAFB,N) Details of the LU factorization of the band matrix A, as com- puted by CGBTRF. 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 cla_gbrpvgrw(3P)