?trtri

Developer Reference for Intel® oneAPI Math Kernel Library for C

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ID 766684

Date 4/28/2026

Version

Public

?trtri

Computes the inverse of a triangular matrix.

Syntax

lapack_intLAPACKE_strtri ( intmatrix_layout , charuplo , chardiag , lapack_intn , float*a , lapack_intlda );

lapack_intLAPACKE_dtrtri ( intmatrix_layout , charuplo , chardiag , lapack_intn , double*a , lapack_intlda );

lapack_intLAPACKE_ctrtri ( intmatrix_layout , charuplo , chardiag , lapack_intn , lapack_complex_float*a , lapack_intlda );

lapack_intLAPACKE_ztrtri ( intmatrix_layout , charuplo , chardiag , lapack_intn , lapack_complex_double*a , lapack_intlda );

Include Files

mkl.h

Description

strtri dtrtri ctrtri ztrtri trtri

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.

LAPACK 95 Interface Notes

There exist FORTRAN 77 and FORTRAN 95 interfaces for this routine. See the Intel® oneMKL Fortran Developer Reference for details.

Application Notes

The computed inverse \(X\) satisfies the following error bounds:

\[|XA - I| \leq c(n)\varepsilon |X||A|\]

\[|XA - I| \leq c(n)\varepsilon |A^{-1}||A||X|,\]

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

The total number of floating-point operations is approximately \((1/3)n^{3}\) for real flavors and \((4/3)n^{3}\) for complex flavors.

NOTE:

Matrix Storage Schemes

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Developer Reference for Intel® oneAPI Math Kernel Library for C

?trtri

Syntax

Include Files

Description

Input Parameters

Output Parameters

Return Values

LAPACK 95 Interface Notes

Application Notes