NAME

       las2 - las2: 2x2 triangular SVD

SYNOPSIS

   Functions
       subroutine dlas2 (f, g, h, ssmin, ssmax)
           DLAS2 computes singular values of a 2-by-2 triangular matrix.
       subroutine slas2 (f, g, h, ssmin, ssmax)
           SLAS2 computes singular values of a 2-by-2 triangular matrix.

Detailed Description

Function Documentation

   subroutine dlas2 (double precision f, double precision g, double precision h, double precision
       ssmin, double precision ssmax)
       DLAS2 computes singular values of a 2-by-2 triangular matrix.

       Purpose:

            DLAS2  computes the singular values of the 2-by-2 matrix
               [  F   G  ]
               [  0   H  ].
            On return, SSMIN is the smaller singular value and SSMAX is the
            larger singular value.

       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
                     The smaller singular value.

           SSMAX

                     SSMAX is DOUBLE PRECISION
                     The larger singular value.

       Author
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       Further Details:

             Barring over/underflow, all output quantities are correct to within
             a few units in the last place (ulps), even in the absence of a guard
             digit in addition/subtraction.

             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 slas2 (real f, real g, real h, real ssmin, real ssmax)
       SLAS2 computes singular values of a 2-by-2 triangular matrix.

       Purpose:

            SLAS2  computes the singular values of the 2-by-2 matrix
               [  F   G  ]
               [  0   H  ].
            On return, SSMIN is the smaller singular value and SSMAX is the
            larger singular value.

       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
                     The smaller singular value.

           SSMAX

                     SSMAX is REAL
                     The larger singular value.

       Author
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       Further Details:

             Barring over/underflow, all output quantities are correct to within
             a few units in the last place (ulps), even in the absence of a guard
             digit in addition/subtraction.

             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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