Man page - tbcon(3)

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Manual

tbcon

NAME
SYNOPSIS
Functions
Detailed Description
Function Documentation
subroutine ctbcon (character norm, character uplo, character diag, integern, integer kd, complex, dimension( ldab, * ) ab, integer ldab, realrcond, complex, dimension( * ) work, real, dimension( * ) rwork,integer info)
subroutine dtbcon (character norm, character uplo, character diag, integern, integer kd, double precision, dimension( ldab, * ) ab, integer ldab,double precision rcond, double precision, dimension( * ) work, integer,dimension( * ) iwork, integer info)
subroutine stbcon (character norm, character uplo, character diag, integern, integer kd, real, dimension( ldab, * ) ab, integer ldab, real rcond,real, dimension( * ) work, integer, dimension( * ) iwork, integer info)
subroutine ztbcon (character norm, character uplo, character diag, integern, integer kd, complex*16, dimension( ldab, * ) ab, integer ldab,double precision rcond, complex*16, dimension( * ) work, doubleprecision, dimension( * ) rwork, integer info)
Author

NAME

tbcon - tbcon: condition number estimate

SYNOPSIS

Functions

subroutine ctbcon (norm, uplo, diag, n, kd, ab, ldab, rcond, work, rwork, info)
CTBCON
subroutine dtbcon (norm, uplo, diag, n, kd, ab, ldab, rcond, work, iwork, info)
DTBCON
subroutine stbcon (norm, uplo, diag, n, kd, ab, ldab, rcond, work, iwork, info)
STBCON
subroutine ztbcon (norm, uplo, diag, n, kd, ab, ldab, rcond, work, rwork, info)
ZTBCON

Detailed Description

Function Documentation

subroutine ctbcon (character norm, character uplo, character diag, integern, integer kd, complex, dimension( ldab, * ) ab, integer ldab, realrcond, complex, dimension( * ) work, real, dimension( * ) rwork,integer info)

CTBCON

Purpose:

CTBCON estimates the reciprocal of the condition number of a
triangular band matrix A, in either the 1-norm or the infinity-norm.

The norm of A is computed and an estimate is obtained for
norm(inv(A)), then the reciprocal of the condition number is
computed as
RCOND = 1 / ( norm(A) * norm(inv(A)) ).

Parameters

NORM

NORM is CHARACTER*1
Specifies whether the 1-norm condition number or the
infinity-norm condition number is required:
= ā€™1ā€™ or ā€™Oā€™: 1-norm;
= ā€™Iā€™: Infinity-norm.

UPLO

UPLO is CHARACTER*1
= ā€™Uā€™: A is upper triangular;
= ā€™Lā€™: A is lower triangular.

DIAG

DIAG is CHARACTER*1
= ā€™Nā€™: A is non-unit triangular;
= ā€™Uā€™: A is unit triangular.

N

N is INTEGER
The order of the matrix A. N >= 0.

KD

KD is INTEGER
The number of superdiagonals or subdiagonals of the
triangular band matrix A. KD >= 0.

AB

AB is COMPLEX array, dimension (LDAB,N)
The upper or lower triangular band matrix A, stored in the
first kd+1 rows of the array. The j-th column of A is stored
in the j-th column of the array AB as follows:
if UPLO = ā€™Uā€™, AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
if UPLO = ā€™Lā€™, AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd).
If DIAG = ā€™Uā€™, the diagonal elements of A are not referenced
and are assumed to be 1.

LDAB

LDAB is INTEGER
The leading dimension of the array AB. LDAB >= KD+1.

RCOND

RCOND is REAL
The reciprocal of the condition number of the matrix A,
computed as RCOND = 1/(norm(A) * norm(inv(A))).

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 dtbcon (character norm, character uplo, character diag, integern, integer kd, double precision, dimension( ldab, * ) ab, integer ldab,double precision rcond, double precision, dimension( * ) work, integer,dimension( * ) iwork, integer info)

DTBCON

Purpose:

DTBCON estimates the reciprocal of the condition number of a
triangular band matrix A, in either the 1-norm or the infinity-norm.

The norm of A is computed and an estimate is obtained for
norm(inv(A)), then the reciprocal of the condition number is
computed as
RCOND = 1 / ( norm(A) * norm(inv(A)) ).

Parameters

NORM

NORM is CHARACTER*1
Specifies whether the 1-norm condition number or the
infinity-norm condition number is required:
= ā€™1ā€™ or ā€™Oā€™: 1-norm;
= ā€™Iā€™: Infinity-norm.

UPLO

UPLO is CHARACTER*1
= ā€™Uā€™: A is upper triangular;
= ā€™Lā€™: A is lower triangular.

DIAG

DIAG is CHARACTER*1
= ā€™Nā€™: A is non-unit triangular;
= ā€™Uā€™: A is unit triangular.

N

N is INTEGER
The order of the matrix A. N >= 0.

KD

KD is INTEGER
The number of superdiagonals or subdiagonals of the
triangular band matrix A. KD >= 0.

AB

AB is DOUBLE PRECISION array, dimension (LDAB,N)
The upper or lower triangular band matrix A, stored in the
first kd+1 rows of the array. The j-th column of A is stored
in the j-th column of the array AB as follows:
if UPLO = ā€™Uā€™, AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
if UPLO = ā€™Lā€™, AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd).
If DIAG = ā€™Uā€™, the diagonal elements of A are not referenced
and are assumed to be 1.

LDAB

LDAB is INTEGER
The leading dimension of the array AB. LDAB >= KD+1.

RCOND

RCOND is DOUBLE PRECISION
The reciprocal of the condition number of the matrix A,
computed as RCOND = 1/(norm(A) * norm(inv(A))).

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 stbcon (character norm, character uplo, character diag, integern, integer kd, real, dimension( ldab, * ) ab, integer ldab, real rcond,real, dimension( * ) work, integer, dimension( * ) iwork, integer info)

STBCON

Purpose:

STBCON estimates the reciprocal of the condition number of a
triangular band matrix A, in either the 1-norm or the infinity-norm.

The norm of A is computed and an estimate is obtained for
norm(inv(A)), then the reciprocal of the condition number is
computed as
RCOND = 1 / ( norm(A) * norm(inv(A)) ).

Parameters

NORM

NORM is CHARACTER*1
Specifies whether the 1-norm condition number or the
infinity-norm condition number is required:
= ā€™1ā€™ or ā€™Oā€™: 1-norm;
= ā€™Iā€™: Infinity-norm.

UPLO

UPLO is CHARACTER*1
= ā€™Uā€™: A is upper triangular;
= ā€™Lā€™: A is lower triangular.

DIAG

DIAG is CHARACTER*1
= ā€™Nā€™: A is non-unit triangular;
= ā€™Uā€™: A is unit triangular.

N

N is INTEGER
The order of the matrix A. N >= 0.

KD

KD is INTEGER
The number of superdiagonals or subdiagonals of the
triangular band matrix A. KD >= 0.

AB

AB is REAL array, dimension (LDAB,N)
The upper or lower triangular band matrix A, stored in the
first kd+1 rows of the array. The j-th column of A is stored
in the j-th column of the array AB as follows:
if UPLO = ā€™Uā€™, AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
if UPLO = ā€™Lā€™, AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd).
If DIAG = ā€™Uā€™, the diagonal elements of A are not referenced
and are assumed to be 1.

LDAB

LDAB is INTEGER
The leading dimension of the array AB. LDAB >= KD+1.

RCOND

RCOND is REAL
The reciprocal of the condition number of the matrix A,
computed as RCOND = 1/(norm(A) * norm(inv(A))).

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 ztbcon (character norm, character uplo, character diag, integern, integer kd, complex*16, dimension( ldab, * ) ab, integer ldab,double precision rcond, complex*16, dimension( * ) work, doubleprecision, dimension( * ) rwork, integer info)

ZTBCON

Purpose:

ZTBCON estimates the reciprocal of the condition number of a
triangular band matrix A, in either the 1-norm or the infinity-norm.

The norm of A is computed and an estimate is obtained for
norm(inv(A)), then the reciprocal of the condition number is
computed as
RCOND = 1 / ( norm(A) * norm(inv(A)) ).

Parameters

NORM

NORM is CHARACTER*1
Specifies whether the 1-norm condition number or the
infinity-norm condition number is required:
= ā€™1ā€™ or ā€™Oā€™: 1-norm;
= ā€™Iā€™: Infinity-norm.

UPLO

UPLO is CHARACTER*1
= ā€™Uā€™: A is upper triangular;
= ā€™Lā€™: A is lower triangular.

DIAG

DIAG is CHARACTER*1
= ā€™Nā€™: A is non-unit triangular;
= ā€™Uā€™: A is unit triangular.

N

N is INTEGER
The order of the matrix A. N >= 0.

KD

KD is INTEGER
The number of superdiagonals or subdiagonals of the
triangular band matrix A. KD >= 0.

AB

AB is COMPLEX*16 array, dimension (LDAB,N)
The upper or lower triangular band matrix A, stored in the
first kd+1 rows of the array. The j-th column of A is stored
in the j-th column of the array AB as follows:
if UPLO = ā€™Uā€™, AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
if UPLO = ā€™Lā€™, AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd).
If DIAG = ā€™Uā€™, the diagonal elements of A are not referenced
and are assumed to be 1.

LDAB

LDAB is INTEGER
The leading dimension of the array AB. LDAB >= KD+1.

RCOND

RCOND is DOUBLE PRECISION
The reciprocal of the condition number of the matrix A,
computed as RCOND = 1/(norm(A) * norm(inv(A))).

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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