Actual source code: test8.c

slepc-3.11.2 2019-07-30
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  1: /*
  2:    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
  3:    SLEPc - Scalable Library for Eigenvalue Problem Computations
  4:    Copyright (c) 2002-2019, 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 inverse square root.\n\n";

 13: #include <slepcfn.h>

 15: /*
 16:    Compute matrix inverse square root B = inv(sqrtm(A))
 17:    Check result as norm(B*B*A-I)
 18:  */
 19: PetscErrorCode TestMatInvSqrt(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:   MatCreateSeqDense(PETSC_COMM_SELF,n,n,NULL,&R);
 34:   PetscObjectSetName((PetscObject)R,"R");
 35:   FNGetScale(fn,&tau,&eta);
 36:   /* compute inverse square root */
 37:   if (inplace) {
 38:     MatCopy(A,S,SAME_NONZERO_PATTERN);
 39:     MatIsHermitianKnown(A,&set,&flg);
 40:     if (set && flg) { MatSetOption(S,MAT_HERMITIAN,PETSC_TRUE); }
 41:     FNEvaluateFunctionMat(fn,S,NULL);
 42:   } else {
 43:     FNEvaluateFunctionMat(fn,A,S);
 44:   }
 45:   if (verbose) {
 46:     PetscPrintf(PETSC_COMM_WORLD,"Matrix A - - - - - - - -\n");
 47:     MatView(A,viewer);
 48:     PetscPrintf(PETSC_COMM_WORLD,"Computed inv(sqrtm(A)) - - - - - - -\n");
 49:     MatView(S,viewer);
 50:   }
 51:   /* check error ||S*S*A-I||_F */
 52:   MatMatMult(S,S,MAT_REUSE_MATRIX,PETSC_DEFAULT,&R);
 53:   if (eta!=1.0) {
 54:     MatScale(R,1.0/(eta*eta));
 55:   }
 56:   MatCreateVecs(A,&v,&f0);
 57:   MatGetColumnVector(S,f0,0);
 58:   MatCopy(R,S,SAME_NONZERO_PATTERN);
 59:   if (tau!=1.0) {
 60:     MatScale(S,tau);
 61:   }
 62:   MatMatMult(S,A,MAT_REUSE_MATRIX,PETSC_DEFAULT,&R);
 63:   MatShift(R,-1.0);
 64:   MatNorm(R,NORM_FROBENIUS,&nrm);
 65:   if (nrm<100*PETSC_MACHINE_EPSILON) {
 66:     PetscPrintf(PETSC_COMM_WORLD,"||S*S*A-I||_F < 100*eps\n");
 67:   } else {
 68:     PetscPrintf(PETSC_COMM_WORLD,"||S*S*A-I||_F = %g\n",(double)nrm);
 69:   }
 70:   /* check FNEvaluateFunctionMatVec() */
 71:   FNEvaluateFunctionMatVec(fn,A,v);
 72:   VecAXPY(v,-1.0,f0);
 73:   VecNorm(v,NORM_2,&nrm);
 74:   if (nrm>100*PETSC_MACHINE_EPSILON) {
 75:     PetscPrintf(PETSC_COMM_WORLD,"Warning: the norm of f(A)*e_1-v is %g\n",(double)nrm);
 76:   }
 77:   MatDestroy(&S);
 78:   MatDestroy(&R);
 79:   VecDestroy(&v);
 80:   VecDestroy(&f0);
 81:   return(0);
 82: }

 84: int main(int argc,char **argv)
 85: {
 87:   FN             fn;
 88:   Mat            A;
 89:   PetscInt       i,j,n=10;
 90:   PetscScalar    x,y,yp,*As;
 91:   PetscViewer    viewer;
 92:   PetscBool      verbose,inplace;
 93:   PetscRandom    myrand;
 94:   PetscReal      v;
 95:   char           strx[50],str[50];

 97:   SlepcInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;
 98:   PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);
 99:   PetscOptionsHasName(NULL,NULL,"-verbose",&verbose);
100:   PetscOptionsHasName(NULL,NULL,"-inplace",&inplace);
101:   PetscPrintf(PETSC_COMM_WORLD,"Matrix inverse square root, n=%D.\n",n);

103:   /* Create function object */
104:   FNCreate(PETSC_COMM_WORLD,&fn);
105:   FNSetType(fn,FNINVSQRT);
106:   FNSetFromOptions(fn);

108:   /* Set up viewer */
109:   PetscViewerASCIIGetStdout(PETSC_COMM_WORLD,&viewer);
110:   FNView(fn,viewer);
111:   if (verbose) {
112:     PetscViewerPushFormat(viewer,PETSC_VIEWER_ASCII_MATLAB);
113:   }

115:   /* Scalar evaluation */
116:   x = 2.2;
117:   SlepcSNPrintfScalar(strx,50,x,PETSC_FALSE);
118:   FNEvaluateFunction(fn,x,&y);
119:   FNEvaluateDerivative(fn,x,&yp);
120:   SlepcSNPrintfScalar(str,50,y,PETSC_FALSE);
121:   PetscPrintf(PETSC_COMM_WORLD,"  f(%s)=%s\n",strx,str);
122:   SlepcSNPrintfScalar(str,50,yp,PETSC_FALSE);
123:   PetscPrintf(PETSC_COMM_WORLD,"  f'(%s)=%s\n",strx,str);

125:   /* Create matrix */
126:   MatCreateSeqDense(PETSC_COMM_SELF,n,n,NULL,&A);
127:   PetscObjectSetName((PetscObject)A,"A");

129:   /* Compute square root of a symmetric matrix A */
130:   MatDenseGetArray(A,&As);
131:   for (i=0;i<n;i++) As[i+i*n]=2.5;
132:   for (j=1;j<3;j++) {
133:     for (i=0;i<n-j;i++) { As[i+(i+j)*n]=1.0; As[(i+j)+i*n]=1.0; }
134:   }
135:   MatDenseRestoreArray(A,&As);
136:   MatSetOption(A,MAT_HERMITIAN,PETSC_TRUE);
137:   TestMatInvSqrt(fn,A,viewer,verbose,inplace);

139:   /* Repeat with upper triangular A */
140:   MatDenseGetArray(A,&As);
141:   for (j=1;j<3;j++) {
142:     for (i=0;i<n-j;i++) As[(i+j)+i*n]=0.0;
143:   }
144:   MatDenseRestoreArray(A,&As);
145:   MatSetOption(A,MAT_HERMITIAN,PETSC_FALSE);
146:   TestMatInvSqrt(fn,A,viewer,verbose,inplace);

148:   /* Repeat with non-symmetic A */
149:   PetscRandomCreate(PETSC_COMM_WORLD,&myrand);
150:   PetscRandomSetFromOptions(myrand);
151:   PetscRandomSetInterval(myrand,0.0,1.0);
152:   MatDenseGetArray(A,&As);
153:   for (j=1;j<3;j++) {
154:     for (i=0;i<n-j;i++) {
155:       PetscRandomGetValueReal(myrand,&v);
156:       As[(i+j)+i*n]=v;
157:     }
158:   }
159:   MatDenseRestoreArray(A,&As);
160:   PetscRandomDestroy(&myrand);
161:   MatSetOption(A,MAT_HERMITIAN,PETSC_FALSE);
162:   TestMatInvSqrt(fn,A,viewer,verbose,inplace);

164:   MatDestroy(&A);
165:   FNDestroy(&fn);
166:   SlepcFinalize();
167:   return ierr;
168: }

170: /*TEST

172:    test:
173:       suffix: 1
174:       nsize: 1
175:       args: -fn_scale 0.9,0.5 -n 10 -fn_method {{0 1 2}shared output}
176:       filter: grep -v "computing matrix functions"
177:       output_file: output/test8_1.out

179:    test:
180:       suffix: 2
181:       nsize: 1
182:       args: -fn_scale 0.9,0.5 -n 10 -inplace -fn_method {{0 1 2}shared output}
183:       filter: grep -v "computing matrix functions"
184:       output_file: output/test8_1.out

186: TEST*/