Actual source code: ex35.c
1: static char help[] = "Test of Colorized Scatter Plot.\n";
3: #include "petscdraw.h"
4: #include "petscvec.h"
5: #include "petscis.h"
7: typedef struct {
8: PetscInt Np; /* total number of particles */
9: PetscInt dim;
10: PetscInt dim_inp;
11: } AppCtx;
13: static PetscErrorCode ProcessOptions(MPI_Comm comm, AppCtx *options)
14: {
16: options->dim = 2;
17: options->dim_inp = 2;
18: options->Np = 100;
19: PetscOptionsBegin(comm, "", "Test of colorized scatter plot", "");
20: PetscOptionsInt("-Np", "Number of particles", "ex35.c", options->Np, &options->Np, PETSC_NULL);
21: PetscOptionsInt("-dim", "Number of dimensions", "ex35.c", options->dim_inp, &options->dim_inp, PETSC_NULL);
22: PetscOptionsEnd();
23: return 0;
24: }
26: /*
27: ref: http://www.mimirgames.com/articles/programming/approximations-of-the-inverse-error-function/
28: */
29: PetscReal erfinv(PetscReal x)
30: {
31: PetscReal *ck, r = 0.;
32: PetscInt maxIter = 100;
34: PetscCalloc1(maxIter, &ck);
35: ck[0] = 1;
36: r = ck[0] * ((PetscSqrtReal(PETSC_PI) / 2.) * x);
37: for (PetscInt k = 1; k < maxIter; ++k) {
38: for (PetscInt m = 0; m <= k - 1; ++m) {
39: PetscReal denom = (m + 1.) * (2. * m + 1.);
40: ck[k] += (ck[m] * ck[k - 1 - m]) / denom;
41: }
42: PetscReal temp = 2. * k + 1.;
43: r += (ck[k] / temp) * PetscPowReal((PetscSqrtReal(PETSC_PI) / 2.) * x, 2. * k + 1.);
44: }
45: PETSC_COMM_SELF, PetscFree(ck);
46: return r;
47: }
49: int main(int argc, char **argv)
50: {
51: PetscInt p, dim, Np;
52: PetscScalar *randVecNums;
53: PetscReal speed, value, *x, *v;
54: PetscRandom rngx, rng1, rng2;
55: Vec randVec, subvecvx, subvecvy;
56: IS isvx, isvy;
57: AppCtx user;
58: PetscDrawAxis axis;
59: PetscDraw positionDraw;
60: PetscDrawSP positionDrawSP;
61: MPI_Comm comm;
64: PetscInitialize(&argc, &argv, NULL, help);
65: comm = PETSC_COMM_WORLD;
66: ProcessOptions(comm, &user);
68: Np = user.Np;
69: dim = user.dim;
71: PetscMalloc2(Np * dim, &x, Np * dim, &v);
73: PetscRandomCreate(comm, &rngx);
74: PetscRandomSetInterval(rngx, 0., 1.);
75: PetscRandomSetFromOptions(rngx);
76: PetscRandomSetSeed(rngx, 1034);
77: PetscRandomSeed(rngx);
79: PetscRandomCreate(comm, &rng1);
80: PetscRandomSetInterval(rng1, 0., 1.);
81: PetscRandomSetFromOptions(rng1);
82: PetscRandomSetSeed(rng1, 3084);
83: PetscRandomSeed(rng1);
85: PetscRandomCreate(comm, &rng2);
86: PetscRandomSetInterval(rng2, 0., 1.);
87: PetscRandomSetFromOptions(rng2);
88: PetscRandomSetSeed(rng2, 2397);
89: PetscRandomSeed(rng2);
91: /* Set particle positions and velocities */
92: if (user.dim_inp == 1) {
93: for (p = 0; p < Np; ++p) {
94: PetscReal temp;
95: PetscRandomGetValueReal(rngx, &value);
96: x[p * dim] = value;
97: x[p * dim + 1] = 0.;
98: temp = erfinv(2 * value - 1);
99: v[p * dim] = temp;
100: v[p * dim + 1] = 0.;
101: }
102: } else if (user.dim_inp == 2) {
103: /*
104: Use Box-Muller to sample a distribution of velocities for the maxwellian.
105: https://en.wikipedia.org/wiki/Box%E2%80%93Muller_transform
106: */
107: VecCreate(comm, &randVec);
108: VecSetSizes(randVec, PETSC_DECIDE, Np * dim);
109: VecSetFromOptions(randVec);
111: ISCreateStride(comm, Np * dim / 2, 0, 2, &isvx);
112: ISCreateStride(comm, Np * dim / 2, 1, 2, &isvy);
113: VecGetSubVector(randVec, isvx, &subvecvx);
114: VecGetSubVector(randVec, isvy, &subvecvy);
115: VecSetRandom(subvecvx, rng1);
116: VecSetRandom(subvecvy, rng2);
117: VecRestoreSubVector(randVec, isvx, &subvecvx);
118: VecRestoreSubVector(randVec, isvy, &subvecvy);
119: VecGetArray(randVec, &randVecNums);
121: for (p = 0; p < Np; ++p) {
122: PetscReal u1, u2, mag, zx, zy;
124: u1 = PetscRealPart(randVecNums[p * dim]);
125: u2 = PetscRealPart(randVecNums[p * dim + 1]);
127: x[p * dim] = u1;
128: x[p * dim + 1] = u2;
130: mag = PetscSqrtReal(-2.0 * PetscLogReal(u1));
132: zx = mag * PetscCosReal(2 * PETSC_PI * u2) + 0;
133: zy = mag * PetscSinReal(2 * PETSC_PI * u2) + 0;
135: v[p * dim] = zx;
136: v[p * dim + 1] = zy;
137: }
138: ISDestroy(&isvx);
139: ISDestroy(&isvy);
140: VecDestroy(&subvecvx);
141: VecDestroy(&subvecvy);
142: VecDestroy(&randVec);
143: } else SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Do not support dimension %" PetscInt_FMT, dim);
145: PetscDrawCreate(comm, NULL, "monitor_particle_positions", 0, 0, 400, 300, &positionDraw);
146: PetscDrawSetFromOptions(positionDraw);
147: PetscDrawSPCreate(positionDraw, 10, &positionDrawSP);
148: PetscDrawSPSetDimension(positionDrawSP, 1);
149: PetscDrawSPGetAxis(positionDrawSP, &axis);
150: PetscDrawSPReset(positionDrawSP);
151: PetscDrawAxisSetLabels(axis, "Particles", "x", "y");
152: PetscDrawSetSave(positionDraw, "ex35_pos.ppm");
153: PetscDrawSPReset(positionDrawSP);
154: PetscDrawSPSetLimits(positionDrawSP, 0, 1, 0, 1);
155: for (p = 0; p < Np; ++p) {
156: speed = PetscSqrtReal(PetscSqr(v[p * dim]) + PetscSqr(v[p * dim + 1]));
157: PetscDrawSPAddPointColorized(positionDrawSP, &x[p * dim], &x[p * dim + 1], &speed);
158: }
159: PetscDrawSPDraw(positionDrawSP, PETSC_TRUE);
160: PetscDrawSave(positionDraw);
162: PetscFree2(x, v);
163: PetscRandomDestroy(&rngx);
164: PetscRandomDestroy(&rng1);
165: PetscRandomDestroy(&rng2);
167: PetscDrawSPDestroy(&positionDrawSP);
168: PetscDrawDestroy(&positionDraw);
169: PetscFinalize();
170: return 0;
171: }
173: /*TEST
174: test:
175: suffix: 1D
176: args: -Np 50\
177: -dim 1
178: test:
179: suffix: 2D
180: args: -Np 50\
181: -dim 2
182: TEST*/