source: branches/2789_MathNetNumerics-Exploration/HeuristicLab.Algorithms.DataAnalysis.Experimental/CubicSplineGCV.cs @ 16536

using System;
using System.Collections.Generic;
using System.Diagnostics;
using System.Linq;
using System.Runtime.InteropServices;
using System.Text;
using System.Threading.Tasks;
using HeuristicLab.Problems.DataAnalysis;

namespace HeuristicLab.Algorithms.DataAnalysis.Experimental {
  public static class CubicSplineGCV {
    // CUBGCV (X,F,DF,N,Y,C,IC,VAR,JOB,SE,WK,IER)
    //   ARGUMENTS    X      - VECTOR OF LENGTH N CONTAINING THE
    //                           ABSCISSAE OF THE N DATA POINTS
    //                           (X(I),F(I)) I=1..N. (INPUT) X
    //                           MUST BE ORDERED SO THAT
    //                           X(I) .LT. X(I+1).
    //                F      - VECTOR OF LENGTH N CONTAINING THE
    //                           ORDINATES (OR FUNCTION VALUES)
    //                           OF THE N DATA POINTS (INPUT).
    //                DF     - VECTOR OF LENGTH N. (INPUT/OUTPUT)
    //                           DF(I) IS THE RELATIVE STANDARD DEVIATION
    //                           OF THE ERROR ASSOCIATED WITH DATA POINT I.
    //                           EACH DF(I) MUST BE POSITIVE.  THE VALUES IN
    //                           DF ARE SCALED BY THE SUBROUTINE SO THAT
    //                           THEIR MEAN SQUARE VALUE IS 1, AND UNSCALED
    //                           AGAIN ON NORMAL EXIT.
    //                           THE MEAN SQUARE VALUE OF THE DF(I) IS RETURNED
    //                           IN WK(7) ON NORMAL EXIT.
    //                           IF THE ABSOLUTE STANDARD DEVIATIONS ARE KNOWN,
    //                           THESE SHOULD BE PROVIDED IN DF AND THE ERROR
    //                           VARIANCE PARAMETER VAR (SEE BELOW) SHOULD THEN
    //                           BE SET TO 1.
    //                           IF THE RELATIVE STANDARD DEVIATIONS ARE UNKNOWN,
    //                           SET EACH DF(I)=1.
    //                N      - NUMBER OF DATA POINTS (INPUT).
    //                           N MUST BE .GE. 3.
    //                Y,C    - SPLINE COEFFICIENTS. (OUTPUT) Y
    //                           IS A VECTOR OF LENGTH N. C IS
    //                           AN N-1 BY 3 MATRIX. THE VALUE
    //                           OF THE SPLINE APPROXIMATION AT T IS
    //                           S(T)=((C(I,3)*D+C(I,2))*D+C(I,1))*D+Y(I)
    //                           WHERE X(I).LE.T.LT.X(I+1) AND
    //                           D = T-X(I).
    //                IC     - ROW DIMENSION OF MATRIX C EXACTLY
    //                           AS SPECIFIED IN THE DIMENSION
    //                           STATEMENT IN THE CALLING PROGRAM. (INPUT)
    //                VAR    - ERROR VARIANCE. (INPUT/OUTPUT)
    //                           IF VAR IS NEGATIVE (I.E. UNKNOWN) THEN
    //                           THE SMOOTHING PARAMETER IS DETERMINED
    //                           BY MINIMIZING THE GENERALIZED CROSS VALIDATION
    //                           AND AN ESTIMATE OF THE ERROR VARIANCE IS
    //                           RETURNED IN VAR.
    //                           IF VAR IS NON-NEGATIVE (I.E. KNOWN) THEN THE
    //                           SMOOTHING PARAMETER IS DETERMINED TO MINIMIZE
    //                           AN ESTIMATE, WHICH DEPENDS ON VAR, OF THE TRUE
    //                           MEAN SQUARE ERROR, AND VAR IS UNCHANGED.
    //                           IN PARTICULAR, IF VAR IS ZERO, THEN AN
    //                           INTERPOLATING NATURAL CUBIC SPLINE IS CALCULATED.
    //                           VAR SHOULD BE SET TO 1 IF ABSOLUTE STANDARD
    //                           DEVIATIONS HAVE BEEN PROVIDED IN DF (SEE ABOVE).
    //                JOB    - JOB SELECTION PARAMETER. (INPUT)
    //                         JOB = 0 SHOULD BE SELECTED IF POINT STANDARD ERROR
    //                           ESTIMATES ARE NOT REQUIRED IN SE.
    //                         JOB = 1 SHOULD BE SELECTED IF POINT STANDARD ERROR
    //                           ESTIMATES ARE REQUIRED IN SE.
    //                SE     - VECTOR OF LENGTH N CONTAINING BAYESIAN STANDARD
    //                           ERROR ESTIMATES OF THE FITTED SPLINE VALUES IN Y.
    //                           SE IS NOT REFERENCED IF JOB=0. (OUTPUT)
    //                WK     - WORK VECTOR OF LENGTH 7*(N + 2). ON NORMAL EXIT THE
    //                           FIRST 7 VALUES OF WK ARE ASSIGNED AS FOLLOWS:-
    //
    //                           WK(1) = SMOOTHING PARAMETER (= RHO/(RHO + 1))
    //                           WK(2) = ESTIMATE OF THE NUMBER OF DEGREES OF
    //                                   FREEDOM OF THE RESIDUAL SUM OF SQUARES
    //                           WK(3) = GENERALIZED CROSS VALIDATION
    //                           WK(4) = MEAN SQUARE RESIDUAL
    //                           WK(5) = ESTIMATE OF THE TRUE MEAN SQUARE ERROR
    //                                   AT THE DATA POINTS
    //                           WK(6) = ESTIMATE OF THE ERROR VARIANCE
    //                           WK(7) = MEAN SQUARE VALUE OF THE DF(I)
    //
    //                           IF WK(1)=0 (RHO=0) AN INTERPOLATING NATURAL CUBIC
    //                           SPLINE HAS BEEN CALCULATED.
    //                           IF WK(1)=1 (RHO=INFINITE) A LEAST SQUARES
    //                           REGRESSION LINE HAS BEEN CALCULATED.
    //                           WK(2) IS AN ESTIMATE OF THE NUMBER OF DEGREES OF
    //                           FREEDOM OF THE RESIDUAL WHICH REDUCES TO THE
    //                           USUAL VALUE OF N-2 WHEN A LEAST SQUARES REGRESSION
    //                           LINE IS CALCULATED.
    //                           WK(3),WK(4),WK(5) ARE CALCULATED WITH THE DF(I)
    //                           SCALED TO HAVE MEAN SQUARE VALUE 1.  THE
    //                           UNSCALED VALUES OF WK(3),WK(4),WK(5) MAY BE
    //                           CALCULATED BY DIVIDING BY WK(7).
    //                           WK(6) COINCIDES WITH THE OUTPUT VALUE OF VAR IF
    //                           VAR IS NEGATIVE ON INPUT.  IT IS CALCULATED WITH
    //                           THE UNSCALED VALUES OF THE DF(I) TO FACILITATE
    //                           COMPARISONS WITH A PRIORI VARIANCE ESTIMATES.
    //
    //                IER    - ERROR PARAMETER. (OUTPUT)
    //                         TERMINAL ERROR
    //                           IER = 129, IC IS LESS THAN N-1.
    //                           IER = 130, N IS LESS THAN 3.
    //                           IER = 131, INPUT ABSCISSAE ARE NOT
    //                             ORDERED SO THAT X(I).LT.X(I+1).
    //                           IER = 132, DF(I) IS NOT POSITIVE FOR SOME I.
    //                           IER = 133, JOB IS NOT 0 OR 1.

    // To build the fortran library (x64) use:
    // > gfortran -m64 642.f -shared -o 642_x64.dll  or
    // > ifort /dll /Qm64 642.f /Fe642_x64.dll
    // check dumpbin /EXPORTS 642_x64.dll
    // and   dumpbin /IMPORTS 642_x64.dll
    [DllImport("642_x64.dll", CallingConvention = CallingConvention.Cdecl, EntryPoint = "cubgcv")]
    public static extern void cubgcv_x64(
      double[] x,
      double[] f,
      double[] df,
      ref int n,
      [Out] double[] y,
      [Out] double[,] c,
      ref int ic,
      ref double var,
      ref int job,
      [Out] double[] se,
      double[,] wk,
      ref int ier);

    // To build the fortran library (x86) use:
    // > gfortran -static -Lc:/mingw/bin/libgcc_s_dw2-1.dll -m32 642.f -shared -o 642_x86.dll
    [DllImport("642_x86.dll", CallingConvention = CallingConvention.Cdecl, EntryPoint = "cubgcv")]
    public static extern void cubgcv_x86(
      double[] x,
      double[] f,
      double[] df,
      ref Int32 n,
      double[] y,
      double[,] c,
      ref Int32 ic,
      ref double var,
      ref Int32 job,
      double[] se,
      double[,] wk,
      ref Int32 ier);


    public class CubGcvReport {
      //
      //   
      //
      //
      //   IF WK(1)=0 (RHO=0) AN INTERPOLATING NATURAL CUBIC
      //   SPLINE HAS BEEN CALCULATED.
      //   IF WK(1)=1 (RHO=INFINITE) A LEAST SQUARES
      //   REGRESSION LINE HAS BEEN CALCULATED.
      //
      public double smoothingParameter;
      //   WK(2) IS AN ESTIMATE OF THE NUMBER OF DEGREES OF
      //   FREEDOM OF THE RESIDUAL WHICH REDUCES TO THE
      //   USUAL VALUE OF N-2 WHEN A LEAST SQUARES REGRESSION
      //   LINE IS CALCULATED.
      public double estimatedRSSDegreesOfFreedom;
      //   WK(3),WK(4),WK(5) ARE CALCULATED WITH THE DF(I)
      //   SCALED TO HAVE MEAN SQUARE VALUE 1.  THE
      //   UNSCALED VALUES OF WK(3),WK(4),WK(5) MAY BE
      //   CALCULATED BY DIVIDING BY WK(7).
      public double generalizedCrossValidation;
      public double meanSquareResiudal;
      public double estimatedTrueMeanSquaredErrorAtDataPoints;

      //   WK(6) COINCIDES WITH THE OUTPUT VALUE OF VAR IF
      //   VAR IS NEGATIVE ON INPUT.  IT IS CALCULATED WITH
      //   THE UNSCALED VALUES OF THE DF(I) TO FACILITATE
      //   COMPARISONS WITH A PRIORI VARIANCE ESTIMATES.
      public double estimatedErrorVariance;
      public double meanSquareOfDf;
      public double[] se;
    }
    public static ReinschSmoothingSplineModel CalculateCubicSpline(double[] x, double[] y,
      string targetVariable, string[] inputVars, 
      out CubGcvReport report) {
      var w = Enumerable.Repeat(1.0, x.Length).ToArray();
      double[] x2, y2, w2;
      Splines.SortAndBin(x, y, w, out x2, out y2, out w2);
      // TODO: use weights correctly

      int n = x2.Length;
      double[] df = Enumerable.Repeat(1.0, n).ToArray();   // set each df if actual standard deviation of data points is not known
      double[,] c = new double[3, n - 1];
      double[] se = new double[n]; // standard errors in points
      double[,] wk = new double[7, (n + 2)]; // work array;
      double[] y_smoothed = new double[n];
      int job = 1; // calc estimates of standard errors in points
      int ic = n - 1;
      int ier = -99;
      double var = -99.0;
      if (Environment.Is64BitProcess) {
        CubicSplineGCV.cubgcv_x64(x2, y2, df, ref n, y_smoothed,
          c, ref ic, ref var, ref job, se, wk, ref ier);
      } else {
        CubicSplineGCV.cubgcv_x86(x2, y2, df, ref n, y_smoothed,
          c, ref ic, ref var, ref job, se, wk, ref ier);


      }

      /*
       *                  IER    - ERROR PARAMETER. (OUTPUT)
       *                           TERMINAL ERROR
       *                             IER = 129, IC IS LESS THAN N-1.
       *                             IER = 130, N IS LESS THAN 3.
       *                             IER = 131, INPUT ABSCISSAE ARE NOT
       *                               ORDERED SO THAT X(I).LT.X(I+1).
       *                             IER = 132, DF(I) IS NOT POSITIVE FOR SOME I.
       *                             IER = 133, JOB IS NOT 0 OR 1.
       *
       */

      if (ier == 131) {
        throw new ArgumentException("x is not ordered");
      } else if (ier != 0) throw new ArgumentException("Error in CUBGCV " + ier);

      //                           OF THE SPLINE APPROXIMATION AT T IS
      //                           S(T)=((C(I,3)*D+C(I,2))*D+C(I,1))*D+Y(I)
      //                           WHERE X(I).LE.T.LT.X(I+1) AND
      //                           D = T-X(I).

      //                           WK(1) = SMOOTHING PARAMETER (= RHO/(RHO + 1))
      //                           WK(2) = ESTIMATE OF THE NUMBER OF DEGREES OF
      //                                   FREEDOM OF THE RESIDUAL SUM OF SQUARES
      //                           WK(3) = GENERALIZED CROSS VALIDATION
      //                           WK(4) = MEAN SQUARE RESIDUAL
      //                           WK(5) = ESTIMATE OF THE TRUE MEAN SQUARE ERROR
      //                                   AT THE DATA POINTS
      //                           WK(6) = ESTIMATE OF THE ERROR VARIANCE
      //                           WK(7) = MEAN SQUARE VALUE OF THE DF(I)
      report = new CubGcvReport();
      report.smoothingParameter = wk[0, 0];
      report.estimatedRSSDegreesOfFreedom = wk[0, 1];
      report.generalizedCrossValidation = wk[0, 2];
      report.meanSquareResiudal = wk[0, 3];
      report.estimatedTrueMeanSquaredErrorAtDataPoints = wk[0, 4];
      report.estimatedErrorVariance = wk[0, 5];
      report.meanSquareOfDf = wk[0, 6];
      report.se = se;
      // Debug.Assert(var == report.estimatedErrorVariance);



      double[] dArr = new double[n];
      double[] cArr = new double[n];
      double[] bArr = new double[n];

      for (int i = 0; i < n - 1; i++) {
        bArr[i] = c[0, i];
        cArr[i] = c[1, i];
        dArr[i] = c[2, i];
      }

      // extrapolate linearly for xx > x[n]
      bArr[n - 1] = bArr[n - 2];
      // extrapolate linearly for xx < x[1]
      dArr[0] = 0;

      return new ReinschSmoothingSplineModel(
        new MyArray<double>(1, y_smoothed),
        new MyArray<double>(1, bArr),
        new MyArray<double>(1, cArr),
        new MyArray<double>(1, dArr),
        new MyArray<double>(1, x2),
        targetVariable, inputVars);


    }

  }
}