ZPBCON - Online Linux Manual Page

Section : 1
Updated : November 2008
Source : LAPACK routine (version 3.2)
Note : LAPACK routine (version 3.2)
NAMEZPBCON - estimates the reciprocal of the condition number (in the 1-norm) of a complex Hermitian positive definite band matrix using the Cholesky factorization A = U**H*U or A = L*L**H computed by ZPBTRF
SYNOPSISSUBROUTINE ZPBCON(  UPLO, N, KD, AB, LDAB, ANORM, RCOND, WORK, RWORK, INFO )  CHARACTER UPLO  INTEGER INFO, KD, LDAB, N  DOUBLE PRECISION ANORM, RCOND  DOUBLE PRECISION RWORK( * )  COMPLEX*16 AB( LDAB, * ), WORK( * )
PURPOSEZPBCON estimates the reciprocal of the condition number (in the 1-norm) of a complex Hermitian positive definite band matrix using the Cholesky factorization A = U**H*U or A = L*L**H computed by ZPBTRF. An estimate is obtained for norm(inv(A)), and the reciprocal of the condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).
ARGUMENTSUPLO (input) CHARACTER*1  = 'U': Upper triangular factor stored in AB;
= 'L': Lower triangular factor stored in AB. N (input) INTEGER  The order of the matrix A. N >= 0. KD (input) INTEGER  The number of superdiagonals of the matrix A if UPLO = 'U', or the number of sub-diagonals if UPLO = 'L'. KD >= 0. AB (input) COMPLEX*16 array, dimension (LDAB,N)  The triangular factor U or L from the Cholesky factorization A = U**H*U or A = L*L**H of the band matrix A, stored in the first KD+1 rows of the array. The j-th column of U or L is stored in the j-th column of the array AB as follows: if UPLO ='U', AB(kd+1+i-j,j) = U(i,j) for max(1,j-kd)<=i<=j; if UPLO ='L', AB(1+i-j,j) = L(i,j) for j<=i<=min(n,j+kd). LDAB (input) INTEGER  The leading dimension of the array AB. LDAB >= KD+1. ANORM (input) DOUBLE PRECISION  The 1-norm (or infinity-norm) of the Hermitian band matrix A. RCOND (output) DOUBLE PRECISION  The reciprocal of the condition number of the matrix A, computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an estimate of the 1-norm of inv(A) computed in this routine. WORK (workspace) COMPLEX*16 array, dimension (2*N)  RWORK (workspace) DOUBLE PRECISION array, dimension (N)  INFO (output) INTEGER  = 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value 0
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