Developer Reference

  • 0.9
  • 09/09/2020
  • Public Content
Contents

?sysv_rk

Computes the solution to system of linear equations A * X = B for
SY
matrices.
lapack_int
LAPACKE_ssysv_rk
(
int
matrix_layout
,
char
uplo
,
lapack_int
n
,
lapack_int
nrhs
,
float
*
A
,
lapack_int
lda
,
float
*
e
,
lapack_int
*
ipiv
,
float
*
B
,
lapack_int
ldb
);
lapack_int
LAPACKE_dsysv_rk
(
int
matrix_layout
,
char
uplo
,
lapack_int
n
,
lapack_int
nrhs
,
double
*
A
,
lapack_int
lda
,
double
*
e
,
lapack_int
*
ipiv
,
double
*
B
,
lapack_int
ldb
);
lapack_int
LAPACKE_csysv_rk
(
int
matrix_layout
,
char
uplo
,
lapack_int
n
,
lapack_int
nrhs
,
lapack_complex_float
*
A
,
lapack_int
lda
,
lapack_complex_float
*
e
,
lapack_int
*
ipiv
,
lapack_complex_float
*
B
,
lapack_int
ldb
);
lapack_int
LAPACKE_zsysv_rk
(
int
matrix_layout
,
char
uplo
,
lapack_int
n
,
lapack_int
nrhs
,
lapack_complex_double
*
A
,
lapack_int
lda
,
lapack_complex_double
*
e
,
lapack_int
*
ipiv
,
lapack_complex_double
*
B
,
lapack_int
ldb
);
Description
?sysv_rk
computes the solution to a real or 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.
The bounded Bunch-Kaufman (rook) diagonal pivoting method is used to factor A as A= P*U*D*(U
T
)*(P
T
), if
uplo
=
'U'
, or A= P*L*D*(L
T
)*(P
T
), if
uplo
=
'L'
, where U (or L) is unit upper (or lower) triangular matrix, U
T
(or L
T
) is the transpose of U (or L), P is a permutation matrix, P
T
is the transpose of P, and D is symmetric and block diagonal with 1-by-1 and 2-by-2 diagonal blocks.
?sytrf_rk
is called to compute the factorization of a real or complex symmetric matrix. The factored form of A is then used to solve the system of equations A * X = B by calling BLAS3 routine
?sytrs_3
.
Input Parameters
matrix_layout
Specifies whether matrix storage layout is row major (
LAPACK_ROW_MAJOR
) or column major (
LAPACK_COL_MAJOR
).
uplo
Specifies whether the upper or lower triangular part of the symmetric matrix A is stored:
  • =
    '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'
, the leading
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'
, the leading
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
).
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 diagonal of the block diagonal matrix D and factors U or L as computed by
?sytrf_rk
:
  • Only
    diagonal elements of the symmetric block diagonal matrix D on the diagonal of A; that is, D(
    k
    ,
    k
    ) = A(
    k
    ,
    k
    ). Superdiagonal (or subdiagonal) elements of D are stored on exit in array
    e
    .
  • If
    uplo
    =
    'U'
    , factor U in the superdiagonal part of A. If
    uplo
    =
    'L'
    , factor L in the subdiagonal part of A. For more information, see the description of the
    ?sytrf_rk
    routine.
e
Array of size
n
.
On exit, contains the output computed by the factorization routine
?sytrf_rk
; that is, the superdiagonal (or subdiagonal) elements of the symmetric block diagonal matrix D with 1-by-1 or 2-by-2 diagonal blocks. If
uplo
=
'U'
, e(
i
) = D(
i
-
1,
i
),
i
=1:N
-
1, and e(1) is set to 0. If
uplo
=
'L'
, e(
i
) = D(
i
+1,
i
),
i
=1:N
-
1, and e(
n
) is set to 0.
For 1-by-1 diagonal block D(
k
), where 1 ≤ k ≤
n
, the element e(
k
) is set to 0 in both the
uplo
=
'U'
and
uplo
=
'L'
cases. For more information, see the description of the
?sytrf_rk
routine.
ipiv
Array of size
n
.
Details of the interchanges and the block structure of D, as determined by
?sytrf_rk
. For more information, see the description of the
?sytrf_rk
routine.
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
=
-k
, the
k
th
argument had an illegal value.
> 0: If
info
=
k
, the matrix A is singular. If
uplo
=
'U'
, column
k
in the upper triangular part of A contains all zeros. If
uplo
=
'L'
, column
k
in the lower triangular part of A contains all zeros. Therefore D(
k
,
k
) is exactly zero, and superdiagonal elements of column
k
of U (or subdiagonal elements of column
k
of L) are all zeros. The factorization has been completed, but the block diagonal matrix D is exactly singular, and division by zero will occur if it is used to solve a system of equations.

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