dlasv2.f

Section: LAPACK (3)
Updated: Tue Nov 14 2017
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NAME

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 precision F, double precision G, double precision H, double precision SSMIN, double precision SSMAX, double precision SNR, 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 is DOUBLE PRECISION
          The (1,1) element of the 2-by-2 matrix.

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

          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:

: December 2016

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 140 of file dlasv2.f.

Author

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