Developer Reference

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

?lasv2

Computes the singular value decomposition of a 2-by-2 triangular matrix.

Syntax

call slasv2
(
f
,
g
,
h
,
ssmin
,
ssmax
,
snr
,
csr
,
snl
,
csl
)
call dlasv2
(
f
,
g
,
h
,
ssmin
,
ssmax
,
snr
,
csr
,
snl
,
csl
)
Include Files
  • mkl.fi
Description
The routine
?lasv2
computes the singular value decomposition of a 2-by-2 triangular matrix
Equation
On return, abs(
ssmax
) is the larger singular value, abs(
ssmin
) is the smaller singular value, and (
csl
,
snl
) and (
csr
,
snr
) are the left and right singular vectors for abs(
ssmax)
, giving the decomposition
Equation
Input Parameters
f
,
g
,
h
REAL
for
slasv2
DOUBLE PRECISION
for
dlasv2
.
The (1,1), (1,2) and (2,2) elements of the 2-by-2 matrix, respectively.
Output Parameters
ssmin
,
ssmax
REAL
for
slasv2
DOUBLE PRECISION
for
dlasv2
.
abs(
ssmin
) and abs(
ssmax
) is the smaller and the larger singular value, respectively.
snl
,
csl
REAL
for
slasv2
DOUBLE PRECISION
for
dlasv2
.
The vector (
csl
,
snl
) is a unit left singular vector for the singular value abs(
ssmax
).
snr
,
csr
REAL
for
slasv2
DOUBLE PRECISION
for
dlasv2
.
The vector (
csr
,
snr
) is a unit right singular vector for the singular value abs(
ssmax
).
Application Notes
Any input parameter may be aliased with any output parameter.
Barring over/underflow and assuming a guard digit in subtraction, all output quantities are correct to within a few units in the last place (ulps).
In ieee arithmetic, the code works correctly if one matrix element is infinite. Overflow will not occur unless the largest singular value itself overflows or is within a few ulps of overflow. (On machines with partial overflow, like the Cray, overflow may occur if the largest singular value is within a factor of 2 of overflow.) Underflow is harmless if underflow is gradual. Otherwise, results may correspond to a matrix modified by perturbations of size near the underflow threshold.

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