?tptri

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 3/31/2023

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?tptri

Computes the inverse of a triangular matrix using packed storage.

Syntax

call stptri( uplo, diag, n, ap, info )

call dtptri( uplo, diag, n, ap, info )

call ctptri( uplo, diag, n, ap, info )

call ztptri( uplo, diag, n, ap, info )

call tptri( ap [,uplo] [,diag] [,info] )

Include Files

mkl.fi, lapack.f90

Description

The routine computes the inverse inv(A) of a packed triangular matrix A.

Input Parameters

uplo	CHARACTER*1. Must be 'U' or 'L'. Indicates whether `A` is upper or lower triangular: If `uplo = 'U'`, then `A` is upper triangular. If `uplo = 'L'`, then `A` is lower triangular.
diag	CHARACTER*1. Must be 'N' or 'U'. If `diag = 'N'`, then `A` is not a unit triangular matrix. If `diag = 'U'`, `A` is unit triangular: diagonal elements of `A` are assumed to be 1 and not referenced in the array `ap`.
n	INTEGER. The order of the matrix `A`; `n≥ 0`.
ap	REAL for stptri DOUBLE PRECISION for dtptri COMPLEX for ctptri DOUBLE COMPLEX for ztptri. Array, size at least `max(1,n(n+1)/2)`. Contains the packed triangular matrix A.

Output Parameters

Overwritten by the packed n-by-n matrix inv(A) .

info

INTEGER.

If info = 0, the execution is successful.

If info = -i, the i-th parameter had an illegal value.

If info = i, the i-th diagonal element of A is zero, A is singular, and the inversion could not be completed.

LAPACK 95 Interface Notes

Routines in Fortran 95 interface have fewer arguments in the calling sequence than their FORTRAN 77 counterparts. For general conventions applied to skip redundant or reconstructible arguments, see LAPACK 95 Interface Conventions.

Specific details for the routine tptri interface are as follows:

ap	Holds the array `A` of size (`n*(n+1)/2`).
uplo	Must be 'U' or 'L'. The default value is 'U'.
diag	Must be 'N' or 'U'. The default value is 'N'.

Application Notes

The computed inverse X satisfies the following error bounds:

|XA - I| ≤ c(n)ε |X||A|

|X - A^-1| ≤ c(n)ε |A^-1||A||X|,

where c(n) is a modest linear function of n; ε is the machine precision; I denotes the identity matrix.

The total number of floating-point operations is approximately (1/3)n³ for real flavors and (4/3)n³ for complex flavors.

Parent topic: Matrix Inversion: LAPACK Computational Routines

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