LAPACK

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 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.

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.