Developer Reference for Intel® oneAPI Math Kernel Library - C

Developer Reference

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

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