?trtri

Developer Reference for Intel® oneAPI Math Kernel Library for C

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ID 766684

Date 12/16/2022

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Computes the inverse of a triangular matrix.

Syntax

lapack_int LAPACKE_strtri (int matrix_layout , char uplo , char diag , lapack_int n , float * a , lapack_int lda );

lapack_int LAPACKE_dtrtri (int matrix_layout , char uplo , char diag , lapack_int n , double * a , lapack_int lda );

lapack_int LAPACKE_ctrtri (int matrix_layout , char uplo , char diag , lapack_int n , lapack_complex_float * a , lapack_int lda );

lapack_int LAPACKE_ztrtri (int matrix_layout , char uplo , char diag , lapack_int n , lapack_complex_double * a , lapack_int lda );

Include Files

Description

The routine computes the inverse inv(A) of a 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 `a`.
n	The order of the matrix `A`; `n≥ 0`.
a	Array: . Contains the matrix `A`.
lda	The first dimension of `a`; `lda≥ max(1, n)`.

Output Parameters

a	Overwritten by the 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|

|XA - I| ≤ 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