spline3.h

/*************************************************************************
Copyright (c) 2007, Sergey Bochkanov (ALGLIB project).

Redistribution and use in source and binary forms, with or without
modification, are permitted provided that the following conditions are
met:

- Redistributions of source code must retain the above copyright
  notice, this list of conditions and the following disclaimer.

- Redistributions in binary form must reproduce the above copyright
  notice, this list of conditions and the following disclaimer listed
  in this license in the documentation and/or other materials
  provided with the distribution.

- Neither the name of the copyright holders nor the names of its
  contributors may be used to endorse or promote products derived from
  this software without specific prior written permission.

THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
"AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
*************************************************************************/

#ifndef _spline3_h
#define _spline3_h

#include "ap.h"

/*************************************************************************
This subroutine builds linear spline coefficients table.

Input parameters:
    X   -   spline nodes, array[0..N-1]
    Y   -   function values, array[0..N-1]
    N   -   points count, N>=2
    
Output parameters:
    C   -   coefficients table.  Used  by  SplineInterpolation  and  other
            subroutines from this file.

  -- ALGLIB PROJECT --
     Copyright 24.06.2007 by Bochkanov Sergey
*************************************************************************/
void buildlinearspline(ap::real_1d_array x,
     ap::real_1d_array y,
     int n,
     ap::real_1d_array& c);


/*************************************************************************
This subroutine builds cubic spline coefficients table.

Input parameters:
    X           -   spline nodes, array[0..N-1]
    Y           -   function values, array[0..N-1]
    N           -   points count, N>=2
    BoundLType  -   boundary condition type for the left boundary
    BoundL      -   left boundary condition (first or second derivative,
                    depending on the BoundLType)
    BoundRType  -   boundary condition type for the right boundary
    BoundR      -   right boundary condition (first or second derivative,
                    depending on the BoundRType)

Output parameters:
    C           -   coefficients table.  Used  by  SplineInterpolation and
                    other subroutines from this file.
                    
The BoundLType/BoundRType parameters can have the following values:
    * 0,   which  corresponds  to  the  parabolically   terminated  spline
      (BoundL/BoundR are ignored).
    * 1, which corresponds to the first derivative boundary condition
    * 2, which corresponds to the second derivative boundary condition

  -- ALGLIB PROJECT --
     Copyright 23.06.2007 by Bochkanov Sergey
*************************************************************************/
void buildcubicspline(ap::real_1d_array x,
     ap::real_1d_array y,
     int n,
     int boundltype,
     double boundl,
     int boundrtype,
     double boundr,
     ap::real_1d_array& c);


/*************************************************************************
This subroutine builds cubic Hermite spline coefficients table.

Input parameters:
    X           -   spline nodes, array[0..N-1]
    Y           -   function values, array[0..N-1]
    D           -   derivatives, array[0..N-1]
    N           -   points count, N>=2

Output parameters:
    C           -   coefficients table.  Used  by  SplineInterpolation and
                    other subroutines from this file.

  -- ALGLIB PROJECT --
     Copyright 23.06.2007 by Bochkanov Sergey
*************************************************************************/
void buildhermitespline(ap::real_1d_array x,
     ap::real_1d_array y,
     ap::real_1d_array d,
     int n,
     ap::real_1d_array& c);


/*************************************************************************
This subroutine builds Akima spline coefficients table.

Input parameters:
    X           -   spline nodes, array[0..N-1]
    Y           -   function values, array[0..N-1]
    N           -   points count, N>=5

Output parameters:
    C           -   coefficients table.  Used  by  SplineInterpolation and
                    other subroutines from this file.

  -- ALGLIB PROJECT --
     Copyright 24.06.2007 by Bochkanov Sergey
*************************************************************************/
void buildakimaspline(ap::real_1d_array x,
     ap::real_1d_array y,
     int n,
     ap::real_1d_array& c);


/*************************************************************************
This subroutine calculates the value of the spline at the given point X.

Input parameters:
    C           -   coefficients table. Built by BuildLinearSpline,
                    BuildHermiteSpline, BuildCubicSpline, BuildAkimaSpline.
    X           -   point

Result:
    S(x)

  -- ALGLIB PROJECT --
     Copyright 23.06.2007 by Bochkanov Sergey
*************************************************************************/
double splineinterpolation(const ap::real_1d_array& c, double x);


/*************************************************************************
This subroutine differentiates the spline.

Input parameters:
    C   -   coefficients table. Built by BuildLinearSpline,
            BuildHermiteSpline, BuildCubicSpline, BuildAkimaSpline.
    X   -   point

Result:
    S   -   S(x)
    DS  -   S'(x)
    D2S -   S''(x)

  -- ALGLIB PROJECT --
     Copyright 24.06.2007 by Bochkanov Sergey
*************************************************************************/
void splinedifferentiation(const ap::real_1d_array& c,
     double x,
     double& s,
     double& ds,
     double& d2s);


/*************************************************************************
This subroutine makes the copy of the spline.

Input parameters:
    C   -   coefficients table. Built by BuildLinearSpline,
            BuildHermiteSpline, BuildCubicSpline, BuildAkimaSpline.

Result:
    CC  -   spline copy

  -- ALGLIB PROJECT --
     Copyright 29.06.2007 by Bochkanov Sergey
*************************************************************************/
void splinecopy(const ap::real_1d_array& c, ap::real_1d_array& cc);


/*************************************************************************
This subroutine unpacks the spline into the coefficients table.

Input parameters:
    C   -   coefficients table. Built by BuildLinearSpline,
            BuildHermiteSpline, BuildCubicSpline, BuildAkimaSpline.
    X   -   point

Result:
    Tbl -   coefficients table, unpacked format, array[0..N-2, 0..5].
            For I = 0...N-2:
                Tbl[I,0] = X[i]
                Tbl[I,1] = X[i+1]
                Tbl[I,2] = C0
                Tbl[I,3] = C1
                Tbl[I,4] = C2
                Tbl[I,5] = C3
            On [x[i], x[i+1]] spline is equals to:
                S(x) = C0 + C1*t + C2*t^2 + C3*t^3
                t = x-x[i]

  -- ALGLIB PROJECT --
     Copyright 29.06.2007 by Bochkanov Sergey
*************************************************************************/
void splineunpack(const ap::real_1d_array& c, int& n, ap::real_2d_array& tbl);


/*************************************************************************
This subroutine performs linear transformation of the spline argument.

Input parameters:
    C   -   coefficients table. Built by BuildLinearSpline,
            BuildHermiteSpline, BuildCubicSpline, BuildAkimaSpline.
    A, B-   transformation coefficients: x = A*t + B
Result:
    C   -   transformed spline

  -- ALGLIB PROJECT --
     Copyright 30.06.2007 by Bochkanov Sergey
*************************************************************************/
void splinelintransx(ap::real_1d_array& c, double a, double b);


/*************************************************************************
This subroutine performs linear transformation of the spline.

Input parameters:
    C   -   coefficients table. Built by BuildLinearSpline,
            BuildHermiteSpline, BuildCubicSpline, BuildAkimaSpline.
    A, B-   transformation coefficients: S2(x) = A*S(x) + B
Result:
    C   -   transformed spline

  -- ALGLIB PROJECT --
     Copyright 30.06.2007 by Bochkanov Sergey
*************************************************************************/
void splinelintransy(ap::real_1d_array& c, double a, double b);


/*************************************************************************
This subroutine integrates the spline.

Input parameters:
    C   -   coefficients table. Built by BuildLinearSpline,
            BuildHermiteSpline, BuildCubicSpline, BuildAkimaSpline.
    X   -   right bound of the integration interval [a, x]
Result:
    integral(S(t)dt,a,x)

  -- ALGLIB PROJECT --
     Copyright 23.06.2007 by Bochkanov Sergey
*************************************************************************/
double splineintegration(const ap::real_1d_array& c, double x);


/*************************************************************************
Obsolete subroutine, left for backward compatibility.
*************************************************************************/
void spline3buildtable(int n,
     const int& diffn,
     ap::real_1d_array x,
     ap::real_1d_array y,
     const double& boundl,
     const double& boundr,
     ap::real_2d_array& ctbl);


/*************************************************************************
Obsolete subroutine, left for backward compatibility.
*************************************************************************/
double spline3interpolate(int n, const ap::real_2d_array& c, const double& x);


#endif