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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