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: PetscOptionsHasName(PETSC_NULL,"-norandom",&flg);
46: if (flg) {
47: use_random = 0;
48: VecSet(u,pfive);
49: } else {
50: PetscRandomCreate(PETSC_COMM_WORLD,&rctx);
51: PetscRandomSetFromOptions(rctx);
52: VecSetRandom(u,rctx);
53: }
55: /* Create and assemble matrix */
56: MatCreate(PETSC_COMM_WORLD,&A);
57: MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,dim,dim);
58: MatSetFromOptions(A);
59: FormTestMatrix(A,n,type);
60: MatMult(A,u,b);
61: PetscOptionsHasName(PETSC_NULL,"-printout",&flg);
62: if (flg) {
63: MatView(A,PETSC_VIEWER_STDOUT_WORLD);
64: VecView(u,PETSC_VIEWER_STDOUT_WORLD);
65: VecView(b,PETSC_VIEWER_STDOUT_WORLD);
66: }
68: /* Create KSP context; set operators and options; solve linear system */
69: KSPCreate(PETSC_COMM_WORLD,&ksp);
70: KSPSetOperators(ksp,A,A,DIFFERENT_NONZERO_PATTERN);
71: KSPSetFromOptions(ksp);
72: KSPSolve(ksp,b,x);
73: KSPView(ksp,PETSC_VIEWER_STDOUT_WORLD);
75: /* Check error */
76: VecAXPY(x,none,u);
77: VecNorm(x,NORM_2,&norm);
78: KSPGetIterationNumber(ksp,&its);
79: PetscPrintf(PETSC_COMM_WORLD,"Norm of error %A,Iterations %D\n",norm,its);
81: /* Free work space */
82: VecDestroy(x); VecDestroy(u);
83: VecDestroy(b); MatDestroy(A);
84: if (use_random) {PetscRandomDestroy(rctx);}
85: KSPDestroy(ksp);
86: PetscFinalize();
87: return 0;
88: }
92: PetscErrorCode FormTestMatrix(Mat A,PetscInt n,TestType type)
93: {
94: #if !defined(PETSC_USE_COMPLEX)
95: SETERRQ(1,"FormTestMatrix: These problems require complex numbers.");
96: #else
98: PetscScalar val[5];
100: PetscInt i,j,Ii,J,col[5],Istart,Iend;
102: MatGetOwnershipRange(A,&Istart,&Iend);
103: if (type == TEST_1) {
104: val[0] = 1.0; val[1] = 4.0; val[2] = -2.0;
105: for (i=1; i<n-1; i++) {
106: col[0] = i-1; col[1] = i; col[2] = i+1;
107: MatSetValues(A,1,&i,3,col,val,INSERT_VALUES);
108: }
109: i = n-1; col[0] = n-2; col[1] = n-1;
110: MatSetValues(A,1,&i,2,col,val,INSERT_VALUES);
111: i = 0; col[0] = 0; col[1] = 1; val[0] = 4.0; val[1] = -2.0;
112: MatSetValues(A,1,&i,2,col,val,INSERT_VALUES);
113: }
114: else if (type == TEST_2) {
115: val[0] = 1.0; val[1] = 0.0; val[2] = 2.0; val[3] = 1.0;
116: for (i=2; i<n-1; i++) {
117: col[0] = i-2; col[1] = i-1; col[2] = i; col[3] = i+1;
118: MatSetValues(A,1,&i,4,col,val,INSERT_VALUES);
119: }
120: i = n-1; col[0] = n-3; col[1] = n-2; col[2] = n-1;
121: MatSetValues(A,1,&i,3,col,val,INSERT_VALUES);
122: i = 1; col[0] = 0; col[1] = 1; col[2] = 2;
123: MatSetValues(A,1,&i,3,col,&val[1],INSERT_VALUES);
124: i = 0;
125: MatSetValues(A,1,&i,2,col,&val[2],INSERT_VALUES);
126: }
127: else if (type == TEST_3) {
128: val[0] = PETSC_i * 2.0;
129: val[1] = 4.0; val[2] = 0.0; val[3] = 1.0; val[4] = 0.7;
130: for (i=1; i<n-3; i++) {
131: col[0] = i-1; col[1] = i; col[2] = i+1; col[3] = i+2; col[4] = i+3;
132: MatSetValues(A,1,&i,5,col,val,INSERT_VALUES);
133: }
134: i = n-3; col[0] = n-4; col[1] = n-3; col[2] = n-2; col[3] = n-1;
135: MatSetValues(A,1,&i,4,col,val,INSERT_VALUES);
136: i = n-2; col[0] = n-3; col[1] = n-2; col[2] = n-1;
137: MatSetValues(A,1,&i,3,col,val,INSERT_VALUES);
138: i = n-1; col[0] = n-2; col[1] = n-1;
139: MatSetValues(A,1,&i,2,col,val,INSERT_VALUES);
140: i = 0; col[0] = 0; col[1] = 1; col[2] = 2; col[3] = 3;
141: MatSetValues(A,1,&i,4,col,&val[1],INSERT_VALUES);
142: }
143: else if (type == HELMHOLTZ_1) {
144: /* Problem domain: unit square: (0,1) x (0,1)
145: Solve Helmholtz equation:
146: -delta u - sigma1*u + i*sigma2*u = f,
147: where delta = Laplace operator
148: Dirichlet b.c.'s on all sides
149: */
150: PetscRandom rctx;
151: PetscReal h2,sigma1 = 5.0;
152: PetscScalar sigma2;
153: PetscOptionsGetReal(PETSC_NULL,"-sigma1",&sigma1,PETSC_NULL);
154: PetscRandomCreate(PETSC_COMM_WORLD,&rctx);
155: PetscRandomSetFromOptions(rctx);
156: h2 = 1.0/((n+1)*(n+1));
157: for (Ii=Istart; Ii<Iend; Ii++) {
158: *val = -1.0; i = Ii/n; j = Ii - i*n;
159: if (i>0) {
160: J = Ii-n; MatSetValues(A,1,&Ii,1,&J,val,ADD_VALUES);}
161: if (i<n-1) {
162: J = Ii+n; MatSetValues(A,1,&Ii,1,&J,val,ADD_VALUES);}
163: if (j>0) {
164: J = Ii-1; MatSetValues(A,1,&Ii,1,&J,val,ADD_VALUES);}
165: if (j<n-1) {
166: J = Ii+1; MatSetValues(A,1,&Ii,1,&J,val,ADD_VALUES);}
167: PetscRandomGetValueImaginary(rctx,&sigma2);
168: *val = 4.0 - sigma1*h2 + sigma2*h2;
169: MatSetValues(A,1,&Ii,1,&Ii,val,ADD_VALUES);
170: }
171: PetscRandomDestroy(rctx);
172: }
173: else if (type == HELMHOLTZ_2) {
174: /* Problem domain: unit square: (0,1) x (0,1)
175: Solve Helmholtz equation:
176: -delta u - sigma1*u = f,
177: where delta = Laplace operator
178: Dirichlet b.c.'s on 3 sides
179: du/dn = i*alpha*u on (1,y), 0<y<1
180: */
181: PetscReal h2,sigma1 = 200.0;
182: PetscScalar alpha_h;
183: PetscOptionsGetReal(PETSC_NULL,"-sigma1",&sigma1,PETSC_NULL);
184: h2 = 1.0/((n+1)*(n+1));
185: alpha_h = (PETSC_i * 10.0) / (PetscReal)(n+1); /* alpha_h = alpha * h */
186: for (Ii=Istart; Ii<Iend; Ii++) {
187: *val = -1.0; i = Ii/n; j = Ii - i*n;
188: if (i>0) {
189: J = Ii-n; MatSetValues(A,1,&Ii,1,&J,val,ADD_VALUES);}
190: if (i<n-1) {
191: J = Ii+n; MatSetValues(A,1,&Ii,1,&J,val,ADD_VALUES);}
192: if (j>0) {
193: J = Ii-1; MatSetValues(A,1,&Ii,1,&J,val,ADD_VALUES);}
194: if (j<n-1) {
195: J = Ii+1; MatSetValues(A,1,&Ii,1,&J,val,ADD_VALUES);}
196: *val = 4.0 - sigma1*h2;
197: if (!((Ii+1)%n)) *val += alpha_h;
198: MatSetValues(A,1,&Ii,1,&Ii,val,ADD_VALUES);
199: }
200: }
201: else SETERRQ(1,"FormTestMatrix: unknown test matrix type");
203: MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
204: MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
205: #endif
207: return 0;
208: }