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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