Developer Reference for Intel® oneAPI Math Kernel Library for C

ID 766684
Date 3/22/2024
Public

A newer version of this document is available. Customers should click here to go to the newest version.

Document Table of Contents

?tptri

Computes the inverse of a triangular matrix using packed storage.

Syntax

lapack_int LAPACKE_stptri (int matrix_layout , char uplo , char diag , lapack_int n , float * ap );

lapack_int LAPACKE_dtptri (int matrix_layout , char uplo , char diag , lapack_int n , double * ap );

lapack_int LAPACKE_ctptri (int matrix_layout , char uplo , char diag , lapack_int n , lapack_complex_float * ap );

lapack_int LAPACKE_ztptri (int matrix_layout , char uplo , char diag , lapack_int n , lapack_complex_double * ap );

Include Files

  • mkl.h

Description

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

Input Parameters

matrix_layout

Specifies whether matrix storage layout is row major (LAPACK_ROW_MAJOR) or column major (LAPACK_COL_MAJOR).

uplo

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

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

The order of the matrix A; n 0.

ap

Array, size at least max(1,n(n+1)/2).

Contains the packed triangular matrix A.

Output Parameters

ap

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

Return Values

This function returns a value info.

If info = 0, the execution is successful.

If info = -i, parameter i 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.

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.