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 );

• mkl.h

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.