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CPBCON(l)) CPBCON(l)NAMECPBCON - estimate the reciprocal of the condition number (in the 1-norm) of a complex Her- mitian positive definite band matrix using the Cholesky factorization A = U**H*U or A = L*L**H computed by CPBTRFSYNOPSISSUBROUTINE CPBCON( UPLO, N, KD, AB, LDAB, ANORM, RCOND, WORK, RWORK, INFO ) CHARACTER UPLO INTEGER INFO, KD, LDAB, N REAL ANORM, RCOND REAL RWORK( * ) COMPLEX AB( LDAB, * ), WORK( * )PURPOSECPBCON estimates the reciprocal of the condition number (in the 1-norm) of a complex Her- mitian 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))).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 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) REAL The 1-norm (or infinity-norm) of the Hermitian band matrix A. 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. WORK (workspace) COMPLEX array, dimension (2*N) RWORK (workspace) REAL array, dimension (N) INFO (output) INTEGER = 0: successful exit < 0: if INFO =, the i-th argument had an illegal value-iLAPACK version 3.015 June 2000 CPBCON(l)

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