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