Developer Reference for Intel® oneAPI Math Kernel Library - C

Developer Reference

  • 2021.1
  • 12/04/2020
  • 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

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