Contents

# ?sptri

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

## Syntax

Include Files
• mkl.h
Description
The routine computes the inverse
inv(
A
)
of a packed symmetric matrix
A
. Before calling this routine, call
?sptrf
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
ap
stores the Bunch-Kaufman factorization
A
=
U*D*U
T
.
If
uplo
=
'L'
, the array
ap
stores the Bunch-Kaufman factorization
A
=
L*D*L
T
.
n
The order of the matrix
A
;
n
0
.
ap
Arrays
ap
(size max(1,
n
(
n
+1)/2)) contains the factorization of the matrix
A
, as returned by
?sptrf
.
ipiv
Array, size at least
max(1,
n
)
. The
ipiv
array, as returned by
?sptrf
.
Output Parameters
ap
Overwritten by the matrix
inv(
A
)
in packed form.
Return Values
This function returns a value
info
.
If
info
= 0
, the execution is successful.
If
info
=
-i
, parameter
i
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*UT*PT*X*P*U - I| ≤c(n)ε(|D||UT|PT|X|P|U| + |D||D-1|)`
for
uplo
=
'U'
, and
`|D*LT*PT*X*P*L - I| ≤c(n)ε(|D||LT|PT|X|P|L| + |D||D-1|)`
for
uplo
=
'L'
. 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