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Commit 9d3636f4 authored by peastman's avatar peastman
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Added 3D spline functions to SplineFitter

parent 9434c6e8
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Showing with 450 additions and 6 deletions
openmmapi/include/openmm/internal/SplineFitter.h
View file @ 9d3636f4
......@@ -9,7 +9,7 @@
* Biological Structures at Stanford, funded under the NIH Roadmap for *
* Medical Research, grant U54 GM072970. See https://simtk.org. *
* *
* Portions copyright (c) 2010 Stanford University and the Authors. *
* Portions copyright (c) 2010-2014 Stanford University and the Authors. *
* Authors: Peter Eastman *
* Contributors: *
* *
......@@ -124,6 +124,52 @@ public:
* @param dy on exit, the y derivative of the spline at the specified point
*/
static void evaluate2DSplineDerivatives(const std::vector<double>& x, const std::vector<double>& y, const std::vector<double>& values, const std::vector<std::vector<double> >& c, double u, double v, double& dx, double& dy);
/**
* Fit a natural cubic spline surface f(x,y,z) to a 3D set of data points. The resulting spline interpolates all the
* data points, has a continuous second derivative everywhere, and has a second derivative of 0 at the boundary.
*
* @param x the values of the first independent variable at the data points to interpolate. They must
* be strictly increasing: x[i] > x[i-1].
* @param y the values of the second independent variable at the data points to interpolate. They must
* be strictly increasing: y[i] > y[i-1].
* @param z the values of the third independent variable at the data points to interpolate. They must
* be strictly increasing: z[i] > z[i-1].
* @param values the values of the dependent variable at the data points to interpolate. They must be ordered
* so that values[i+xsize*j+xsize*ysize*k] = f(x[i],y[j],z[k]), where xsize is the length of x
* and ysize is the length of y.
* @param c on exit, this contains the spline coefficients at each of the data points
*/
static void create3DNaturalSpline(const std::vector<double>& x, const std::vector<double>& y, const std::vector<double>& z, const std::vector<double>& values, std::vector<std::vector<double> >& c);
/**
* Evaluate a 3D spline generated by one of the other methods in this class.
*
* @param x the values of the first independent variable at the data points to interpolate
* @param y the values of the second independent variable at the data points to interpolate
* @param z the values of the third independent variable at the data points to interpolate
* @param values the values of the dependent variable at the data points to interpolate
* @param c the vector of spline coefficients that was calculated by one of the other methods
* @param u the value of the first independent variable at which to evaluate the spline
* @param v the value of the second independent variable at which to evaluate the spline
* @param w the value of the third independent variable at which to evaluate the spline
* @return the value of the spline at the specified point
*/
static double evaluate3DSpline(const std::vector<double>& x, const std::vector<double>& y, const std::vector<double>& z, const std::vector<double>& values, const std::vector<std::vector<double> >& c, double u, double v, double w);
/**
* Evaluate the derivatives of a 3D spline generated by one of the other methods in this class.
*
* @param x the values of the first independent variable at the data points to interpolate
* @param y the values of the second independent variable at the data points to interpolate
* @param z the values of the third independent variable at the data points to interpolate
* @param values the values of the dependent variable at the data points to interpolate
* @param c the vector of spline coefficients that was calculated by one of the other methods
* @param u the value of the first independent variable at which to evaluate the spline
* @param v the value of the second independent variable at which to evaluate the spline
* @param w the value of the third independent variable at which to evaluate the spline
* @param dx on exit, the x derivative of the spline at the specified point
* @param dy on exit, the y derivative of the spline at the specified point
* @param dz on exit, the z derivative of the spline at the specified point
*/
static void evaluate3DSplineDerivatives(const std::vector<double>& x, const std::vector<double>& y, const std::vector<double>& z, const std::vector<double>& values, const std::vector<std::vector<double> >& c, double u, double v, double w, double& dx, double& dy, double &dz);
private:
static void solveTridiagonalMatrix(const std::vector<double>& a, const std::vector<double>& b, const std::vector<double>& c, const std::vector<double>& rhs, std::vector<double>& sol);
};
......
openmmapi/src/SplineFitter.cpp
View file @ 9d3636f4
......@@ -6,7 +6,7 @@
* Biological Structures at Stanford, funded under the NIH Roadmap for *
* Medical Research, grant U54 GM072970. See https://simtk.org. *
* *
* Portions copyright (c) 2010 Stanford University and the Authors. *
* Portions copyright (c) 2010-2014 Stanford University and the Authors. *
* Authors: Peter Eastman *
* Contributors: *
* *
......@@ -319,7 +319,7 @@ double SplineFitter::evaluate2DSpline(const vector<double>& x, const vector<doub
double db = (v-y[lowery])/deltay;
const vector<double>& coeff = c[lowerx+(xsize-1)*lowery];
// Evaluate the spline to determine the value and gradients.
// Evaluate the spline to determine the value.
double value = 0;
for (int i = 3; i >= 0; i--)
......@@ -359,7 +359,7 @@ void SplineFitter::evaluate2DSplineDerivatives(const vector<double>& x, const ve
double db = (v-y[lowery])/deltay;
const vector<double>& coeff = c[lowerx+(xsize-1)*lowery];
// Evaluate the spline to determine the value and gradients.
// Evaluate the spline to determine the derivatives.
dx = 0;
dy = 0;
......@@ -370,3 +370,355 @@ void SplineFitter::evaluate2DSplineDerivatives(const vector<double>& x, const ve
dx /= deltax;
dy /= deltay;
}
void SplineFitter::create3DNaturalSpline(const vector<double>& x, const vector<double>& y, const vector<double>& z, const vector<double>& values, vector<vector<double> >& c) {
int xsize = x.size(), ysize = y.size(), zsize = z.size();
int xysize = xsize*ysize;
if (xsize < 2 || ysize < 2 || zsize < 2)
throw OpenMMException("create2DNaturalSpline: must have at least two points along each axis");
if (values.size() != xsize*ysize*zsize)
throw OpenMMException("create2DNaturalSpline: incorrect number of values");
vector<double> d1(xsize*ysize*zsize), d2(xsize*ysize*zsize), d3(xsize*ysize*zsize);
vector<double> d12(xsize*ysize*zsize), d13(xsize*ysize*zsize), d23(xsize*ysize*zsize), d123(xsize*ysize*zsize);
vector<double> t(xsize), deriv(xsize);
// Compute derivatives with respect to x.
for (int i = 0; i < ysize; i++) {
for (int j = 0; j < zsize; j++) {
for (int k = 0; k < xsize; k++)
t[k] = values[k+xsize*i+xysize*j];
SplineFitter::createNaturalSpline(x, t, deriv);
for (int k = 0; k < xsize; k++)
d1[k+xsize*i+xysize*j] = SplineFitter::evaluateSplineDerivative(x, t, deriv, x[k]);
}
}
// Compute derivatives with respect to y.
t.resize(ysize);
deriv.resize(ysize);
for (int i = 0; i < xsize; i++) {
for (int j = 0; j < zsize; j++) {
for (int k = 0; k < ysize; k++)
t[k] = values[i+xsize*k+xysize*j];
SplineFitter::createNaturalSpline(y, t, deriv);
for (int k = 0; k < ysize; k++)
d2[i+xsize*k+xysize*j] = SplineFitter::evaluateSplineDerivative(y, t, deriv, y[k]);
}
}
// Compute derivatives with respect to z.
t.resize(zsize);
deriv.resize(zsize);
for (int i = 0; i < xsize; i++) {
for (int j = 0; j < ysize; j++) {
for (int k = 0; k < zsize; k++)
t[k] = values[i+xsize*j+xysize*k];
SplineFitter::createNaturalSpline(z, t, deriv);
for (int k = 0; k < zsize; k++)
d3[i+xsize*j+xysize*k] = SplineFitter::evaluateSplineDerivative(z, t, deriv, z[k]);
}
}
// Compute second derivatives with respect to x and y.
t.resize(xsize);
deriv.resize(xsize);
for (int i = 0; i < ysize; i++) {
for (int j = 0; j < zsize; j++) {
for (int k = 0; k < xsize; k++)
t[k] = d2[k+xsize*i+xysize*j];
SplineFitter::createNaturalSpline(x, t, deriv);
for (int k = 0; k < xsize; k++)
d12[k+xsize*i+xysize*j] = SplineFitter::evaluateSplineDerivative(x, t, deriv, x[k]);
}
}
// Compute second derivatives with respect to y and z.
t.resize(ysize);
deriv.resize(ysize);
for (int i = 0; i < zsize; i++) {
for (int j = 0; j < xsize; j++) {
for (int k = 0; k < ysize; k++)
t[k] = d3[j+xsize*k+xysize*i];
SplineFitter::createNaturalSpline(y, t, deriv);
for (int k = 0; k < ysize; k++)
d23[j+xsize*k+xysize*i] = SplineFitter::evaluateSplineDerivative(y, t, deriv, y[k]);
}
}
// Compute second derivatives with respect to x and z.
t.resize(zsize);
deriv.resize(zsize);
for (int i = 0; i < xsize; i++) {
for (int j = 0; j < ysize; j++) {
for (int k = 0; k < zsize; k++)
t[k] = d1[i+xsize*j+xysize*k];
SplineFitter::createNaturalSpline(z, t, deriv);
for (int k = 0; k < zsize; k++)
d13[i+xsize*j+xysize*k] = SplineFitter::evaluateSplineDerivative(z, t, deriv, z[k]);
}
}
// Compute third derivatives with respect to x, y, and z.
t.resize(xsize);
deriv.resize(xsize);
for (int i = 0; i < ysize; i++) {
for (int j = 0; j < zsize; j++) {
for (int k = 0; k < xsize; k++)
t[k] = d23[k+xsize*i+xysize*j];
SplineFitter::createNaturalSpline(x, t, deriv);
for (int k = 0; k < xsize; k++)
d123[k+xsize*i+xysize*j] = SplineFitter::evaluateSplineDerivative(x, t, deriv, x[k]);
}
}
// Now compute the coefficients. This involves multiplying by a sparse 64x64 matrix, given
// here in packed form.
const int wt[] = {
1,0,1,
1,8,1,
4,0,-3,1,3,8,-2,9,-1,
4,0,2,1,-2,8,1,9,1,
1,16,1,
1,32,1,
4,16,-3,17,3,32,-2,33,-1,
4,16,2,17,-2,32,1,33,1,
4,0,-3,2,3,16,-2,18,-1,
4,8,-3,10,3,32,-2,34,-1,
16,0,9,1,-9,2,-9,3,9,8,6,9,3,10,-6,11,-3,16,6,17,-6,18,3,19,-3,32,4,33,2,34,2,35,1,
16,0,-6,1,6,2,6,3,-6,8,-3,9,-3,10,3,11,3,16,-4,17,4,18,-2,19,2,32,-2,33,-2,34,-1,35,-1,
4,0,2,2,-2,16,1,18,1,
4,8,2,10,-2,32,1,34,1,
16,0,-6,1,6,2,6,3,-6,8,-4,9,-2,10,4,11,2,16,-3,17,3,18,-3,19,3,32,-2,33,-1,34,-2,35,-1,
16,0,4,1,-4,2,-4,3,4,8,2,9,2,10,-2,11,-2,16,2,17,-2,18,2,19,-2,32,1,33,1,34,1,35,1,
1,24,1,
1,40,1,
4,24,-3,25,3,40,-2,41,-1,
4,24,2,25,-2,40,1,41,1,
1,48,1,
1,56,1,
4,48,-3,49,3,56,-2,57,-1,
4,48,2,49,-2,56,1,57,1,
4,24,-3,26,3,48,-2,50,-1,
4,40,-3,42,3,56,-2,58,-1,
16,24,9,25,-9,26,-9,27,9,40,6,41,3,42,-6,43,-3,48,6,49,-6,50,3,51,-3,56,4,57,2,58,2,59,1,
16,24,-6,25,6,26,6,27,-6,40,-3,41,-3,42,3,43,3,48,-4,49,4,50,-2,51,2,56,-2,57,-2,58,-1,59,-1,
4,24,2,26,-2,48,1,50,1,
4,40,2,42,-2,56,1,58,1,
16,24,-6,25,6,26,6,27,-6,40,-4,41,-2,42,4,43,2,48,-3,49,3,50,-3,51,3,56,-2,57,-1,58,-2,59,-1,
16,24,4,25,-4,26,-4,27,4,40,2,41,2,42,-2,43,-2,48,2,49,-2,50,2,51,-2,56,1,57,1,58,1,59,1,
4,0,-3,4,3,24,-2,28,-1,
4,8,-3,12,3,40,-2,44,-1,
16,0,9,1,-9,4,-9,5,9,8,6,9,3,12,-6,13,-3,24,6,25,-6,28,3,29,-3,40,4,41,2,44,2,45,1,
16,0,-6,1,6,4,6,5,-6,8,-3,9,-3,12,3,13,3,24,-4,25,4,28,-2,29,2,40,-2,41,-2,44,-1,45,-1,
4,16,-3,20,3,48,-2,52,-1,
4,32,-3,36,3,56,-2,60,-1,
16,16,9,17,-9,20,-9,21,9,32,6,33,3,36,-6,37,-3,48,6,49,-6,52,3,53,-3,56,4,57,2,60,2,61,1,
16,16,-6,17,6,20,6,21,-6,32,-3,33,-3,36,3,37,3,48,-4,49,4,52,-2,53,2,56,-2,57,-2,60,-1,61,-1,
16,0,9,2,-9,4,-9,6,9,16,6,18,3,20,-6,22,-3,24,6,26,-6,28,3,30,-3,48,4,50,2,52,2,54,1,
16,8,9,10,-9,12,-9,14,9,32,6,34,3,36,-6,38,-3,40,6,42,-6,44,3,46,-3,56,4,58,2,60,2,62,1,
64,0,-27,1,27,2,27,3,-27,4,27,5,-27,6,-27,7,27,8,-18,9,-9,10,18,11,9,12,18,13,9,14,-18,15,-9,16,-18,17,18,18,-9,19,9,20,18,21,-18,22,9,23,-9,24,-18,25,18,26,18,27,-18,28,-9,29,9,30,9,31,-9,32,-12,33,-6,34,-6,35,-3,36,12,37,6,38,6,39,3,40,-12,41,-6,42,12,43,6,44,-6,45,-3,46,6,47,3,48,-12,49,12,50,-6,51,6,52,-6,53,6,54,-3,55,3,56,-8,57,-4,58,-4,59,-2,60,-4,61,-2,62,-2,63,-1,
64,0,18,1,-18,2,-18,3,18,4,-18,5,18,6,18,7,-18,8,9,9,9,10,-9,11,-9,12,-9,13,-9,14,9,15,9,16,12,17,-12,18,6,19,-6,20,-12,21,12,22,-6,23,6,24,12,25,-12,26,-12,27,12,28,6,29,-6,30,-6,31,6,32,6,33,6,34,3,35,3,36,-6,37,-6,38,-3,39,-3,40,6,41,6,42,-6,43,-6,44,3,45,3,46,-3,47,-3,48,8,49,-8,50,4,51,-4,52,4,53,-4,54,2,55,-2,56,4,57,4,58,2,59,2,60,2,61,2,62,1,63,1,
16,0,-6,2,6,4,6,6,-6,16,-3,18,-3,20,3,22,3,24,-4,26,4,28,-2,30,2,48,-2,50,-2,52,-1,54,-1,
16,8,-6,10,6,12,6,14,-6,32,-3,34,-3,36,3,38,3,40,-4,42,4,44,-2,46,2,56,-2,58,-2,60,-1,62,-1,
64,0,18,1,-18,2,-18,3,18,4,-18,5,18,6,18,7,-18,8,12,9,6,10,-12,11,-6,12,-12,13,-6,14,12,15,6,16,9,17,-9,18,9,19,-9,20,-9,21,9,22,-9,23,9,24,12,25,-12,26,-12,27,12,28,6,29,-6,30,-6,31,6,32,6,33,3,34,6,35,3,36,-6,37,-3,38,-6,39,-3,40,8,41,4,42,-8,43,-4,44,4,45,2,46,-4,47,-2,48,6,49,-6,50,6,51,-6,52,3,53,-3,54,3,55,-3,56,4,57,2,58,4,59,2,60,2,61,1,62,2,63,1,
64,0,-12,1,12,2,12,3,-12,4,12,5,-12,6,-12,7,12,8,-6,9,-6,10,6,11,6,12,6,13,6,14,-6,15,-6,16,-6,17,6,18,-6,19,6,20,6,21,-6,22,6,23,-6,24,-8,25,8,26,8,27,-8,28,-4,29,4,30,4,31,-4,32,-3,33,-3,34,-3,35,-3,36,3,37,3,38,3,39,3,40,-4,41,-4,42,4,43,4,44,-2,45,-2,46,2,47,2,48,-4,49,4,50,-4,51,4,52,-2,53,2,54,-2,55,2,56,-2,57,-2,58,-2,59,-2,60,-1,61,-1,62,-1,63,-1,
4,0,2,4,-2,24,1,28,1,
4,8,2,12,-2,40,1,44,1,
16,0,-6,1,6,4,6,5,-6,8,-4,9,-2,12,4,13,2,24,-3,25,3,28,-3,29,3,40,-2,41,-1,44,-2,45,-1,
16,0,4,1,-4,4,-4,5,4,8,2,9,2,12,-2,13,-2,24,2,25,-2,28,2,29,-2,40,1,41,1,44,1,45,1,
4,16,2,20,-2,48,1,52,1,
4,32,2,36,-2,56,1,60,1,
16,16,-6,17,6,20,6,21,-6,32,-4,33,-2,36,4,37,2,48,-3,49,3,52,-3,53,3,56,-2,57,-1,60,-2,61,-1,
16,16,4,17,-4,20,-4,21,4,32,2,33,2,36,-2,37,-2,48,2,49,-2,52,2,53,-2,56,1,57,1,60,1,61,1,
16,0,-6,2,6,4,6,6,-6,16,-4,18,-2,20,4,22,2,24,-3,26,3,28,-3,30,3,48,-2,50,-1,52,-2,54,-1,
16,8,-6,10,6,12,6,14,-6,32,-4,34,-2,36,4,38,2,40,-3,42,3,44,-3,46,3,56,-2,58,-1,60,-2,62,-1,
64,0,18,1,-18,2,-18,3,18,4,-18,5,18,6,18,7,-18,8,12,9,6,10,-12,11,-6,12,-12,13,-6,14,12,15,6,16,12,17,-12,18,6,19,-6,20,-12,21,12,22,-6,23,6,24,9,25,-9,26,-9,27,9,28,9,29,-9,30,-9,31,9,32,8,33,4,34,4,35,2,36,-8,37,-4,38,-4,39,-2,40,6,41,3,42,-6,43,-3,44,6,45,3,46,-6,47,-3,48,6,49,-6,50,3,51,-3,52,6,53,-6,54,3,55,-3,56,4,57,2,58,2,59,1,60,4,61,2,62,2,63,1,
64,0,-12,1,12,2,12,3,-12,4,12,5,-12,6,-12,7,12,8,-6,9,-6,10,6,11,6,12,6,13,6,14,-6,15,-6,16,-8,17,8,18,-4,19,4,20,8,21,-8,22,4,23,-4,24,-6,25,6,26,6,27,-6,28,-6,29,6,30,6,31,-6,32,-4,33,-4,34,-2,35,-2,36,4,37,4,38,2,39,2,40,-3,41,-3,42,3,43,3,44,-3,45,-3,46,3,47,3,48,-4,49,4,50,-2,51,2,52,-4,53,4,54,-2,55,2,56,-2,57,-2,58,-1,59,-1,60,-2,61,-2,62,-1,63,-1,
16,0,4,2,-4,4,-4,6,4,16,2,18,2,20,-2,22,-2,24,2,26,-2,28,2,30,-2,48,1,50,1,52,1,54,1,
16,8,4,10,-4,12,-4,14,4,32,2,34,2,36,-2,38,-2,40,2,42,-2,44,2,46,-2,56,1,58,1,60,1,62,1,
64,0,-12,1,12,2,12,3,-12,4,12,5,-12,6,-12,7,12,8,-8,9,-4,10,8,11,4,12,8,13,4,14,-8,15,-4,16,-6,17,6,18,-6,19,6,20,6,21,-6,22,6,23,-6,24,-6,25,6,26,6,27,-6,28,-6,29,6,30,6,31,-6,32,-4,33,-2,34,-4,35,-2,36,4,37,2,38,4,39,2,40,-4,41,-2,42,4,43,2,44,-4,45,-2,46,4,47,2,48,-3,49,3,50,-3,51,3,52,-3,53,3,54,-3,55,3,56,-2,57,-1,58,-2,59,-1,60,-2,61,-1,62,-2,63,-1,
64,0,8,1,-8,2,-8,3,8,4,-8,5,8,6,8,7,-8,8,4,9,4,10,-4,11,-4,12,-4,13,-4,14,4,15,4,16,4,17,-4,18,4,19,-4,20,-4,21,4,22,-4,23,4,24,4,25,-4,26,-4,27,4,28,4,29,-4,30,-4,31,4,32,2,33,2,34,2,35,2,36,-2,37,-2,38,-2,39,-2,40,2,41,2,42,-2,43,-2,44,2,45,2,46,-2,47,-2,48,2,49,-2,50,2,51,-2,52,2,53,-2,54,2,55,-2,56,1,57,1,58,1,59,1,60,1,61,1,62,1,63,1
};
vector<vector<int> > weight(64);
int index = 0;
for (int i = 0; i < 64; i++) {
int numElements = wt[index++];
for (int j = 0; j < numElements; j++) {
weight[i].push_back(wt[index++]);
weight[i].push_back(wt[index++]);
}
}
vector<double> rhs(64);
c.resize((xsize-1)*(ysize-1)*(zsize-1));
for (int i = 0; i < xsize-1; i++) {
for (int j = 0; j < ysize-1; j++) {
for (int k = 0; k < zsize-1; k++) {
// Compute the 64 coefficients for patch (i, j, k).
int nexti = i+1;
int nextj = j+1;
int nextk = k+1;
double deltax = x[nexti]-x[i];
double deltay = y[nextj]-y[j];
double deltaz = z[nextj]-z[j];
double e[] = {values[i+j*xsize+k*xysize], values[nexti+j*xsize+k*xysize], values[i+nextj*xsize+k*xysize], values[nexti+nextj*xsize+k*xysize], values[i+j*xsize+nextk*xysize], values[nexti+j*xsize+nextk*xysize], values[i+nextj*xsize+nextk*xysize], values[nexti+nextj*xsize+nextk*xysize]};
double e1[] = {d1[i+j*xsize+k*xysize], d1[nexti+j*xsize+k*xysize], d1[i+nextj*xsize+k*xysize], d1[nexti+nextj*xsize+k*xysize], d1[i+j*xsize+nextk*xysize], d1[nexti+j*xsize+nextk*xysize], d1[i+nextj*xsize+nextk*xysize], d1[nexti+nextj*xsize+nextk*xysize]};
double e2[] = {d2[i+j*xsize+k*xysize], d2[nexti+j*xsize+k*xysize], d2[i+nextj*xsize+k*xysize], d2[nexti+nextj*xsize+k*xysize], d2[i+j*xsize+nextk*xysize], d2[nexti+j*xsize+nextk*xysize], d2[i+nextj*xsize+nextk*xysize], d2[nexti+nextj*xsize+nextk*xysize]};
double e3[] = {d3[i+j*xsize+k*xysize], d3[nexti+j*xsize+k*xysize], d3[i+nextj*xsize+k*xysize], d3[nexti+nextj*xsize+k*xysize], d3[i+j*xsize+nextk*xysize], d3[nexti+j*xsize+nextk*xysize], d3[i+nextj*xsize+nextk*xysize], d3[nexti+nextj*xsize+nextk*xysize]};
double e12[] = {d12[i+j*xsize+k*xysize], d12[nexti+j*xsize+k*xysize], d12[i+nextj*xsize+k*xysize], d12[nexti+nextj*xsize+k*xysize], d12[i+j*xsize+nextk*xysize], d12[nexti+j*xsize+nextk*xysize], d12[i+nextj*xsize+nextk*xysize], d12[nexti+nextj*xsize+nextk*xysize]};
double e13[] = {d13[i+j*xsize+k*xysize], d13[nexti+j*xsize+k*xysize], d13[i+nextj*xsize+k*xysize], d13[nexti+nextj*xsize+k*xysize], d13[i+j*xsize+nextk*xysize], d13[nexti+j*xsize+nextk*xysize], d13[i+nextj*xsize+nextk*xysize], d13[nexti+nextj*xsize+nextk*xysize]};
double e23[] = {d23[i+j*xsize+k*xysize], d23[nexti+j*xsize+k*xysize], d23[i+nextj*xsize+k*xysize], d23[nexti+nextj*xsize+k*xysize], d23[i+j*xsize+nextk*xysize], d23[nexti+j*xsize+nextk*xysize], d23[i+nextj*xsize+nextk*xysize], d23[nexti+nextj*xsize+nextk*xysize]};
double e123[] = {d123[i+j*xsize+k*xysize], d123[nexti+j*xsize+k*xysize], d123[i+nextj*xsize+k*xysize], d123[nexti+nextj*xsize+k*xysize], d123[i+j*xsize+nextk*xysize], d123[nexti+j*xsize+nextk*xysize], d123[i+nextj*xsize+nextk*xysize], d123[nexti+nextj*xsize+nextk*xysize]};
for (int m = 0; m < 8; m++) {
rhs[m] = e[m];
rhs[m+8] = e1[m]*deltax;
rhs[m+16] = e2[m]*deltay;
rhs[m+24] = e3[m]*deltaz;
rhs[m+32] = e12[m]*deltax*deltay;
rhs[m+40] = e13[m]*deltax*deltaz;
rhs[m+48] = e23[m]*deltay*deltaz;
rhs[m+56] = e123[m]*deltax*deltay*deltaz;
}
vector<double>& coeff = c[i+j*(xsize-1)+k*(xsize-1)*(ysize-1)];
coeff.resize(64);
for (int m = 0; m < 64; m++) {
double sum = 0.0;
int numElements = weight[m].size();
for (int n = 0; n < numElements; n += 2)
sum += weight[m][n+1]*rhs[weight[m][n]];
coeff[m] = sum;
}
}
}
}
}
double SplineFitter::evaluate3DSpline(const vector<double>& x, const vector<double>& y, const vector<double>& z, const vector<double>& values, const vector<vector<double> >& c, double u, double v, double w) {
int xsize = x.size();
int ysize = y.size();
int zsize = z.size();
if (u < x[0] || u > x[xsize-1] || v < y[0] || v > y[ysize-1] || w < z[0] || w > z[zsize-1])
throw OpenMMException("evaluate3DSpline: specified point is outside the range defined by the spline");
// Perform a binary search to identify the interval containing the point to evaluate.
int lowerx = 0;
int upperx = xsize-1;
while (upperx-lowerx > 1) {
int middle = (upperx+lowerx)/2;
if (x[middle] > u)
upperx = middle;
else
lowerx = middle;
}
int lowery = 0;
int uppery = ysize-1;
while (uppery-lowery > 1) {
int middle = (uppery+lowery)/2;
if (y[middle] > v)
uppery = middle;
else
lowery = middle;
}
int lowerz = 0;
int upperz = zsize-1;
while (upperz-lowerz > 1) {
int middle = (upperz+lowerz)/2;
if (z[middle] > w)
upperz = middle;
else
lowerz = middle;
}
double deltax = x[upperx]-x[lowerx];
double deltay = y[uppery]-y[lowery];
double deltaz = z[upperz]-z[lowerz];
double da = (u-x[lowerx])/deltax;
double db = (v-y[lowery])/deltay;
double dc = (w-z[lowerz])/deltaz;
const vector<double>& coeff = c[lowerx+(xsize-1)*lowery+(xsize-1)*(ysize-1)*lowerz];
// Evaluate the spline to determine the value and gradients.
double value[] = {0, 0, 0, 0};
for (int i = 3; i >= 0; i--) {
for (int j = 0; j < 4; j++) {
int base = 4*i + 16*j;
value[j] = db*value[j] + ((coeff[base+3]*da + coeff[base+2])*da + coeff[base+1])*da + coeff[base];
}
}
return value[0] + dc*(value[1] + dc*(value[2] + dc*value[3]));
}
void SplineFitter::evaluate3DSplineDerivatives(const vector<double>& x, const vector<double>& y, const vector<double>& z, const vector<double>& values, const vector<vector<double> >& c, double u, double v, double w, double& dx, double& dy, double& dz) {
int xsize = x.size();
int ysize = y.size();
int zsize = z.size();
if (u < x[0] || u > x[xsize-1] || v < y[0] || v > y[ysize-1] || w < z[0] || w > z[zsize-1])
throw OpenMMException("evaluate3DSpline: specified point is outside the range defined by the spline");
// Perform a binary search to identify the interval containing the point to evaluate.
int lowerx = 0;
int upperx = xsize-1;
while (upperx-lowerx > 1) {
int middle = (upperx+lowerx)/2;
if (x[middle] > u)
upperx = middle;
else
lowerx = middle;
}
int lowery = 0;
int uppery = ysize-1;
while (uppery-lowery > 1) {
int middle = (uppery+lowery)/2;
if (y[middle] > v)
uppery = middle;
else
lowery = middle;
}
int lowerz = 0;
int upperz = zsize-1;
while (upperz-lowerz > 1) {
int middle = (upperz+lowerz)/2;
if (z[middle] > w)
upperz = middle;
else
lowerz = middle;
}
double deltax = x[upperx]-x[lowerx];
double deltay = y[uppery]-y[lowery];
double deltaz = z[upperz]-z[lowerz];
double da = (u-x[lowerx])/deltax;
double db = (v-y[lowery])/deltay;
double dc = (w-z[lowerz])/deltaz;
const vector<double>& coeff = c[lowerx+(xsize-1)*lowery+(xsize-1)*(ysize-1)*lowerz];
// Evaluate the spline to determine the derivatives.
double derivx[] = {0, 0, 0, 0};
double derivy[] = {0, 0, 0, 0};
double derivz[] = {0, 0, 0, 0};
for (int i = 3; i >= 0; i--) {
for (int j = 0; j < 4; j++) {
int base = 4*i + 16*j;
derivx[j] = db*derivx[j] + (3.0*coeff[base+3]*da + 2.0*coeff[base+2])*da + coeff[base+1];
derivz[j] = db*derivz[j] + ((coeff[base+3]*da + coeff[base+2])*da + coeff[base+1])*da + coeff[base];
base = i + 16*j;
derivy[j] = da*derivy[j] + (3.0*coeff[base+12]*db + 2.0*coeff[base+8])*db + coeff[base+4];
}
}
dx = derivx[0] + dc*(derivx[1] + dc*(derivx[2] + dc*derivx[3]));
dy = derivy[0] + dc*(derivy[1] + dc*(derivy[2] + dc*derivy[3]));
dz = derivz[1] + dc*(2.0*derivz[2] + 3.0*dc*derivz[3]);
dx /= deltax;
dy /= deltay;
dz /= deltaz;
}
tests/TestSplineFitter.cpp
View file @ 9d3636f4
......@@ -106,8 +106,8 @@ void test2DSpline() {
}
for (int i = 0; i < 10; i++) {
for (int j = 0; j < 10; j++) {
double s = x[0]+(i+1)*(x[xsize-1]-x[0])/11.0;
double t = y[0]+(j+1)*(y[ysize-1]-y[0])/11.0;
double s = x[0]+(i+1)*(x[xsize-1]-x[0])/12.0;
double t = y[0]+(j+1)*(y[ysize-1]-y[0])/12.0;
double value = SplineFitter::evaluate2DSpline(x, y, f, c, s, t);
ASSERT_EQUAL_TOL(sin(s)*cos(0.4*t), value, 0.02);
double dx, dy;
......@@ -118,11 +118,57 @@ void test2DSpline() {
}
}
void test3DSpline() {
const int xsize = 8;
const int ysize = 9;
const int zsize = 10;
vector<double> x(xsize);
vector<double> y(ysize);
vector<double> z(zsize);
vector<double> f(xsize*ysize*zsize);
for (int i = 0; i < xsize; i++)
x[i] = 0.2*i+0.02*sin(0.4*double(i));
for (int i = 0; i < ysize; i++)
y[i] = 0.2*i+0.02*sin(0.45*double(i));
for (int i = 0; i < zsize; i++)
z[i] = 0.2*i+0.02*sin(0.5*double(i));
for (int i = 0; i < xsize; i++)
for (int j = 0; j < ysize; j++)
for (int k = 0; k < zsize; k++)
f[i+j*xsize+k*xsize*ysize] = sin(x[i])*cos(0.4*y[j])*(1+z[k]);
vector<vector<double> > c;
SplineFitter::create3DNaturalSpline(x, y, z, f, c);
for (int i = 0; i < xsize; i++)
for (int j = 0; j < ysize; j++) {
for (int k = 0; k < zsize; k++) {
double value = SplineFitter::evaluate3DSpline(x, y, z, f, c, x[i], y[j], z[k]);
ASSERT_EQUAL_TOL(f[i+j*xsize+k*xsize*ysize], value, 1e-6);
}
}
for (int i = 0; i < 10; i++) {
for (int j = 0; j < 10; j++) {
for (int k = 0; k < 10; k++) {
double s = x[0]+(i+1)*(x[xsize-1]-x[0])/12.0;
double t = y[0]+(j+1)*(y[ysize-1]-y[0])/12.0;
double u = z[0]+(k+1)*(z[zsize-1]-z[0])/12.0;
double value = SplineFitter::evaluate3DSpline(x, y, z, f, c, s, t, u);
ASSERT_EQUAL_TOL(sin(s)*cos(0.4*t)*(1+u), value, 0.02);
double dx, dy, dz;
SplineFitter::evaluate3DSplineDerivatives(x, y, z, f, c, s, t, u, dx, dy, dz);
ASSERT_EQUAL_TOL(cos(s)*cos(0.4*t)*(1+u), dx, 0.1);
ASSERT_EQUAL_TOL(-0.4*sin(s)*sin(0.4*t)*(1+u), dy, 0.1);
ASSERT_EQUAL_TOL(sin(s)*cos(0.4*t), dz, 0.1);
}
}
}
}
int main() {
try {
testNaturalSpline();
testPeriodicSpline();
test2DSpline();
test3DSpline();
}
catch(const exception& e) {
cout << "exception: " << e.what() << endl;
......
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