Developer Reference for Intel® oneAPI Math Kernel Library - C

Developer Reference

  • 0.9
  • 09/09/2020
  • Public Content
Contents

?pftri

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

Syntax

lapack_int
LAPACKE_spftri
(
int
matrix_layout
,
char
transr
,
char
uplo
,
lapack_int
n
,
float
*
a
);
lapack_int
LAPACKE_dpftri
(
int
matrix_layout
,
char
transr
,
char
uplo
,
lapack_int
n
,
double
*
a
);
lapack_int
LAPACKE_cpftri
(
int
matrix_layout
,
char
transr
,
char
uplo
,
lapack_int
n
,
lapack_complex_float
*
a
);
lapack_int
LAPACKE_zpftri
(
int
matrix_layout
,
char
transr
,
char
uplo
,
lapack_int
n
,
lapack_complex_double
*
a
);
Include Files
  • mkl.h
Description
The routine computes the inverse
inv(
A
)
 of a symmetric positive definite or, for complex data, Hermitian positive-definite matrix
A
 using the Cholesky factorization:
A
 =
U
T
*U
 for real data,
A
 =
U
H
*U
 for complex data
if
uplo
=
'U'
A
 =
L*L
T
 for real data,
A
 =
L*L
H
 for complex data
if
uplo
=
'L'
Before calling this routine, call
?pftrf
 to factorize
A
.
The matrix
A
 is in the Rectangular Full Packed (RFP) format. For the description of the RFP format, see Matrix Storage Schemes.
Input Parameters
matrix_layout
Specifies whether matrix storage layout is row major (
LAPACK_ROW_MAJOR
) or column major (
LAPACK_COL_MAJOR
).
transr
Must be
'N'
,
'T'
 (for real data) or
'C'
 (for complex data).
If
transr
 =
'N'
, the Normal
transr
 of RFP
U
 (if
uplo
 =
'U'
) or
L
 (if
uplo
 =
'L'
) is stored.
If
transr
 =
'T'
, the Transpose
transr
 of RFP
U
 (if
uplo
 =
'U'
) or
L
 (if
uplo
 =
'L'
 is stored.
If
transr
 =
'C'
, the Conjugate-Transpose
transr
 of RFP
U
 (if
uplo
 =
'U'
) or
L
 (if
uplo
 =
'L'
 is stored.
uplo
Must be
'U'
 or
'L'
.
Indicates how the input matrix
A
 has been factored:
If
uplo
 =
'U'
,
A
 =
U
T
*
U
 for real data or
A
 =
U
H
*
U
 for complex data, and
U
 is stored.
If
uplo
 =
'L'
,
A
 =
L
*
L
T
 for real data or
A
 =
L
*
L
H
 for complex data, and
L
 is stored.
n
The order of the matrix
A
;
n
≥
 0.
a
Array, size
(
n
*(
n
+1)/2)
. The array
a
 contains the factor
U
 or
L
 matrix
A
 in the RFP format.
Output Parameters
a
The symmetric/Hermitian inverse of the original matrix in the same storage format.
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
,
i
)
 element of the factor
U
 or
L
 is zero, and the inverse could not be computed.

Product and Performance Information

1

Intel's compilers may or may not optimize to the same degree for non-Intel microprocessors for optimizations that are not unique to Intel microprocessors. These optimizations include SSE2, SSE3, and SSSE3 instruction sets and other optimizations. Intel does not guarantee the availability, functionality, or effectiveness of any optimization on microprocessors not manufactured by Intel. Microprocessor-dependent optimizations in this product are intended for use with Intel microprocessors. Certain optimizations not specific to Intel microarchitecture are reserved for Intel microprocessors. Please refer to the applicable product User and Reference Guides for more information regarding the specific instruction sets covered by this notice.

Notice revision #20110804