Man page - tptrs(3)

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Manual

tptrs

NAME
SYNOPSIS
Functions
Detailed Description
Function Documentation
subroutine ctptrs (character uplo, character trans, character diag, integern, integer nrhs, complex, dimension( * ) ap, complex, dimension( ldb, *) b, integer ldb, integer info)
subroutine dtptrs (character uplo, character trans, character diag, integern, integer nrhs, double precision, dimension( * ) ap, double precision,dimension( ldb, * ) b, integer ldb, integer info)
subroutine stptrs (character uplo, character trans, character diag, integern, integer nrhs, real, dimension( * ) ap, real, dimension( ldb, * ) b,integer ldb, integer info)
subroutine ztptrs (character uplo, character trans, character diag, integern, integer nrhs, complex*16, dimension( * ) ap, complex*16, dimension(ldb, * ) b, integer ldb, integer info)
Author

NAME

tptrs - tptrs: triangular solve

SYNOPSIS

Functions

subroutine ctptrs (uplo, trans, diag, n, nrhs, ap, b, ldb, info)
CTPTRS
subroutine dtptrs (uplo, trans, diag, n, nrhs, ap, b, ldb, info)
DTPTRS
subroutine stptrs (uplo, trans, diag, n, nrhs, ap, b, ldb, info)
STPTRS
subroutine ztptrs (uplo, trans, diag, n, nrhs, ap, b, ldb, info)
ZTPTRS

Detailed Description

Function Documentation

subroutine ctptrs (character uplo, character trans, character diag, integern, integer nrhs, complex, dimension( * ) ap, complex, dimension( ldb, *) b, integer ldb, integer info)

CTPTRS

Purpose:

CTPTRS solves a triangular system of the form

A * X = B, A**T * X = B, or A**H * X = B,

where A is a triangular matrix of order N stored in packed format, and B is an N-by-NRHS matrix.

This subroutine verifies that A is nonsingular, but callers should note that only exact
singularity is detected. It is conceivable for one or more diagonal elements of A to be
subnormally tiny numbers without this subroutine signalling an error.

If a possible loss of numerical precision due to near-singular matrices is a concern, the
caller should verify that A is nonsingular within some tolerance before calling this subroutine.

Parameters

UPLO

UPLO is CHARACTER*1
= ’U’: A is upper triangular;
= ’L’: A is lower triangular.

TRANS

TRANS is CHARACTER*1
Specifies the form of the system of equations:
= ’N’: A * X = B (No transpose)
= ’T’: A**T * X = B (Transpose)
= ’C’: A**H * X = B (Conjugate transpose)

DIAG

DIAG is CHARACTER*1
= ’N’: A is non-unit triangular;
= ’U’: A is unit triangular.

N

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

NRHS

NRHS is INTEGER
The number of right hand sides, i.e., the number of columns
of the matrix B. NRHS >= 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 = ’U’, AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
if UPLO = ’L’, AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n.

B

B is COMPLEX array, dimension (LDB,NRHS)
On entry, the right hand side matrix B.
On exit, if INFO = 0, the solution matrix X.

LDB

LDB is INTEGER
The leading dimension of the array B. LDB >= max(1,N).

INFO

INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: if INFO = i, the i-th diagonal element of A is exactly zero,
indicating that the matrix is singular and the
solutions X have not been computed.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

subroutine dtptrs (character uplo, character trans, character diag, integern, integer nrhs, double precision, dimension( * ) ap, double precision,dimension( ldb, * ) b, integer ldb, integer info)

DTPTRS

Purpose:

DTPTRS solves a triangular system of the form

A * X = B or A**T * X = B,

where A is a triangular matrix of order N stored in packed format, and B is an N-by-NRHS matrix.

This subroutine verifies that A is nonsingular, but callers should note that only exact
singularity is detected. It is conceivable for one or more diagonal elements of A to be
subnormally tiny numbers without this subroutine signalling an error.

If a possible loss of numerical precision due to near-singular matrices is a concern, the
caller should verify that A is nonsingular within some tolerance before calling this subroutine.

Parameters

UPLO

UPLO is CHARACTER*1
= ’U’: A is upper triangular;
= ’L’: A is lower triangular.

TRANS

TRANS is CHARACTER*1
Specifies the form of the system of equations:
= ’N’: A * X = B (No transpose)
= ’T’: A**T * X = B (Transpose)
= ’C’: A**H * X = B (Conjugate transpose = Transpose)

DIAG

DIAG is CHARACTER*1
= ’N’: A is non-unit triangular;
= ’U’: A is unit triangular.

N

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

NRHS

NRHS is INTEGER
The number of right hand sides, i.e., the number of columns
of the matrix B. NRHS >= 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 = ’U’, AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
if UPLO = ’L’, AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n.

B

B is DOUBLE PRECISION array, dimension (LDB,NRHS)
On entry, the right hand side matrix B.
On exit, if INFO = 0, the solution matrix X.

LDB

LDB is INTEGER
The leading dimension of the array B. LDB >= max(1,N).

INFO

INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: if INFO = i, the i-th diagonal element of A is exactly zero,
indicating that the matrix is singular and the
solutions X have not been computed.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

subroutine stptrs (character uplo, character trans, character diag, integern, integer nrhs, real, dimension( * ) ap, real, dimension( ldb, * ) b,integer ldb, integer info)

STPTRS

Purpose:

STPTRS solves a triangular system of the form

A * X = B or A**T * X = B,

where A is a triangular matrix of order N stored in packed format, and B is an N-by-NRHS matrix.

This subroutine verifies that A is nonsingular, but callers should note that only exact
singularity is detected. It is conceivable for one or more diagonal elements of A to be
subnormally tiny numbers without this subroutine signalling an error.

If a possible loss of numerical precision due to near-singular matrices is a concern, the
caller should verify that A is nonsingular within some tolerance before calling this subroutine.

Parameters

UPLO

UPLO is CHARACTER*1
= ’U’: A is upper triangular;
= ’L’: A is lower triangular.

TRANS

TRANS is CHARACTER*1
Specifies the form of the system of equations:
= ’N’: A * X = B (No transpose)
= ’T’: A**T * X = B (Transpose)
= ’C’: A**H * X = B (Conjugate transpose = Transpose)

DIAG

DIAG is CHARACTER*1
= ’N’: A is non-unit triangular;
= ’U’: A is unit triangular.

N

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

NRHS

NRHS is INTEGER
The number of right hand sides, i.e., the number of columns
of the matrix B. NRHS >= 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 = ’U’, AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
if UPLO = ’L’, AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n.

B

B is REAL array, dimension (LDB,NRHS)
On entry, the right hand side matrix B.
On exit, if INFO = 0, the solution matrix X.

LDB

LDB is INTEGER
The leading dimension of the array B. LDB >= max(1,N).

INFO

INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: if INFO = i, the i-th diagonal element of A is exactly zero,
indicating that the matrix is singular and the
solutions X have not been computed.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

subroutine ztptrs (character uplo, character trans, character diag, integern, integer nrhs, complex*16, dimension( * ) ap, complex*16, dimension(ldb, * ) b, integer ldb, integer info)

ZTPTRS

Purpose:

ZTPTRS solves a triangular system of the form

A * X = B, A**T * X = B, or A**H * X = B,

where A is a triangular matrix of order N stored in packed format, and B is an N-by-NRHS matrix.

This subroutine verifies that A is nonsingular, but callers should note that only exact
singularity is detected. It is conceivable for one or more diagonal elements of A to be
subnormally tiny numbers without this subroutine signalling an error.

If a possible loss of numerical precision due to near-singular matrices is a concern, the
caller should verify that A is nonsingular within some tolerance before calling this subroutine.

Parameters

UPLO

UPLO is CHARACTER*1
= ’U’: A is upper triangular;
= ’L’: A is lower triangular.

TRANS

TRANS is CHARACTER*1
Specifies the form of the system of equations:
= ’N’: A * X = B (No transpose)
= ’T’: A**T * X = B (Transpose)
= ’C’: A**H * X = B (Conjugate transpose)

DIAG

DIAG is CHARACTER*1
= ’N’: A is non-unit triangular;
= ’U’: A is unit triangular.

N

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

NRHS

NRHS is INTEGER
The number of right hand sides, i.e., the number of columns
of the matrix B. NRHS >= 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 = ’U’, AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
if UPLO = ’L’, AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n.

B

B is COMPLEX*16 array, dimension (LDB,NRHS)
On entry, the right hand side matrix B.
On exit, if INFO = 0, the solution matrix X.

LDB

LDB is INTEGER
The leading dimension of the array B. LDB >= max(1,N).

INFO

INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: if INFO = i, the i-th diagonal element of A is exactly zero,
indicating that the matrix is singular and the
solutions X have not been computed.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Author

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