void ChebyshevDiffMatrix(int N, elem::Matrix<T>& D, double a = -1, double b = 1) {
elem::Matrix<T> X;
ChebyshevPoints(N, X);
double *x = X.Buffer();
const double s = 2.0 / (b - a);
D.Resize(N+1, N+1);
for(int j = 0; j <= N; j++)
for(int i = 0; i <= N; i++) {
int d = i - j;
double v = 2.0 / (b - a);
if (i == 0 && j == 0)
v *= (2.0 * N * N + 1.0) / 6.0;
else if (i == N && j == N)
v *= -(2.0 * N * N + 1.0) / 6.0;
else {
if (i == 0 || i == N)
v *= 2.0;
if (j ==0 || j == N)
v /= 2.0;
if (d == 0)
v *= -x[j] / (2.0 * (1 - x[j] * x[j]));
else if (d % 2 == 0)
v *= 1.0 / (x[i] - x[j]);
else
v *= -1.0 / (x[i] - x[j]);
}
D.Set(i, j, v);
}
}
void ChebyshevPoints(int N, elem::Matrix<T>& X, double a = -1, double b = 1) {
const double s = (b - a) / 2.0;
const double pi = boost::math::constants::pi<double>();
X.Resize(N+1, 1);
for(int j = 0; j <= N; j++)
X.Set(j, 0,
(std::cos(j * pi / N) + a + 1) * s);
if (N % 2 == 0)
X.Set(N / 2, 0, 0.0);
}
void realize_matrix_view(elem::Matrix<value_type>& A,
int i, int j, int height, int width,
int col_stride, int row_stride) const {
A.Resize(height, width);
value_type *data = A.Buffer();
#ifdef SKYLARK_HAVE_OPENMP
#pragma omp parallel for
#endif
for(size_t j_loc = 0; j_loc < width; j_loc++) {
size_t j_glob = j + j_loc * row_stride;
for (size_t i_loc = 0; i_loc < height; i_loc++) {
size_t i_glob = i + i_loc * col_stride;
size_t tmp = j_glob * _S;
tmp += i_glob;
value_type sample = entries[tmp];
tmp = j_loc * height;
data[tmp + i_loc] = scale * sample;
}
}
}
