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

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.