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/*******************************************************************************
* 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.
*
********************************************************************************
*/
/*
DGEEV Example.
==============
Program computes the eigenvalues and left and right eigenvectors of a general
rectangular matrix A:
-1.01 0.86 -4.60 3.31 -4.81
3.98 0.53 -7.04 5.29 3.55
3.30 8.26 -3.89 8.20 -1.51
4.43 4.96 -7.66 -7.33 6.18
7.31 -6.43 -6.16 2.47 5.58
Description.
============
The routine computes for an n-by-n real nonsymmetric matrix A, the
eigenvalues and, optionally, the left and/or right eigenvectors. The right
eigenvector v(j) of A satisfies
A*v(j)= lambda(j)*v(j)
where lambda(j) is its eigenvalue. The left eigenvector u(j) of A satisfies
u(j)H*A = lambda(j)*u(j)H
where u(j)H denotes the conjugate transpose of u(j). The computed
eigenvectors are normalized to have Euclidean norm equal to 1 and
largest component real.
Example Program Results.
========================
DGEEV Example Program Results
Eigenvalues
( 2.86, 10.76) ( 2.86,-10.76) ( -0.69, 4.70) ( -0.69, -4.70) -10.46
Left eigenvectors
( 0.04, 0.29) ( 0.04, -0.29) ( -0.13, -0.33) ( -0.13, 0.33) 0.04
( 0.62, 0.00) ( 0.62, 0.00) ( 0.69, 0.00) ( 0.69, 0.00) 0.56
( -0.04, -0.58) ( -0.04, 0.58) ( -0.39, -0.07) ( -0.39, 0.07) -0.13
( 0.28, 0.01) ( 0.28, -0.01) ( -0.02, -0.19) ( -0.02, 0.19) -0.80
( -0.04, 0.34) ( -0.04, -0.34) ( -0.40, 0.22) ( -0.40, -0.22) 0.18
Right eigenvectors
( 0.11, 0.17) ( 0.11, -0.17) ( 0.73, 0.00) ( 0.73, 0.00) 0.46
( 0.41, -0.26) ( 0.41, 0.26) ( -0.03, -0.02) ( -0.03, 0.02) 0.34
( 0.10, -0.51) ( 0.10, 0.51) ( 0.19, -0.29) ( 0.19, 0.29) 0.31
( 0.40, -0.09) ( 0.40, 0.09) ( -0.08, -0.08) ( -0.08, 0.08) -0.74
( 0.54, 0.00) ( 0.54, 0.00) ( -0.29, -0.49) ( -0.29, 0.49) 0.16
*/
// #include <stdlib.h>
// #include <stdio.h>
#include <iostream>
#include <fstream>
// #include <iomanip>
using namespace std;
/* DGEEV prototype */
/*
extern void dgeev_( char* jobvl, char* jobvr, int* n, double* a,
int* lda, double* wr, double* wi, double* vl, int* ldvl,
double* vr, int* ldvr, double* work, int* lwork, int* info );
*/
// dgeev_ is a symbol in the LAPACK library files
extern "C"
{
extern int dgeev_(char*,char*,int*,double*,int*,double*, double*, double*, int*, double*, int*, double*, int*, int*);
}
/* Auxiliary routines prototypes */
extern void print_eigenvalues( char* desc, int n, double* wr, double* wi );
extern void print_eigenvectors( char* desc, int n, double* wi, double* v, int ldv );
/* Parameters */
#define N 5
#define LDA N
#define LDVL N
#define LDVR N
double * ReadMatrix( char *filename, int *numRows, int *numColums)
{
int n,m;
double *data;
// read in a text file that contains a real matrix stored in column major format
// but read it into row major format
ifstream fin(filename);
if (!fin.is_open()){
cout << "Failed to open " << filename << endl;
return NULL;
}
fin >> n >> m; // n is the number of rows, m the number of columns
data = new double[n*m];
*numRows = n;
*numColums = m;
for (int i=0;i<n;i++)
{
for (int j=0;j<m;j++)
{
// fin >> data[j*n+i]; // column order ?
fin >> data[i*n+j]; // row order ?
}
}
if (fin.fail() || fin.eof()){
cout << "Error while reading " << filename << endl;
cout << "n=" << n << " m=" << m;
return NULL;
}
fin.close();
// check that matrix is square
if (n != m){
cout << "Matrix is not square" <<endl;
return NULL;
}
return data;
}
void PrintMatrix( double *data, int n, int m)
{
printf("Matrix %dx%d loaded \n", n, m);
for ( int i = 0 ; i < n ; i++ )
{
for ( int j = 0 ; j < m ; j++ )
{
// printf("%f ", data[j*n+i]);
printf("%.2f ", data[i*n+j]);
}
printf("\n");
}
printf("\n");
}
/* Main program */
int main( int argc, char **argv )
{
/* Locals */
int n = N, lda = LDA, ldvl = LDVL, ldvr = LDVR;
int info, lwork;
double wkopt;
double* work;
/* Local arrays */
double wr[N], wi[N], vl[LDVL*N], vr[LDVR*N];
char Nchar = 'N';
char Vchar = 'V';
double a0[LDA*N] = {
-1.01, 3.98, 3.30, 4.43, 7.31,
0.86, 0.53, 8.26, 4.96, -6.43,
-4.60, -7.04, -3.89, -7.66, -6.16,
3.31, 5.29, 8.20, -7.33, 2.47,
-4.81, 3.55, -1.51, 6.18, 5.58
};
double *a;
int nRows, nColums;
/* Executable statements */
printf( " DGEEV Example Program Results\n\n" );
if ( argc > 1 )
{
a = ReadMatrix( argv[1], &nRows, &nColums);
n = nRows;
lda = n;
ldvl = n;
ldvr = n;
}
else
{
a = a0;
nRows = nColums = n = N;
lda = LDA;
ldvl = LDVL;
ldvr = LDVR;
}
PrintMatrix(a, nRows, nColums);
/* Query and allocate the optimal workspace */
lwork = -1;
dgeev_( "Vectors", "Vectors", &n, a, &lda, wr, wi, vl, &ldvl, vr, &ldvr, &wkopt, &lwork, &info );
lwork = (int)wkopt;
work = (double*)malloc( lwork*sizeof(double) );
/* Solve eigenproblem */
dgeev_( "Vectors", "Vectors", &n, a, &lda, wr, wi, vl, &ldvl, vr, &ldvr, work, &lwork, &info );
/* Check for convergence */
if( info > 0 ) {
printf( "The algorithm failed to compute eigenvalues.\n" );
exit( 1 );
}
/* Print eigenvalues */
print_eigenvalues( "Eigenvalues", n, wr, wi );
/* Print left eigenvectors */
print_eigenvectors( "Left eigenvectors", n, wi, vl, ldvl );
/* Print right eigenvectors */
print_eigenvectors( "Right eigenvectors", n, wi, vr, ldvr );
/* Free workspace */
free( (void*)work );
exit( 0 );
} /* End of DGEEV Example */
/* Auxiliary routine: printing eigenvalues */
void print_eigenvalues( char* desc, int n, double* wr, double* wi ) {
int j;
printf( "\n %s\n", desc );
for( j = 0; j < n; j++ ) {
if( wi[j] == (double)0.0 ) {
printf( " %6.2f", wr[j] );
} else {
printf( " (%6.2f,%6.2f)", wr[j], wi[j] );
}
}
printf( "\n" );
}
/* Auxiliary routine: printing eigenvectors */
void print_eigenvectors( char* desc, int n, double* wi, double* v, int ldv )
{
int i, j;
printf( "\n %s\n", desc );
for( i = 0; i < n; i++ ) {
j = 0;
while( j < n ) {
if( wi[j] == (double)0.0 ) {
printf( " %6.2f", v[i+j*ldv] );
j++;
} else {
printf( " (%6.2f,%6.2f)", v[i+j*ldv], v[i+(j+1)*ldv] );
printf( " (%6.2f,%6.2f)", v[i+j*ldv], -v[i+(j+1)*ldv] );
j += 2;
}g++ -o test_lapack3 test_lapack3.cpp -llapack
}
printf( "\n" );
}
} |
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