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.

   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.

Author

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