Contents

# ?stedc

Computes all eigenvalues and eigenvectors of a symmetric tridiagonal matrix using the divide and conquer method.

## Syntax

Include Files
• mkl.h
Description
The routine computes all the eigenvalues and (optionally) all the eigenvectors of a symmetric tridiagonal matrix using the divide and conquer method. The eigenvectors of a full or band real symmetric or complex Hermitian matrix can also be found if sytrd/hetrd or sptrd/hptrd or sbtrd/hbtrd has been used to reduce this matrix to tridiagonal form.
Input Parameters
matrix_layout
Specifies whether matrix storage layout is row major (
LAPACK_ROW_MAJOR
) or column major (
LAPACK_COL_MAJOR
).
compz
Must be
'N'
or
'I'
or
'V'
.
If
compz
=
'N'
, the routine computes eigenvalues only.
If
compz
=
'I'
, the routine computes the eigenvalues and eigenvectors of the tridiagonal matrix.
If
compz
=
'V'
, the routine computes the eigenvalues and eigenvectors of original symmetric/Hermitian matrix. On entry, the array
z
must contain the orthogonal/unitary matrix used to reduce the original matrix to tridiagonal form.
n
The order of the symmetric tridiagonal matrix
(
n
0).
d
,
e
Arrays:
d
contains the diagonal elements of the tridiagonal matrix.
The dimension of
d
must be at least max(1,
n
).
e
contains the subdiagonal elements of the tridiagonal matrix.
The dimension of
e
must be at least max(1,
n
-1).
z
Array
z
is of size max(1,
ldz
*
n
).
If
compz
=
'V'
, then, on entry,
z
must contain the orthogonal/unitary matrix used to reduce the original matrix to tridiagonal form.
ldz
z
. Constraints:
ldz
1 if
compz
=
'N'
;
ldz
max(1,
n
) if
compz
=
'V'
or
'I'
.
Output Parameters
d
The
n
eigenvalues in ascending order, unless
info
0
.
info
.
e
On exit, the array is overwritten; see
info
.
z
If
info
= 0
, then if
compz
=
'V'
,
z
contains the orthonormal eigenvectors of the original symmetric/Hermitian matrix, and if
compz
=
'I'
,
z
contains the orthonormal eigenvectors of the symmetric tridiagonal matrix. If
compz
=
'N'
,
z
is not referenced.
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
, the algorithm failed to compute an eigenvalue while working on the submatrix lying in rows and columns
i
/(
n
+1) through mod(
i
,
n
+1).

#### Product and Performance Information

1

Performance varies by use, configuration and other factors. Learn more at www.Intel.com/PerformanceIndex.