1 static char help[] = "Test LAPACK routine DSYEV() or DSYEVX(). \n\ 2 Reads PETSc matrix A \n\ 3 then computes selected eigenvalues, and optionally, eigenvectors of \n\ 4 a real generalized symmetric-definite eigenproblem \n\ 5 A*x = lambda*x \n\ 6 Input parameters include\n\ 7 -f <input_file> : file to load\n\ 8 e.g. ./ex116 -f $DATAFILESPATH/matrices/small \n\n"; 9 10 #include <petscmat.h> 11 #include <petscblaslapack.h> 12 13 extern PetscErrorCode CkEigenSolutions(PetscInt,Mat,PetscInt,PetscInt,PetscReal*,Vec*,PetscReal*); 14 15 int main(int argc,char **args) 16 { 17 Mat A,A_dense; 18 Vec *evecs; 19 PetscViewer fd; /* viewer */ 20 char file[1][PETSC_MAX_PATH_LEN]; /* input file name */ 21 PetscBool flg,TestSYEVX=PETSC_TRUE; 22 PetscErrorCode ierr; 23 PetscBool isSymmetric; 24 PetscScalar *arrayA,*evecs_array,*work,*evals; 25 PetscMPIInt size; 26 PetscInt m,n,i,cklvl=2; 27 PetscBLASInt nevs,il,iu,in; 28 PetscReal vl,vu,abstol=1.e-8; 29 PetscBLASInt *iwork,*ifail,lwork,lierr,bn; 30 PetscReal tols[2]; 31 32 ierr = PetscInitialize(&argc,&args,(char*)0,help);if (ierr) return ierr; 33 CHKERRMPI(MPI_Comm_size(PETSC_COMM_WORLD,&size)); 34 PetscCheckFalse(size != 1,PETSC_COMM_WORLD,PETSC_ERR_SUP,"This is a uniprocessor example only!"); 35 36 CHKERRQ(PetscOptionsHasName(NULL,NULL, "-test_syev", &flg)); 37 if (flg) { 38 TestSYEVX = PETSC_FALSE; 39 } 40 41 /* Determine files from which we read the two matrices */ 42 CHKERRQ(PetscOptionsGetString(NULL,NULL,"-f",file[0],sizeof(file[0]),&flg)); 43 44 /* Load matrix A */ 45 CHKERRQ(PetscViewerBinaryOpen(PETSC_COMM_WORLD,file[0],FILE_MODE_READ,&fd)); 46 CHKERRQ(MatCreate(PETSC_COMM_WORLD,&A)); 47 CHKERRQ(MatSetType(A,MATSEQAIJ)); 48 CHKERRQ(MatLoad(A,fd)); 49 CHKERRQ(PetscViewerDestroy(&fd)); 50 CHKERRQ(MatGetSize(A,&m,&n)); 51 52 /* Check whether A is symmetric */ 53 CHKERRQ(PetscOptionsHasName(NULL,NULL, "-check_symmetry", &flg)); 54 if (flg) { 55 Mat Trans; 56 CHKERRQ(MatTranspose(A,MAT_INITIAL_MATRIX, &Trans)); 57 CHKERRQ(MatEqual(A, Trans, &isSymmetric)); 58 PetscCheck(isSymmetric,PETSC_COMM_SELF,PETSC_ERR_USER,"A must be symmetric"); 59 CHKERRQ(MatDestroy(&Trans)); 60 } 61 62 /* Solve eigenvalue problem: A_dense*x = lambda*B*x */ 63 /*==================================================*/ 64 /* Convert aij matrix to MatSeqDense for LAPACK */ 65 CHKERRQ(MatConvert(A,MATSEQDENSE,MAT_INITIAL_MATRIX,&A_dense)); 66 67 CHKERRQ(PetscBLASIntCast(8*n,&lwork)); 68 CHKERRQ(PetscBLASIntCast(n,&bn)); 69 CHKERRQ(PetscMalloc1(n,&evals)); 70 CHKERRQ(PetscMalloc1(lwork,&work)); 71 CHKERRQ(MatDenseGetArray(A_dense,&arrayA)); 72 73 if (!TestSYEVX) { /* test syev() */ 74 CHKERRQ(PetscPrintf(PETSC_COMM_SELF," LAPACKsyev: compute all %" PetscInt_FMT " eigensolutions...\n",m)); 75 LAPACKsyev_("V","U",&bn,arrayA,&bn,evals,work,&lwork,&lierr); 76 evecs_array = arrayA; 77 CHKERRQ(PetscBLASIntCast(m,&nevs)); 78 il = 1; 79 CHKERRQ(PetscBLASIntCast(m,&iu)); 80 } else { /* test syevx() */ 81 il = 1; 82 CHKERRQ(PetscBLASIntCast(0.2*m,&iu)); 83 CHKERRQ(PetscBLASIntCast(n,&in)); 84 CHKERRQ(PetscPrintf(PETSC_COMM_SELF," LAPACKsyevx: compute %" PetscBLASInt_FMT " to %" PetscBLASInt_FMT "-th eigensolutions...\n",il,iu)); 85 CHKERRQ(PetscMalloc1(m*n+1,&evecs_array)); 86 CHKERRQ(PetscMalloc1(6*n+1,&iwork)); 87 ifail = iwork + 5*n; 88 89 /* in the case "I", vl and vu are not referenced */ 90 vl = 0.0; vu = 8.0; 91 LAPACKsyevx_("V","I","U",&bn,arrayA,&bn,&vl,&vu,&il,&iu,&abstol,&nevs,evals,evecs_array,&in,work,&lwork,iwork,ifail,&lierr); 92 CHKERRQ(PetscFree(iwork)); 93 } 94 CHKERRQ(MatDenseRestoreArray(A_dense,&arrayA)); 95 PetscCheckFalse(nevs <= 0,PETSC_COMM_SELF,PETSC_ERR_CONV_FAILED, "nev=%" PetscBLASInt_FMT ", no eigensolution has found", nevs); 96 97 /* View eigenvalues */ 98 CHKERRQ(PetscOptionsHasName(NULL,NULL, "-eig_view", &flg)); 99 if (flg) { 100 CHKERRQ(PetscPrintf(PETSC_COMM_SELF," %" PetscBLASInt_FMT " evals: \n",nevs)); 101 for (i=0; i<nevs; i++) CHKERRQ(PetscPrintf(PETSC_COMM_SELF,"%" PetscInt_FMT " %g\n",(PetscInt)(i+il),(double)evals[i])); 102 } 103 104 /* Check residuals and orthogonality */ 105 CHKERRQ(PetscMalloc1(nevs+1,&evecs)); 106 for (i=0; i<nevs; i++) { 107 CHKERRQ(VecCreate(PETSC_COMM_SELF,&evecs[i])); 108 CHKERRQ(VecSetSizes(evecs[i],PETSC_DECIDE,n)); 109 CHKERRQ(VecSetFromOptions(evecs[i])); 110 CHKERRQ(VecPlaceArray(evecs[i],evecs_array+i*n)); 111 } 112 113 tols[0] = tols[1] = PETSC_SQRT_MACHINE_EPSILON; 114 CHKERRQ(CkEigenSolutions(cklvl,A,il-1,iu-1,evals,evecs,tols)); 115 116 /* Free work space. */ 117 for (i=0; i<nevs; i++) CHKERRQ(VecDestroy(&evecs[i])); 118 CHKERRQ(PetscFree(evecs)); 119 CHKERRQ(MatDestroy(&A_dense)); 120 CHKERRQ(PetscFree(work)); 121 if (TestSYEVX) CHKERRQ(PetscFree(evecs_array)); 122 123 /* Compute SVD: A_dense = U*SIGMA*transpose(V), 124 JOBU=JOBV='S': the first min(m,n) columns of U and V are returned in the arrayU and arrayV; */ 125 /*==============================================================================================*/ 126 { 127 /* Convert aij matrix to MatSeqDense for LAPACK */ 128 PetscScalar *arrayU,*arrayVT,*arrayErr,alpha=1.0,beta=-1.0; 129 Mat Err; 130 PetscBLASInt minMN,maxMN,im,in; 131 PetscInt j; 132 PetscReal norm; 133 134 CHKERRQ(MatConvert(A,MATSEQDENSE,MAT_INITIAL_MATRIX,&A_dense)); 135 136 minMN = PetscMin(m,n); 137 maxMN = PetscMax(m,n); 138 lwork = 5*minMN + maxMN; 139 CHKERRQ(PetscMalloc4(m*minMN,&arrayU,m*minMN,&arrayVT,m*minMN,&arrayErr,lwork,&work)); 140 141 /* Create matrix Err for checking error */ 142 CHKERRQ(MatCreate(PETSC_COMM_WORLD,&Err)); 143 CHKERRQ(MatSetSizes(Err,PETSC_DECIDE,PETSC_DECIDE,m,minMN)); 144 CHKERRQ(MatSetType(Err,MATSEQDENSE)); 145 CHKERRQ(MatSeqDenseSetPreallocation(Err,(PetscScalar*)arrayErr)); 146 147 /* Save A to arrayErr for checking accuracy later. arrayA will be destroyed by LAPACKgesvd_() */ 148 CHKERRQ(MatDenseGetArray(A_dense,&arrayA)); 149 CHKERRQ(PetscArraycpy(arrayErr,arrayA,m*minMN)); 150 151 CHKERRQ(PetscBLASIntCast(m,&im)); 152 CHKERRQ(PetscBLASIntCast(n,&in)); 153 /* Compute A = U*SIGMA*VT */ 154 LAPACKgesvd_("S","S",&im,&in,arrayA,&im,evals,arrayU,&minMN,arrayVT,&minMN,work,&lwork,&lierr); 155 CHKERRQ(MatDenseRestoreArray(A_dense,&arrayA)); 156 if (!lierr) { 157 CHKERRQ(PetscPrintf(PETSC_COMM_SELF," 1st 10 of %" PetscBLASInt_FMT " singular values: \n",minMN)); 158 for (i=0; i<10; i++) CHKERRQ(PetscPrintf(PETSC_COMM_SELF,"%" PetscInt_FMT " %g\n",i,(double)evals[i])); 159 } else { 160 CHKERRQ(PetscPrintf(PETSC_COMM_SELF,"LAPACKgesvd_ fails!")); 161 } 162 163 /* Check Err = (U*Sigma*V^T - A) using BLASgemm() */ 164 /* U = U*Sigma */ 165 for (j=0; j<minMN; j++) { /* U[:,j] = sigma[j]*U[:,j] */ 166 for (i=0; i<m; i++) arrayU[j*m+i] *= evals[j]; 167 } 168 /* Err = U*VT - A = alpha*U*VT + beta*Err */ 169 BLASgemm_("N","N",&im,&minMN,&minMN,&alpha,arrayU,&im,arrayVT,&minMN,&beta,arrayErr,&im); 170 CHKERRQ(MatNorm(Err,NORM_FROBENIUS,&norm)); 171 CHKERRQ(PetscPrintf(PETSC_COMM_SELF," || U*Sigma*VT - A || = %g\n",(double)norm)); 172 173 CHKERRQ(PetscFree4(arrayU,arrayVT,arrayErr,work)); 174 CHKERRQ(PetscFree(evals)); 175 CHKERRQ(MatDestroy(&A_dense)); 176 CHKERRQ(MatDestroy(&Err)); 177 } 178 179 CHKERRQ(MatDestroy(&A)); 180 ierr = PetscFinalize(); 181 return ierr; 182 } 183 /*------------------------------------------------ 184 Check the accuracy of the eigen solution 185 ----------------------------------------------- */ 186 /* 187 input: 188 cklvl - check level: 189 1: check residual 190 2: 1 and check B-orthogonality locally 191 A - matrix 192 il,iu - lower and upper index bound of eigenvalues 193 eval, evec - eigenvalues and eigenvectors stored in this process 194 tols[0] - reporting tol_res: || A * evec[i] - eval[i]*evec[i] || 195 tols[1] - reporting tol_orth: evec[i]^T*evec[j] - delta_ij 196 */ 197 PetscErrorCode CkEigenSolutions(PetscInt cklvl,Mat A,PetscInt il,PetscInt iu,PetscReal *eval,Vec *evec,PetscReal *tols) 198 { 199 PetscInt i,j,nev; 200 Vec vt1,vt2; /* tmp vectors */ 201 PetscReal norm,tmp,dot,norm_max,dot_max; 202 203 PetscFunctionBegin; 204 nev = iu - il; 205 if (nev <= 0) PetscFunctionReturn(0); 206 207 /*ierr = VecView(evec[0],PETSC_VIEWER_STDOUT_WORLD);*/ 208 CHKERRQ(VecDuplicate(evec[0],&vt1)); 209 CHKERRQ(VecDuplicate(evec[0],&vt2)); 210 211 switch (cklvl) { 212 case 2: 213 dot_max = 0.0; 214 for (i = il; i<iu; i++) { 215 CHKERRQ(VecCopy(evec[i], vt1)); 216 for (j=il; j<iu; j++) { 217 CHKERRQ(VecDot(evec[j],vt1,&dot)); 218 if (j == i) { 219 dot = PetscAbsScalar(dot - 1); 220 } else { 221 dot = PetscAbsScalar(dot); 222 } 223 if (dot > dot_max) dot_max = dot; 224 if (dot > tols[1]) { 225 CHKERRQ(VecNorm(evec[i],NORM_INFINITY,&norm)); 226 CHKERRQ(PetscPrintf(PETSC_COMM_SELF,"|delta(%" PetscInt_FMT ",%" PetscInt_FMT ")|: %g, norm: %g\n",i,j,(double)dot,(double)norm)); 227 } 228 } 229 } 230 CHKERRQ(PetscPrintf(PETSC_COMM_SELF," max|(x_j^T*x_i) - delta_ji|: %g\n",(double)dot_max)); 231 232 case 1: 233 norm_max = 0.0; 234 for (i = il; i< iu; i++) { 235 CHKERRQ(MatMult(A, evec[i], vt1)); 236 CHKERRQ(VecCopy(evec[i], vt2)); 237 tmp = -eval[i]; 238 CHKERRQ(VecAXPY(vt1,tmp,vt2)); 239 CHKERRQ(VecNorm(vt1, NORM_INFINITY, &norm)); 240 norm = PetscAbsScalar(norm); 241 if (norm > norm_max) norm_max = norm; 242 /* sniff, and bark if necessary */ 243 if (norm > tols[0]) { 244 CHKERRQ(PetscPrintf(PETSC_COMM_SELF," residual violation: %" PetscInt_FMT ", resi: %g\n",i, (double)norm)); 245 } 246 } 247 CHKERRQ(PetscPrintf(PETSC_COMM_SELF," max_resi: %g\n", (double)norm_max)); 248 break; 249 default: 250 CHKERRQ(PetscPrintf(PETSC_COMM_SELF,"Error: cklvl=%" PetscInt_FMT " is not supported \n",cklvl)); 251 } 252 CHKERRQ(VecDestroy(&vt2)); 253 CHKERRQ(VecDestroy(&vt1)); 254 PetscFunctionReturn(0); 255 } 256 257 /*TEST 258 259 build: 260 requires: !complex 261 262 test: 263 requires: datafilespath !complex double !defined(PETSC_USE_64BIT_INDICES) 264 args: -f ${DATAFILESPATH}/matrices/small 265 output_file: output/ex116_1.out 266 267 test: 268 suffix: 2 269 requires: datafilespath !complex double !defined(PETSC_USE_64BIT_INDICES) 270 args: -f ${DATAFILESPATH}/matrices/small -test_syev -check_symmetry 271 272 TEST*/ 273