zla_gbrcond_x - compute the infinity norm condition number of op(A)*diag(x) for general banded matrices
DOUBLE PRECISION FUNCTION ZLA_GBRCOND_X( TRANS, N, KL, KU, AB, LDAB, AFB, LDAFB, IPIV, X, INFO, WORK, RWORK ) CHARACTER*1 TRANS INTEGER N, KL, KU, KD, KE, LDAB, LDAFB, INFO INTEGER IPIV(*) DOUBLE COMPLEX AB(LDAB,*), AFB(LDAFB,*), WORK(*), X(*) DOUBLE PRECISION RWORK(*) DOUBLE PRECISION FUNCTION ZLA_GBRCOND_X_64( TRANS, N, KL, KU, AB, LDAB, AFB, LDAFB, IPIV, X, INFO, WORK, RWORK ) CHARACTER*1 TRANS INTEGER*8 N, KL, KU, KD, KE, LDAB, LDAFB, INFO INTEGER*8 IPIV(*) DOUBLE COMPLEX AB(LDAB,*), AFB(LDAFB,*), WORK(*), X(*) DOUBLE PRECISION RWORK(*) F95 INTERFACE REAL(8) FUNCTION LA_GBRCOND_X( TRANS, N, KL, KU, AB, LDAB, AFB, LDAFB, IPIV, X, INFO, WORK, RWORK ) INTEGER :: N, KL, KU, LDAB, LDAFB, INFO CHARACTER(LEN=1) :: TRANS INTEGER, DIMENSION(:) :: IPIV COMPLEX(8), DIMENSION(:) :: X, WORK REAL(8), DIMENSION(:) :: RWORK COMPLEX(8), DIMENSION(:,:) :: AB, AFB REAL(8) FUNCTION LA_GBRCOND_X_64( TRANS, N, KL, KU, AB, LDAB, AFB, LDAFB, IPIV, X, INFO, WORK, RWORK ) INTEGER(8) :: N, KL, KU, LDAB, LDAFB, INFO CHARACTER(LEN=1) :: TRANS INTEGER(8), DIMENSION(:) :: IPIV COMPLEX(8), DIMENSION(:) :: X, WORK REAL(8), DIMENSION(:) :: RWORK COMPLEX(8), DIMENSION(:,:) :: AB, AFB C INTERFACE #include <sunperf.h> double zla_gbrcond_x (char trans, int n, int kl, int ku, doublecomplex *ab, int ldab, doublecomplex *afb, int ldafb, int *ipiv, dou- blecomplex *x, int *info); double zla_gbrcond_x_64 (char trans, long n, long kl, long ku, double- complex *ab, long ldab, doublecomplex *afb, long ldafb, long *ipiv, doublecomplex *x, long *info);
Oracle Solaris Studio Performance Library zla_gbrcond_x(3P)
NAME
zla_gbrcond_x - compute the infinity norm condition number of
op(A)*diag(x) for general banded matrices
SYNOPSIS
DOUBLE PRECISION FUNCTION ZLA_GBRCOND_X( TRANS, N, KL, KU, AB, LDAB,
AFB, LDAFB, IPIV, X, INFO, WORK, RWORK )
CHARACTER*1 TRANS
INTEGER N, KL, KU, KD, KE, LDAB, LDAFB, INFO
INTEGER IPIV(*)
DOUBLE COMPLEX AB(LDAB,*), AFB(LDAFB,*), WORK(*), X(*)
DOUBLE PRECISION RWORK(*)
DOUBLE PRECISION FUNCTION ZLA_GBRCOND_X_64( TRANS, N, KL, KU, AB, LDAB,
AFB, LDAFB, IPIV, X, INFO, WORK, RWORK )
CHARACTER*1 TRANS
INTEGER*8 N, KL, KU, KD, KE, LDAB, LDAFB, INFO
INTEGER*8 IPIV(*)
DOUBLE COMPLEX AB(LDAB,*), AFB(LDAFB,*), WORK(*), X(*)
DOUBLE PRECISION RWORK(*)
F95 INTERFACE
REAL(8) FUNCTION LA_GBRCOND_X( TRANS, N, KL, KU, AB, LDAB, AFB, LDAFB,
IPIV, X, INFO, WORK, RWORK )
INTEGER :: N, KL, KU, LDAB, LDAFB, INFO
CHARACTER(LEN=1) :: TRANS
INTEGER, DIMENSION(:) :: IPIV
COMPLEX(8), DIMENSION(:) :: X, WORK
REAL(8), DIMENSION(:) :: RWORK
COMPLEX(8), DIMENSION(:,:) :: AB, AFB
REAL(8) FUNCTION LA_GBRCOND_X_64( TRANS, N, KL, KU, AB, LDAB, AFB,
LDAFB, IPIV, X, INFO, WORK, RWORK )
INTEGER(8) :: N, KL, KU, LDAB, LDAFB, INFO
CHARACTER(LEN=1) :: TRANS
INTEGER(8), DIMENSION(:) :: IPIV
COMPLEX(8), DIMENSION(:) :: X, WORK
REAL(8), DIMENSION(:) :: RWORK
COMPLEX(8), DIMENSION(:,:) :: AB, AFB
C INTERFACE
#include <sunperf.h>
double zla_gbrcond_x (char trans, int n, int kl, int ku, doublecomplex
*ab, int ldab, doublecomplex *afb, int ldafb, int *ipiv, dou-
blecomplex *x, int *info);
double zla_gbrcond_x_64 (char trans, long n, long kl, long ku, double-
complex *ab, long ldab, doublecomplex *afb, long ldafb, long
*ipiv, doublecomplex *x, long *info);
PURPOSE
zla_gbrcond_x Computes the infinity norm condition number of
op(A)*diag(X) where X is a COMPLEX*16 vector.
ARGUMENTS
TRANS (input)
TRANS is CHARACTER*1
Specifies the form of the system of equations:
= 'N': A * X = B (No transpose)
= 'T': A**T * X = B (Transpose)
= 'C': A**H * X = B (Conjugate Transpose = Transpose)
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.
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.
IPIV (input)
IPIV is INTEGER array, dimension (N)
The pivot indices from the factorization A=P*L*U as computed
by ZGBTRF; row i of the matrix was interchanged with row
IPIV(i).
X (input)
X is COMPLEX*16 array, dimension (N)
The vector X in the formula op(A)*diag(X).
INFO (output)
INFO is INTEGER
= 0: Successful exit.
i > 0: The ith argument is invalid.
WORK (input)
WORK is COMPLEX*16 array, dimension (2*N).
Workspace.
RWORK (input)
RWORK is DOUBLE PRECISION array, dimension (N).
Workspace.
7 Nov 2015 zla_gbrcond_x(3P)