.TH CPBCON 1 "November 2006" " LAPACK routine (version 3.1) " " LAPACK routine (version 3.1) " .SH NAME CPBCON - 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 CPBTRF .SH SYNOPSIS .TP 19 SUBROUTINE CPBCON( UPLO, N, KD, AB, LDAB, ANORM, RCOND, WORK, RWORK, INFO ) .TP 19 .ti +4 CHARACTER UPLO .TP 19 .ti +4 INTEGER INFO, KD, LDAB, N .TP 19 .ti +4 REAL ANORM, RCOND .TP 19 .ti +4 REAL RWORK( * ) .TP 19 .ti +4 COMPLEX AB( LDAB, * ), WORK( * ) .SH PURPOSE CPBCON 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 CPBTRF. An estimate is obtained for norm(inv(A)), and the reciprocal of the condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))). .SH ARGUMENTS .TP 8 UPLO (input) CHARACTER*1 = \(aqU\(aq: Upper triangular factor stored in AB; .br = \(aqL\(aq: Lower triangular factor stored in AB. .TP 8 N (input) INTEGER The order of the matrix A. N >= 0. .TP 8 KD (input) INTEGER The number of superdiagonals of the matrix A if UPLO = \(aqU\(aq, or the number of sub-diagonals if UPLO = \(aqL\(aq. KD >= 0. .TP 8 AB (input) COMPLEX 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 =\(aqU\(aq, AB(kd+1+i-j,j) = U(i,j) for max(1,j-kd)<=i<=j; if UPLO =\(aqL\(aq, AB(1+i-j,j) = L(i,j) for j<=i<=min(n,j+kd). .TP 8 LDAB (input) INTEGER The leading dimension of the array AB. LDAB >= KD+1. .TP 8 ANORM (input) REAL The 1-norm (or infinity-norm) of the Hermitian band matrix A. .TP 8 RCOND (output) REAL 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. .TP 8 WORK (workspace) COMPLEX array, dimension (2*N) .TP 8 RWORK (workspace) REAL array, dimension (N) .TP 8 INFO (output) INTEGER = 0: successful exit .br < 0: if INFO = -i, the i-th argument had an illegal value