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antigradient2.c
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antigradient2.c
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/*
* ANTIGRADIENT
*
* See the help text in antigradient.m for a description.
*
* Author: Gunnar Farnebäck
* Medical Informatics
* Linköping University, Sweden
*/
#include "mex.h"
#include <string.h>
#define RECURSION_SIZE_LIMIT 4
/* This can without cost be overdimensioned. */
#define MAX_LEVELS 30
/* Helper macro. */
#define VAL(x, y) ((x) ? (y) : 0)
struct data
{
mxArray *A_array;
double *lhs[MAX_LEVELS];
};
struct data data;
static void
clear_global_data()
{
int k;
data.A_array = NULL;
for (k = 0; k < MAX_LEVELS; k++)
data.lhs[k] = NULL;
}
/*************** 2D ****************/
static void
logmatrix2D(double *M, int m, int n, char *name, char *logfunction)
{
mxArray *M_array;
int dims[2];
int i;
mxArray *input_arrays[2];
dims[0] = m;
dims[1] = n;
M_array = mxCreateNumericArray(2, dims, mxDOUBLE_CLASS, mxREAL);
for (i = 0; i < m * n; i++)
mxGetPr(M_array)[i] = M[i];
input_arrays[0] = M_array;
input_arrays[1] = mxCreateString(name);
mexCallMATLAB(0, NULL, 2, input_arrays, logfunction);
}
static void
solve_directly2D(double *lhs, double *rhs, double *f_out, int M, int N)
{
int s = M * N;
int dims[2];
mxArray *b_array;
double *b;
int i, j;
mxArray *x_array;
mxArray *input_arrays[2];
if (data.A_array == NULL)
{
double *A;
dims[0] = s;
dims[1] = s;
data.A_array = mxCreateNumericArray(2, dims, mxDOUBLE_CLASS, mxREAL);
A = mxGetPr(data.A_array);
for (j = 0; j < N; j++)
for (i = 0; i < M; i++)
{
int index = j * M + i;
A[index + s * index] = lhs[9 * index] + (lhs[9 * index] == 0.0);
if (i > 0)
A[index + s * (index - 1)] = lhs[9 * index + 1];
if (i < M-1)
A[index + s * (index + 1)] = lhs[9 * index + 2];
if (j > 0)
A[index + s * (index - M)] = lhs[9 * index + 3];
if (j < N-1)
A[index + s * (index + M)] = lhs[9 * index + 4];
if (i > 0 && j > 0)
A[index + s * (index - M - 1)] = lhs[9 * index + 5];
if (i > 0 && j < N-1)
A[index + s * (index + M - 1)] = lhs[9 * index + 6];
if (i < M-1 && j > 0)
A[index + s * (index - M + 1)] = lhs[9 * index + 7];
if (i < M-1 && j < N-1)
A[index + s * (index + M + 1)] = lhs[9 * index + 8];
}
for (i = 0; i < s*s; i++)
A[i] += 1.0 / (s*s);
}
dims[0] = s;
dims[1] = 1;
b_array = mxCreateNumericArray(2, dims, mxDOUBLE_CLASS, mxREAL);
b = mxGetPr(b_array);
memcpy(b, rhs, M * N * sizeof(*rhs));
input_arrays[0] = data.A_array;
input_arrays[1] = b_array;
mexCallMATLAB(1, &x_array, 2, input_arrays, "\\");
memcpy(f_out, mxGetPr(x_array), s * sizeof(*f_out));
mxDestroyArray(x_array);
mxDestroyArray(b_array);
}
/* Gauss-Seidel smoothing iteration. Red-black ordering. */
static void
gauss_seidel2D(double *f, double *A, double *d, int M, int N)
{
int pass;
int i, j;
int index;
for (pass = 0; pass <= 1; pass++)
{
for (j = 0; j < N; j++)
for (i = 0; i < M; i++)
{
double new_f;
if ((i + j) % 2 != pass)
continue;
index = i + j * M;
if (A[9 * index] == 0.0)
continue;
new_f = d[index];
if (i > 0)
new_f -= A[9 * index + 1] * f[index - 1];
if (i < M-1)
new_f -= A[9 * index + 2] * f[index + 1];
if (j > 0)
new_f -= A[9 * index + 3] * f[index - M];
if (j < N-1)
new_f -= A[9 * index + 4] * f[index + M];
if (i > 0 && j > 0)
new_f -= A[9 * index + 5] * f[index - 1 - M];
if (i > 0 && j < N-1)
new_f -= A[9 * index + 6] * f[index - 1 + M];
if (i < M-1 && j > 0)
new_f -= A[9 * index + 7] * f[index + 1 - M];
if (i < M-1 && j < N-1)
new_f -= A[9 * index + 8] * f[index + 1 + M];
f[index] = new_f / A[9 * index];
}
}
}
static void
compute_residual2D(double *r, double *A, double *d, double *f, int M, int N)
{
int i, j;
for (j = 0; j < N; j++)
for (i = 0; i < M; i++)
{
int index = j * M + i;
double residual = 0.0;
if (A[9 * index] != 0.0)
{
residual = d[index] - A[9 * index] * f[index];
if (i > 0)
residual -= A[9 * index + 1] * f[index - 1];
if (i < M-1)
residual -= A[9 * index + 2] * f[index + 1];
if (j > 0)
residual -= A[9 * index + 3] * f[index - M];
if (j < N-1)
residual -= A[9 * index + 4] * f[index + M];
if (i > 0 && j > 0)
residual -= A[9 * index + 5] * f[index - 1 - M];
if (i > 0 && j < N-1)
residual -= A[9 * index + 6] * f[index - 1 + M];
if (i < M-1 && j > 0)
residual -= A[9 * index + 7] * f[index + 1 - M];
if (i < M-1 && j < N-1)
residual -= A[9 * index + 8] * f[index + 1 + M];
}
r[index] = residual;
}
}
static void
downsample2D(double *rhs, int M, int N,
double *rhs_coarse, int Mhalf, int Nhalf,
double *weight, double *coarse_weight)
{
int i, j;
int index1;
int index2;
double c, n, s, w, e, nw, ne, sw, se;
double sum;
if (M % 2 == 0 && N % 2 == 0)
{
for (j = 0; j < Nhalf; j++)
for (i = 0; i < Mhalf; i++)
{
index1 = (j * Mhalf + i);
index2 = (2 * j * M + 2 * i);
nw = weight[index2];
ne = weight[index2 + M];
sw = weight[index2 + 1];
se = weight[index2 + M + 1];
sum = nw + ne + sw + se;
coarse_weight[index1] = sum;
if (sum > 0)
{
rhs_coarse[index1] = 4 / sum * (nw * rhs[index2]
+ ne * rhs[index2 + M]
+ sw * rhs[index2 + 1]
+ se * rhs[index2 + M + 1]);
}
}
}
if (M % 2 == 1 && N % 2 == 0)
{
for (j = 0; j < Nhalf; j++)
for (i = 0; i < Mhalf; i++)
{
double result;
index1 = (j * Mhalf + i);
index2 = (2 * j * M + 2 * i);
nw = 0.5 * VAL(i > 0, weight[index2 - 1]);
ne = 0.5 * VAL(i > 0, weight[index2 + M - 1]);
w = weight[index2];
e = weight[index2 + M];
sw = 0.5 * VAL(i < Mhalf - 1, weight[index2 + 1]);
se = 0.5 * VAL(i < Mhalf - 1, weight[index2 + M + 1]);
sum = nw + ne + w + e + sw + se;
coarse_weight[index1] = sum;
if (sum > 0)
{
result = w * rhs[index2] + e * rhs[index2 + M];
if (i > 0)
result += nw * rhs[index2 - 1] + ne * rhs[index2 + M - 1];
if (i < Mhalf - 1)
result += sw * rhs[index2 + 1] + se * rhs[index2 + M + 1];
rhs_coarse[index1] = 4 / sum * result;
}
}
}
if (M % 2 == 0 && N % 2 == 1)
{
for (j = 0; j < Nhalf; j++)
for (i = 0; i < Mhalf; i++)
{
double result;
index1 = (j * Mhalf + i);
index2 = (2 * j * M + 2 * i);
nw = 0.5 * VAL(j > 0, weight[index2 - M]);
sw = 0.5 * VAL(j > 0, weight[index2 - M + 1]);
n = weight[index2];
s = weight[index2 + 1];
ne = 0.5 * VAL(j < Nhalf - 1, weight[index2 + M]);
se = 0.5 * VAL(j < Nhalf - 1, weight[index2 + M + 1]);
sum = nw + sw + n + s + ne + se;
coarse_weight[index1] = sum;
if (sum > 0)
{
result = n * rhs[index2] + s * rhs[index2 + 1];
if (j > 0)
result += nw * rhs[index2 - M] + sw * rhs[index2 - M + 1];
if (j < Nhalf - 1)
result += ne * rhs[index2 + M] + se * rhs[index2 + M + 1];
rhs_coarse[index1] = 4 / sum * result;
}
}
}
if (M % 2 == 1 && N % 2 == 1)
{
for (j = 0; j < Nhalf; j++)
for (i = 0; i < Mhalf; i++)
{
double result;
index1 = (j * Mhalf + i);
index2 = (2 * j * M + 2 * i);
c = weight[index2];
n = 0.5 * VAL(i > 0, weight[index2 - 1]);
s = 0.5 * VAL(i < Mhalf - 1, weight[index2 + 1]);
w = 0.5 * VAL(j > 0, weight[index2 - M]);
e = 0.5 * VAL(j < Nhalf - 1, weight[index2 + M]);
nw = 0.25 * VAL(i > 0 && j > 0, weight[index2 - M - 1]);
ne = 0.25 * VAL(i > 0 && j < Nhalf - 1, weight[index2 + M - 1]);
sw = 0.25 * VAL(i < Mhalf - 1 && j > 0, weight[index2 - M + 1]);
se = 0.25 * VAL(i < Mhalf - 1 && j < Nhalf - 1, weight[index2 + M + 1]);
sum = c + n + s + w + e + nw + ne + sw + se;
coarse_weight[index1] = sum;
if (sum > 0)
{
result = c * rhs[index2];
if (n > 0)
result += n * rhs[index2 - 1];
if (s > 0)
result += s * rhs[index2 + 1];
if (w > 0)
result += w * rhs[index2 - M];
if (e > 0)
result += e * rhs[index2 + M];
if (nw > 0)
result += nw * rhs[index2 - M - 1];
if (ne > 0)
result += ne * rhs[index2 + M - 1];
if (sw > 0)
result += sw * rhs[index2 - M + 1];
if (se > 0)
result += se * rhs[index2 + M + 1];
rhs_coarse[index1] = 4 / sum * result;
}
}
}
}
static void
galerkin2D(int level, int M, int N, int Mhalf, int Nhalf,
double *weight, double *coarse_weight)
{
int i, j;
double *lhs;
double *lhs_coarse;
if (data.lhs[level + 1] != NULL)
return;
data.lhs[level + 1] = mxCalloc(9 * Mhalf * Nhalf,
sizeof(*data.lhs[level + 1]));
lhs = data.lhs[level];
lhs_coarse = data.lhs[level + 1];
for (j = 0; j < Nhalf; j++)
for (i = 0; i < Mhalf; i++)
{
int index1 = (j * Mhalf + i);
int index2 = (2 * j * M + 2 * i);
double stencil1[3][3];
double stencil2[5][5];
double stencil3[3][3];
double mask1[3][3];
int u, v;
for (u = 0; u < 5; u++)
for (v = 0; v < 5; v++)
{
stencil2[u][v] = 0;
if (u < 3 && v < 3)
{
stencil1[u][v] = 0;
stencil3[u][v] = 0;
}
}
mask1[1][1] = coarse_weight[index1];
mask1[0][1] = VAL(i > 0, coarse_weight[index1 - 1]);
mask1[2][1] = VAL(i < Mhalf - 1, coarse_weight[index1 + 1]);
mask1[1][0] = VAL(j > 0, coarse_weight[index1 - Mhalf]);
mask1[1][2] = VAL(j < Nhalf - 1, coarse_weight[index1 + Mhalf]);
mask1[0][0] = VAL(i > 0 && j > 0, coarse_weight[index1 - Mhalf - 1]);
mask1[0][2] = VAL(i > 0 && j < Nhalf - 1, coarse_weight[index1 + Mhalf - 1]);
mask1[2][0] = VAL(i < Mhalf - 1 && j > 0, coarse_weight[index1 - Mhalf + 1]);
mask1[2][2] = VAL(i < Mhalf - 1 && j < Nhalf - 1, coarse_weight[index1 + Mhalf + 1]);
if (M % 2 == 0 && N % 2 == 0)
{
double nw = weight[index2];
double ne = weight[index2 + M];
double sw = weight[index2 + 1];
double se = weight[index2 + M + 1];
double mean = (nw + sw + ne + se) / 4;
/* If mean is 0 here we can short-circuit. */
if (mean == 0)
continue;
stencil1[1][1] = nw / mean;
stencil1[1][2] = ne / mean;
stencil1[2][1] = sw / mean;
stencil1[2][2] = se / mean;
}
if (M % 2 == 1 && N % 2 == 0)
{
double nw = 0.5 * VAL(i > 0, weight[index2 - 1]);
double ne = 0.5 * VAL(i > 0, weight[index2 + M - 1]);
double w = weight[index2];
double e = weight[index2 + M];
double sw = 0.5 * VAL(i < Mhalf - 1, weight[index2 + 1]);
double se = 0.5 * VAL(i < Mhalf - 1, weight[index2 + M + 1]);
double mean = (w + e + nw + ne + sw + se) / 4;
/* If mean is 0 here we can short-circuit. */
if (mean == 0)
continue;
stencil1[1][1] = w / mean;
stencil1[1][2] = e / mean;
stencil1[2][1] = sw / mean;
stencil1[2][2] = se / mean;
stencil1[0][1] = nw / mean;
stencil1[0][2] = ne / mean;
}
if (M % 2 == 0 && N % 2 == 1)
{
double nw = 0.5 * VAL(j > 0, weight[index2 - M]);
double sw = 0.5 * VAL(j > 0, weight[index2 - M + 1]);
double n = weight[index2];
double s = weight[index2 + 1];
double ne = 0.5 * VAL(j < Nhalf - 1, weight[index2 + M]);
double se = 0.5 * VAL(j < Nhalf - 1, weight[index2 + M + 1]);
double mean = (n + s + nw + ne + sw + se) / 4;
/* If mean is 0 here we can short-circuit. */
if (mean == 0)
continue;
stencil1[1][1] = n / mean;
stencil1[2][1] = s / mean;
stencil1[1][2] = ne / mean;
stencil1[2][2] = se / mean;
stencil1[1][0] = nw / mean;
stencil1[2][0] = sw / mean;
}
if (M % 2 == 1 && N % 2 == 1)
{
double c = weight[index2];
double n = 0.5 * VAL(i > 0, weight[index2 - 1]);
double s = 0.5 * VAL(i < Mhalf - 1, weight[index2 + 1]);
double w = 0.5 * VAL(j > 0, weight[index2 - M]);
double e = 0.5 * VAL(j < Nhalf - 1, weight[index2 + M]);
double nw = 0.25 * VAL(i > 0 && j > 0, weight[index2 - M - 1]);
double ne = 0.25 * VAL(i > 0 && j < Nhalf - 1, weight[index2 + M - 1]);
double sw = 0.25 * VAL(i < Mhalf - 1 && j > 0, weight[index2 - M + 1]);
double se = 0.25 * VAL(i < Mhalf - 1 && j < Nhalf - 1, weight[index2 + M + 1]);
double mean = (c + s + e + w + n + se + sw + ne + nw) / 4;
/* If mean is 0 here we can short-circuit. */
if (mean == 0)
continue;
stencil1[0][0] = nw / mean;
stencil1[0][1] = n / mean;
stencil1[0][2] = ne / mean;
stencil1[1][0] = w / mean;
stencil1[1][1] = c / mean;
stencil1[1][2] = e / mean;
stencil1[2][0] = sw / mean;
stencil1[2][1] = s / mean;
stencil1[2][2] = se / mean;
}
for (u = 0; u < 3; u++)
for (v = 0; v < 3; v++)
{
if (stencil1[u][v] != 0)
{
int index = 9 * (index2 + (u-1) + M*(v-1));
if (lhs[index] != 0.0)
{
stencil2[u+1][v+1] += stencil1[u][v] * lhs[index];
stencil2[u ][v+1] += stencil1[u][v] * lhs[index + 1];
stencil2[u+2][v+1] += stencil1[u][v] * lhs[index + 2];
stencil2[u+1][v ] += stencil1[u][v] * lhs[index + 3];
stencil2[u+1][v+2] += stencil1[u][v] * lhs[index + 4];
stencil2[u ][v ] += stencil1[u][v] * lhs[index + 5];
stencil2[u ][v+2] += stencil1[u][v] * lhs[index + 6];
stencil2[u+2][v ] += stencil1[u][v] * lhs[index + 7];
stencil2[u+2][v+2] += stencil1[u][v] * lhs[index + 8];
}
}
}
if (M % 2 == 0 && N % 2 == 0)
{
for (u = 1; u < 5; u++)
for (v = 1; v < 5; v++)
{
double alpha1, alpha2;
double nw, ne, sw, se;
int uu, vv;
double sum;
if (u % 2 == 0)
alpha1 = 0.75;
else
alpha1 = 0.25;
if (v % 2 == 0)
alpha2 = 0.75;
else
alpha2 = 0.25;
uu = (u-1)/2;
vv = (v-1)/2;
nw = (1 - alpha1) * (1 - alpha2) * mask1[uu ][vv ];
ne = (1 - alpha1) * alpha2 * mask1[uu ][vv+1];
sw = alpha1 * (1 - alpha2) * mask1[uu+1][vv ];
se = alpha1 * alpha2 * mask1[uu+1][vv+1];
sum = nw + ne + sw + se;
if (sum > 0)
{
stencil3[uu ][vv ] += nw * stencil2[u][v] / sum;
stencil3[uu ][vv+1] += ne * stencil2[u][v] / sum;
stencil3[uu+1][vv ] += sw * stencil2[u][v] / sum;
stencil3[uu+1][vv+1] += se * stencil2[u][v] / sum;
}
}
}
if (M % 2 == 1 && N % 2 == 0)
{
for (u = 0; u < 5; u++)
for (v = 1; v < 5; v++)
{
double alpha1, alpha2;
double nw, ne, sw, se;
int uu, vv;
double sum;
if (u % 2 == 0)
alpha1 = 0;
else
alpha1 = 0.5;
if (v % 2 == 0)
alpha2 = 0.75;
else
alpha2 = 0.25;
uu = u/2;
vv = (v-1)/2;
nw = (1 - alpha1) * (1 - alpha2) * mask1[uu ][vv ];
ne = (1 - alpha1) * alpha2 * mask1[uu ][vv+1];
sw = 0;
se = 0;
if (alpha1 > 0)
{
sw = alpha1 * (1 - alpha2) * mask1[uu+1][vv ];
se = alpha1 * alpha2 * mask1[uu+1][vv+1];
}
sum = nw + ne + sw + se;
if (sum > 0)
{
stencil3[uu ][vv ] += nw * stencil2[u][v] / sum;
stencil3[uu ][vv+1] += ne * stencil2[u][v] / sum;
if (alpha1 > 0)
{
stencil3[uu+1][vv ] += sw * stencil2[u][v] / sum;
stencil3[uu+1][vv+1] += se * stencil2[u][v] / sum;
}
}
}
}
if (M % 2 == 0 && N % 2 == 1)
{
for (u = 1; u < 5; u++)
for (v = 0; v < 5; v++)
{
double alpha1, alpha2;
double nw, ne, sw, se;
int uu, vv;
double sum;
if (u % 2 == 0)
alpha1 = 0.75;
else
alpha1 = 0.25;
if (v % 2 == 0)
alpha2 = 0;
else
alpha2 = 0.5;
uu = (u-1)/2;
vv = v/2;
nw = (1 - alpha1) * (1 - alpha2) * mask1[uu ][vv ];
sw = alpha1 * (1 - alpha2) * mask1[uu+1][vv ];
ne = 0;
se = 0;
if (alpha2 > 0)
{
ne = (1 - alpha1) * alpha2 * mask1[uu ][vv+1];
se = alpha1 * alpha2 * mask1[uu+1][vv+1];
}
sum = nw + ne + sw + se;
if (sum > 0)
{
stencil3[uu ][vv ] += nw * stencil2[u][v] / sum;
stencil3[uu+1][vv ] += sw * stencil2[u][v] / sum;
if (alpha2 > 0)
{
stencil3[uu ][vv+1] += ne * stencil2[u][v] / sum;
stencil3[uu+1][vv+1] += se * stencil2[u][v] / sum;
}
}
}
}
if (M % 2 == 1 && N % 2 == 1)
{
for (u = 0; u < 5; u++)
for (v = 0; v < 5; v++)
{
double alpha1, alpha2;
double nw, ne, sw, se;
int uu, vv;
double sum;
if (u % 2 == 0)
alpha1 = 0;
else
alpha1 = 0.5;
if (v % 2 == 0)
alpha2 = 0;
else
alpha2 = 0.5;
uu = u/2;
vv = v/2;
nw = (1 - alpha1) * (1 - alpha2) * mask1[uu ][vv ];
sw = 0;
if (alpha1 > 0)
sw = alpha1 * (1 - alpha2) * mask1[uu+1][vv ];
ne = 0;
if (alpha2 > 0)
ne = (1 - alpha1) * alpha2 * mask1[uu ][vv+1];
se = 0;
if (alpha1 > 0 && alpha2 > 0)
se = alpha1 * alpha2 * mask1[uu+1][vv+1];
sum = nw + ne + sw + se;
if (sum > 0)
{
stencil3[uu ][vv ] += nw * stencil2[u][v] / sum;
if (alpha1 > 0)
stencil3[uu+1][vv ] += sw * stencil2[u][v] / sum;
if (alpha2 > 0)
stencil3[uu ][vv+1] += ne * stencil2[u][v] / sum;
if (alpha1 > 0 && alpha2 > 0)
stencil3[uu+1][vv+1] += se * stencil2[u][v] / sum;
}
}
}
lhs_coarse[9 * index1] = stencil3[1][1];
lhs_coarse[9 * index1 + 1] = stencil3[0][1];
lhs_coarse[9 * index1 + 2] = stencil3[2][1];
lhs_coarse[9 * index1 + 3] = stencil3[1][0];
lhs_coarse[9 * index1 + 4] = stencil3[1][2];
lhs_coarse[9 * index1 + 5] = stencil3[0][0];
lhs_coarse[9 * index1 + 6] = stencil3[0][2];
lhs_coarse[9 * index1 + 7] = stencil3[2][0];
lhs_coarse[9 * index1 + 8] = stencil3[2][2];
for (u = 1; u < 9; u++)
if (lhs_coarse[9 * index1 + u] < 0)
{
lhs_coarse[9 * index1] += lhs_coarse[9 * index1 + u];
lhs_coarse[9 * index1 + u] = 0;
}
}
}
/* Upsample and apply correction. Bilinear interpolation. */
static void
upsample2D(int M, int N,
double *v, int Mhalf, int Nhalf,
double *f_out, double *weight, double *coarse_weight)
{
int i, j;
int index1, index2;
if (M % 2 == 0 && N % 2 == 0)
{
for (j = 0; j < N; j++)
for (i = 0; i < M; i++)
{
double alpha1, alpha2;
double nw, ne, sw, se;
double sum;
index1 = j * M + i;
index2 = ((j + 1) / 2 - 1) * Mhalf + (i + 1) / 2 - 1;
if (weight[index1] == 0)
continue;
if (i % 2 == 0)
alpha1 = 0.75;
else
alpha1 = 0.25;
if (j % 2 == 0)
alpha2 = 0.75;
else
alpha2 = 0.25;
nw = (1 - alpha1) * (1 - alpha2) * VAL(i > 0 && j > 0, coarse_weight[index2]);
ne = (1 - alpha1) * alpha2 * VAL(i > 0 && j < N - 1, coarse_weight[index2 + Mhalf]);
sw = alpha1 * (1 - alpha2) * VAL(i < M - 1 && j > 0, coarse_weight[index2 + 1]);
se = alpha1 * alpha2 * VAL(i < M - 1 && j < N - 1, coarse_weight[index2 + Mhalf + 1]);
sum = nw + ne + sw + se;
if (sum > 0)
{
double contribution = 0;
if (nw > 0)
contribution += nw * v[index2];
if (ne > 0)
contribution += ne * v[index2 + Mhalf];
if (sw > 0)
contribution += sw * v[index2 + 1];
if (se > 0)
contribution += se * v[index2 + Mhalf + 1];
f_out[index1] += contribution / sum;
}
}
}
if (M % 2 == 1 && N % 2 == 0)
{
for (j = 0; j < N; j++)
for (i = 0; i < M; i++)
{
double alpha1, alpha2;
double nw, ne, sw, se;
double sum;
index1 = j * M + i;
index2 = ((j + 1) / 2 - 1) * Mhalf + i / 2;
if (weight[index1] == 0)
continue;
if (i % 2 == 0)
alpha1 = 0.0;
else
alpha1 = 0.5;
if (j % 2 == 0)
alpha2 = 0.75;
else
alpha2 = 0.25;
nw = (1 - alpha1) * (1 - alpha2) * VAL(j > 0, coarse_weight[index2]);
ne = (1 - alpha1) * alpha2 * VAL(j < N - 1, coarse_weight[index2 + Mhalf]);
sw = alpha1 * (1 - alpha2) * VAL(i < M - 1 && j > 0, coarse_weight[index2 + 1]);
se = alpha1 * alpha2 * VAL(i < M - 1 && j < N - 1, coarse_weight[index2 + Mhalf + 1]);
sum = nw + ne + sw + se;
if (sum > 0)
{
double contribution = 0;
if (nw > 0)
contribution += nw * v[index2];
if (ne > 0)
contribution += ne * v[index2 + Mhalf];
if (sw > 0)
contribution += sw * v[index2 + 1];
if (se > 0)
contribution += se * v[index2 + Mhalf + 1];
f_out[index1] += contribution / sum;
}
}
}
if (M % 2 == 0 && N % 2 == 1)
{
for (j = 0; j < N; j++)
for (i = 0; i < M; i++)
{
double alpha1, alpha2;
double nw, ne, sw, se;
double sum;
index1 = j * M + i;
index2 = (j / 2) * Mhalf + (i + 1) / 2 - 1;
if (weight[index1] == 0)
continue;
if (i % 2 == 0)
alpha1 = 0.75;
else
alpha1 = 0.25;
if (j % 2 == 0)
alpha2 = 0.0;
else
alpha2 = 0.5;
nw = (1 - alpha1) * (1 - alpha2) * VAL(i > 0, coarse_weight[index2]);
ne = (1 - alpha1) * alpha2 * VAL(i > 0 && j < N - 1, coarse_weight[index2 + Mhalf]);
sw = alpha1 * (1 - alpha2) * VAL(i < M - 1, coarse_weight[index2 + 1]);
se = alpha1 * alpha2 * VAL(i < M - 1 && j < N - 1, coarse_weight[index2 + Mhalf + 1]);
sum = nw + ne + sw + se;
if (sum > 0)
{
double contribution = 0;
if (nw > 0)
contribution += nw * v[index2];
if (ne > 0)
contribution += ne * v[index2 + Mhalf];
if (sw > 0)
contribution += sw * v[index2 + 1];
if (se > 0)
contribution += se * v[index2 + Mhalf + 1];
f_out[index1] += contribution / sum;
}
}
}
if (M % 2 == 1 && N % 2 == 1)
{
for (j = 0; j < N; j++)
for (i = 0; i < M; i++)
{
double alpha1, alpha2;
double nw, ne, sw, se;
double sum;
index1 = j * M + i;
index2 = (j / 2) * Mhalf + i / 2;
if (weight[index1] == 0)
continue;
if (i % 2 == 0)
alpha1 = 0.0;
else
alpha1 = 0.5;
if (j % 2 == 0)
alpha2 = 0.0;
else
alpha2 = 0.5;
nw = (1 - alpha1) * (1 - alpha2) * coarse_weight[index2];
ne = (1 - alpha1) * alpha2 * VAL(j < N - 1, coarse_weight[index2 + Mhalf]);
sw = alpha1 * (1 - alpha2) * VAL(i < M - 1, coarse_weight[index2 + 1]);
se = alpha1 * alpha2 * VAL(i < M - 1 && j < N - 1, coarse_weight[index2 + Mhalf + 1]);
sum = nw + ne + sw + se;
if (sum > 0)
{
double contribution = 0;
if (nw > 0)
contribution += nw * v[index2];
if (ne > 0)
contribution += ne * v[index2 + Mhalf];
if (sw > 0)
contribution += sw * v[index2 + 1];
if (se > 0)
contribution += se * v[index2 + Mhalf + 1];
f_out[index1] += contribution / sum;
}
}
}
}
/* Recursive multigrid function.*/
static void
poisson_multigrid2D(double *f, int level, double *rhs, double *weight,
int n1, int n2, int nm,
double *f_out,
int M, int N, int *directly_solved)
{
int k;
double *r;
double *r_downsampled;
double *coarse_weight;
double *lhs = data.lhs[level];
double *v;
int Mhalf;
int Nhalf;
/* Solve a sufficiently small problem directly. */
if (M < RECURSION_SIZE_LIMIT || N < RECURSION_SIZE_LIMIT)
{
solve_directly2D(lhs, rhs, f_out, M, N);
*directly_solved = 1;
return;
}
*directly_solved = 0;
/* Initialize solution. */
memcpy(f_out, f, M * N * sizeof(*f_out));
/* Pre-smoothing. */
for (k = 0; k < n1; k++)
gauss_seidel2D(f_out, lhs, rhs, M, N);
/* Compute residual. */
r = mxCalloc(M * N, sizeof(*r));
compute_residual2D(r, lhs, rhs, f_out, M, N);
/* Downsample residual. */
Mhalf = (M + 1) / 2;
Nhalf = (N + 1) / 2;
r_downsampled = mxCalloc(Mhalf * Nhalf, sizeof(*r_downsampled));
coarse_weight = mxCalloc(Mhalf * Nhalf, sizeof(*coarse_weight));
downsample2D(r, M, N, r_downsampled, Mhalf, Nhalf, weight, coarse_weight);
galerkin2D(level, M, N, Mhalf, Nhalf, weight, coarse_weight);
/* Recurse to compute a correction. */
v = mxCalloc(Mhalf * Nhalf, sizeof(*v));
for (k = 0; k < nm; k++)
{
int directly_solved;
poisson_multigrid2D(v, level + 1, r_downsampled, coarse_weight,
n1, n2, nm, v, Mhalf, Nhalf, &directly_solved);
if (directly_solved)
break;
}
upsample2D(M, N, v, Mhalf, Nhalf, f_out, weight, coarse_weight);
/* Post-smoothing. */
for (k = 0; k < n2; k++)
gauss_seidel2D(f_out, lhs, rhs, M, N);
/* Set the mean value to zero.
*
* FIXME: This should not be needed (I believe) and might indicate
* some bug elsewhere.
*/
if (1)