Developer Reference

Contents

?sytri

Computes the inverse of a symmetric matrix using
U
*
D
*
U
T
or
L
*
D
*
L
T
Bunch-Kaufman factorization.

Syntax

lapack_int
LAPACKE_ssytri
(
int
matrix_layout
,
char
uplo
,
lapack_int
n
,
float
*
a
,
lapack_int
lda
,
const
lapack_int
*
ipiv
);
lapack_int
LAPACKE_dsytri
(
int
matrix_layout
,
char
uplo
,
lapack_int
n
,
double
*
a
,
lapack_int
lda
,
const
lapack_int
*
ipiv
);
lapack_int
LAPACKE_csytri
(
int
matrix_layout
,
char
uplo
,
lapack_int
n
,
lapack_complex_float
*
a
,
lapack_int
lda
,
const
lapack_int
*
ipiv
);
lapack_int
LAPACKE_zsytri
(
int
matrix_layout
,
char
uplo
,
lapack_int
n
,
lapack_complex_double
*
a
,
lapack_int
lda
,
const
lapack_int
*
ipiv
);
Include Files
  • mkl.h
Description
The routine computes the inverse
inv(
A
)
of a symmetric matrix
A
. Before calling this routine, call
?sytrf
to factorize
A
.
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 Bunch-Kaufman factorization
A
=
U*D*U
T
.
If
uplo
=
'L'
, the array
a
stores the Bunch-Kaufman factorization
A
=
L*D*L
T
.
n
The order of the matrix
A
;
n
0
.
a
a
(size max(1,
lda
*
n
))
contains the factorization of the matrix
A
, as returned by
?sytrf
.
lda
The leading dimension of
a
;
lda
max(1,
n
)
.
ipiv
Array, size at least
max(1,
n
)
.
The
ipiv
array, as returned by
?sytrf
.
Output Parameters
a
Overwritten by the
n
-by-
n
matrix
inv(
A
)
.
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
, the
i
-th diagonal element of
D
is zero,
D
is singular, and the inversion could not be completed.
Application Notes
The computed inverse
X
satisfies the following error bounds:
|
D*U
T
*P
T
*X*P*U
-
I
|
c
(
n
)
ε
(|
D
||
U
T
|
P
T
|
X
|
P
|
U
| + |
D
||
D
-1
|)
for
uplo
=
'U'
, and
|
D*L
T
*P
T
*X*P*L
-
I
|
c
(
n
)
ε
(|
D
||
L
T
|
P
T
|
X
|
P
|
L
| + |
D
||
D
-1
|)
for . Here
c
(
n
)
is a modest linear function of
n
, and
ε
is the machine precision;
I
denotes the identity matrix.
The total number of floating-point operations is approximately
(2/3)
n
3
for real flavors and
(8/3)
n
3
for complex flavors.

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