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lasv2 - Man Page

lasv2: 2x2 triangular SVD

subroutine dlasv2 (f, g, h, ssmin, ssmax, snr, csr, snl, csl)
DLASV2 computes the singular value decomposition of a 2-by-2 triangular matrix.
subroutine slasv2 (f, g, h, ssmin, ssmax, snr, csr, snl, csl)
SLASV2 computes the singular value decomposition of a 2-by-2 triangular matrix.

Detailed Description

Function 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.

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.

  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 135 of file dlasv2.f.

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.