slasv2.f man page

slasv2.f

Synopsis

Functions/Subroutines

subroutine slasv2 (F, G, H, SSMIN, SSMAX, SNR, CSR, SNL, CSL)
SLASV2 computes the singular value decomposition of a 2-by-2 triangular matrix.

Function/Subroutine Documentation

subroutine slasv2 (real F, real G, real H, real SSMIN, real SSMAX, real SNR, 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.

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 slasv2.f.

Author

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Referenced By

The man page slasv2(3) is an alias of slasv2.f(3).

Tue Nov 14 2017 Version 3.8.0 LAPACK