Developer Reference

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

?lanv2

Computes the Schur factorization of a real 2-by-2 nonsymmetric matrix in standard form.

Syntax

call slanv2
(
a
,
b
,
c
,
d
,
rt1r
,
rt1i
,
rt2r
,
rt2i
,
cs
,
sn
)
call dlanv2
(
a
,
b
,
c
,
d
,
rt1r
,
rt1i
,
rt2r
,
rt2i
,
cs
,
sn
)
Include Files
  • mkl.fi
Description
The routine computes the Schur factorization of a real 2-by-2 nonsymmetric matrix in standard form:
Equation
where either
  1. cc
    = 0
    so that
    aa
    and
    dd
    are real eigenvalues of the matrix, or
  2. aa
    =
    dd
    and
    bb
    *
    cc
    < 0
    , so that
    aa
    ±
    sqrt(
    bb
    *
    cc
    )
    are complex conjugate eigenvalues.
The routine was adjusted to reduce the risk of cancellation errors, when computing real eigenvalues, and to ensure, if possible, that
abs(
rt1r
)
abs(
rt2r
)
.
Input Parameters
a
,
b
,
c
,
d
REAL
for
slanv2
DOUBLE PRECISION
for
dlanv2
.
On entry, elements of the input matrix.
Output Parameters
a
,
b
,
c
,
d
On exit, overwritten by the elements of the standardized Schur form.
rt1r
,
rt1i
,
rt2r
,
rt2i
REAL
for
slanv2
DOUBLE PRECISION
for
dlanv2
.
The real and imaginary parts of the eigenvalues.
If the eigenvalues are a complex conjugate pair,
rt1i
> 0
.
cs
,
sn
REAL
for
slanv2
DOUBLE PRECISION
for
dlanv2
.
Parameters of the rotation matrix.

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