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  • 2022.1
  • 12/20/2021
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ZHEEVR Example Program in C

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Any license * under such intellectual property rights must be express and approved by Intel * in writing. * ******************************************************************************** */ /* ZHEEVR Example. ============== Program computes eigenvalues specified by a selected range of values and corresponding eigenvectors of a complex Hermitian matrix A using the Relatively Robust Representations, where A is: ( -2.16, 0.00) ( -0.16, -4.86) ( -7.23, -9.38) ( -0.04, 6.86) ( -0.16, 4.86) ( 7.45, 0.00) ( 4.39, 6.29) ( -8.11, -4.41) ( -7.23, 9.38) ( 4.39, -6.29) ( -9.03, 0.00) ( -6.89, -7.66) ( -0.04, -6.86) ( -8.11, 4.41) ( -6.89, 7.66) ( 7.76, 0.00) Description. ============ The routine computes selected eigenvalues and, optionally, eigenvectors of an n-by-n complex Hermitian matrix A. The eigenvector v(j) of A satisfies A*v(j) = lambda(j)*v(j) where lambda(j) is its eigenvalue. The computed eigenvectors are orthonormal. Eigenvalues and eigenvectors can be selected by specifying either a range of values or a range of indices for the desired eigenvalues. Example Program Results. ======================== ZHEEVR Example Program Results The total number of eigenvalues found: 2 Selected eigenvalues -4.18 3.57 Selected eigenvectors (stored columnwise) ( 0.68, 0.00) ( 0.38, 0.00) ( 0.03, 0.18) ( 0.54, -0.57) ( -0.03, 0.21) ( -0.40, 0.04) ( 0.20, 0.64) ( -0.14, -0.26) */ #include <stdlib.h> #include <stdio.h> /* Complex datatype */ struct _dcomplex { double re, im; }; typedef struct _dcomplex dcomplex; /* ZHEEVR prototype */ extern void zheevr( char* jobz, char* range, char* uplo, int* n, dcomplex* a, int* lda, double* vl, double* vu, int* il, int* iu, double* abstol, int* m, double* w, dcomplex* z, int* ldz, int* isuppz, dcomplex* work, int* lwork, double* rwork, int* lrwork, int* iwork, int* liwork, int* info ); /* Auxiliary routines prototypes */ extern void print_matrix( char* desc, int m, int n, dcomplex* a, int lda ); extern void print_rmatrix( char* desc, int m, int n, double* a, int lda ); /* Parameters */ #define N 4 #define LDA N #define LDZ N /* Main program */ int main() { /* Locals */ int n = N, lda = LDA, ldz = LDZ, il, iu, m, info, lwork, lrwork, liwork; double abstol, vl, vu; int iwkopt; int* iwork; double rwkopt; double* rwork; dcomplex wkopt; dcomplex* work; /* Local arrays */ int isuppz[N]; double w[N]; dcomplex z[LDZ*N]; dcomplex a[LDA*N] = { {-2.16, 0.00}, {-0.16, 4.86}, {-7.23, 9.38}, {-0.04, -6.86}, { 0.00, 0.00}, { 7.45, 0.00}, { 4.39, -6.29}, {-8.11, 4.41}, { 0.00, 0.00}, { 0.00, 0.00}, {-9.03, 0.00}, {-6.89, 7.66}, { 0.00, 0.00}, { 0.00, 0.00}, { 0.00, 0.00}, { 7.76, 0.00} }; /* Executable statements */ printf( " ZHEEVR Example Program Results\n" ); /* Negative abstol means using the default value */ abstol = -1.0; /* Set VL, VU to compute eigenvalues in half-open (VL,VU] interval */ vl = -5.0; vu = 5.0; /* Query and allocate the optimal workspace */ lwork = -1; lrwork = -1; liwork = -1; zheevr( "Vectors", "Values", "Lower", &n, a, &lda, &vl, &vu, &il, &iu, &abstol, &m, w, z, &ldz, isuppz, &wkopt, &lwork, &rwkopt, &lrwork, &iwkopt, &liwork, &info ); lwork = (int)wkopt.re; work = (dcomplex*)malloc( lwork*sizeof(dcomplex) ); lrwork = (int)rwkopt; rwork = (double*)malloc( lrwork*sizeof(double) ); liwork = iwkopt; iwork = (int*)malloc( liwork*sizeof(int) ); /* Solve eigenproblem */ zheevr( "Vectors", "Values", "Lower", &n, a, &lda, &vl, &vu, &il, &iu, &abstol, &m, w, z, &ldz, isuppz, work, &lwork, rwork, &lrwork, iwork, &liwork, &info ); /* Check for convergence */ if( info > 0 ) { printf( "The algorithm failed to compute eigenvalues.\n" ); exit( 1 ); } /* Print the number of eigenvalues found */ printf( "\n The total number of eigenvalues found:%2i\n", m ); /* Print eigenvalues */ print_rmatrix( "Selected eigenvalues", 1, m, w, 1 ); /* Print eigenvectors */ print_matrix( "Selected eigenvectors (stored columnwise)", n, m, z, ldz ); /* Free workspace */ free( (void*)iwork ); free( (void*)rwork ); free( (void*)work ); exit( 0 ); } /* End of ZHEEVR Example */ /* Auxiliary routine: printing a matrix */ void print_matrix( char* desc, int m, int n, dcomplex* a, int lda ) { int i, j; printf( "\n %s\n", desc ); for( i = 0; i < m; i++ ) { for( j = 0; j < n; j++ ) printf( " (%6.2f,%6.2f)", a[i+j*lda].re, a[i+j*lda].im ); printf( "\n" ); } } /* Auxiliary routine: printing a real matrix */ void print_rmatrix( char* desc, int m, int n, double* a, int lda ) { int i, j; printf( "\n %s\n", desc ); for( i = 0; i < m; i++ ) { for( j = 0; j < n; j++ ) printf( " %6.2f", a[i+j*lda] ); printf( "\n" ); } }

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