mkl_?getrinp

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 3/31/2023

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Computes the inverse of an LU-factored general matrix without pivoting.

Syntax

call mkl_sgetrinp( n, a, lda, work, lwork, info )

call mkl_dgetrinp( n, a, lda, work, lwork, info )

call mkl_cgetrinp( n, a, lda, work, lwork, info )

call mkl_zgetrinp( n, a, lda, work, lwork, info )

Include Files

Description

The routine computes the inverse inv(A) of a general matrix A. Before calling this routine, call mkl_?getrfnp to factorize A.

Input Parameters

n	INTEGER. The order of the matrix `A`; `n≥ 0`.
a, work	REAL for mkl_sgetrinp DOUBLE PRECISION for mkl_dgetrinp COMPLEX for mkl_cgetrinp DOUBLE COMPLEX for mkl_zgetrinp. Arrays: `a(lda,)`, `work()`. `a(lda,)` contains the factorization of the matrix `A`, as returned by mkl_?getrfnp: `A = LU`. The second dimension of `a` must be at least `max(1,n)`. `work(*)` is a workspace array of dimension at least `max(1,lwork)`.
lda	INTEGER. The leading dimension of `a`; `lda≥ max(1, n)`.
lwork	INTEGER. The size of the `work` array; `lwork`≥`n`. If `lwork = -1`, then a workspace query is assumed; the routine only calculates the optimal size of the `work` array, returns this value as the first entry of the `work` array, and no error message related to `lwork` is issued by xerbla.

See Application Notes below for the suggested value of lwork.

Output Parameters

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

work(1)

If info = 0, on exit work(1) contains the minimum value of lwork required for optimum performance. Use this lwork for subsequent runs.

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 the factor U is zero, U is singular, and the inversion could not be completed.

Application Notes

The total number of floating-point operations is approximately (4/3)n³ for real flavors and (16/3)n³ for complex flavors.

Parent topic: Matrix Inversion: LAPACK Computational Routines