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dlasv2 examples
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Man Page Details
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NAME
       DLASV2 - the singular value decomposition of a 2-by-2 triangular matrix
       [ F G ]  [ 0 H ]

SYNOPSIS
       SUBROUTINE DLASV2( F, G, H, SSMIN, SSMAX, SNR, CSR, SNL, CSL )

           DOUBLE         PRECISION CSL, CSR, F, G, H, SNL, SNR, SSMAX, SSMIN

  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 ].

  Arguments
  =========

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

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

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

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

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

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

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

  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.

