Computes the inverse of a triangular matrix.


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

  • mkl.h


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

Input Parameters


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


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.


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.


The order of the matrix A; n 0.


Array: . Contains the matrix A.


The first dimension of a; lda max(1, n).

Output Parameters


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.

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