| Line | Branch | Exec | Source |
|---|---|---|---|
| 1 | /* | ||
| 2 | - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - | ||
| 3 | SLEPc - Scalable Library for Eigenvalue Problem Computations | ||
| 4 | Copyright (c) 2002-, Universitat Politecnica de Valencia, Spain | ||
| 5 | |||
| 6 | This file is part of SLEPc. | ||
| 7 | SLEPc is distributed under a 2-clause BSD license (see LICENSE). | ||
| 8 | - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - | ||
| 9 | */ | ||
| 10 | /* | ||
| 11 | Define the function | ||
| 12 | |||
| 13 | f(x) = (1-x^2) exp(-x/(1+x^2)) | ||
| 14 | |||
| 15 | with the following tree: | ||
| 16 | |||
| 17 | f(x) f(x) (combined by product) | ||
| 18 | / \ g(x) = 1-x^2 (polynomial) | ||
| 19 | g(x) h(x) h(x) (combined by composition) | ||
| 20 | / \ r(x) = -x/(1+x^2) (rational) | ||
| 21 | r(x) e(x) e(x) = exp(x) (exponential) | ||
| 22 | */ | ||
| 23 | |||
| 24 | static char help[] = "Test combined function.\n\n"; | ||
| 25 | |||
| 26 | #include <slepcfn.h> | ||
| 27 | |||
| 28 | /* | ||
| 29 | Compute matrix function B = (I-A^2) exp(-(I+A^2)\A) | ||
| 30 | */ | ||
| 31 | 48 | PetscErrorCode TestMatCombine(FN fn,Mat A,PetscViewer viewer,PetscBool verbose,PetscBool inplace) | |
| 32 | { | ||
| 33 | 48 | PetscBool set,flg; | |
| 34 | 48 | PetscInt n; | |
| 35 | 48 | Mat F,Acopy; | |
| 36 | 48 | Vec v,f0; | |
| 37 | 48 | PetscReal nrm; | |
| 38 | |||
| 39 |
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48 | PetscFunctionBeginUser; |
| 40 |
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48 | PetscCall(MatGetSize(A,&n,NULL)); |
| 41 |
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48 | PetscCall(MatDuplicate(A,MAT_DO_NOT_COPY_VALUES,&F)); |
| 42 |
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48 | PetscCall(PetscObjectSetName((PetscObject)F,"F")); |
| 43 | /* compute matrix function */ | ||
| 44 |
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48 | if (inplace) { |
| 45 |
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24 | PetscCall(MatCopy(A,F,SAME_NONZERO_PATTERN)); |
| 46 |
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24 | PetscCall(MatIsHermitianKnown(A,&set,&flg)); |
| 47 |
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24 | if (set && flg) PetscCall(MatSetOption(F,MAT_HERMITIAN,PETSC_TRUE)); |
| 48 |
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24 | PetscCall(FNEvaluateFunctionMat(fn,F,NULL)); |
| 49 | } else { | ||
| 50 |
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24 | PetscCall(MatDuplicate(A,MAT_COPY_VALUES,&Acopy)); |
| 51 |
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24 | PetscCall(FNEvaluateFunctionMat(fn,A,F)); |
| 52 | /* check that A has not been modified */ | ||
| 53 |
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24 | PetscCall(MatAXPY(Acopy,-1.0,A,SAME_NONZERO_PATTERN)); |
| 54 |
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24 | PetscCall(MatNorm(Acopy,NORM_1,&nrm)); |
| 55 |
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24 | if (nrm>100*PETSC_MACHINE_EPSILON) PetscCall(PetscPrintf(PETSC_COMM_WORLD,"Warning: the input matrix has changed by %g\n",(double)nrm)); |
| 56 |
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24 | PetscCall(MatDestroy(&Acopy)); |
| 57 | } | ||
| 58 |
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48 | if (verbose) { |
| 59 | ✗ | PetscCall(PetscPrintf(PETSC_COMM_WORLD,"Matrix A - - - - - - - -\n")); | |
| 60 | ✗ | PetscCall(MatView(A,viewer)); | |
| 61 | ✗ | PetscCall(PetscPrintf(PETSC_COMM_WORLD,"Computed f(A) - - - - - - -\n")); | |
| 62 | ✗ | PetscCall(MatView(F,viewer)); | |
| 63 | } | ||
| 64 | /* print matrix norm for checking */ | ||
| 65 |
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48 | PetscCall(MatNorm(F,NORM_1,&nrm)); |
| 66 |
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48 | PetscCall(PetscPrintf(PETSC_COMM_WORLD,"The 1-norm of f(A) is %6.3f\n",(double)nrm)); |
| 67 | /* check FNEvaluateFunctionMatVec() */ | ||
| 68 |
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48 | PetscCall(MatCreateVecs(A,&v,&f0)); |
| 69 |
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48 | PetscCall(MatGetColumnVector(F,f0,0)); |
| 70 |
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48 | PetscCall(FNEvaluateFunctionMatVec(fn,A,v)); |
| 71 |
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48 | PetscCall(VecAXPY(v,-1.0,f0)); |
| 72 |
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48 | PetscCall(VecNorm(v,NORM_2,&nrm)); |
| 73 |
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48 | if (nrm>100*PETSC_MACHINE_EPSILON) PetscCall(PetscPrintf(PETSC_COMM_WORLD,"Warning: the norm of f(A)*e_1-v is %g\n",(double)nrm)); |
| 74 |
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48 | PetscCall(MatDestroy(&F)); |
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48 | PetscCall(VecDestroy(&v)); |
| 76 |
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48 | PetscCall(VecDestroy(&f0)); |
| 77 |
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8 | PetscFunctionReturn(PETSC_SUCCESS); |
| 78 | } | ||
| 79 | |||
| 80 | 24 | int main(int argc,char **argv) | |
| 81 | { | ||
| 82 | 24 | FN f,g,h,e,r,fcopy; | |
| 83 | 24 | Mat A=NULL; | |
| 84 | 24 | PetscInt i,j,n=10,np,nq; | |
| 85 | 24 | PetscScalar x,y,yp,*As,p[10],q[10]; | |
| 86 | 24 | char strx[50],str[50]; | |
| 87 | 24 | PetscViewer viewer; | |
| 88 | 24 | PetscBool verbose,inplace,matcuda; | |
| 89 | |||
| 90 |
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24 | PetscFunctionBeginUser; |
| 91 |
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24 | PetscCall(SlepcInitialize(&argc,&argv,NULL,help)); |
| 92 |
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24 | PetscCall(PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL)); |
| 93 |
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24 | PetscCall(PetscOptionsHasName(NULL,NULL,"-verbose",&verbose)); |
| 94 |
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24 | PetscCall(PetscOptionsHasName(NULL,NULL,"-inplace",&inplace)); |
| 95 |
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24 | PetscCall(PetscOptionsHasName(NULL,NULL,"-matcuda",&matcuda)); |
| 96 |
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24 | PetscCall(PetscPrintf(PETSC_COMM_WORLD,"Combined function, n=%" PetscInt_FMT ".\n",n)); |
| 97 | |||
| 98 | /* Create function */ | ||
| 99 | |||
| 100 | /* e(x) = exp(x) */ | ||
| 101 |
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24 | PetscCall(FNCreate(PETSC_COMM_WORLD,&e)); |
| 102 |
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24 | PetscCall(FNSetType(e,FNEXP)); |
| 103 |
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24 | PetscCall(FNSetFromOptions(e)); |
| 104 | /* r(x) = x/(1+x^2) */ | ||
| 105 |
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24 | PetscCall(FNCreate(PETSC_COMM_WORLD,&r)); |
| 106 |
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24 | PetscCall(FNSetType(r,FNRATIONAL)); |
| 107 |
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24 | PetscCall(FNSetFromOptions(r)); |
| 108 | 24 | np = 2; nq = 3; | |
| 109 | 24 | p[0] = -1.0; p[1] = 0.0; | |
| 110 | 24 | q[0] = 1.0; q[1] = 0.0; q[2] = 1.0; | |
| 111 |
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24 | PetscCall(FNRationalSetNumerator(r,np,p)); |
| 112 |
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24 | PetscCall(FNRationalSetDenominator(r,nq,q)); |
| 113 | /* h(x) */ | ||
| 114 |
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24 | PetscCall(FNCreate(PETSC_COMM_WORLD,&h)); |
| 115 |
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24 | PetscCall(FNSetType(h,FNCOMBINE)); |
| 116 |
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24 | PetscCall(FNSetFromOptions(h)); |
| 117 |
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24 | PetscCall(FNCombineSetChildren(h,FN_COMBINE_COMPOSE,r,e)); |
| 118 | /* g(x) = 1-x^2 */ | ||
| 119 |
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24 | PetscCall(FNCreate(PETSC_COMM_WORLD,&g)); |
| 120 |
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24 | PetscCall(FNSetType(g,FNRATIONAL)); |
| 121 |
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24 | PetscCall(FNSetFromOptions(g)); |
| 122 | 24 | np = 3; | |
| 123 | 24 | p[0] = -1.0; p[1] = 0.0; p[2] = 1.0; | |
| 124 |
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24 | PetscCall(FNRationalSetNumerator(g,np,p)); |
| 125 | /* f(x) */ | ||
| 126 |
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24 | PetscCall(FNCreate(PETSC_COMM_WORLD,&f)); |
| 127 |
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24 | PetscCall(FNSetType(f,FNCOMBINE)); |
| 128 |
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24 | PetscCall(FNSetFromOptions(f)); |
| 129 |
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24 | PetscCall(FNCombineSetChildren(f,FN_COMBINE_MULTIPLY,g,h)); |
| 130 | |||
| 131 | /* Set up viewer */ | ||
| 132 |
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24 | PetscCall(PetscViewerASCIIGetStdout(PETSC_COMM_WORLD,&viewer)); |
| 133 |
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24 | PetscCall(FNView(f,viewer)); |
| 134 |
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24 | if (verbose) PetscCall(PetscViewerPushFormat(viewer,PETSC_VIEWER_ASCII_MATLAB)); |
| 135 | |||
| 136 | /* Scalar evaluation */ | ||
| 137 | 24 | x = 2.2; | |
| 138 |
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24 | PetscCall(SlepcSNPrintfScalar(strx,sizeof(strx),x,PETSC_FALSE)); |
| 139 |
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24 | PetscCall(FNEvaluateFunction(f,x,&y)); |
| 140 |
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24 | PetscCall(FNEvaluateDerivative(f,x,&yp)); |
| 141 |
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24 | PetscCall(SlepcSNPrintfScalar(str,sizeof(str),y,PETSC_FALSE)); |
| 142 |
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24 | PetscCall(PetscPrintf(PETSC_COMM_WORLD," f(%s)=%s\n",strx,str)); |
| 143 |
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24 | PetscCall(SlepcSNPrintfScalar(str,sizeof(str),yp,PETSC_FALSE)); |
| 144 |
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24 | PetscCall(PetscPrintf(PETSC_COMM_WORLD," f'(%s)=%s\n",strx,str)); |
| 145 | |||
| 146 | /* Test duplication */ | ||
| 147 |
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24 | PetscCall(FNDuplicate(f,PetscObjectComm((PetscObject)f),&fcopy)); |
| 148 | |||
| 149 | /* Create matrices */ | ||
| 150 |
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24 | if (matcuda) { |
| 151 | #if defined(PETSC_HAVE_CUDA) | ||
| 152 |
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4 | PetscCall(MatCreateSeqDenseCUDA(PETSC_COMM_SELF,n,n,NULL,&A)); |
| 153 | #endif | ||
| 154 |
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20 | } else PetscCall(MatCreateSeqDense(PETSC_COMM_SELF,n,n,NULL,&A)); |
| 155 |
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24 | PetscCall(PetscObjectSetName((PetscObject)A,"A")); |
| 156 | |||
| 157 | /* Fill A with a symmetric Toeplitz matrix */ | ||
| 158 |
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24 | PetscCall(MatDenseGetArray(A,&As)); |
| 159 |
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264 | for (i=0;i<n;i++) As[i+i*n]=2.0; |
| 160 |
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72 | for (j=1;j<3;j++) { |
| 161 |
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456 | for (i=0;i<n-j;i++) { As[i+(i+j)*n]=1.0; As[(i+j)+i*n]=1.0; } |
| 162 | } | ||
| 163 |
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24 | PetscCall(MatDenseRestoreArray(A,&As)); |
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24 | PetscCall(MatSetOption(A,MAT_HERMITIAN,PETSC_TRUE)); |
| 165 |
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24 | PetscCall(TestMatCombine(fcopy,A,viewer,verbose,inplace)); |
| 166 | |||
| 167 | /* Repeat with same matrix as non-symmetric */ | ||
| 168 |
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24 | PetscCall(MatSetOption(A,MAT_HERMITIAN,PETSC_FALSE)); |
| 169 |
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24 | PetscCall(TestMatCombine(fcopy,A,viewer,verbose,inplace)); |
| 170 | |||
| 171 |
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24 | PetscCall(MatDestroy(&A)); |
| 172 |
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24 | PetscCall(FNDestroy(&f)); |
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24 | PetscCall(FNDestroy(&fcopy)); |
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24 | PetscCall(FNDestroy(&g)); |
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24 | PetscCall(FNDestroy(&h)); |
| 176 |
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24 | PetscCall(FNDestroy(&e)); |
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24 | PetscCall(FNDestroy(&r)); |
| 178 |
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24 | PetscCall(SlepcFinalize()); |
| 179 | return 0; | ||
| 180 | } | ||
| 181 | |||
| 182 | /*TEST | ||
| 183 | |||
| 184 | testset: | ||
| 185 | output_file: output/test6_1.out | ||
| 186 | test: | ||
| 187 | suffix: 1 | ||
| 188 | test: | ||
| 189 | suffix: 1_cuda | ||
| 190 | args: -matcuda | ||
| 191 | requires: cuda | ||
| 192 | test: | ||
| 193 | suffix: 2 | ||
| 194 | args: -inplace | ||
| 195 | test: | ||
| 196 | suffix: 2_cuda | ||
| 197 | args: -inplace -matcuda | ||
| 198 | requires: cuda | ||
| 199 | |||
| 200 | TEST*/ | ||
| 201 |