Man page - lasv2(3)

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lasv2

NAME
SYNOPSIS
Functions
Detailed Description
Function Documentation
subroutine dlasv2 (double precision f, double precision g, double precisionh, double precision ssmin, double precision ssmax, double precisionsnr, double precision csr, double precision snl, double precision csl)
subroutine slasv2 (real f, real g, real h, real ssmin, real ssmax, realsnr, real csr, real snl, real csl)
Author

NAME

lasv2 - lasv2: 2x2 triangular SVD

SYNOPSIS

Functions

subroutine dlasv2 (f, g, h, ssmin, ssmax, snr, csr, snl, csl)
DLASV2 computes the singular value decomposition of a 2-by-2 triangular matrix.
subroutine slasv2 (f, g, h, ssmin, ssmax, snr, csr, snl, csl)
SLASV2 computes the singular value decomposition of a 2-by-2 triangular matrix.

Detailed Description

Function Documentation

subroutine dlasv2 (double precision f, double precision g, double precisionh, double precision ssmin, double precision ssmax, double precisionsnr, double precision csr, double precision snl, double precision csl)

DLASV2 computes the singular value decomposition of a 2-by-2 triangular matrix.

Purpose:

DLASV2 computes the singular value decomposition of a 2-by-2
triangular matrix
[ F G ]
[ 0 H ].
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

[ CSL SNL ] [ F G ] [ CSR -SNR ] = [ SSMAX 0 ]
[-SNL CSL ] [ 0 H ] [ SNR CSR ] [ 0 SSMIN ].

Parameters

F

F is DOUBLE PRECISION
The (1,1) element of the 2-by-2 matrix.

G

G is DOUBLE PRECISION
The (1,2) element of the 2-by-2 matrix.

H

H is DOUBLE PRECISION
The (2,2) element of the 2-by-2 matrix.

SSMIN

SSMIN is DOUBLE PRECISION
abs(SSMIN) is the smaller singular value.

SSMAX

SSMAX is DOUBLE PRECISION
abs(SSMAX) is the larger singular value.

SNL

SNL is DOUBLE PRECISION

CSL

CSL is DOUBLE PRECISION
The vector (CSL, SNL) is a unit left singular vector for the
singular value abs(SSMAX).

SNR

SNR is DOUBLE PRECISION

CSR

CSR is DOUBLE PRECISION
The vector (CSR, SNR) is a unit right singular vector for the
singular value abs(SSMAX).

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Further Details:

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.

Underflow is harmless if underflow is gradual. Otherwise, results
may correspond to a matrix modified by perturbations of size near
the underflow threshold.

subroutine slasv2 (real f, real g, real h, real ssmin, real ssmax, realsnr, real csr, real snl, real csl)

SLASV2 computes the singular value decomposition of a 2-by-2 triangular matrix.

Purpose:

SLASV2 computes the singular value decomposition of a 2-by-2
triangular matrix
[ F G ]
[ 0 H ].
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

[ CSL SNL ] [ F G ] [ CSR -SNR ] = [ SSMAX 0 ]
[-SNL CSL ] [ 0 H ] [ SNR CSR ] [ 0 SSMIN ].

Parameters

F

F is REAL
The (1,1) element of the 2-by-2 matrix.

G

G is REAL
The (1,2) element of the 2-by-2 matrix.

H

H is REAL
The (2,2) element of the 2-by-2 matrix.

SSMIN

SSMIN is REAL
abs(SSMIN) is the smaller singular value.

SSMAX

SSMAX is REAL
abs(SSMAX) is the larger singular value.

SNL

SNL is REAL

CSL

CSL is REAL
The vector (CSL, SNL) is a unit left singular vector for the
singular value abs(SSMAX).

SNR

SNR is REAL

CSR

CSR is REAL
The vector (CSR, SNR) is a unit right singular vector for the
singular value abs(SSMAX).

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Further Details:

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.

Underflow is harmless if underflow is gradual. Otherwise, results
may correspond to a matrix modified by perturbations of size near
the underflow threshold.

Author

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