Actual source code: test8.c

slepc-3.17.1 2022-04-11
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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 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: {
 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 inverse 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 inv(sqrtm(A)) - - - - - - -\n");
 44:     MatView(S,viewer);
 45:   }
 46:   /* check error ||S*S*A-I||_F */
 47:   MatMatMult(S,S,MAT_INITIAL_MATRIX,PETSC_DEFAULT,&R);
 48:   if (eta!=1.0) MatScale(R,1.0/(eta*eta));
 49:   MatCreateVecs(A,&v,&f0);
 50:   MatGetColumnVector(S,f0,0);
 51:   MatCopy(R,S,SAME_NONZERO_PATTERN);
 52:   MatDestroy(&R);
 53:   if (tau!=1.0) MatScale(S,tau);
 54:   MatMatMult(S,A,MAT_INITIAL_MATRIX,PETSC_DEFAULT,&R);
 55:   MatShift(R,-1.0);
 56:   MatNorm(R,NORM_FROBENIUS,&nrm);
 57:   MatDestroy(&R);
 58:   if (nrm<100*PETSC_MACHINE_EPSILON) PetscPrintf(PETSC_COMM_WORLD,"||S*S*A-I||_F < 100*eps\n");
 59:   else PetscPrintf(PETSC_COMM_WORLD,"||S*S*A-I||_F = %g\n",(double)nrm);
 60:   /* check FNEvaluateFunctionMatVec() */
 61:   FNEvaluateFunctionMatVec(fn,A,v);
 62:   VecAXPY(v,-1.0,f0);
 63:   VecNorm(v,NORM_2,&nrm);
 64:   if (nrm>100*PETSC_MACHINE_EPSILON) PetscPrintf(PETSC_COMM_WORLD,"Warning: the norm of f(A)*e_1-v is %g\n",(double)nrm);
 65:   MatDestroy(&S);
 66:   VecDestroy(&v);
 67:   VecDestroy(&f0);
 68:   PetscFunctionReturn(0);
 69: }

 71: int main(int argc,char **argv)
 72: {
 73:   FN             fn;
 74:   Mat            A;
 75:   PetscInt       i,j,n=10;
 76:   PetscScalar    x,y,yp,*As;
 77:   PetscViewer    viewer;
 78:   PetscBool      verbose,inplace;
 79:   PetscRandom    myrand;
 80:   PetscReal      v;
 81:   char           strx[50],str[50];

 83:   SlepcInitialize(&argc,&argv,(char*)0,help);
 84:   PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);
 85:   PetscOptionsHasName(NULL,NULL,"-verbose",&verbose);
 86:   PetscOptionsHasName(NULL,NULL,"-inplace",&inplace);
 87:   PetscPrintf(PETSC_COMM_WORLD,"Matrix inverse square root, n=%" PetscInt_FMT ".\n",n);

 89:   /* Create function object */
 90:   FNCreate(PETSC_COMM_WORLD,&fn);
 91:   FNSetType(fn,FNINVSQRT);
 92:   FNSetFromOptions(fn);

 94:   /* Set up viewer */
 95:   PetscViewerASCIIGetStdout(PETSC_COMM_WORLD,&viewer);
 96:   FNView(fn,viewer);
 97:   if (verbose) PetscViewerPushFormat(viewer,PETSC_VIEWER_ASCII_MATLAB);

 99:   /* Scalar evaluation */
100:   x = 2.2;
101:   SlepcSNPrintfScalar(strx,sizeof(strx),x,PETSC_FALSE);
102:   FNEvaluateFunction(fn,x,&y);
103:   FNEvaluateDerivative(fn,x,&yp);
104:   SlepcSNPrintfScalar(str,sizeof(str),y,PETSC_FALSE);
105:   PetscPrintf(PETSC_COMM_WORLD,"  f(%s)=%s\n",strx,str);
106:   SlepcSNPrintfScalar(str,sizeof(str),yp,PETSC_FALSE);
107:   PetscPrintf(PETSC_COMM_WORLD,"  f'(%s)=%s\n",strx,str);

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

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

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

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

148:   MatDestroy(&A);
149:   FNDestroy(&fn);
150:   SlepcFinalize();
151:   return 0;
152: }

154: /*TEST

156:    testset:
157:       args: -fn_scale 0.9,0.5 -n 10
158:       filter: grep -v "computing matrix functions"
159:       requires: !__float128
160:       output_file: output/test8_1.out
161:       test:
162:          suffix: 1
163:          args: -fn_method {{0 1 2 3}}
164:       test:
165:          suffix: 1_cuda
166:          args: -fn_method 4
167:          requires: cuda
168:       test:
169:          suffix: 1_magma
170:          args: -fn_method {{5 6}}
171:          requires: cuda magma
172:       test:
173:          suffix: 2
174:          args: -inplace -fn_method {{0 1 2 3}}
175:       test:
176:          suffix: 2_cuda
177:          args: -inplace -fn_method 4
178:          requires: cuda
179:       test:
180:          suffix: 2_magma
181:          args: -inplace -fn_method {{5 6}}
182:          requires: cuda magma

184: TEST*/