Developer Reference for Intel® oneAPI Math Kernel Library - C

Developer Reference

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

?potri

Computes the inverse of a symmetric (Hermitian) positive-definite matrix using the Cholesky factorization.

Syntax

lapack_int
LAPACKE_spotri
(
int
matrix_layout
,
char
uplo
,
lapack_int
n
,
float
*
a
,
lapack_int
lda
);
lapack_int
LAPACKE_dpotri
(
int
matrix_layout
,
char
uplo
,
lapack_int
n
,
double
*
a
,
lapack_int
lda
);
lapack_int
LAPACKE_cpotri
(
int
matrix_layout
,
char
uplo
,
lapack_int
n
,
lapack_complex_float
*
a
,
lapack_int
lda
);
lapack_int
LAPACKE_zpotri
(
int
matrix_layout
,
char
uplo
,
lapack_int
n
,
lapack_complex_double
*
a
,
lapack_int
lda
);
Include Files
  • mkl.h
Description
The routine computes the inverse
inv(
A
)
 of a symmetric positive definite or, for complex flavors, Hermitian positive-definite matrix
A
. Before calling this routine, call
?potrf
 to factorize
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 how the input matrix
A
 has been factored:
If
uplo
 =
'U'
, the upper triangle of
A
 is stored.
If
uplo
 =
'L'
, the lower triangle of
A
 is stored.
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
?potrf
.
lda
The leading dimension of
a
.
lda
≥
 max(1,
n
).
Output Parameters
a
Overwritten by the upper or lower triangle of the inverse of
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 Cholesky factor (and therefore the factor itself) is zero, and the inversion could not be completed.
Application Notes
The computed inverse
X
 satisfies the following error bounds: 
||XA - I||
2

					≤
					c(n)ε
					κ
					
2
(A), ||AX -  I||
2

					≤
					c(n)ε
					κ
					
2
(A),
where
c
(
n
)
 is a modest linear function of
n
, and
ε
 is the machine precision;
I
 denotes the identity matrix.
The 2-norm
||
A
||
2
 of a matrix
A
 is defined by
||
A
||
2
 =
max
x
·
x
=1
(
A
x
·
A
x
)
1/2
, and the condition number
κ
2
(
A
)
 is defined by
κ
2
(
A
) = ||
A
||
2
 ||
A
-1
||
2
.
The total number of floating-point operations is approximately
(2/3)
n
3
 for real flavors and
(8/3)
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.