Developer Reference

  • 2022.1
  • 12/20/2021
  • Public Content
Contents

CHEEVX 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. * ******************************************************************************** */ /* CHEEVX Example. ============== Program computes eigenvalues specified by a selected range of values and corresponding eigenvectors of a complex Hermitian matrix A: ( 6.51, 0.00) ( -5.92, 9.53) ( -2.46, 2.91) ( 8.84, 3.21) ( -5.92, -9.53) ( -1.73, 0.00) ( 6.50, 2.09) ( 1.32, 8.81) ( -2.46, -2.91) ( 6.50, -2.09) ( 6.90, 0.00) ( -0.59, 2.47) ( 8.84, -3.21) ( 1.32, -8.81) ( -0.59, -2.47) ( -2.85, 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. ======================== CHEEVX Example Program Results The total number of eigenvalues found: 3 Selected eigenvalues 0.09 9.53 18.75 Selected eigenvectors (stored columnwise) ( 0.18, 0.00) ( -0.54, 0.00) ( 0.67, 0.00) ( -0.40, -0.31) ( -0.21, -0.17) ( -0.30, -0.43) ( 0.60, 0.40) ( -0.35, -0.28) ( -0.39, -0.34) ( -0.34, 0.26) ( -0.57, 0.35) ( 0.05, 0.05) */ #include <stdlib.h> #include <stdio.h> /* Complex datatype */ struct _fcomplex { float re, im; }; typedef struct _fcomplex fcomplex; /* CHEEVX prototype */ extern void cheevx( char* jobz, char* range, char* uplo, int* n, fcomplex* a, int* lda, float* vl, float* vu, int* il, int* iu, float* abstol, int* m, float* w, fcomplex* z, int* ldz, fcomplex* work, int* lwork, float* rwork, int* iwork, int* ifail, int* info ); /* Auxiliary routines prototypes */ extern void print_matrix( char* desc, int m, int n, fcomplex* a, int lda ); extern void print_rmatrix( char* desc, int m, int n, float* 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; float abstol, vl, vu; fcomplex wkopt; fcomplex* work; /* Local arrays */ /* iwork dimension should be at least 5*n */ int iwork[5*N], ifail[N]; /* rwork dimension should be at least 7*n */ float w[N], rwork[7*N]; fcomplex z[LDZ*N]; fcomplex a[LDA*N] = { { 6.51f, 0.00f}, {-5.92f, -9.53f}, {-2.46f, -2.91f}, { 8.84f, -3.21f}, { 0.00f, 0.00f}, {-1.73f, 0.00f}, { 6.50f, -2.09f}, { 1.32f, -8.81f}, { 0.00f, 0.00f}, { 0.00f, 0.00f}, { 6.90f, 0.00f}, {-0.59f, -2.47f}, { 0.00f, 0.00f}, { 0.00f, 0.00f}, { 0.00f, 0.00f}, {-2.85f, 0.00f} }; /* Executable statements */ printf( " CHEEVX 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 = 0.0; vu = 100.0; /* Query and allocate the optimal workspace */ lwork = -1; cheevx( "Vectors", "Values", "Lower", &n, a, &lda, &vl, &vu, &il, &iu, &abstol, &m, w, z, &ldz, &wkopt, &lwork, rwork, iwork, ifail, &info ); lwork = (int)wkopt.re; work = (fcomplex*)malloc( lwork*sizeof(fcomplex) ); /* Solve eigenproblem */ cheevx( "Vectors", "Values", "Lower", &n, a, &lda, &vl, &vu, &il, &iu, &abstol, &m, w, z, &ldz, work, &lwork, rwork, iwork, ifail, &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*)work ); exit( 0 ); } /* End of CHEEVX Example */ /* Auxiliary routine: printing a matrix */ void print_matrix( char* desc, int m, int n, fcomplex* 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, float* 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" ); } }

Product and Performance Information

1

Performance varies by use, configuration and other factors. Learn more at www.Intel.com/PerformanceIndex.