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  • 12/20/2021
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DGEEV Example Program in C

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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> /* 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 ); /* 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 /* Main program */ int main() { /* Locals */ int n = N, lda = LDA, ldvl = LDVL, ldvr = LDVR, info, lwork; double wkopt; double* work; /* Local arrays */ double wr[N], wi[N], vl[LDVL*N], vr[LDVR*N]; double a[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 }; /* Executable statements */ printf( " DGEEV Example Program Results\n" ); /* 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; } } printf( "\n" ); } }

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