Developer Reference for Intel® oneAPI Math Kernel Library - C

Developer Reference

  • 2021.1
  • 12/04/2020
  • Public Content
Contents

?getri

Computes the inverse of an LU-factored general matrix.

Syntax

lapack_int
LAPACKE_sgetri
(
int
matrix_layout
,
lapack_int
n
,
float
*
a
,
lapack_int
lda
,
const
lapack_int
*
ipiv
);
lapack_int
LAPACKE_dgetri
(
int
matrix_layout
,
lapack_int
n
,
double
*
a
,
lapack_int
lda
,
const
lapack_int
*
ipiv
);
lapack_int
LAPACKE_cgetri
(
int
matrix_layout
,
lapack_int
n
,
lapack_complex_float
*
a
,
lapack_int
lda
,
const
lapack_int
*
ipiv
);
lapack_int
LAPACKE_zgetri
(
int
matrix_layout
,
lapack_int
n
,
lapack_complex_double
*
a
,
lapack_int
lda
,
const
lapack_int
*
ipiv
);
Include Files
  • mkl.h
Description
The routine computes the inverse
inv(
A
)
 of a general matrix
A
. Before calling this routine, call
?getrf
 to factorize
A
.
Input Parameters
matrix_layout
Specifies whether matrix storage layout is row major (
LAPACK_ROW_MAJOR
) or column major (
LAPACK_COL_MAJOR
).
n
The order of the matrix
A
;
n
≥
 0
.
a
Array
a
(size max(1,
lda
*
n
))
 contains the factorization of the matrix
A
, as returned by
?getrf
:
A
 =
P*L*U
. The second dimension of
a
 must be at least
max(1,
n
)
.
lda
The leading dimension of
a
;
lda
≥
 max(1,
n
)
.
ipiv
Array, size at least
max(1,
n
)
.
The
ipiv
 array, as returned by
?getrf
.
Output Parameters
a
Overwritten by the
n
-by-
n
 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 the factor
U
 is zero,
U
 is singular, and the inversion could not be completed.
Application Notes
The computed inverse
X
 satisfies the following error bound: 
|XA - I| ≤ c(n)ε|X|P|L||U|,
where
c
(
n
)
 is a modest linear function of
n
;
ε
 is the machine precision;
I
 denotes the identity matrix;
P
,
L
, and
U
 are the factors of the matrix factorization
A
 =
P*L*U
.
The total number of floating-point operations is approximately
(4/3)
n
3
 for real flavors and
(16/3)
n
3
 for complex flavors.

Product and Performance Information

1

Performance varies by use, configuration and other factors. Learn more at www.Intel.com/PerformanceIndex.