Actual source code: test7.c

slepc-3.13.1 2020-04-12
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  1: /*
  2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
  3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
  4:    Copyright (c) 2002-2020, Universitat Politecnica de Valencia, Spain

  6:    This file is part of SLEPc.
  7:    SLEPc is distributed under a 2-clause BSD license (see LICENSE).
  8:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
  9: */

 11: static char help[] = "Test matrix square root.\n\n";

 13: #include <slepcfn.h>

 15: /*
 16:    Compute matrix square root B = sqrtm(A)
 17:    Check result as norm(B*B-A)
 18:  */
 19: PetscErrorCode TestMatSqrt(FN fn,Mat A,PetscViewer viewer,PetscBool verbose,PetscBool inplace)
 20: {
 22:   PetscScalar    tau,eta;
 23:   PetscReal      nrm;
 24:   PetscBool      set,flg;
 25:   PetscInt       n;
 26:   Mat            S,R;
 27:   Vec            v,f0;

 30:   MatGetSize(A,&n,NULL);
 31:   MatCreateSeqDense(PETSC_COMM_SELF,n,n,NULL,&S);
 32:   PetscObjectSetName((PetscObject)S,"S");
 33:   FNGetScale(fn,&tau,&eta);
 34:   /* compute square root */
 35:   if (inplace) {
 36:     MatCopy(A,S,SAME_NONZERO_PATTERN);
 37:     MatIsHermitianKnown(A,&set,&flg);
 38:     if (set && flg) { MatSetOption(S,MAT_HERMITIAN,PETSC_TRUE); }
 39:     FNEvaluateFunctionMat(fn,S,NULL);
 40:   } else {
 41:     FNEvaluateFunctionMat(fn,A,S);
 42:   }
 43:   if (verbose) {
 44:     PetscPrintf(PETSC_COMM_WORLD,"Matrix A - - - - - - - -\n");
 45:     MatView(A,viewer);
 46:     PetscPrintf(PETSC_COMM_WORLD,"Computed sqrtm(A) - - - - - - -\n");
 47:     MatView(S,viewer);
 48:   }
 49:   /* check error ||S*S-A||_F */
 50:   MatMatMult(S,S,MAT_INITIAL_MATRIX,PETSC_DEFAULT,&R);
 51:   if (eta!=1.0) {
 52:     MatScale(R,1.0/(eta*eta));
 53:   }
 54:   MatAXPY(R,-tau,A,SAME_NONZERO_PATTERN);
 55:   MatNorm(R,NORM_FROBENIUS,&nrm);
 56:   if (nrm<100*PETSC_MACHINE_EPSILON) {
 57:     PetscPrintf(PETSC_COMM_WORLD,"||S*S-A||_F < 100*eps\n");
 58:   } else {
 59:     PetscPrintf(PETSC_COMM_WORLD,"||S*S-A||_F = %g\n",(double)nrm);
 60:   }
 61:   /* check FNEvaluateFunctionMatVec() */
 62:   MatCreateVecs(A,&v,&f0);
 63:   MatGetColumnVector(S,f0,0);
 64:   FNEvaluateFunctionMatVec(fn,A,v);
 65:   VecAXPY(v,-1.0,f0);
 66:   VecNorm(v,NORM_2,&nrm);
 67:   if (nrm>100*PETSC_MACHINE_EPSILON) {
 68:     PetscPrintf(PETSC_COMM_WORLD,"Warning: the norm of f(A)*e_1-v is %g\n",(double)nrm);
 69:   }
 70:   MatDestroy(&S);
 71:   MatDestroy(&R);
 72:   VecDestroy(&v);
 73:   VecDestroy(&f0);
 74:   return(0);
 75: }

 77: int main(int argc,char **argv)
 78: {
 80:   FN             fn;
 81:   Mat            A;
 82:   PetscInt       i,j,n=10;
 83:   PetscScalar    *As;
 84:   PetscViewer    viewer;
 85:   PetscBool      verbose,inplace;
 86:   PetscRandom    myrand;
 87:   PetscReal      v;

 89:   SlepcInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;
 90:   PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);
 91:   PetscOptionsHasName(NULL,NULL,"-verbose",&verbose);
 92:   PetscOptionsHasName(NULL,NULL,"-inplace",&inplace);
 93:   PetscPrintf(PETSC_COMM_WORLD,"Matrix square root, n=%D.\n",n);

 95:   /* Create function object */
 96:   FNCreate(PETSC_COMM_WORLD,&fn);
 97:   FNSetType(fn,FNSQRT);
 98:   FNSetFromOptions(fn);

100:   /* Set up viewer */
101:   PetscViewerASCIIGetStdout(PETSC_COMM_WORLD,&viewer);
102:   FNView(fn,viewer);
103:   if (verbose) {
104:     PetscViewerPushFormat(viewer,PETSC_VIEWER_ASCII_MATLAB);
105:   }

107:   /* Create matrix */
108:   MatCreateSeqDense(PETSC_COMM_SELF,n,n,NULL,&A);
109:   PetscObjectSetName((PetscObject)A,"A");

111:   /* Compute square root of a symmetric matrix A */
112:   MatDenseGetArray(A,&As);
113:   for (i=0;i<n;i++) As[i+i*n]=2.5;
114:   for (j=1;j<3;j++) {
115:     for (i=0;i<n-j;i++) { As[i+(i+j)*n]=1.0; As[(i+j)+i*n]=1.0; }
116:   }
117:   MatDenseRestoreArray(A,&As);
118:   MatSetOption(A,MAT_HERMITIAN,PETSC_TRUE);
119:   TestMatSqrt(fn,A,viewer,verbose,inplace);

121:   /* Repeat with upper triangular A */
122:   MatDenseGetArray(A,&As);
123:   for (j=1;j<3;j++) {
124:     for (i=0;i<n-j;i++) As[(i+j)+i*n]=0.0;
125:   }
126:   MatDenseRestoreArray(A,&As);
127:   MatSetOption(A,MAT_HERMITIAN,PETSC_FALSE);
128:   TestMatSqrt(fn,A,viewer,verbose,inplace);

130:   /* Repeat with non-symmetic A */
131:   PetscRandomCreate(PETSC_COMM_WORLD,&myrand);
132:   PetscRandomSetFromOptions(myrand);
133:   PetscRandomSetInterval(myrand,0.0,1.0);
134:   MatDenseGetArray(A,&As);
135:   for (j=1;j<3;j++) {
136:     for (i=0;i<n-j;i++) {
137:       PetscRandomGetValueReal(myrand,&v);
138:       As[(i+j)+i*n]=v;
139:     }
140:   }
141:   MatDenseRestoreArray(A,&As);
142:   PetscRandomDestroy(&myrand);
143:   MatSetOption(A,MAT_HERMITIAN,PETSC_FALSE);
144:   TestMatSqrt(fn,A,viewer,verbose,inplace);

146:   MatDestroy(&A);
147:   FNDestroy(&fn);
148:   SlepcFinalize();
149:   return ierr;
150: }

152: /*TEST

154:    test:
155:       suffix: 1
156:       nsize: 1
157:       args: -fn_scale .05,2 -n 100 -fn_method {{0 1 2}shared output}
158:       filter: grep -v "computing matrix functions"
159:       output_file: output/test7_1.out
160:       timeoutfactor: 2

162:    test:
163:       suffix: 1_sadeghi
164:       nsize: 1
165:       args: -fn_scale .05,2 -n 100 -fn_method 3
166:       requires: !single
167:       filter: grep -v "computing matrix functions"
168:       output_file: output/test7_1.out

170:    test:
171:       suffix: 2
172:       nsize: 1
173:       args: -fn_scale .05,2 -n 100 -inplace -fn_method {{0 1 2}shared output}
174:       filter: grep -v "computing matrix functions"
175:       output_file: output/test7_1.out
176:       timeoutfactor: 2

178:    test:
179:       suffix: 2_sadeghi
180:       nsize: 1
181:       args: -fn_scale .05,2 -n 100 -inplace -fn_method 3
182:       requires: !single
183:       filter: grep -v "computing matrix functions"
184:       output_file: output/test7_1.out

186:    test:
187:       suffix: 3
188:       nsize: 3
189:       args: -fn_scale .05,2 -n 100 -fn_parallel synchronized
190:       filter: grep -v "computing matrix functions" | grep -v "SYNCHRONIZED" | sed -e "s/3 MPI/1 MPI/g"
191:       output_file: output/test7_1.out

193:    test:
194:       suffix: 4
195:       nsize: 3
196:       args: -fn_scale .05,2 -n 100 -inplace -fn_parallel synchronized
197:       filter: grep -v "computing matrix functions" | grep -v "SYNCHRONIZED" | sed -e "s/3 MPI/1 MPI/g"
198:       output_file: output/test7_1.out

200: TEST*/