Developer Reference for Intel® oneAPI Math Kernel Library - C

Developer Reference

Contents

?sysv

Computes the solution to the system of linear equations with a real or complex symmetric coefficient matrix A and multiple right-hand sides.

Syntax

lapack_int
LAPACKE_ssysv
(
int
matrix_layout
,
char
uplo
,
lapack_int
n
,
lapack_int
nrhs
,
float
*
a
,
lapack_int
lda
,
lapack_int
*
ipiv
,
float
*
b
,
lapack_int
ldb
);
lapack_int
LAPACKE_dsysv
(
int
matrix_layout
,
char
uplo
,
lapack_int
n
,
lapack_int
nrhs
,
double
*
a
,
lapack_int
lda
,
lapack_int
*
ipiv
,
double
*
b
,
lapack_int
ldb
);
lapack_int
LAPACKE_csysv
(
int
matrix_layout
,
char
uplo
,
lapack_int
n
,
lapack_int
nrhs
,
lapack_complex_float
*
a
,
lapack_int
lda
,
lapack_int
*
ipiv
,
lapack_complex_float
*
b
,
lapack_int
ldb
);
lapack_int
LAPACKE_zsysv
(
int
matrix_layout
,
char
uplo
,
lapack_int
n
,
lapack_int
nrhs
,
lapack_complex_double
*
a
,
lapack_int
lda
,
lapack_int
*
ipiv
,
lapack_complex_double
*
b
,
lapack_int
ldb
);
Include Files
  • mkl.h
Description
The routine solves for
X
 the real or complex system of linear equations
A*X
 =
B
, where
A
 is an
n
-by-
n
 symmetric matrix, the columns of matrix
B
 are individual right-hand sides, and the columns of
X
 are the corresponding solutions.
The diagonal pivoting method is used to factor
A
 as
A
 =
U*D*U
T
 or
A
 =
L*D*L
T
, where
U
 (or
L
) is a product of permutation and unit upper (lower) triangular matrices, and
D
 is symmetric and block diagonal with 1-by-1 and 2-by-2 diagonal blocks.
The factored form of
A
 is then used to solve the system of equations
A*X
 =
B
.
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 whether the upper or lower triangular part of
A
 is stored:
If
uplo
 =
'U'
, the upper triangle of
A
 is stored.
If
uplo
 =
'L'
, the lower triangle of
A
 is stored.
n
The order of matrix
A
;
n
≥
 0.
nrhs
The number of right-hand sides; the number of columns in
B
;
nrhs
≥
 0
.
a
,
b
Arrays:
a
(size max(1,
lda
*
n
))
,
b
of size max(1,
ldb
*
nrhs
) for column major layout and max(1,
ldb
*
n
) for row major layout
.
The array
a
 contains the upper or the lower triangular part of the symmetric matrix
A
 (see
uplo
).
The array
b
 contains the matrix
B
 whose columns are the right-hand sides for the systems of equations.
lda
The leading dimension of
a
;
lda
≥
 max(1,
n
)
.
ldb
The leading dimension of
b
;
ldb
≥
 max(1,
n
) for column major layout and
ldb
≥
nrhs
 for row major layout
.
Output Parameters
a
If
info
 = 0
,
a
 is overwritten by the block-diagonal matrix
D
 and the multipliers used to obtain the factor
U
 (or
L
) from the factorization of
A
 as computed by
?sytrf
.
b
If
info
 = 0
,
b
 is overwritten by the solution matrix
X
.
ipiv
Array, size at least
max(1,
n
)
. Contains details of the interchanges and the block structure of
D
, as determined by
?sytrf
.
If
ipiv
[
i
-1] =
k
 >0
, then
d
i
i
 is a 1-by-1 diagonal block, and the
i
-th row and column of
A
 was interchanged with the
k
-th row and column.
If
uplo
 =
'U'
 and
ipiv
[
i
] =
ipiv
[
i
-1] = -
m
 < 0, then
D
 has a 2-by-2 block in rows/columns
i
 and
i
+1
, and (
i
)-th row and column of
A
 was interchanged with the
m-
th row and column.
If
uplo
 =
'L'
and
ipiv
[
i
] =
ipiv
[
i
-1] = -
m
 < 0, then
D
 has a 2-by-2 block in rows/columns
i
 and
i
+1
, and (
i
+1
)-th row and column of
A
 was interchanged with the
m
-th row and column.
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
,
d
i
i
 is 0. The factorization has been completed, but
D
 is exactly singular, so the solution could not be computed.

Product and Performance Information

1

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