Man page - tpcon(3)

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Manual

tpcon

NAME
SYNOPSIS
Functions
Detailed Description
Function Documentation
subroutine ctpcon (character norm, character uplo, character diag, integern, complex, dimension( * ) ap, real rcond, complex, dimension( * )work, real, dimension( * ) rwork, integer info)
subroutine dtpcon (character norm, character uplo, character diag, integern, double precision, dimension( * ) ap, double precision rcond, doubleprecision, dimension( * ) work, integer, dimension( * ) iwork, integerinfo)
subroutine stpcon (character norm, character uplo, character diag, integern, real, dimension( * ) ap, real rcond, real, dimension( * ) work,integer, dimension( * ) iwork, integer info)
subroutine ztpcon (character norm, character uplo, character diag, integern, complex*16, dimension( * ) ap, double precision rcond, complex*16,dimension( * ) work, double precision, dimension( * ) rwork, integerinfo)
Author

NAME

tpcon - tpcon: condition number estimate

SYNOPSIS

Functions

subroutine ctpcon (norm, uplo, diag, n, ap, rcond, work, rwork, info)
CTPCON
subroutine dtpcon (norm, uplo, diag, n, ap, rcond, work, iwork, info)
DTPCON
subroutine stpcon (norm, uplo, diag, n, ap, rcond, work, iwork, info)
STPCON
subroutine ztpcon (norm, uplo, diag, n, ap, rcond, work, rwork, info)
ZTPCON

Detailed Description

Function Documentation

subroutine ctpcon (character norm, character uplo, character diag, integern, complex, dimension( * ) ap, real rcond, complex, dimension( * )work, real, dimension( * ) rwork, integer info)

CTPCON

Purpose:

CTPCON estimates the reciprocal of the condition number of a packed
triangular 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.

AP

AP is COMPLEX array, dimension (N*(N+1)/2)
The upper or lower triangular matrix A, packed columnwise in
a linear array. The j-th column of A is stored in the array
AP as follows:
if UPLO = ā€™Uā€™, AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
if UPLO = ā€™Lā€™, AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
If DIAG = ā€™Uā€™, the diagonal elements of A are not referenced
and are assumed to be 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 dtpcon (character norm, character uplo, character diag, integern, double precision, dimension( * ) ap, double precision rcond, doubleprecision, dimension( * ) work, integer, dimension( * ) iwork, integerinfo)

DTPCON

Purpose:

DTPCON estimates the reciprocal of the condition number of a packed
triangular 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.

AP

AP is DOUBLE PRECISION array, dimension (N*(N+1)/2)
The upper or lower triangular matrix A, packed columnwise in
a linear array. The j-th column of A is stored in the array
AP as follows:
if UPLO = ā€™Uā€™, AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
if UPLO = ā€™Lā€™, AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
If DIAG = ā€™Uā€™, the diagonal elements of A are not referenced
and are assumed to be 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 stpcon (character norm, character uplo, character diag, integern, real, dimension( * ) ap, real rcond, real, dimension( * ) work,integer, dimension( * ) iwork, integer info)

STPCON

Purpose:

STPCON estimates the reciprocal of the condition number of a packed
triangular 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.

AP

AP is REAL array, dimension (N*(N+1)/2)
The upper or lower triangular matrix A, packed columnwise in
a linear array. The j-th column of A is stored in the array
AP as follows:
if UPLO = ā€™Uā€™, AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
if UPLO = ā€™Lā€™, AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
If DIAG = ā€™Uā€™, the diagonal elements of A are not referenced
and are assumed to be 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 ztpcon (character norm, character uplo, character diag, integern, complex*16, dimension( * ) ap, double precision rcond, complex*16,dimension( * ) work, double precision, dimension( * ) rwork, integerinfo)

ZTPCON

Purpose:

ZTPCON estimates the reciprocal of the condition number of a packed
triangular 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.

AP

AP is COMPLEX*16 array, dimension (N*(N+1)/2)
The upper or lower triangular matrix A, packed columnwise in
a linear array. The j-th column of A is stored in the array
AP as follows:
if UPLO = ā€™Uā€™, AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
if UPLO = ā€™Lā€™, AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
If DIAG = ā€™Uā€™, the diagonal elements of A are not referenced
and are assumed to be 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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