Actual source code: test7.c

slepc-3.17.0 2022-03-31
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  1: /*
  2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
  3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
  4:    Copyright (c) 2002-, 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: {
 21:   PetscScalar    tau,eta;
 22:   PetscReal      nrm;
 23:   PetscBool      set,flg;
 24:   PetscInt       n;
 25:   Mat            S,R;
 26:   Vec            v,f0;

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

 67: int main(int argc,char **argv)
 68: {
 69:   FN             fn;
 70:   Mat            A;
 71:   PetscInt       i,j,n=10;
 72:   PetscScalar    *As;
 73:   PetscViewer    viewer;
 74:   PetscBool      verbose,inplace;
 75:   PetscRandom    myrand;
 76:   PetscReal      v;

 78:   SlepcInitialize(&argc,&argv,(char*)0,help);
 79:   PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);
 80:   PetscOptionsHasName(NULL,NULL,"-verbose",&verbose);
 81:   PetscOptionsHasName(NULL,NULL,"-inplace",&inplace);
 82:   PetscPrintf(PETSC_COMM_WORLD,"Matrix square root, n=%" PetscInt_FMT ".\n",n);

 84:   /* Create function object */
 85:   FNCreate(PETSC_COMM_WORLD,&fn);
 86:   FNSetType(fn,FNSQRT);
 87:   FNSetFromOptions(fn);

 89:   /* Set up viewer */
 90:   PetscViewerASCIIGetStdout(PETSC_COMM_WORLD,&viewer);
 91:   FNView(fn,viewer);
 92:   if (verbose) PetscViewerPushFormat(viewer,PETSC_VIEWER_ASCII_MATLAB);

 94:   /* Create matrix */
 95:   MatCreateSeqDense(PETSC_COMM_SELF,n,n,NULL,&A);
 96:   PetscObjectSetName((PetscObject)A,"A");

 98:   /* Compute square root of a symmetric matrix A */
 99:   MatDenseGetArray(A,&As);
100:   for (i=0;i<n;i++) As[i+i*n]=2.5;
101:   for (j=1;j<3;j++) {
102:     for (i=0;i<n-j;i++) { As[i+(i+j)*n]=1.0; As[(i+j)+i*n]=1.0; }
103:   }
104:   MatDenseRestoreArray(A,&As);
105:   MatSetOption(A,MAT_HERMITIAN,PETSC_TRUE);
106:   TestMatSqrt(fn,A,viewer,verbose,inplace);

108:   /* Repeat with upper triangular A */
109:   MatDenseGetArray(A,&As);
110:   for (j=1;j<3;j++) {
111:     for (i=0;i<n-j;i++) As[(i+j)+i*n]=0.0;
112:   }
113:   MatDenseRestoreArray(A,&As);
114:   MatSetOption(A,MAT_HERMITIAN,PETSC_FALSE);
115:   TestMatSqrt(fn,A,viewer,verbose,inplace);

117:   /* Repeat with non-symmetic A */
118:   PetscRandomCreate(PETSC_COMM_WORLD,&myrand);
119:   PetscRandomSetFromOptions(myrand);
120:   PetscRandomSetInterval(myrand,0.0,1.0);
121:   MatDenseGetArray(A,&As);
122:   for (j=1;j<3;j++) {
123:     for (i=0;i<n-j;i++) {
124:       PetscRandomGetValueReal(myrand,&v);
125:       As[(i+j)+i*n]=v;
126:     }
127:   }
128:   MatDenseRestoreArray(A,&As);
129:   PetscRandomDestroy(&myrand);
130:   MatSetOption(A,MAT_HERMITIAN,PETSC_FALSE);
131:   TestMatSqrt(fn,A,viewer,verbose,inplace);

133:   MatDestroy(&A);
134:   FNDestroy(&fn);
135:   SlepcFinalize();
136:   return 0;
137: }

139: /*TEST

141:    testset:
142:       args: -fn_scale .05,2 -n 100
143:       filter: grep -v "computing matrix functions"
144:       output_file: output/test7_1.out
145:       timeoutfactor: 2
146:       test:
147:          suffix: 1
148:          args: -fn_method {{0 1 2}}
149:       test:
150:          suffix: 1_sadeghi
151:          args: -fn_method 3
152:          requires: !single
153:       test:
154:          suffix: 1_cuda
155:          args: -fn_method 4
156:          requires: cuda !single
157:       test:
158:          suffix: 1_magma
159:          args: -fn_method {{5 6}}
160:          requires: cuda magma !single
161:       test:
162:          suffix: 2
163:          args: -inplace -fn_method {{0 1 2}}
164:       test:
165:          suffix: 2_sadeghi
166:          args: -inplace -fn_method 3
167:          requires: !single
168:       test:
169:          suffix: 2_cuda
170:          args: -inplace -fn_method 4
171:          requires: cuda !single
172:       test:
173:          suffix: 2_magma
174:          args: -inplace -fn_method {{5 6}}
175:          requires: cuda magma !single

177:    testset:
178:       nsize: 3
179:       args: -fn_scale .05,2 -n 100 -fn_parallel synchronized
180:       filter: grep -v "computing matrix functions" | grep -v "SYNCHRONIZED" | sed -e "s/3 MPI/1 MPI/g"
181:       output_file: output/test7_1.out
182:       test:
183:          suffix: 3
184:       test:
185:          suffix: 3_inplace
186:          args: -inplace

188: TEST*/