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antigradient.c
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antigradient.c
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#include "mex.h"
#include <string.h>
#define RECURSION_SIZE_LIMIT 4
/*
* ANTIGRADIENT
*
* See the help text in antigradient.m for a description.
*
* Author: Gunnar Farnebäck
* Medical Informatics
* Linköping University, Sweden
* gunnar@imt.liu.se
*/
/*************** 2D ****************/
void
solve_directly2D(double *f, double *rhs, double *f_out,
mwSize M, mwSize N)
{
mwSize s = M * N;
mwSize dims[2];
mxArray *A_array;
mxArray *b_array;
double *A;
double *b;
mwSize k;
mwSize i, j;
mxArray *x_array;
mxArray *input_arrays[2];
dims[0] = s;
dims[1] = s;
A_array = mxCreateNumericArray(2, dims, mxDOUBLE_CLASS, mxREAL);
A = mxGetPr(A_array);
dims[1] = 1;
b_array = mxCreateNumericArray(2, dims, mxDOUBLE_CLASS, mxREAL);
b = mxGetPr(b_array);
k = 0;
for (j = 0; j < N; j++)
for (i = 0; i < M; i++)
{
A[k + s * (j*M+i)] = -4;
if (i > 0)
A[k + s * (j*M+i-1)] = 1 + (i == M-1);
if (i < M-1)
A[k + s * (j*M+i+1)] = 1 + (i == 0);
if (j > 0)
A[k + s * ((j-1)*M+i)] = 1 + (j == N-1);
if (j < N-1)
A[k + s * ((j+1)*M+i)] = 1 + (j == 0);
b[k] = rhs[i+j*M];
k++;
}
for (i = 0; i < s*s; i++)
A[i] += 1.0 / (s*s);
input_arrays[0] = A_array;
input_arrays[1] = b_array;
mexCallMATLAB(1, &x_array, 2, input_arrays, "\\");
memcpy(f_out, mxGetPr(x_array), s * sizeof(*f));
mxDestroyArray(x_array);
mxDestroyArray(A_array);
mxDestroyArray(b_array);
}
/* Gauss-Seidel smoothing iteration. Red-black ordering. */
void
gauss_seidel2D(double *f, double *d, mwSize M, mwSize N)
{
int pass;
mwSize i, j;
mwSize 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;
new_f = -d[index];
if (i == 0)
new_f += f[index + 1];
else
new_f += f[index - 1];
if (i == M-1)
new_f += f[index - 1];
else
new_f += f[index + 1];
if (j == 0)
new_f += f[index + M];
else
new_f += f[index - M];
if (j == N-1)
new_f += f[index - M];
else
new_f += f[index + M];
f[index] = 0.25 * new_f;
}
}
}
void
downsample2D(double *rhs, mwSize M, mwSize N,
double *rhs_coarse, mwSize Mhalf, mwSize Nhalf)
{
mwSize i, j;
mwSize index1;
mwSize index2;
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);
rhs_coarse[index1] = (rhs[index2]
+ rhs[index2 + M]
+ rhs[index2 + 1]
+ rhs[index2 + M + 1]);
}
}
if (M % 2 == 1 && N % 2 == 0)
{
for (j = 0; j < Nhalf; j++)
{
index1 = (j * Mhalf);
index2 = (2 * j * M);
rhs_coarse[index1] = (rhs[index2]
+ rhs[index2 + M]
+ rhs[index2 + 1]
+ rhs[index2 + M + 1]);
for (i = 1; i < Mhalf - 1; i++)
{
index1++;
index2 += 2;
rhs_coarse[index1] = (rhs[index2]
+ rhs[index2 + M]
+ 0.5 * (rhs[index2 - 1]
+ rhs[index2 + 1]
+ rhs[index2 + M - 1]
+ rhs[index2 + M + 1]));
}
index1++;
index2 += 2;
rhs_coarse[index1] = (rhs[index2]
+ rhs[index2 + M]
+ rhs[index2 - 1]
+ rhs[index2 + M - 1]);
}
}
if (M % 2 == 0 && N % 2 == 1)
{
for (i = 0; i < Mhalf; i++)
{
index1 = i;
index2 = 2 * i;
rhs_coarse[index1] = (rhs[index2]
+ rhs[index2 + 1]
+ rhs[index2 + M]
+ rhs[index2 + M + 1]);
}
for (j = 1; j < Nhalf - 1; j++)
{
for (i = 0; i < Mhalf; i++)
{
index1 = (j * Mhalf + i);
index2 = (2 * j * M + 2 * i);
rhs_coarse[index1] = (rhs[index2]
+ rhs[index2 + 1]
+ 0.5 * (rhs[index2 - M]
+ rhs[index2 + M]
+ rhs[index2 - M + 1]
+ rhs[index2 + M + 1]));
}
}
for (i = 0; i < Mhalf; i++)
{
index1 = (j * Mhalf + i);
index2 = (2 * j * M + 2 * i);
rhs_coarse[index1] = (rhs[index2]
+ rhs[index2 + 1]
+ rhs[index2 - M]
+ rhs[index2 - M + 1]);
}
}
if (M % 2 == 1 && N % 2 == 1)
{
for (j = 1; j < Nhalf - 1; j++)
{
for (i = 1; i < Mhalf - 1; i++)
{
index1 = (j * Mhalf + i);
index2 = (2 * j * M + 2 * i);
rhs_coarse[index1] = (rhs[index2]
+ 0.5 * (rhs[index2 - 1]
+ rhs[index2 + 1]
+ rhs[index2 - M]
+ rhs[index2 + M])
+ 0.25* (rhs[index2 - M - 1]
+ rhs[index2 - M + 1]
+ rhs[index2 + M - 1]
+ rhs[index2 + M + 1]));
}
}
for (i = 1; i < Mhalf - 1; i++)
{
index1 = i;
index2 = 2 * i;
rhs_coarse[index1] = (rhs[index2]
+ rhs[index2 + M]
+ 0.5 * (rhs[index2 - 1]
+ rhs[index2 + 1]
+ rhs[index2 + M - 1]
+ rhs[index2 + M + 1]));
index1 = ((Nhalf - 1) * Mhalf + i);
index2 = (2 * (Nhalf - 1) * M + 2 * i);
rhs_coarse[index1] = (rhs[index2]
+ rhs[index2 - M]
+ 0.5 * (rhs[index2 - 1]
+ rhs[index2 + 1]
+ rhs[index2 - M - 1]
+ rhs[index2 - M + 1]));
}
for (j = 1; j < Nhalf - 1; j++)
{
index1 = (j * Mhalf);
index2 = (2 * j * M);
rhs_coarse[index1] = (rhs[index2]
+ rhs[index2 + 1]
+ 0.5 * (rhs[index2 - M]
+ rhs[index2 + M]
+ rhs[index2 - M + 1]
+ rhs[index2 + M + 1]));
index1 = (j * Mhalf + Mhalf - 1);
index2 = (2 * j * M + 2 * (Mhalf - 1));
rhs_coarse[index1] = (rhs[index2]
+ rhs[index2 - 1]
+ 0.5 * (rhs[index2 - M]
+ rhs[index2 + M]
+ rhs[index2 - M - 1]
+ rhs[index2 + M - 1]));
}
index1 = 0;
index2 = 0;
rhs_coarse[index1] = (rhs[index2]
+ rhs[index2 + 1]
+ rhs[index2 + M]
+ rhs[index2 + M + 1]);
index1 = (Nhalf - 1) * Mhalf;
index2 = 2 * (Nhalf - 1) * M;
rhs_coarse[index1] = (rhs[index2]
+ rhs[index2 + 1]
+ rhs[index2 - M]
+ rhs[index2 - M + 1]);
index1 = (Mhalf - 1);
index2 = (2 * (Mhalf - 1));
rhs_coarse[index1] = (rhs[index2]
+ rhs[index2 - 1]
+ rhs[index2 + M]
+ rhs[index2 + M - 1]);
index1 = ((Nhalf - 1) * Mhalf + Mhalf - 1);
index2 = (2 * (Nhalf - 1) * M + 2 * (Mhalf - 1));
rhs_coarse[index1] = (rhs[index2]
+ rhs[index2 - 1]
+ rhs[index2 - M]
+ rhs[index2 - M - 1]);
}
}
/* Upsample and apply correction. Bilinear interpolation. */
void
upsample2D(double *rhs, mwSize M, mwSize N,
double *v, mwSize Mhalf, mwSize Nhalf,
double *f_out)
{
mwSize i, j;
mwSize index1, index2;
mwSize ce, no, so, we, ea, nw, sw, ne, se;
mwSize CE, NO, SO, WE, EA, SW, NE, SE;
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);
ce = index1;
no = index1 - 1;
so = index1 + 1;
we = index1 - Mhalf;
ea = index1 + Mhalf;
nw = index1 - Mhalf - 1;
sw = index1 - Mhalf + 1;
ne = index1 + Mhalf - 1;
se = index1 + Mhalf + 1;
CE = index2;
SO = index2 + 1;
EA = index2 + M;
SE = index2 + M + 1;
/* Fine pixels northwest of coarse pixel center. */
if (i == 0)
{
if (j == 0) /* NW corner. */
f_out[CE] += v[ce] - 0.25 * rhs[CE];
else /* North edge. */
f_out[CE] += 0.75 * v[ce] + 0.25 * (v[we] - rhs[CE]);
}
else
{
if (j == 0) /* West edge. */
f_out[CE] += 0.75 * v[ce] + 0.25 * (v[no] - rhs[CE]);
else /* Inner point. */
f_out[CE] += (0.5625 * v[ce] + 0.1875 * (v[no] + v[we]) + 0.0625 * v[nw]);
}
/* Fine pixels southwest of coarse pixel center. */
if (i == Mhalf - 1)
{
if (j == 0) /* SW corner. */
f_out[SO] += v[ce] - 0.25 * rhs[SO];
else /* South edge. */
f_out[SO] += 0.75 * v[ce] + 0.25 * (v[we] - rhs[SO]);
}
else
{
if (j == 0) /* West edge. */
f_out[SO] += 0.75 * v[ce] + 0.25 * (v[so] - rhs[SO]);
else /* Inner point. */
f_out[SO] += 0.5625 * v[ce] + 0.1875 * (v[so] + v[we]) + 0.0625 * v[sw];
}
/* Fine pixels northeast of coarse pixel center. */
if (i == 0)
{
if (j == Nhalf - 1) /* NE corner. */
f_out[EA] += v[ce] - 0.25 * rhs[EA];
else /* North edge. */
f_out[EA] += 0.75 * v[ce] + 0.25 * (v[ea] - rhs[EA]);
}
else
{
if (j == Nhalf - 1) /* East edge. */
f_out[EA] += 0.75 * v[ce] + 0.25 * (v[no] - rhs[EA]);
else /* Inner point. */
f_out[EA] += 0.5625 * v[ce] + 0.1875 * (v[no] + v[ea]) + 0.0625 * v[ne];
}
/* Fine pixels southeast of coarse pixel center. */
if (i == Mhalf - 1)
{
if (j == Nhalf - 1) /* SE corner. */
f_out[SE] += v[ce] - 0.25 * rhs[SE];
else /* South edge.*/
f_out[SE] += 0.75 * v[ce] + 0.25 * (v[ea] - rhs[SE]);
}
else
{
if (j == Nhalf - 1) /* East edge. */
f_out[SE] += 0.75 * v[ce] + 0.25 * (v[so] - rhs[SE]);
else /* Inner point. */
f_out[SE] += 0.5625 * v[ce] + 0.1875 * (v[so] + v[ea]) + 0.0625 * v[se];
}
}
}
if (M % 2 == 1 && 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);
ce = index1;
so = index1 + 1;
we = index1 - Mhalf;
ea = index1 + Mhalf;
sw = index1 - Mhalf + 1;
se = index1 + Mhalf + 1;
CE = index2;
SO = index2 + 1;
EA = index2 + M;
SE = index2 + M + 1;
NO = index2 - 1;
NE = index2 + M - 1;
/* Fine pixels west of coarse pixel center. */
if (j == 0) /* West edge. */
{
if (i == 0) /* NW corner */
f_out[CE] += v[ce] - 0.125 * (rhs[SO] + rhs[CE] - rhs[EA]);
else if (i == Mhalf - 1) /* SW corner */
f_out[CE] += v[ce] - 0.125 * (rhs[NO] + rhs[CE] - rhs[EA]);
else
f_out[CE] += v[ce] - 0.25 * rhs[CE];
}
else /* Inner point. */
f_out[CE] += 0.75 * v[ce] + 0.25 * v[we];
/* Fine pixels southsouthwest of coarse pixel center. */
if (i < Mhalf - 1)
{
if (j == 0) /* West edge. */
f_out[SO] += 0.5 * (v[ce] + v[so]) - 0.25 * rhs[SO];
else /* Inner point. */
f_out[SO] += 0.375 * (v[ce] + v[so]) + 0.125 * (v[we] + v[sw]);
}
/* Fine pixels east of coarse pixel center. */
if (j == Nhalf - 1) /* East edge. */
{
if (i == 0) /* NE corner */
f_out[EA] += v[ce] - 0.125 * (rhs[SE] + rhs[EA] - rhs[CE]);
else if (i == Mhalf - 1) /* SE corner */
f_out[EA] += v[ce] - 0.125 * (rhs[NE] + rhs[EA] - rhs[CE]);
else
f_out[EA] += v[ce] - 0.25 * rhs[EA];
}
else /* Inner point. */
f_out[EA] += 0.75 * v[ce] + 0.25 * v[ea];
/* Fine pixels southsoutheast of coarse pixel center. */
if (i < Mhalf - 1)
{
if (j == Nhalf - 1) /* East edge. */
f_out[SE] += 0.5 * (v[ce] + v[so]) - 0.25 * rhs[SE];
else /* Inner point. */
f_out[SE] += 0.375 * (v[ce] + v[so]) + 0.125 * (v[ea] + v[se]);
}
}
}
if (M % 2 == 0 && N % 2 == 1)
{
for (j = 0; j < Nhalf; j++)
for (i = 0; i < Mhalf; i++)
{
index1 = (j * Mhalf + i);
index2 = (2 * j * M + 2 * i);
ce = index1;
so = index1 + 1;
no = index1 - 1;
ea = index1 + Mhalf;
se = index1 + Mhalf + 1;
ne = index1 + Mhalf - 1;
CE = index2;
SO = index2 + 1;
EA = index2 + M;
SE = index2 + M + 1;
WE = index2 - M;
SW = index2 - M + 1;
/* Fine pixels north of coarse pixel center. */
if (i == 0) /* North edge. */
{
if (j == 0) /* NW corner */
f_out[CE] += v[ce] - 0.125 * (rhs[EA] + rhs[CE] - rhs[SO]);
else if (j == Nhalf - 1) /* NE corner */
f_out[CE] += v[ce] - 0.125 * (rhs[WE] + rhs[CE] - rhs[SO]);
else
f_out[CE] += v[ce] - 0.25 * rhs[CE];
}
else /* Inner point. */
f_out[CE] += 0.75 * v[ce] + 0.25 * v[no];
/* Fine pixels eastnortheast of coarse pixel center. */
if (j < Nhalf - 1)
{
if (i == 0) /* North edge. */
f_out[EA] += 0.5 * (v[ce] + v[ea]) - 0.25 * rhs[EA];
else /* Inner point. */
f_out[EA] += 0.375 * (v[ce] + v[ea]) + 0.125 * (v[no] + v[ne]);
}
/* Fine pixels south of coarse pixel center. */
if (i == Mhalf - 1) /* South edge. */
{
if (j == 0) /* SW corner */
f_out[SO] += v[ce] - 0.125 * (rhs[SE] + rhs[SO] - rhs[CE]);
else if (j == Nhalf - 1) /* SE corner */
f_out[SO] += v[ce] - 0.125 * (rhs[SW] + rhs[SO] - rhs[CE]);
else
f_out[SO] += v[ce] - 0.25 * rhs[SO];
}
else /* Inner point. */
f_out[SO] += 0.75 * v[ce] + 0.25 * v[so];
/* Fine pixels eastsoutheast of coarse pixel center. */
if (j < Nhalf - 1)
{
if (i == Mhalf - 1) /* South edge. */
f_out[SE] += 0.5 * (v[ce] + v[ea]) - 0.25 * rhs[SE];
else /* Inner point. */
f_out[SE] += 0.375 * (v[ce] + v[ea]) + 0.125 * (v[so] + v[se]);
}
}
}
if (M % 2 == 1 && N % 2 == 1)
{
for (j = 0; j < Nhalf; j++)
for (i = 0; i < Mhalf; i++)
{
index1 = (j * Mhalf + i);
index2 = (2 * j * M + 2 * i);
ce = index1;
so = index1 + 1;
ea = index1 + Mhalf;
se = index1 + Mhalf + 1;
CE = index2;
SO = index2 + 1;
EA = index2 + M;
SE = index2 + M + 1;
/* Fine pixels on coarse pixel center. */
f_out[CE] += v[ce];
/* Fine pixels south of coarse pixel center. */
if (i < Mhalf - 1)
f_out[SO] += 0.5 * (v[ce] + v[so]);
/* Fine pixels east of coarse pixel center. */
if (j < Nhalf - 1) /* South edge. */
f_out[EA] += 0.5 * (v[ce] + v[ea]);
/* Fine pixels southeast of coarse pixel center. */
if (i < Mhalf - 1 && j < Nhalf - 1)
f_out[SE] += 0.25 * (v[ce] + v[ea] + v[so] + v[se]);
}
}
}
/* Recursive multigrid function.*/
void
poisson_multigrid2D(double *f, double *d,
int n1, int n2, int nm,
double *f_out,
mwSize M, mwSize N, int *directly_solved)
{
mwSize i, j;
mwSize k;
double *r;
double *r_downsampled;
double *v;
mwSize Mhalf;
mwSize Nhalf;
/* Solve a sufficiently small problem directly. */
if (M < RECURSION_SIZE_LIMIT || N < RECURSION_SIZE_LIMIT)
{
solve_directly2D(f, d, 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, d, M, N);
/* Compute residual. */
r = mxCalloc(M * N, sizeof(*r));
for (j = 0; j < N; j++)
for (i = 0; i < M; i++)
{
mwSize index = j * M + i;
double residual = d[index] + 4 * f_out[index];
if (i == 0)
residual -= f_out[index + 1];
else
residual -= f_out[index - 1];
if (i == M - 1)
residual -= f_out[index - 1];
else
residual -= f_out[index + 1];
if (j == 0)
residual -= f_out[index + M];
else
residual -= f_out[index - M];
if (j == N - 1)
residual -= f_out[index - M];
else
residual -= f_out[index + M];
r[index] = residual;
}
/* Downsample residual. */
Mhalf = (M + 1) / 2;
Nhalf = (N + 1) / 2;
r_downsampled = mxCalloc(Mhalf * Nhalf, sizeof(*r_downsampled));
downsample2D(r, M, N, r_downsampled, Mhalf, Nhalf);
/* Recurse to compute a correction. */
v = mxCalloc(Mhalf * Nhalf, sizeof(*v));
for (k = 0; k < nm; k++)
{
int directly_solved;
poisson_multigrid2D(v, r_downsampled, n1, n2, nm, v, Mhalf, Nhalf,
&directly_solved);
if (directly_solved)
break;
}
upsample2D(r, M, N, v, Mhalf, Nhalf, f_out);
/* Post-smoothing. */
for (k = 0; k < n2; k++)
gauss_seidel2D(f_out, d, M, N);
mxFree(r);
mxFree(r_downsampled);
mxFree(v);
}
/* It is assumed that f_out is initialized to zero when called. */
void
poisson_full_multigrid2D(double *rhs, int number_of_iterations,
mwSize M, mwSize N, double *f_out)
{
double *rhs_downsampled;
double *f_coarse;
mwSize k;
/* Unless already coarsest scale, first recurse to coarser scale. */
if (M >= RECURSION_SIZE_LIMIT && N >= RECURSION_SIZE_LIMIT)
{
/* Downsample right hand side. */
mwSize Mhalf = (M + 1) / 2;
mwSize Nhalf = (N + 1) / 2;
rhs_downsampled = mxCalloc(Mhalf * Nhalf, sizeof(*rhs_downsampled));
downsample2D(rhs, M, N, rhs_downsampled, Mhalf, Nhalf);
f_coarse = mxCalloc(Mhalf * Nhalf, sizeof(*f_coarse));
poisson_full_multigrid2D(rhs_downsampled, number_of_iterations,
Mhalf, Nhalf, f_coarse);
/* Upsample the coarse result. */
upsample2D(rhs, M, N, f_coarse, Mhalf, Nhalf, f_out);
mxFree(f_coarse);
mxFree(rhs_downsampled);
}
/* Perform number_of_iterations standard multigrid cycles. */
for (k = 0; k < number_of_iterations; k++)
{
int directly_solved;
poisson_multigrid2D(f_out, rhs, 2, 2, 2, f_out, M, N,
&directly_solved);
if (directly_solved)
break;
}
}
void
antigradient2D(double *g, double mu, int number_of_iterations,
mwSize M, mwSize N, double *f_out)
{
double *rhs;
double sum;
double mean;
mwSize i, j;
/* Compute right hand side of Poisson problem with Neumann
* boundary conditions, discretized by finite differences.
*/
rhs = mxCalloc(M * N, sizeof(*rhs));
for (j = 0; j < N; j++)
for (i = 0; i < M; i++)
{
mwSize index1 = j * M + i;
mwSize index2 = index1 + M * N;
double d = 0.0;
if (i == 0)
d = g[index1 + 1] + g[index1];
else if (i == M - 1)
d = - g[index1] - g[index1 - 1];
else
d = 0.5 * (g[index1 + 1] - g[index1 - 1]);
if (j == 0)
d += g[index2 + M] + g[index2];
else if (j == N - 1)
d += - g[index2] - g[index2 - M];
else
d += 0.5 * (g[index2 + M] - g[index2 - M]);
rhs[index1] = d;
}
/* Solve the equation system with the full multigrid algorithm.
* Use W cycles and 2 presmoothing and 2 postsmoothing
* Gauss-Seidel iterations.
*/
poisson_full_multigrid2D(rhs, number_of_iterations, M, N, f_out);
/* Fix the mean value. */
sum = 0.0;
for (i = 0; i < M * N; i++)
sum += f_out[i];
mean = sum / (M * N);
for (i = 0; i < M * N; i++)
{
f_out[i] -= mean;
f_out[i] += mu;
}
}
/*************** 3D ****************/
void
solve_directly3D(double *f, double *rhs,
double *f_out,
mwSize M, mwSize N, mwSize P)
{
mwSize s = M * N * P;
mwSize dims[2];
mxArray *A_array;
mxArray *b_array;
double *A;
double *b;
mwSize k;
mwSize i, j, p;
mxArray *x_array;
mxArray *input_arrays[2];
dims[0] = s;
dims[1] = s;
A_array = mxCreateNumericArray(2, dims, mxDOUBLE_CLASS, mxREAL);
A = mxGetPr(A_array);
dims[1] = 1;
b_array = mxCreateNumericArray(2, dims, mxDOUBLE_CLASS, mxREAL);
b = mxGetPr(b_array);
k = 0;
for (p = 0; p < P; p++)
for (j = 0; j < N; j++)
for (i = 0; i < M; i++)
{
A[k + s * ((p*N+j)*M+i)] = -6;
if (i > 0)
A[k + s * ((p*N+j)*M+i-1)] = 1 + (i == M-1);
if (i < M-1)
A[k + s * ((p*N+j)*M+i+1)] = 1 + (i == 0);
if (j > 0)
A[k + s * ((p*N+(j-1))*M+i)] = 1 + (j == N-1);
if (j < N-1)
A[k + s * ((p*N+(j+1))*M+i)] = 1 + (j == 0);
if (p > 0)
A[k + s * (((p-1)*N+j)*M+i)] = 1 + (p == P-1);
if (p < P-1)
A[k + s * (((p+1)*N+j)*M+i)] = 1 + (p == 0);
b[k] = rhs[(p*N+j)*M+i];
k++;
}
for (i = 0; i < s*s; i++)
A[i] += 1.0 / (s*s);
input_arrays[0] = A_array;
input_arrays[1] = b_array;
mexCallMATLAB(1, &x_array, 2, input_arrays, "\\");
memcpy(f_out, mxGetPr(x_array), s * sizeof(*f));
mxDestroyArray(x_array);
mxDestroyArray(A_array);
mxDestroyArray(b_array);
}
/* Gauss-Seidel smoothing iteration. Red-black ordering. */
void
gauss_seidel3D(double *f, double *d, mwSize M, mwSize N, mwSize P)
{
int pass;
mwSize i, j, p;
mwSize index;
mwSize MN = M * N;
for (pass = 0; pass <= 1; pass++)
{
for (p = 0; p < P; p++)
for (j = 0; j < N; j++)
for (i = 0; i < M; i++)
{
double new_f;
if ((i + j + p) % 2 != pass)
continue;
index = (p * N + j) * M + i;
new_f = -d[index];
if (i == 0)
new_f += f[index + 1];
else
new_f += f[index - 1];
if (i == M-1)
new_f += f[index - 1];
else
new_f += f[index + 1];
if (j == 0)
new_f += f[index + M];
else
new_f += f[index - M];
if (j == N-1)
new_f += f[index - M];
else
new_f += f[index + M];
if (p == 0)
new_f += f[index + MN];
else
new_f += f[index - MN];
if (p == P-1)
new_f += f[index - MN];
else
new_f += f[index + MN];
f[index] = (1 / 6.0) * new_f;
}
}
}
void
downsample3D(double *rhs, mwSize M, mwSize N, mwSize P,
double *rhs_coarse, mwSize Mhalf, mwSize Nhalf, mwSize Phalf)
{
mwSize i, j, p;
mwSize index1;
mwSize index2;
mwSize MN = M * N;
if (M % 2 == 0 && N % 2 == 0 && P % 2 == 0)
{
for (p = 0; p < Phalf; p++)
{
for (j = 0; j < Nhalf; j++)
{
for (i = 0; i < Mhalf; i++)
{
index1 = (p * Nhalf + j) * Mhalf + i;
index2 = (2 * p * N + 2 * j) * M + 2 * i;
rhs_coarse[index1] = (0.5 * (rhs[index2]
+ rhs[index2 + 1]
+ rhs[index2 + M]
+ rhs[index2 + M + 1]
+ rhs[index2 + MN]
+ rhs[index2 + MN + 1]
+ rhs[index2 + MN + M]
+ rhs[index2 + MN + M + 1]));
}
}
}
}
if (M % 2 == 1 && N % 2 == 0 && P % 2 == 0)
{
for (p = 0; p < Phalf; p++)
{
for (j = 0; j < Nhalf; j++)
{
index1 = (p * Nhalf + j) * Mhalf + 0;
index2 = (2 * p * N + 2 * j) * M + 2 * 0;
rhs_coarse[index1] = (0.5 * (rhs[index2]
+ rhs[index2 + 1]
+ rhs[index2 + M]
+ rhs[index2 + M + 1]
+ rhs[index2 + MN]
+ rhs[index2 + MN + 1]
+ rhs[index2 + MN + M]
+ rhs[index2 + MN + M + 1]));
for (i = 1; i < Mhalf - 1; i++)
{
index1 = (p * Nhalf + j) * Mhalf + i;
index2 = (2 * p * N + 2 * j) * M + 2 * i;
rhs_coarse[index1] = (0.5 * (rhs[index2]
+ rhs[index2 + M]
+ rhs[index2 + MN]
+ rhs[index2 + MN + M])
+ 0.25 * (rhs[index2 + 1]
+ rhs[index2 - 1]
+ rhs[index2 + M + 1]
+ rhs[index2 + M - 1]
+ rhs[index2 + MN + 1]
+ rhs[index2 + MN - 1]
+ rhs[index2 + MN + M + 1]
+ rhs[index2 + MN + M - 1]));
}
index1 = (p * Nhalf + j) * Mhalf + (Mhalf - 1);
index2 = (2 * p * N + 2 * j) * M + 2 * (Mhalf - 1);
rhs_coarse[index1] = (0.5 * (rhs[index2]
+ rhs[index2 - 1]
+ rhs[index2 + M]
+ rhs[index2 + M - 1]
+ rhs[index2 + MN]
+ rhs[index2 + MN - 1]
+ rhs[index2 + MN + M]
+ rhs[index2 + MN + M - 1]));
}
}
}
if (M % 2 == 0 && N % 2 == 1 && P % 2 == 0)
{
for (p = 0; p < Phalf; p++)
{
for (i = 0; i < Mhalf; i++)
{
index1 = (p * Nhalf + 0) * Mhalf + i;
index2 = (2 * p * N + 2 * 0) * M + 2 * i;
rhs_coarse[index1] = (0.5 * (rhs[index2]
+ rhs[index2 + 1]
+ rhs[index2 + M]
+ rhs[index2 + M + 1]
+ rhs[index2 + MN]
+ rhs[index2 + MN + 1]
+ rhs[index2 + MN + M]
+ rhs[index2 + MN + M + 1]));
}
for (j = 1; j < Nhalf - 1; j++)
{
for (i = 0; i < Mhalf; i++)
{
index1 = (p * Nhalf + j) * Mhalf + i;
index2 = (2 * p * N + 2 * j) * M + 2 * i;
rhs_coarse[index1] = (0.5 * (rhs[index2]
+ rhs[index2 + 1]
+ rhs[index2 + MN]
+ rhs[index2 + MN + 1])
+ 0.25 * (rhs[index2 + M]
+ rhs[index2 + M + 1]
+ rhs[index2 - M]
+ rhs[index2 - M + 1]
+ rhs[index2 + MN + M]
+ rhs[index2 + MN + M + 1]
+ rhs[index2 + MN - M]
+ rhs[index2 + MN - M + 1]));
}
}
for (i = 0; i < Mhalf; i++)
{
index1 = (p * Nhalf + (Nhalf - 1)) * Mhalf + i;
index2 = (2 * p * N + 2 * (Nhalf - 1)) * M + 2 * i;
rhs_coarse[index1] = (0.5 * (rhs[index2]
+ rhs[index2 + 1]
+ rhs[index2 - M]
+ rhs[index2 - M + 1]
+ rhs[index2 + MN]
+ rhs[index2 + MN + 1]
+ rhs[index2 + MN - M]