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slasv2.f(3) LAPACK slasv2.f(3)

NAME

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 (realF, realG, realH, realSSMIN, realSSMAX, realSNR, realCSR, realSNL, realCSL)

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:
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 slasv2.f.

Author

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Wed Oct 15 2014 Version 3.4.2