Man page - pbcon(3)

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Manual

pbcon

NAME
SYNOPSIS
Functions
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)
subroutine dpbcon (character uplo, integer n, integer kd, double precision,dimension( ldab, * ) ab, integer ldab, double precision anorm, doubleprecision rcond, double precision, dimension( * ) work, integer,dimension( * ) iwork, integer info)
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)
subroutine zpbcon (character uplo, integer n, integer kd, complex*16,dimension( ldab, * ) ab, integer ldab, double precision anorm, doubleprecision rcond, complex*16, dimension( * ) work, double precision,dimension( * ) rwork, integer info)
Author

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
= ā€™Uā€™: Upper triangular factor stored in AB;
= ā€™Lā€™: 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 = ā€™Uā€™,
or the number of sub-diagonals if UPLO = ā€™Lā€™. 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 =ā€™Uā€™, AB(kd+1+i-j,j) = U(i,j) for max(1,j-kd)<=i<=j;
if UPLO =ā€™Lā€™, 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.

subroutine dpbcon (character uplo, integer n, integer kd, double precision,dimension( ldab, * ) ab, integer ldab, double precision anorm, doubleprecision 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
= ā€™Uā€™: Upper triangular factor stored in AB;
= ā€™Lā€™: 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 = ā€™Uā€™,
or the number of subdiagonals if UPLO = ā€™Lā€™. 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 =ā€™Uā€™, AB(kd+1+i-j,j) = U(i,j) for max(1,j-kd)<=i<=j;
if UPLO =ā€™Lā€™, 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.

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
= ā€™Uā€™: Upper triangular factor stored in AB;
= ā€™Lā€™: 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 = ā€™Uā€™,
or the number of subdiagonals if UPLO = ā€™Lā€™. 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 =ā€™Uā€™, AB(kd+1+i-j,j) = U(i,j) for max(1,j-kd)<=i<=j;
if UPLO =ā€™Lā€™, 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.

subroutine zpbcon (character uplo, integer n, integer kd, complex*16,dimension( ldab, * ) ab, integer ldab, double precision anorm, doubleprecision 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
= ā€™Uā€™: Upper triangular factor stored in AB;
= ā€™Lā€™: 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 = ā€™Uā€™,
or the number of sub-diagonals if UPLO = ā€™Lā€™. 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 =ā€™Uā€™, AB(kd+1+i-j,j) = U(i,j) for max(1,j-kd)<=i<=j;
if UPLO =ā€™Lā€™, 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.

Author

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