Developer Reference

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

?sytrs

Solves a system of linear equations with a UDU
T
- or LDL
T
-factored symmetric coefficient matrix.

Syntax

lapack_int
LAPACKE_ssytrs
(
int
matrix_layout
,
char
uplo
,
lapack_int
n
,
lapack_int
nrhs
,
const
float
*
a
,
lapack_int
lda
,
const
lapack_int
*
ipiv
,
float
*
b
,
lapack_int
ldb
);
lapack_int
LAPACKE_dsytrs
(
int
matrix_layout
,
char
uplo
,
lapack_int
n
,
lapack_int
nrhs
,
const
double
*
a
,
lapack_int
lda
,
const
lapack_int
*
ipiv
,
double
*
b
,
lapack_int
ldb
);
lapack_int
LAPACKE_csytrs
(
int
matrix_layout
,
char
uplo
,
lapack_int
n
,
lapack_int
nrhs
,
const
lapack_complex_float
*
a
,
lapack_int
lda
,
const
lapack_int
*
ipiv
,
lapack_complex_float
*
b
,
lapack_int
ldb
);
lapack_int
LAPACKE_zsytrs
(
int
matrix_layout
,
char
uplo
,
lapack_int
n
,
lapack_int
nrhs
,
const
lapack_complex_double
*
a
,
lapack_int
lda
,
const
lapack_int
*
ipiv
,
lapack_complex_double
*
b
,
lapack_int
ldb
);
Include Files
  • mkl.h
Description
The routine solves for
X
the system of linear equations
A*X
=
B
with a symmetric matrix
A
, given the Bunch-Kaufman factorization of
A
:
if
uplo
=
'U'
,
A
=
U*D*U
T
if
uplo
=
'L'
,
A
=
L*D*L
T
,
where
U
and
L
are upper and lower triangular matrices with unit diagonal and
D
is a symmetric block-diagonal matrix. The system is solved with multiple right-hand sides stored in the columns of the matrix
B
. You must supply to this routine the factor
U
(or
L
) and the array
ipiv
returned by the factorization routine
?sytrf
.
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 how the input matrix
A
has been factored:
If
uplo
=
'U'
, the array
a
stores the upper triangular factor
U
of the factorization
A
=
U*D*U
T
.
If
uplo
=
'L'
, the array
a
stores the lower triangular factor
L
of the factorization
A
=
L*D*L
T
.
n
The order of matrix
A
;
n
0.
nrhs
The number of right-hand sides;
nrhs
0.
ipiv
Array, size at least
max(1,
n
)
. The
ipiv
array, as returned by
?sytrf
.
a
The array
a
of size max(1,
lda
*
n
)
contains the factor
U
or
L
(see
uplo
). .
b
The array
b
contains the matrix
B
whose columns are the right-hand sides for the system of equations.
The size of
b
is at least max(1,
ldb
*
nrhs
) for column major layout and max(1,
ldb
*
n
) for row major layout.
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
b
Overwritten by the solution matrix
X
.
Return Values
This function returns a value
info
.
If
info
=0
, the execution is successful.
If
info
=
-i
, parameter
i
had an illegal value.
Application Notes
For each right-hand side
b
, the computed solution is the exact solution of a perturbed system of equations
(
A
+
E
)
x
=
b
, where
|E| ≤ c(n)ε P|U||D||U
T
|P
T
or |E| ≤ c(n)ε P|L||D||U
T
|P
T
c
(
n
)
is a modest linear function of
n
, and
ε
is the machine precision.
If
x
0
is the true solution, the computed solution
x
satisfies this error bound:
Equation
where
cond(
A
,
x
)
= || |
A
-1
||
A
| |
x
| ||
/ ||
x
||
||
A
-1
||
||
A
||
=
κ
(
A
).
Note that
cond(
A
,
x
)
can be much smaller than
κ
(
A
)
.
The total number of floating-point operations for one right-hand side vector is approximately
2
n
2
for real flavors or
8
n
2
for complex flavors.
To estimate the condition number
κ
(
A
)
, call
?sycon
.
To refine the solution and estimate the error, call
?syrfs
.

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