DLASV2 (3lapack)

compute 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.