Contents

# ?sysv_aa

Computes the solution to a system of linear equations A * X = B for symmetric matrices.
Description
The
?sysv
routine computes the solution to a complex system of linear equations A * X = B, where A is an
n
-by-
n
symmetric matrix and X and B are
n
-by-
nrhs
matrices.
Aasen's algorithm is used to factor A as A = U * T * U
T
, if
uplo
=
'U'
, or A = L * T * L
T
, if
uplo
=
'L'
, where U (or L) is a product of permutation and unit upper (lower) triangular matrices, and T is symmetric tri-diagonal. 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
• =
'U'
: The upper triangle of A is stored.
• =
'L'
: The lower triangle of A is stored.
n
The number of linear equations; that is, 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 of size max(1,
lda
*
n
).
On entry, the symmetric matrix A. If
uplo
=
'U'
n
-by-
n
upper triangular part of A contains the upper triangular part of the matrix A, and the strictly lower triangular part of A is not referenced. If
uplo
=
'L'
n
-by-
n
lower triangular part of A contains the lower triangular part of the matrix A, and the strictly upper triangular part of A is not referenced.
lda
The leading dimension of the array
A
.
B
Array of size max(1,
ldb
*
nrhs
) for column-major layout and max(1,
ldb
*
n
) for row-major layout.
On entry, the
n
-by-
nrhs
right-hand side matrix B.
ldb
The leading dimension of the array
B
.
ldb
≥ max(1,
n
) for column-major layout and
ldb
nrhs
for row-major layout.
Output Parameters
A
On exit, if
info
= 0, the tridiagonal matrix T and the multipliers used to obtain the factor U or L from the factorization A = U*T*U
T
or A = L*T*L
T
as computed by
?sytrf
.
ipiv
Array of size
n
.
On exit, it contains the details of the interchanges; that is, the row and column
k
of A were interchanged with the row and column ipiv(
k
).
B
On exit, if
info
= 0, the
n
-by-
nrhs
solution matrix X.
Return Values
This function returns a value
info
.
= 0: Successful exit.
< 0: If
info
=
-i
, the
i
th
> 0: If
info
=
i
, D(
i
,
i
) is exactly zero. The factorization has been completed, but the block diagonal matrix D is exactly singular, so the solution could not be computed.

#### 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