Developer Reference

Contents

?pptri

Computes the inverse of a packed symmetric (Hermitian) positive-definite matrix using Cholesky factorization.

Syntax

lapack_int
LAPACKE_spptri
(
int
matrix_layout
,
char
uplo
,
lapack_int
n
,
float
*
ap
);
lapack_int
LAPACKE_dpptri
(
int
matrix_layout
,
char
uplo
,
lapack_int
n
,
double
*
ap
);
lapack_int
LAPACKE_cpptri
(
int
matrix_layout
,
char
uplo
,
lapack_int
n
,
lapack_complex_float
*
ap
);
lapack_int
LAPACKE_zpptri
(
int
matrix_layout
,
char
uplo
,
lapack_int
n
,
lapack_complex_double
*
ap
);
Include Files
  • mkl.h
Description
The routine computes the inverse
inv(
A
)
of a symmetric positive definite or, for complex flavors, Hermitian positive-definite matrix
A
in packed form. Before calling this routine, call
?pptrf
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 whether
the upper or lower triangular factor is stored in
ap
:
If
uplo
=
'U'
, then the upper triangular factor is stored.
If
uplo
=
'L'
, then the lower triangular factor is stored.
n
The order of the matrix
A
;
n
0
.
ap
Array, size at least max(1,
n
(
n
+1)/2).
Contains the factorization of the packed matrix
A
, as returned by
?pptrf
.
The dimension
ap
must be at least max(1,
n
(
n
+1)/2).
Output Parameters
ap
Overwritten by the packed
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 the Cholesky factor (and therefore the factor itself) is zero, and the inversion could not be completed.
Application Notes
The computed inverse
X
satisfies the following error bounds:
||
XA
-
I
||
2
c
(
n
)
ε
κ
2
(
A
), ||
AX
-
I
||
2
c
(
n
)
ε
κ
2
(
A
),
where
c
(
n
)
is a modest linear function of
n
, and
ε
is the machine precision;
I
denotes the identity matrix.
The 2-norm
||
A
||
2
of a matrix
A
is defined by
||
A
||
2
=
max
x
·
x
=1
(
A
x
·
A
x
)
1/2
, and the condition number
κ
2
(
A
)
is defined by
κ
2
(
A
) = ||
A
||
2
||
A
-1
||
2
.
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