## Developer Reference

• 2020.2
• 07/15/2020
• Public Content
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
uplo
CHARACTER*1
• =
'U'
: The upper triangle of A is stored.
• =
'L'
: The lower triangle of A is stored.
n
INTEGER
The number of linear equations; that is, the order of the matrix A.
n
≥ 0.
nrhs
INTEGER
The number of right-hand sides; that is, the number of columns of the matrix B.
nrhs
≥ 0.
A
REAL
for
ssysv_aa
DOUBLE PRECISION
for
dsysv_aa
COMPLEX
for
csysv_aa
COMPLEX*16
for
zsysv_aa
Array, dimension (
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
INTEGER
The leading dimension of the array
A
.
lda
≥ max(1,
n
).
B
REAL
for
ssysv_aa
DOUBLE PRECISION
for
dsysv_aa
COMPLEX
for
csysv_aa
COMPLEX*16
for
zsysv_aa
Array, dimension (
ldb
,
nrhs
).
On entry, the
n
-by-
nrhs
right-hand side matrix B.
ldb
INTEGER
The leading dimension of the array
B
.
ldb
≥ max(1,
n
).
lwork
INTEGER
The length of the array
work
.
If
lwork
=
-1
, a workspace query is assumed; the routine calculates only the optimal size of the work array and returns this value as the first entry of the work array, and no error message related to
lwork
is issued by XERBLA.
Output Parameters
A
REAL
for
ssysv_aa
DOUBLE PRECISION
for
dsysv_aa
COMPLEX
for
csysv_aa