Actual source code: ex17.c
2: static char help[] = "Solves a linear system with KSP. This problem is\n\
3: intended to test the complex numbers version of various solvers.\n\n";
5: #include petscksp.h
7: typedef enum {TEST_1,TEST_2,TEST_3,HELMHOLTZ_1,HELMHOLTZ_2} TestType;
12: int main(int argc,char **args)
13: {
14: Vec x,b,u; /* approx solution, RHS, exact solution */
15: Mat A; /* linear system matrix */
16: KSP ksp; /* KSP context */
18: PetscInt n = 10,its, dim,p = 1,use_random;
19: PetscScalar none = -1.0,pfive = 0.5;
20: PetscReal norm;
21: PetscRandom rctx;
22: TestType type;
23: PetscTruth flg;
25: PetscInitialize(&argc,&args,(char *)0,help);
26: PetscOptionsGetInt(PETSC_NULL,"-n",&n,PETSC_NULL);
27: PetscOptionsGetInt(PETSC_NULL,"-p",&p,PETSC_NULL);
28: switch (p) {
29: case 1: type = TEST_1; dim = n; break;
30: case 2: type = TEST_2; dim = n; break;
31: case 3: type = TEST_3; dim = n; break;
32: case 4: type = HELMHOLTZ_1; dim = n*n; break;
33: case 5: type = HELMHOLTZ_2; dim = n*n; break;
34: default: type = TEST_1; dim = n;
35: }
37: /* Create vectors */
38: VecCreate(PETSC_COMM_WORLD,&x);
39: VecSetSizes(x,PETSC_DECIDE,dim);
40: VecSetFromOptions(x);
41: VecDuplicate(x,&b);
42: VecDuplicate(x,&u);
44: use_random = 1;
45: flg = PETSC_FALSE;
46: PetscOptionsGetTruth(PETSC_NULL,"-norandom",&flg,PETSC_NULL);
47: if (flg) {
48: use_random = 0;
49: VecSet(u,pfive);
50: } else {
51: PetscRandomCreate(PETSC_COMM_WORLD,&rctx);
52: PetscRandomSetFromOptions(rctx);
53: VecSetRandom(u,rctx);
54: }
56: /* Create and assemble matrix */
57: MatCreate(PETSC_COMM_WORLD,&A);
58: MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,dim,dim);
59: MatSetFromOptions(A);
60: FormTestMatrix(A,n,type);
61: MatMult(A,u,b);
62: flg = PETSC_FALSE;
63: PetscOptionsGetTruth(PETSC_NULL,"-printout",&flg,PETSC_NULL);
64: if (flg) {
65: MatView(A,PETSC_VIEWER_STDOUT_WORLD);
66: VecView(u,PETSC_VIEWER_STDOUT_WORLD);
67: VecView(b,PETSC_VIEWER_STDOUT_WORLD);
68: }
70: /* Create KSP context; set operators and options; solve linear system */
71: KSPCreate(PETSC_COMM_WORLD,&ksp);
72: KSPSetOperators(ksp,A,A,DIFFERENT_NONZERO_PATTERN);
73: KSPSetFromOptions(ksp);
74: KSPSolve(ksp,b,x);
75: KSPView(ksp,PETSC_VIEWER_STDOUT_WORLD);
77: /* Check error */
78: VecAXPY(x,none,u);
79: VecNorm(x,NORM_2,&norm);
80: KSPGetIterationNumber(ksp,&its);
81: PetscPrintf(PETSC_COMM_WORLD,"Norm of error %A,Iterations %D\n",norm,its);
83: /* Free work space */
84: VecDestroy(x); VecDestroy(u);
85: VecDestroy(b); MatDestroy(A);
86: if (use_random) {PetscRandomDestroy(rctx);}
87: KSPDestroy(ksp);
88: PetscFinalize();
89: return 0;
90: }
94: PetscErrorCode FormTestMatrix(Mat A,PetscInt n,TestType type)
95: {
96: #if !defined(PETSC_USE_COMPLEX)
97: SETERRQ(1,"FormTestMatrix: These problems require complex numbers.");
98: #else
100: PetscScalar val[5];
102: PetscInt i,j,Ii,J,col[5],Istart,Iend;
104: MatGetOwnershipRange(A,&Istart,&Iend);
105: if (type == TEST_1) {
106: val[0] = 1.0; val[1] = 4.0; val[2] = -2.0;
107: for (i=1; i<n-1; i++) {
108: col[0] = i-1; col[1] = i; col[2] = i+1;
109: MatSetValues(A,1,&i,3,col,val,INSERT_VALUES);
110: }
111: i = n-1; col[0] = n-2; col[1] = n-1;
112: MatSetValues(A,1,&i,2,col,val,INSERT_VALUES);
113: i = 0; col[0] = 0; col[1] = 1; val[0] = 4.0; val[1] = -2.0;
114: MatSetValues(A,1,&i,2,col,val,INSERT_VALUES);
115: }
116: else if (type == TEST_2) {
117: val[0] = 1.0; val[1] = 0.0; val[2] = 2.0; val[3] = 1.0;
118: for (i=2; i<n-1; i++) {
119: col[0] = i-2; col[1] = i-1; col[2] = i; col[3] = i+1;
120: MatSetValues(A,1,&i,4,col,val,INSERT_VALUES);
121: }
122: i = n-1; col[0] = n-3; col[1] = n-2; col[2] = n-1;
123: MatSetValues(A,1,&i,3,col,val,INSERT_VALUES);
124: i = 1; col[0] = 0; col[1] = 1; col[2] = 2;
125: MatSetValues(A,1,&i,3,col,&val[1],INSERT_VALUES);
126: i = 0;
127: MatSetValues(A,1,&i,2,col,&val[2],INSERT_VALUES);
128: }
129: else if (type == TEST_3) {
130: val[0] = PETSC_i * 2.0;
131: val[1] = 4.0; val[2] = 0.0; val[3] = 1.0; val[4] = 0.7;
132: for (i=1; i<n-3; i++) {
133: col[0] = i-1; col[1] = i; col[2] = i+1; col[3] = i+2; col[4] = i+3;
134: MatSetValues(A,1,&i,5,col,val,INSERT_VALUES);
135: }
136: i = n-3; col[0] = n-4; col[1] = n-3; col[2] = n-2; col[3] = n-1;
137: MatSetValues(A,1,&i,4,col,val,INSERT_VALUES);
138: i = n-2; col[0] = n-3; col[1] = n-2; col[2] = n-1;
139: MatSetValues(A,1,&i,3,col,val,INSERT_VALUES);
140: i = n-1; col[0] = n-2; col[1] = n-1;
141: MatSetValues(A,1,&i,2,col,val,INSERT_VALUES);
142: i = 0; col[0] = 0; col[1] = 1; col[2] = 2; col[3] = 3;
143: MatSetValues(A,1,&i,4,col,&val[1],INSERT_VALUES);
144: }
145: else if (type == HELMHOLTZ_1) {
146: /* Problem domain: unit square: (0,1) x (0,1)
147: Solve Helmholtz equation:
148: -delta u - sigma1*u + i*sigma2*u = f,
149: where delta = Laplace operator
150: Dirichlet b.c.'s on all sides
151: */
152: PetscRandom rctx;
153: PetscReal h2,sigma1 = 5.0;
154: PetscScalar sigma2;
155: PetscOptionsGetReal(PETSC_NULL,"-sigma1",&sigma1,PETSC_NULL);
156: PetscRandomCreate(PETSC_COMM_WORLD,&rctx);
157: PetscRandomSetFromOptions(rctx);
158: PetscRandomSetInterval(rctx,0.0,PETSC_i);
159: h2 = 1.0/((n+1)*(n+1));
160: for (Ii=Istart; Ii<Iend; Ii++) {
161: *val = -1.0; i = Ii/n; j = Ii - i*n;
162: if (i>0) {
163: J = Ii-n; MatSetValues(A,1,&Ii,1,&J,val,ADD_VALUES);}
164: if (i<n-1) {
165: J = Ii+n; MatSetValues(A,1,&Ii,1,&J,val,ADD_VALUES);}
166: if (j>0) {
167: J = Ii-1; MatSetValues(A,1,&Ii,1,&J,val,ADD_VALUES);}
168: if (j<n-1) {
169: J = Ii+1; MatSetValues(A,1,&Ii,1,&J,val,ADD_VALUES);}
170: PetscRandomGetValue(rctx,&sigma2);
171: *val = 4.0 - sigma1*h2 + sigma2*h2;
172: MatSetValues(A,1,&Ii,1,&Ii,val,ADD_VALUES);
173: }
174: PetscRandomDestroy(rctx);
175: }
176: else if (type == HELMHOLTZ_2) {
177: /* Problem domain: unit square: (0,1) x (0,1)
178: Solve Helmholtz equation:
179: -delta u - sigma1*u = f,
180: where delta = Laplace operator
181: Dirichlet b.c.'s on 3 sides
182: du/dn = i*alpha*u on (1,y), 0<y<1
183: */
184: PetscReal h2,sigma1 = 200.0;
185: PetscScalar alpha_h;
186: PetscOptionsGetReal(PETSC_NULL,"-sigma1",&sigma1,PETSC_NULL);
187: h2 = 1.0/((n+1)*(n+1));
188: alpha_h = (PETSC_i * 10.0) / (PetscReal)(n+1); /* alpha_h = alpha * h */
189: for (Ii=Istart; Ii<Iend; Ii++) {
190: *val = -1.0; i = Ii/n; j = Ii - i*n;
191: if (i>0) {
192: J = Ii-n; MatSetValues(A,1,&Ii,1,&J,val,ADD_VALUES);}
193: if (i<n-1) {
194: J = Ii+n; MatSetValues(A,1,&Ii,1,&J,val,ADD_VALUES);}
195: if (j>0) {
196: J = Ii-1; MatSetValues(A,1,&Ii,1,&J,val,ADD_VALUES);}
197: if (j<n-1) {
198: J = Ii+1; MatSetValues(A,1,&Ii,1,&J,val,ADD_VALUES);}
199: *val = 4.0 - sigma1*h2;
200: if (!((Ii+1)%n)) *val += alpha_h;
201: MatSetValues(A,1,&Ii,1,&Ii,val,ADD_VALUES);
202: }
203: }
204: else SETERRQ(1,"FormTestMatrix: unknown test matrix type");
206: MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
207: MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
208: #endif
210: return 0;
211: }