Developer Reference

  • 2020.2
  • 07/15/2020
  • Public Content
Contents

?laesy

Computes the eigenvalues and eigenvectors of a 2-by-2 complex symmetric matrix, and checks that the norm of the matrix of eigenvectors is larger than a threshold value.

Syntax

call claesy
(
a
,
b
,
c
,
rt1
,
rt2
,
evscal
,
cs1
,
sn1
)
call zlaesy
(
a
,
b
,
c
,
rt1
,
rt2
,
evscal
,
cs1
,
sn1
)
Include Files
  • mkl.fi
Description
The routine performs the eigendecomposition of a 2-by-2 symmetric matrix
Equation
provided the norm of the matrix of eigenvectors is larger than some threshold value.
rt1
is the eigenvalue of larger absolute value, and
rt2
of smaller absolute value. If the eigenvectors are computed, then on return (
cs1
,
sn1
) is the unit eigenvector for
rt1
, hence
Equation
Input Parameters
a
,
b
,
c
COMPLEX
for
claesy
DOUBLE COMPLEX
for
zlaesy
Elements of the input matrix.
Output Parameters
rt1
,
rt2
COMPLEX
for
claesy
DOUBLE COMPLEX
for
zlaesy
Eigenvalues of larger and smaller modulus, respectively.
evscal
COMPLEX
for
claesy
DOUBLE COMPLEX
for
zlaesy
The complex value by which the eigenvector matrix was scaled to make it orthonormal. If
evscal
is zero, the eigenvectors were not computed. This means one of two things: the 2-by-2 matrix could not be diagonalized, or the norm of the matrix of eigenvectors before scaling was larger than the threshold value
thresh
(set to 0.1E0).
cs1
,
sn1
COMPLEX
for
claesy
DOUBLE COMPLEX
for
zlaesy
If
evscal
is not zero, then (
cs1
,
sn1
) is the unit right eigenvector for
rt1
.

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