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

/******************************************************************************* * Copyright (C) 2009-2015 Intel Corporation. All Rights Reserved. * The information and material ("Material") provided below is owned by Intel * Corporation or its suppliers or licensors, and title to such Material remains * with Intel Corporation or its suppliers or licensors. The Material contains * proprietary information of Intel or its suppliers and licensors. The Material * is protected by worldwide copyright laws and treaty provisions. No part of * the Material may be copied, reproduced, published, uploaded, posted, * transmitted, or distributed in any way without Intel's prior express written * permission. No license under any patent, copyright or other intellectual * property rights in the Material is granted to or conferred upon you, either * expressly, by implication, inducement, estoppel or otherwise. Any license * under such intellectual property rights must be express and approved by Intel * in writing. * ******************************************************************************** */ /* ZHEEVD Example. ============== Program computes all eigenvalues and eigenvectors of a complex Hermitian matrix A using divide and conquer algorithm, where A is: ( 3.40, 0.00) ( -2.36, -1.93) ( -4.68, 9.55) ( 5.37, -1.23) ( -2.36, 1.93) ( 6.94, 0.00) ( 8.13, -1.47) ( 2.07, -5.78) ( -4.68, -9.55) ( 8.13, 1.47) ( -2.14, 0.00) ( 4.68, 7.44) ( 5.37, 1.23) ( 2.07, 5.78) ( 4.68, -7.44) ( -7.42, 0.00) Description. ============ The routine computes all 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. If the eigenvectors are requested, then this routine uses a divide and conquer algorithm to compute eigenvalues and eigenvectors. Example Program Results. ======================== ZHEEVD Example Program Results Eigenvalues -21.97 -0.05 6.46 16.34 Eigenvectors (stored columnwise) ( 0.41, 0.00) ( -0.34, 0.00) ( -0.69, 0.00) ( 0.49, 0.00) ( 0.02, -0.30) ( 0.32, -0.21) ( -0.57, -0.22) ( -0.59, -0.21) ( 0.18, 0.57) ( -0.42, -0.32) ( 0.06, 0.16) ( -0.35, -0.47) ( -0.62, -0.09) ( -0.58, 0.35) ( -0.15, -0.31) ( -0.10, -0.12) */ #include <stdlib.h> #include <stdio.h> /* Complex datatype */ struct _dcomplex { double re, im; }; typedef struct _dcomplex dcomplex; /* ZHEEVD prototype */ extern void zheevd( char* jobz, char* uplo, int* n, dcomplex* a, int* lda, double* w, 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 /* Main program */ int main() { /* Locals */ int n = N, lda = LDA, info, lwork, lrwork, liwork; int iwkopt; int* iwork; double rwkopt; double* rwork; dcomplex wkopt; dcomplex* work; /* Local arrays */ double w[N]; dcomplex a[LDA*N] = { { 3.40, 0.00}, {-2.36, 1.93}, {-4.68, -9.55}, { 5.37, 1.23}, { 0.00, 0.00}, { 6.94, 0.00}, { 8.13, 1.47}, { 2.07, 5.78}, { 0.00, 0.00}, { 0.00, 0.00}, {-2.14, 0.00}, { 4.68, -7.44}, { 0.00, 0.00}, { 0.00, 0.00}, { 0.00, 0.00}, {-7.42, 0.00} }; /* Executable statements */ printf( " ZHEEVD Example Program Results\n" ); /* Query and allocate the optimal workspace */ lwork = -1; lrwork = -1; liwork = -1; zheevd( "Vectors", "Lower", &n, a, &lda, w, &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 */ zheevd( "Vectors", "Lower", &n, a, &lda, w, work, &lwork, rwork, &lrwork, iwork, &liwork, &info ); /* Check for convergence */ if( info > 0 ) { printf( "The algorithm failed to compute eigenvalues.\n" ); exit( 1 ); } /* Print eigenvalues */ print_rmatrix( "Eigenvalues", 1, n, w, 1 ); /* Print eigenvectors */ print_matrix( "Eigenvectors (stored columnwise)", n, n, a, lda ); /* Free workspace */ free( (void*)iwork ); free( (void*)rwork ); free( (void*)work ); exit( 0 ); } /* End of ZHEEVD 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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