?trtri

Computes the inverse of a triangular matrix.

Syntax

FORTRAN 77:

call strtri( uplo, diag, n, a, lda, info )

call dtrtri( uplo, diag, n, a, lda, info )

call ctrtri( uplo, diag, n, a, lda, info )

call ztrtri( uplo, diag, n, a, lda, info )

FORTRAN 95:

call trtri( a [,uplo] [,diag] [,info] )

lapack_int LAPACKE_<?>trtri( int matrix_order, char uplo, char diag, lapack_int n, <datatype>* a, lapack_int lda );

Include Files

Fortran: mkl_lapack.fi and mkl_lapack.h
Fortran 95: lapack.f90
C: mkl_lapacke.h

Description

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

Input Parameters

The data types are given for the Fortran interface. A <datatype> placeholder, if present, is used for the C interface data types in the C interface section above. See C Interface Conventions for the C interface principal conventions and type definitions.

uplo	CHARACTER*1. 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	CHARACTER*1. 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	INTEGER. The order of the matrix `A`; `n ≥ 0`.
a	REAL for strtri DOUBLE PRECISION for dtrtri COMPLEX for ctrtri DOUBLE COMPLEX for ztrtri. Array: DIMENSION `(,*)`. Contains the matrix `A`. The second dimension of `a` must be at least `max(1,n)`.
lda	INTEGER. The first dimension of `a`; `lda ≥ max(1, n)`.

Output Parameters

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

info

INTEGER.

If info = 0, the execution is successful.

If info = -i, the i-th parameter 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.

Fortran 95 Interface Notes

Routines in Fortran 95 interface have fewer arguments in the calling sequence than their FORTRAN 77 counterparts. For general conventions applied to skip redundant or reconstructible arguments, see Fortran 95 Interface Conventions.

Specific details for the routine trtri interface are as follows:

a	Holds the matrix `A` of size (`n,n`).
uplo	Must be 'U' or 'L'. The default value is 'U'.
diag	Must be 'N' or 'U'. The default value is 'N'.

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.