pbcon(3) Library Functions Manual pbcon(3) NAME pbcon - pbcon: condition number estimate SYNOPSIS Functions subroutine cpbcon (uplo, n, kd, ab, ldab, anorm, rcond, work, rwork, info) CPBCON subroutine dpbcon (uplo, n, kd, ab, ldab, anorm, rcond, work, iwork, info) DPBCON subroutine spbcon (uplo, n, kd, ab, ldab, anorm, rcond, work, iwork, info) SPBCON subroutine zpbcon (uplo, n, kd, ab, ldab, anorm, rcond, work, rwork, info) ZPBCON Detailed Description Function Documentation subroutine cpbcon (character uplo, integer n, integer kd, complex, dimension( ldab, * ) ab, integer ldab, real anorm, real rcond, complex, dimension( * ) work, real, dimension( * ) rwork, integer info) CPBCON 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))). !> Parameters UPLO !> UPLO is CHARACTER*1 !> = 'U': Upper triangular factor stored in AB; !> = 'L': Lower triangular factor stored in AB. !> N !> N is INTEGER !> The order of the matrix A. N >= 0. !> KD !> KD is INTEGER !> The number of superdiagonals of the matrix A if UPLO = 'U', !> or the number of sub-diagonals if UPLO = 'L'. KD >= 0. !> AB !> AB is 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 !> LDAB is INTEGER !> The leading dimension of the array AB. LDAB >= KD+1. !> ANORM !> ANORM is REAL !> The 1-norm (or infinity-norm) of the Hermitian band matrix A. !> RCOND !> RCOND is 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 !> WORK is COMPLEX array, dimension (2*N) !> RWORK !> RWORK is REAL array, dimension (N) !> INFO !> INFO is INTEGER !> = 0: successful exit !> < 0: if INFO = -i, the i-th argument had an illegal value !> Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Definition at line 131 of file cpbcon.f. subroutine dpbcon (character uplo, integer n, integer kd, double precision, dimension( ldab, * ) ab, integer ldab, double precision anorm, double precision rcond, double precision, dimension( * ) work, integer, dimension( * ) iwork, integer info) DPBCON Purpose: !> !> DPBCON estimates the reciprocal of the condition number (in the !> 1-norm) of a real symmetric positive definite band matrix using the !> Cholesky factorization A = U**T*U or A = L*L**T computed by DPBTRF. !> !> An estimate is obtained for norm(inv(A)), and the reciprocal of the !> condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))). !> Parameters UPLO !> UPLO is CHARACTER*1 !> = 'U': Upper triangular factor stored in AB; !> = 'L': Lower triangular factor stored in AB. !> N !> N is INTEGER !> The order of the matrix A. N >= 0. !> KD !> KD is INTEGER !> The number of superdiagonals of the matrix A if UPLO = 'U', !> or the number of subdiagonals if UPLO = 'L'. KD >= 0. !> AB !> AB is DOUBLE PRECISION array, dimension (LDAB,N) !> The triangular factor U or L from the Cholesky factorization !> A = U**T*U or A = L*L**T 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 !> LDAB is INTEGER !> The leading dimension of the array AB. LDAB >= KD+1. !> ANORM !> ANORM is DOUBLE PRECISION !> The 1-norm (or infinity-norm) of the symmetric band matrix A. !> RCOND !> RCOND is 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 !> WORK is DOUBLE PRECISION array, dimension (3*N) !> IWORK !> IWORK is INTEGER array, dimension (N) !> INFO !> INFO is INTEGER !> = 0: successful exit !> < 0: if INFO = -i, the i-th argument had an illegal value !> Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Definition at line 130 of file dpbcon.f. subroutine spbcon (character uplo, integer n, integer kd, real, dimension( ldab, * ) ab, integer ldab, real anorm, real rcond, real, dimension( * ) work, integer, dimension( * ) iwork, integer info) SPBCON Purpose: !> !> SPBCON estimates the reciprocal of the condition number (in the !> 1-norm) of a real symmetric positive definite band matrix using the !> Cholesky factorization A = U**T*U or A = L*L**T computed by SPBTRF. !> !> An estimate is obtained for norm(inv(A)), and the reciprocal of the !> condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))). !> Parameters UPLO !> UPLO is CHARACTER*1 !> = 'U': Upper triangular factor stored in AB; !> = 'L': Lower triangular factor stored in AB. !> N !> N is INTEGER !> The order of the matrix A. N >= 0. !> KD !> KD is INTEGER !> The number of superdiagonals of the matrix A if UPLO = 'U', !> or the number of subdiagonals if UPLO = 'L'. KD >= 0. !> AB !> AB is REAL array, dimension (LDAB,N) !> The triangular factor U or L from the Cholesky factorization !> A = U**T*U or A = L*L**T 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 !> LDAB is INTEGER !> The leading dimension of the array AB. LDAB >= KD+1. !> ANORM !> ANORM is REAL !> The 1-norm (or infinity-norm) of the symmetric band matrix A. !> RCOND !> RCOND is 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 !> WORK is REAL array, dimension (3*N) !> IWORK !> IWORK is INTEGER array, dimension (N) !> INFO !> INFO is INTEGER !> = 0: successful exit !> < 0: if INFO = -i, the i-th argument had an illegal value !> Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Definition at line 130 of file spbcon.f. subroutine zpbcon (character uplo, integer n, integer kd, complex*16, dimension( ldab, * ) ab, integer ldab, double precision anorm, double precision rcond, complex*16, dimension( * ) work, double precision, dimension( * ) rwork, integer info) ZPBCON Purpose: !> !> ZPBCON 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))). !> Parameters UPLO !> UPLO is CHARACTER*1 !> = 'U': Upper triangular factor stored in AB; !> = 'L': Lower triangular factor stored in AB. !> N !> N is INTEGER !> The order of the matrix A. N >= 0. !> KD !> KD is INTEGER !> The number of superdiagonals of the matrix A if UPLO = 'U', !> or the number of sub-diagonals if UPLO = 'L'. KD >= 0. !> AB !> AB is 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 !> LDAB is INTEGER !> The leading dimension of the array AB. LDAB >= KD+1. !> ANORM !> ANORM is DOUBLE PRECISION !> The 1-norm (or infinity-norm) of the Hermitian band matrix A. !> RCOND !> RCOND is 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 !> WORK is COMPLEX*16 array, dimension (2*N) !> RWORK !> RWORK is DOUBLE PRECISION array, dimension (N) !> INFO !> INFO is INTEGER !> = 0: successful exit !> < 0: if INFO = -i, the i-th argument had an illegal value !> Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Definition at line 131 of file zpbcon.f. Author Generated automatically by Doxygen for LAPACK from the source code. LAPACK Version 3.12.0 pbcon(3)