text: //Intel® Math Kernel Library LAPACK Examples
  
  /*******************************************************************************
   *  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.
   *
   ********************************************************************************
   */
  /*
   ZHEEV Example.
   ==============
   
   Program computes all eigenvalues and eigenvectors of a complex Hermitian
   matrix A:
   
   (  9.14,  0.00) ( -4.37, -9.22) ( -1.98, -1.72) ( -8.96, -9.50)
   ( -4.37,  9.22) ( -3.35,  0.00) (  2.25, -9.51) (  2.57,  2.40)
   ( -1.98,  1.72) (  2.25,  9.51) ( -4.82,  0.00) ( -3.24,  2.04)
   ( -8.96,  9.50) (  2.57, -2.40) ( -3.24, -2.04) (  8.44,  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.
   
   Example Program Results.
   ========================
   
   ZHEEV Example Program Results
   
   Eigenvalues
   -16.00  -6.76   6.67  25.51
   
   Eigenvectors (stored columnwise)
   (  0.34,  0.00) ( -0.55,  0.00) (  0.31,  0.00) ( -0.70,  0.00)
   (  0.44, -0.54) (  0.26,  0.18) (  0.45,  0.29) (  0.22, -0.28)
   ( -0.48, -0.37) ( -0.52, -0.02) ( -0.05,  0.57) (  0.15,  0.08)
   (  0.10, -0.12) ( -0.50,  0.28) ( -0.23, -0.48) (  0.34, -0.49)
   */
  #include <stdlib.h>
  #include <stdio.h>
  
  /* Complex datatype */
  struct _dcomplex { double re, im; };
  typedef struct _dcomplex dcomplex;
  
  /* ZHEEV prototype */
  extern void zheev( char* jobz, char* uplo, int* n, dcomplex* a, int* lda,
                    double* w, dcomplex* work, int* lwork, double* rwork, 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;
      dcomplex wkopt;
      dcomplex* work;
      /* Local arrays */
      /* rwork dimension should be at least max(1,3*n-2) */
      double w[N], rwork[3*N-2];
      dcomplex a[LDA*N] = {
          { 9.14,  0.00}, {-4.37,  9.22}, {-1.98,  1.72}, {-8.96,  9.50},
          { 0.00,  0.00}, {-3.35,  0.00}, { 2.25,  9.51}, { 2.57, -2.40},
          { 0.00,  0.00}, { 0.00,  0.00}, {-4.82,  0.00}, {-3.24, -2.04},
          { 0.00,  0.00}, { 0.00,  0.00}, { 0.00,  0.00}, { 8.44,  0.00}
      };
      /* Executable statements */
      printf( " ZHEEV Example Program Results\n" );
      /* Query and allocate the optimal workspace */
      lwork = -1;
      zheev( "Vectors", "Lower", &n, a, &lda, w, &wkopt, &lwork, rwork, &info );
      lwork = (int)wkopt.re;
      work = (dcomplex*)malloc( lwork*sizeof(dcomplex) );
      /* Solve eigenproblem */
      zheev( "Vectors", "Lower", &n, a, &lda, w, work, &lwork, rwork, &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*)work );
      exit( 0 );
  } /* End of ZHEEV 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" );
      }
  }
  