NAME

       lanv2 - lanv2: 2x2 Schur factor

SYNOPSIS

   Functions
       subroutine dlanv2 (a, b, c, d, rt1r, rt1i, rt2r, rt2i, cs, sn)
           DLANV2 computes the Schur factorization of a real 2-by-2 nonsymmetric matrix in
           standard form.
       subroutine slanv2 (a, b, c, d, rt1r, rt1i, rt2r, rt2i, cs, sn)
           SLANV2 computes the Schur factorization of a real 2-by-2 nonsymmetric matrix in
           standard form.

Detailed Description

Function Documentation

   subroutine dlanv2 (double precision a, double precision b, double precision c, double
       precision d, double precision rt1r, double precision rt1i, double precision rt2r, double
       precision rt2i, double precision cs, double precision sn)
       DLANV2 computes the Schur factorization of a real 2-by-2 nonsymmetric matrix in standard
       form.

       Purpose:

            DLANV2 computes the Schur factorization of a real 2-by-2 nonsymmetric
            matrix in standard form:

                 [ A  B ] = [ CS -SN ] [ AA  BB ] [ CS  SN ]
                 [ C  D ]   [ SN  CS ] [ CC  DD ] [-SN  CS ]

            where either
            1) CC = 0 so that AA and DD are real eigenvalues of the matrix, or
            2) AA = DD and BB*CC < 0, so that AA + or - sqrt(BB*CC) are complex
            conjugate eigenvalues.

       Parameters
           A

                     A is DOUBLE PRECISION

           B

                     B is DOUBLE PRECISION

           C

                     C is DOUBLE PRECISION

           D

                     D is DOUBLE PRECISION
                     On entry, the elements of the input matrix.
                     On exit, they are overwritten by the elements of the
                     standardised Schur form.

           RT1R

                     RT1R is DOUBLE PRECISION

           RT1I

                     RT1I is DOUBLE PRECISION

           RT2R

                     RT2R is DOUBLE PRECISION

           RT2I

                     RT2I is DOUBLE PRECISION
                     The real and imaginary parts of the eigenvalues. If the
                     eigenvalues are a complex conjugate pair, RT1I > 0.

           CS

                     CS is DOUBLE PRECISION

           SN

                     SN is DOUBLE PRECISION
                     Parameters of the rotation matrix.

       Author
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       Further Details:

             Modified by V. Sima, Research Institute for Informatics, Bucharest,
             Romania, to reduce the risk of cancellation errors,
             when computing real eigenvalues, and to ensure, if possible, that
             abs(RT1R) >= abs(RT2R).

   subroutine slanv2 (real a, real b, real c, real d, real rt1r, real rt1i, real rt2r, real rt2i,
       real cs, real sn)
       SLANV2 computes the Schur factorization of a real 2-by-2 nonsymmetric matrix in standard
       form.

       Purpose:

            SLANV2 computes the Schur factorization of a real 2-by-2 nonsymmetric
            matrix in standard form:

                 [ A  B ] = [ CS -SN ] [ AA  BB ] [ CS  SN ]
                 [ C  D ]   [ SN  CS ] [ CC  DD ] [-SN  CS ]

            where either
            1) CC = 0 so that AA and DD are real eigenvalues of the matrix, or
            2) AA = DD and BB*CC < 0, so that AA + or - sqrt(BB*CC) are complex
            conjugate eigenvalues.

       Parameters
           A

                     A is REAL

           B

                     B is REAL

           C

                     C is REAL

           D

                     D is REAL
                     On entry, the elements of the input matrix.
                     On exit, they are overwritten by the elements of the
                     standardised Schur form.

           RT1R

                     RT1R is REAL

           RT1I

                     RT1I is REAL

           RT2R

                     RT2R is REAL

           RT2I

                     RT2I is REAL
                     The real and imaginary parts of the eigenvalues. If the
                     eigenvalues are a complex conjugate pair, RT1I > 0.

           CS

                     CS is REAL

           SN

                     SN is REAL
                     Parameters of the rotation matrix.

       Author
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       Further Details:

             Modified by V. Sima, Research Institute for Informatics, Bucharest,
             Romania, to reduce the risk of cancellation errors,
             when computing real eigenvalues, and to ensure, if possible, that
             abs(RT1R) >= abs(RT2R).

Author

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