SRC/slasv2.f(3)

NAME
SRC/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 (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.

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.

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 slasv2.f.

Author

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