Man page - tptri(3)

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Manual

tptri

NAME
SYNOPSIS
Functions
Detailed Description
Function Documentation
subroutine ctptri (character uplo, character diag, integer n, complex,dimension( * ) ap, integer info)
subroutine dtptri (character uplo, character diag, integer n, doubleprecision, dimension( * ) ap, integer info)
subroutine stptri (character uplo, character diag, integer n, real,dimension( * ) ap, integer info)
subroutine ztptri (character uplo, character diag, integer n, complex*16,dimension( * ) ap, integer info)
Author

NAME

tptri - tptri: triangular inverse

SYNOPSIS

Functions

subroutine ctptri (uplo, diag, n, ap, info)
CTPTRI
subroutine dtptri (uplo, diag, n, ap, info)
DTPTRI
subroutine stptri (uplo, diag, n, ap, info)
STPTRI
subroutine ztptri (uplo, diag, n, ap, info)
ZTPTRI

Detailed Description

Function Documentation

subroutine ctptri (character uplo, character diag, integer n, complex,dimension( * ) ap, integer info)

CTPTRI

Purpose:

CTPTRI computes the inverse of a complex upper or lower triangular
matrix A stored in packed format.

Parameters

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)
On entry, the upper or lower triangular matrix A, stored
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)*((2*n-j)/2) = A(i,j) for j<=i<=n.
See below for further details.
On exit, the (triangular) inverse of the original matrix, in
the same packed storage format.

INFO

INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: if INFO = i, A(i,i) is exactly zero. The triangular
matrix is singular and its inverse can not be computed.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Further Details:

A triangular matrix A can be transferred to packed storage using one
of the following program segments:

UPLO = ā€™Uā€™: UPLO = ā€™Lā€™:

JC = 1 JC = 1
DO 2 J = 1, N DO 2 J = 1, N
DO 1 I = 1, J DO 1 I = J, N
AP(JC+I-1) = A(I,J) AP(JC+I-J) = A(I,J)
1 CONTINUE 1 CONTINUE
JC = JC + J JC = JC + N - J + 1
2 CONTINUE 2 CONTINUE

subroutine dtptri (character uplo, character diag, integer n, doubleprecision, dimension( * ) ap, integer info)

DTPTRI

Purpose:

DTPTRI computes the inverse of a real upper or lower triangular
matrix A stored in packed format.

Parameters

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)
On entry, the upper or lower triangular matrix A, stored
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)*((2*n-j)/2) = A(i,j) for j<=i<=n.
See below for further details.
On exit, the (triangular) inverse of the original matrix, in
the same packed storage format.

INFO

INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: if INFO = i, A(i,i) is exactly zero. The triangular
matrix is singular and its inverse can not be computed.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Further Details:

A triangular matrix A can be transferred to packed storage using one
of the following program segments:

UPLO = ā€™Uā€™: UPLO = ā€™Lā€™:

JC = 1 JC = 1
DO 2 J = 1, N DO 2 J = 1, N
DO 1 I = 1, J DO 1 I = J, N
AP(JC+I-1) = A(I,J) AP(JC+I-J) = A(I,J)
1 CONTINUE 1 CONTINUE
JC = JC + J JC = JC + N - J + 1
2 CONTINUE 2 CONTINUE

subroutine stptri (character uplo, character diag, integer n, real,dimension( * ) ap, integer info)

STPTRI

Purpose:

STPTRI computes the inverse of a real upper or lower triangular
matrix A stored in packed format.

Parameters

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)
On entry, the upper or lower triangular matrix A, stored
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)*((2*n-j)/2) = A(i,j) for j<=i<=n.
See below for further details.
On exit, the (triangular) inverse of the original matrix, in
the same packed storage format.

INFO

INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: if INFO = i, A(i,i) is exactly zero. The triangular
matrix is singular and its inverse can not be computed.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Further Details:

A triangular matrix A can be transferred to packed storage using one
of the following program segments:

UPLO = ā€™Uā€™: UPLO = ā€™Lā€™:

JC = 1 JC = 1
DO 2 J = 1, N DO 2 J = 1, N
DO 1 I = 1, J DO 1 I = J, N
AP(JC+I-1) = A(I,J) AP(JC+I-J) = A(I,J)
1 CONTINUE 1 CONTINUE
JC = JC + J JC = JC + N - J + 1
2 CONTINUE 2 CONTINUE

subroutine ztptri (character uplo, character diag, integer n, complex*16,dimension( * ) ap, integer info)

ZTPTRI

Purpose:

ZTPTRI computes the inverse of a complex upper or lower triangular
matrix A stored in packed format.

Parameters

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)
On entry, the upper or lower triangular matrix A, stored
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)*((2*n-j)/2) = A(i,j) for j<=i<=n.
See below for further details.
On exit, the (triangular) inverse of the original matrix, in
the same packed storage format.

INFO

INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: if INFO = i, A(i,i) is exactly zero. The triangular
matrix is singular and its inverse can not be computed.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Further Details:

A triangular matrix A can be transferred to packed storage using one
of the following program segments:

UPLO = ā€™Uā€™: UPLO = ā€™Lā€™:

JC = 1 JC = 1
DO 2 J = 1, N DO 2 J = 1, N
DO 1 I = 1, J DO 1 I = J, N
AP(JC+I-1) = A(I,J) AP(JC+I-J) = A(I,J)
1 CONTINUE 1 CONTINUE
JC = JC + J JC = JC + N - J + 1
2 CONTINUE 2 CONTINUE

Author

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