csaps-cpp/src/csaps.cpp at master · Davidtober/csaps-cpp · GitHub

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#include <cmath>

#include <algorithm>

#include <stdexcept>

#include "csaps.h"

namespace csaps

{

DoubleArray Diff(const DoubleArray &vec)

{

const Size n = vec.size() - 1;

return vec.tail(n) - vec.head(n);

}

IndexArray Digitize(const DoubleArray &arr, const DoubleArray &bins)

{

// This code works if `arr` and `bins` are monotonically increasing

IndexArray indexes = IndexArray::Zero(arr.size());

auto IsInsideBin = [arr, bins](Index item, Index index)

{

const double prc = 1.e-8;

double a = arr(item);

double bl = bins(index - 1);

double br = bins(index);

// bins[i-1] <= a < bins[i]

return (a > bl || std::abs(a - bl) < std::abs(std::min(a, bl)) * prc) && a < br;

};

Index kstart = 1;

for (Index i = 0; i < arr.size(); ++i) {

for (Index k = kstart; k < bins.size(); ++k) {

if (IsInsideBin(i, k)) {

indexes(i) = k;

kstart = k;

break;

}

return indexes;

}

DoubleSparseMatrix MakeSparseDiagMatrix(const DoubleArray2D& diags, const IndexArray& offsets, Size rows, Size cols)

{

auto GetNumElemsAndIndex = [rows, cols](Index offset, Index &i, Index &j)

{

if (offset < 0) {

i = -offset;

j = 0;

}

else {

i = 0;

j = offset;

}

return std::min(rows - i, cols - j);

};

DoubleSparseMatrix m(rows, cols);

for (Index k = 0; k < offsets.size(); ++k) {

Index offset = offsets(k);

Index i, j;

Index n = GetNumElemsAndIndex(offset, i, j);

// When rows == cols or rows > cols, the function takes elements of the

// super-diagonal from the lower part of the corresponding diag array, and

// elements of the sub-diagonal from the upper part of the corresponding diag array.

// When rows < cols, the function does the opposite, taking elements of the

// super-diagonal from the upper part of the corresponding diag array, and

// elements of the sub-diagonal from the lower part of the corresponding diag array.

DoubleArray diag(n);

if (offset < 0) {

if (rows >= cols) {

diag = diags.row(k).head(n);

}

else {

diag = diags.row(k).tail(n);

}

else {

if (rows >= cols) {

diag = diags.row(k).tail(n);

}

else {

diag = diags.row(k).head(n);

}

for (Index l = 0; l < n; ++l) {

m.insert(i+l, j+l) = diag(l);

}

return m;

}

csaps::DoubleArray SolveLinearSystem(const DoubleSparseMatrix &A, const DoubleArray &b)

{

Eigen::SparseLU<DoubleSparseMatrix> solver;

// Compute the ordering permutation vector from the structural pattern of A

solver.analyzePattern(A);

// Compute the numerical factorization

solver.factorize(A);

// Use the factors to solve the linear system

DoubleArray x = solver.solve(b.matrix()).array();

return x;

}

UnivariateCubicSmoothingSpline::UnivariateCubicSmoothingSpline(const DoubleArray &xdata, const DoubleArray &ydata)

: UnivariateCubicSmoothingSpline(xdata, ydata, DoubleArray(), -1.0)

{

}

UnivariateCubicSmoothingSpline::UnivariateCubicSmoothingSpline(const DoubleArray &xdata, const DoubleArray &ydata, const DoubleArray &weights)

: UnivariateCubicSmoothingSpline(xdata, ydata, weights, -1.0)

{

}

UnivariateCubicSmoothingSpline::UnivariateCubicSmoothingSpline(const DoubleArray &xdata, const DoubleArray &ydata, double smooth)

: UnivariateCubicSmoothingSpline(xdata, ydata, DoubleArray(), smooth)

{

}

UnivariateCubicSmoothingSpline::UnivariateCubicSmoothingSpline(const DoubleArray &xdata, const DoubleArray &ydata, const DoubleArray &weights, double smooth)

: m_xdata(xdata)

, m_ydata(ydata)

, m_weights(weights)

, m_smooth(smooth)

{

if (m_xdata.size() < 2) {

throw std::runtime_error("There must be at least 2 data points");

}

if (m_weights.size() == 0) {

m_weights = DoubleArray::Constant(m_xdata.size(), 1.0);

}

if (m_smooth > 1.0) {

throw std::runtime_error("Smoothing parameter must be less than or equal 1.0");

}

if (m_xdata.size() != m_ydata.size() || m_xdata.size() != m_weights.size()) {

throw std::runtime_error("Lenghts of the input data vectors are not equal");

}

MakeSpline();

}

DoubleArray UnivariateCubicSmoothingSpline::operator()(const DoubleArray &xidata)

{

if (xidata.size() < 2) {

throw std::runtime_error("There must be at least 2 data points");

}

return Evaluate(xidata);

}

DoubleArray UnivariateCubicSmoothingSpline::operator()(const Size pcount, DoubleArray &xidata)

{

if (pcount < 2) {

throw std::runtime_error("There must be at least 2 data points");

}

xidata.resize(pcount);

xidata << DoubleArray::LinSpaced(pcount, m_xdata(0), m_xdata(m_xdata.size()-1));

return Evaluate(xidata);

}

void UnivariateCubicSmoothingSpline::MakeSpline()

{

const Size pcount = m_xdata.size();

const Size pcount_m1 = pcount - 1;

const Size pcount_m2 = pcount - 2;

DoubleArray dx = Diff(m_xdata);

DoubleArray dy = Diff(m_ydata);

DoubleArray divdydx = dy / dx;

double p = m_smooth;

if (pcount > 2) {

// Create diagonal sparse matrices

const Size n = dx.size() - 1;

DoubleArray2D diags(3, n);

DoubleArray head_r = dx.head(n);

DoubleArray tail_r = dx.tail(n);

diags.row(0) = tail_r;

diags.row(1) = 2 * (tail_r + head_r);

diags.row(2) = head_r;

IndexArray offsets(3);

offsets << -1, 0, 1;

DoubleSparseMatrix r = MakeSparseDiagMatrix(diags, offsets, pcount_m2, pcount_m2);

DoubleArray odx = 1. / dx;

DoubleArray head_qt = odx.head(n);

DoubleArray tail_qt = odx.tail(n);

diags.row(0) = head_qt;

diags.row(1) = -(tail_qt + head_qt);

diags.row(2) = tail_qt;

offsets << 0, 1, 2;

DoubleSparseMatrix qt = MakeSparseDiagMatrix(diags, offsets, pcount_m2, pcount);

DoubleArray ow = 1. / m_weights;

DoubleArray osqw = 1. / m_weights.sqrt();

offsets.resize(1);

offsets << 0;

DoubleSparseMatrix w = MakeSparseDiagMatrix(ow.transpose(), offsets, pcount, pcount);

DoubleSparseMatrix qw = MakeSparseDiagMatrix(osqw.transpose(), offsets, pcount, pcount);

DoubleSparseMatrix qtw = qt * qw;

DoubleSparseMatrix qtwq = qtw * qtw.transpose();

auto Trace = [](const DoubleSparseMatrix &m)

{

return m.diagonal().sum();

};

double p = m_smooth;

if (p < 0) {

p = 1. / (1. + Trace(r) / (6. * Trace(qtwq)));

}

DoubleSparseMatrix A = ((6. * (1. - p)) * qtwq) + (p * r);

A.makeCompressed();

DoubleArray b = Diff(divdydx);

// Solve linear system Ab = u

DoubleArray u = SolveLinearSystem(A, b);

DoubleArray d1 = DoubleArray::Zero(u.size() + 2);

d1.segment(1, u.size()) = u; d1 = Diff(d1) / dx;

DoubleArray d2 = DoubleArray::Zero(d1.size() + 2);

d2.segment(1, d1.size()) = d1; d2 = Diff(d2);

DoubleArray yi = m_ydata - ((6. * (1. - p)) * w * d2.matrix()).array();

DoubleArray c3 = DoubleArray::Zero(u.size() + 2);

c3.segment(1, u.size()) = p * u;

DoubleArray c2 = Diff(yi) / dx - dx * (2. * c3.head(pcount_m1) + c3.tail(pcount_m1));

m_coeffs.resize(pcount_m1, 4);

m_coeffs.col(0) = Diff(c3) / dx;

m_coeffs.col(1) = 3. * c3.head(pcount_m1);

m_coeffs.col(2) = c2;

m_coeffs.col(3) = yi.head(pcount_m1);

}

else {

p = 1.0;

m_coeffs.resize(1, 2);

m_coeffs(0, 0) = divdydx(0);

m_coeffs(0, 1) = m_ydata(0);

}

m_smooth = p;

}

DoubleArray UnivariateCubicSmoothingSpline::Evaluate(const DoubleArray & xidata)

{

const Size x_size = m_xdata.size();

DoubleArray mesh = m_xdata.segment(1, x_size - 2);

DoubleArray edges(x_size);

edges(0) = -DoubleLimits::infinity();

edges.segment(1, x_size - 2) = mesh;

edges(x_size - 1) = DoubleLimits::infinity();

IndexArray indexes = Digitize(xidata, edges);

// Use 0 as the start index

indexes -= 1;

const Size xi_size = xidata.size();

DoubleArray xidata_loc(xi_size);

DoubleArray yidata(xi_size);

for (Index i = 0; i < xi_size; ++i) {

Index index = indexes(i);

// Go to local coordinates

xidata_loc(i) = xidata(i) - m_xdata(index);

// Initial values

yidata(i) = m_coeffs(index, 0);

}

DoubleArray coeffs(xi_size);

for (Index i = 1; i < m_coeffs.cols(); ++i) {

for (Index k = 0; k < xi_size; ++k) {

coeffs(k) = m_coeffs(indexes(k), i);

}

yidata = xidata_loc * yidata + coeffs;

}

return yidata;

}

} // namespace csaps

csaps-cpp/src/csaps.cpp at master · Davidtober/csaps-cpp · GitHub

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