dlasv2.f man page

dlasv2.f —

Synopsis

Functions/Subroutines

subroutine dlasv2 (F, G, H, SSMIN, SSMAX, SNR, CSR, SNL, CSL)
DLASV2 computes the singular value decomposition of a 2-by-2 triangular matrix.

Function/Subroutine Documentation

subroutine dlasv2 (double precisionF, double precisionG, double precisionH, double precisionSSMIN, double precisionSSMAX, double precisionSNR, double precisionCSR, double precisionSNL, double precisionCSL)

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.

Date:

September 2012

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. (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.

Definition at line 139 of file dlasv2.f.

Author

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Referenced By

dlasv2(3) is an alias of dlasv2.f(3).

Sat Nov 16 2013 Version 3.4.2 LAPACK