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make_matrix.h
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212 lines (172 loc) · 4.63 KB
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#ifndef MAKE_MATRIX_H
#define MAKE_MATRIX_H
#include "../config.h"
#include "../error.h"
#include "matrix_utils.h"
/*
*
* This is part of the Mathieu function suite -- a reimplementation
* of the Mathieu functions for Scipy. This file holds the functions
* which make the recursion matrices.
*
* Stuart Brorson, Summer 2025.
*
*/
#define SQRT2 1.414213562373095
namespace xsf {
namespace mathieu {
/*-----------------------------------------------
This creates the recurrence relation matrix for
the even-even Mathieu fcns (ce_2n).
Inputs:
N = matrix size (related to max order desired).
q = shape parameter.
Output:
A = recurrence matrix (must be calloc'ed in caller).
Return:
return code = SF_ERROR_OK if OK.
-------------------------------------------------*/
int make_matrix_ee(int N, double q, double *A) {
int j;
int i;
// Symmetrize matrix here, then fix in caller.
i = MATRIX_IDX(N, 0, 1);
A[i] = SQRT2*q;
i = MATRIX_IDX(N, 1, 0);
A[i] = SQRT2*q;
i = MATRIX_IDX(N, 1, 1);
A[i] = 4.0;
i = MATRIX_IDX(N, 1, 2);
A[i] = q;
for (j=2; j<=N-2; j++) {
i = MATRIX_IDX(N, j, j-1);
A[i] = q;
i = MATRIX_IDX(N, j, j);
A[i] = (2.0*j)*(2.0*j);
i = MATRIX_IDX(N, j, j+1);
A[i] = q;
}
i = MATRIX_IDX(N, N-1, N-2);
A[i] = q;
i = MATRIX_IDX(N, N-1, N-1);
A[i] = (2.0*(N-1))*(2.0*(N-1));
return SF_ERROR_OK;
}
/*-----------------------------------------------
This creates the recurrence relation matrix for the
even-odd Mathieu fcns (ce_2n+1).
Inputs:
N = matrix size (related to max order desired).
q = shape parameter.
Output:
A = recurrence matrix (calloc in caller).
Return:
return code = SF_ERROR_OK if OK.
-------------------------------------------------*/
int make_matrix_eo(int N, double q, double *A) {
int j;
int i;
i = MATRIX_IDX(N, 0, 0);
A[i] = 1.0+q;
i = MATRIX_IDX(N, 0, 1);
A[i] = q;
i = MATRIX_IDX(N, 1, 0);
A[i] = q;
i = MATRIX_IDX(N, 1, 1);
A[i] = 9.0;
i = MATRIX_IDX(N, 1, 2);
A[i] = q;
for (j=2; j<=N-2; j++) {
i = MATRIX_IDX(N, j, j-1);
A[i] = q;
i = MATRIX_IDX(N, j, j);
A[i] = (2.0*j+1.0)*(2.0*j+1.0);
i = MATRIX_IDX(N, j, j+1);
A[i] = q;
}
i = MATRIX_IDX(N, N-1, N-2);
A[i] = q;
i = MATRIX_IDX(N, N-1, N-1);
A[i] = (2.0*(N-1)+1.0)*(2.0*(N-1)+1.0);
return SF_ERROR_OK;
}
/*-----------------------------------------------
This creates the recurrence relation matrix for
the odd-even Mathieu fcns (se_2n) -- sometimes called
se_2n+2.
Inputs:
N = matrix size (related to max order desired).
q = shape parameter.
Output:
A = recurrence matrix (calloc in caller).
Return:
return code = SF_ERROR_OK if OK.
-------------------------------------------------*/
int make_matrix_oe(int N, double q, double *A) {
int j;
int i;
i = MATRIX_IDX(N, 0, 0);
A[i] = 4.0;
i = MATRIX_IDX(N, 0, 1);
A[i] = q;
i = MATRIX_IDX(N, 1, 0);
A[i] = q;
i = MATRIX_IDX(N, 1, 1);
A[i] = 16.0;
i = MATRIX_IDX(N, 1, 2);
A[i] = q;
for (j=2; j<=N-2; j++) {
i = MATRIX_IDX(N, j, j-1);
A[i] = q;
i = MATRIX_IDX(N, j, j);
A[i] = (2.0*(j+1))*(2.0*(j+1));
i = MATRIX_IDX(N, j, j+1);
A[i] = q;
}
i = MATRIX_IDX(N, N-1, N-2);
A[i] = q;
i = MATRIX_IDX(N, N-1, N-1);
A[i] = (2.0*N)*(2.0*N);
return SF_ERROR_OK;
}
/*-----------------------------------------------
This creates the recurrence relation matrix for
the odd-odd Mathieu fcns (se_2n+1).
Inputs:
N = matrix size (related to max order desired).
q = shape parameter.
Output:
A = recurrence matrix (calloc in caller).
Return:
return code = SF_ERROR_OK if OK.
-------------------------------------------------*/
int make_matrix_oo(int N, double q, double *A) {
int j;
int i;
i = MATRIX_IDX(N, 0, 0);
A[i] = 1.0 - q;
i = MATRIX_IDX(N, 0, 1);
A[i] = q;
i = MATRIX_IDX(N, 1, 0);
A[i] = q;
i = MATRIX_IDX(N, 1, 1);
A[i] = 9.0;
i = MATRIX_IDX(N, 1, 2);
A[i] = q;
for (j=2; j<=N-2; j++) {
i = MATRIX_IDX(N, j, j-1);
A[i] = q;
i = MATRIX_IDX(N, j, j);
A[i] = (2.0*j+1.0)*(2.0*j+1.0);
i = MATRIX_IDX(N, j, j+1);
A[i] = q;
}
i = MATRIX_IDX(N, N-1, N-2);
A[i] = q;
i = MATRIX_IDX(N, N-1, N-1);
A[i] = (2.0*N-1.0)*(2.0*N-1.0);
return SF_ERROR_OK;
}
} // namespace mathieu
} // namespace xsf
#endif // #ifndef MAKE_MATRIX_H