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Annotation of OpenXM_contrib/PHC/Ada/Schubert/osculating_planes.ads, Revision 1.1

1.1     ! maekawa     1: with Standard_Floating_Numbers;          use Standard_Floating_Numbers;
        !             2: with Standard_Floating_Matrices;         use Standard_Floating_Matrices;
        !             3:
        !             4: package Osculating_Planes is
        !             5:
        !             6: -- DESCRIPTION :
        !             7: --   This package provides routines for generating osculating planes.
        !             8:
        !             9:   function Standard_Basis ( n,d : natural; s : double_float ) return Matrix;
        !            10:
        !            11:   -- DESCRIPTION :
        !            12:   --   Returns a d-plane in n-space using the standard monomial basis.
        !            13:   --   The first column contains the first n standard monomials.
        !            14:   --   The kth column contains the kth derivative, scaled such that the
        !            15:   --   diagonal elements are all one.  All polynomials are evaluated at s.
        !            16:
        !            17:   function Chebychev_Basis ( n,d : natural; s : double_float ) return Matrix;
        !            18:
        !            19:   -- DESCRIPTION :
        !            20:   --   Returns a d-plane in n-space using the Chebychev polynomials.
        !            21:   --   The first column contains the first n Chebychev polynomials.
        !            22:   --   The kth column contains the kth derivative, scaled such that the
        !            23:   --   diagonal elements are all one.  All polynomials are evaluated at s.
        !            24:
        !            25:   function Orthogonal_Basis ( n,d : natural; s : double_float ) return Matrix;
        !            26:
        !            27:   -- DESCRIPTION :
        !            28:   --   Returns a d-plane in n-space as an orthognal matrix.
        !            29:
        !            30:   procedure Sampled_Chebychev_Basis
        !            31:                                ( n,d,m : in natural; mat : out Matrix;
        !            32:                   s,ratio : out double_float );
        !            33:
        !            34:   -- DESCRIPTION :
        !            35:   --   Generates m values for s and keeps the one with lowest ratio
        !            36:   --   max/min for all d-minors in the matrix.
        !            37:
        !            38: end Osculating_Planes;