Developer Reference for Intel® oneAPI Math Kernel Library - C

Developer Reference

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

?pftrs

Solves a system of linear equations with a Cholesky-factored symmetric (Hermitian) positive-definite coefficient matrix using the Rectangular Full Packed (RFP) format.

Syntax

lapack_int
LAPACKE_spftrs
(
int
matrix_layout
,
char
transr
,
char
uplo
,
lapack_int
n
,
lapack_int
nrhs
,
const
float
*
a
,
float
*
b
,
lapack_int
ldb
);
lapack_int
LAPACKE_dpftrs
(
int
matrix_layout
,
char
transr
,
char
uplo
,
lapack_int
n
,
lapack_int
nrhs
,
const
double
*
a
,
double
*
b
,
lapack_int
ldb
);
lapack_int
LAPACKE_cpftrs
(
int
matrix_layout
,
char
transr
,
char
uplo
,
lapack_int
n
,
lapack_int
nrhs
,
const
lapack_complex_float
*
a
,
lapack_complex_float
*
b
,
lapack_int
ldb
);
lapack_int
LAPACKE_zpftrs
(
int
matrix_layout
,
char
transr
,
char
uplo
,
lapack_int
n
,
lapack_int
nrhs
,
const
lapack_complex_double
*
a
,
lapack_complex_double
*
b
,
lapack_int
ldb
);
Include Files
  • mkl.h
Description
The routine solves a system of linear equations
A*X
 =
B
 with a symmetric positive-definite or, for complex data, Hermitian positive-definite matrix
A
 using the Cholesky factorization of
A
:
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
?pftrs
, you must call
?pftrf
 to compute the Cholesky factorization of
A
.
L
 stands for a lower triangular matrix and
U
 for an upper triangular matrix.
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 untransposed factor of
A
is stored in RFP format.
If
transr
 =
'T'
, the transposed factor of
A
is stored in RFP format.
If
transr
 =
'C'
, the conjugate-transposed factor of
A
is stored in RFP format.
uplo
Must be
'U'
 or
'L'
.
Indicates how the input matrix
A
 has been factored:
If
uplo
 =
'U'
,
U
 is stored, where
A
 =
U
T
*
U
 for real data,
A
 =
U
H
*
U
 for complex data.
If
uplo
 =
'L'
,
L
 is stored, where
A
 =
L
*
L
T
 for real data,
A
 =
L
*
L
H
 for complex data
n
The order of the matrix
A
;
n
≥
 0.
nrhs
The number of right-hand sides, that is, the number of columns of the matrix
B
;
nrhs
≥
 0.
a
Array
a
 of size max(1,
n
*(
n
 + 1)/2).
The array
a
 contains, in the RFP format, the factor
U
 or
L
 obtained by factorization of matrix
A
.
b
The array
b
 of size max(1,
ldb
*
nrhs
) for column major layout and max(1,
ldb
*
n
) for row major layout contains the matrix
B
 whose columns are the right-hand sides for the systems of equations.
ldb
The leading dimension of
b
;
ldb
≥
 max(1,
n
) for column major layout and
ldb
≥
nrhs
 for row major layout
.
Output Parameters
b
The solution matrix
X
.
Return Values
This function returns a value
info
.
If
info
=0
, the execution is successful.
If
info
 =
-i
, parameter
i
 had an illegal value.

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