Contents

?spev

Computes all eigenvalues and, optionally, eigenvectors of a real symmetric matrix in packed storage.

Syntax

Include Files
• mkl.h
Description
The routine computes all the eigenvalues and, optionally, eigenvectors of a real symmetric matrix
A
in packed storage.
Input Parameters
matrix_layout
Specifies whether matrix storage layout is row major (
LAPACK_ROW_MAJOR
) or column major (
LAPACK_COL_MAJOR
).
jobz
Must be
'N'
or
'V'
.
If
job
=
'N'
, then only eigenvalues are computed.
If
job
=
'V'
, then eigenvalues and eigenvectors are computed.
uplo
Must be
'U'
or
'L'
.
If
uplo
=
'U'
,
ap
stores the packed upper triangular part of
A
.
If
uplo
=
'L'
,
ap
stores the packed lower triangular part of
A
.
n
The order of the matrix
A
(
n
0
).
ap
Array
ap
contains the packed upper or lower triangle of symmetric matrix
A
, as specified by
uplo
.
The size of
ap
must be at least max(1,
n
*(
n
+1)/2).
ldz
The leading dimension of the output array
z
. Constraints:
if
jobz
=
'N'
, then
ldz
1
;
if
jobz
=
'V'
, then
ldz
max(1,
n
)
.
Output Parameters
w
,
z
Arrays:
w
, size at least max(1,
n
).
If
info
= 0
,
w
contains the eigenvalues of the matrix
A
in ascending order.
z
(size max(1,
ldz
*
n
))
.
If
jobz
=
'V'
, then if
info
= 0
,
z
contains the orthonormal eigenvectors of the matrix
A
, with the
i
-th column of
z
holding the eigenvector associated with
w
[
i
- 1]
.
If
jobz
=
'N'
, then
z
is not referenced.
ap
On exit, this array is overwritten by the values generated during the reduction to tridiagonal form. The elements of the diagonal and the off-diagonal of the tridiagonal matrix overwrite the corresponding elements of
A
.
Return Values
This function returns a value
info
.
If
info
=0
, the execution is successful.
If
info
=
-i
, the
i
-th parameter had an illegal value.
If
info
=
i
, then the algorithm failed to converge;
i
indicates the number of elements of an intermediate tridiagonal form which did not converge to zero.

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