Developer Reference for Intel® oneAPI Math Kernel Library - C

Developer Reference

  • 2021.1
  • 12/04/2020
  • Public Content
Contents

?stedc

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

Syntax

lapack_int LAPACKE_sstedc
(
int
matrix_layout
,
char
compz
,
lapack_int
n
,
float*
d
,
float*
e
,
float*
z
,
lapack_int
ldz
);
lapack_int LAPACKE_dstedc
(
int
matrix_layout
,
char
compz
,
lapack_int
n
,
double*
d
,
double*
e
,
double*
z
,
lapack_int
ldz
);
lapack_int LAPACKE_cstedc
(
int
matrix_layout
,
char
compz
,
lapack_int
n
,
float*
d
,
float*
e
,
lapack_complex_float*
z
,
lapack_int
ldz
);
lapack_int LAPACKE_zstedc
(
int
matrix_layout
,
char
compz
,
lapack_int
n
,
double*
d
,
double*
e
,
lapack_complex_double*
z
,
lapack_int
ldz
);
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
The leading dimension of
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
.
See also
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.