.TH DTPTRI 1 "November 2006" " LAPACK routine (version 3.1) " " LAPACK routine (version 3.1) "
.SH NAME
DTPTRI - the inverse of a real upper or lower triangular matrix A stored in packed format
.SH SYNOPSIS
.TP 19
SUBROUTINE DTPTRI(
UPLO, DIAG, N, AP, INFO )
.TP 19
.ti +4
CHARACTER
DIAG, UPLO
.TP 19
.ti +4
INTEGER
INFO, N
.TP 19
.ti +4
DOUBLE
PRECISION AP( * )
.SH PURPOSE
DTPTRI computes the inverse of a real upper or lower triangular
matrix A stored in packed format.
.SH ARGUMENTS
.TP 8
UPLO (input) CHARACTER*1
= \(aqU\(aq: A is upper triangular;
.br
= \(aqL\(aq: A is lower triangular.
.TP 8
DIAG (input) CHARACTER*1
.br
= \(aqN\(aq: A is non-unit triangular;
.br
= \(aqU\(aq: A is unit triangular.
.TP 8
N (input) INTEGER
The order of the matrix A. N >= 0.
.TP 8
AP (input/output) 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 = \(aqU\(aq, AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
if UPLO = \(aqL\(aq, 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.
.TP 8
INFO (output) INTEGER
= 0: successful exit
.br
< 0: if INFO = -i, the i-th argument had an illegal value
.br
> 0: if INFO = i, A(i,i) is exactly zero. The triangular
matrix is singular and its inverse can not be computed.
.SH FURTHER DETAILS
A triangular matrix A can be transferred to packed storage using one
of the following program segments:
.br
UPLO = \(aqU\(aq: UPLO = \(aqL\(aq:
.br
JC = 1 JC = 1
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DO 2 J = 1, N DO 2 J = 1, N
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DO 1 I = 1, J DO 1 I = J, N
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AP(JC+I-1) = A(I,J) AP(JC+I-J) = A(I,J)
1 CONTINUE 1 CONTINUE
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JC = JC + J JC = JC + N - J + 1
2 CONTINUE 2 CONTINUE
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