lasv2(3)

NAME
lasv2 - lasv2: 2x2 triangular SVD

SYNOPSIS

  Functions
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

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

    G

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

    H

    !>          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.

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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