dgges dgges_r dggesx dggesx_r dggev dggevx

dggev() void dggev ( char  jobvl, char  jobvr, int  n, int  lda, double  a[], int  ldb, double  b[], double  alphar[], double  alphai[], double  beta[], int  ldvl, double  vl[], int  ldvr, double  vr[], double  work[], int  lwork, int *  info  ) (Simple driver) Generalized eigenvalue problem of general matrices Purpose This routine computes for a pair of n x n real nonsymmetric matrices (A, B) the generalized eigenvalues, and optionally, the left and/or right generalized eigenvectors. A generalized eigenvalue for a pair of matrices (A, B) is a scalar lambda or a ratio alpha/beta = lambda, such that A - lambda*B is singular. It is usually represented as the pair (alpha, beta), as there is a reasonable interpretation for beta = 0, and even for both being zero. The right generalized eigenvector v(j) corresponding to the generalized eigenvalue lambda(j) of (A, B) satisfies A * v(j) = lambda(j) * B * v(j) The left generalized eigenvector u(j) corresponding to the generalized eigenvalue lambda(j) of (A, B) satisfies u(j)^H * A = lambda(j) * u(j)^H * B where u(j)^H is the conjugate-transpose of u(j). Parameters [in] jobvl = 'N': Do not compute the left generalized eigenvectors. = 'V': Compute the left generalized eigenvectors. [in] jobvr = 'N': Do not compute the right generalized eigenvectors. = 'V': Compute the right generalized eigenvectors. [in] n Order of the matrices A, B, VL and VR. (n >= 0) (If n = 0, returns without computation) [in] lda Leading dimension of the two dimensional array a[][]. (lda >= max(1, n)) [in,out] a[][] Array a[la][lda] (la >= n) [in] Matrix A in the pair (A, B). [out] a[][] has been overwritten. [in] ldb Leading dimension of the two dimensional array b[][]. (ldb >= max(1, n)) [in,out] b[][] Array b[lb][ldb] (lb >= n) [in] Matrix B in the pair (A, B). [out] b[][] has been overwritten. [out] alphar[] Array alphar[lalphar] (lalphar >= n) [out] alphai[] Array alphai[lalphai] (lalphai >= n) [out] beta[] Array beta[lbeta] (lbeta >= n) (alphar[j] + alphai[j]*i)/beta[j], j = 0, ..., n-1, will be the generalized eigenvalues. If alphai[j] is zero, then the j-th eigenvalue is real. If positive, then the j-th and (j+1)-st eigenvalues are a complex conjugate pair, with alphai[j+1] negative. Note: The quotients alphar[j]/beta[j] and alphai[j]/beta[j] may easily over- or underflow, and beta[j] may even be zero. Thus, the user should avoid naively computing the ratio alpha/beta. However, alphar and alphai will be always less than and usually comparable with norm(A) in magnitude, and beta always less than and usually comparable with norm(B). [in] ldvl Leading dimension of the two dimensional array vl[][]. (ldvl >= 1 if jobvl = 'N', ldvl >= n if jobvl = 'V') [out] vl[][] Array vl[lvl][ldvl] (lvl >= n) jobvl = 'V': The left eigenvectors u(j) are stored one after another in the columns of vl[][], in the same order as their eigenvalues.   If the j-th eigenvalue is real, then u(j) = vl[j][*], the j-th column of vl[][].   If j-th and (j+1)-th eigenvalues form a complex conjugate pair, then u(j) = vl[j][*] + vl[j+1][*]*i and u(j+1) = vl[j][*] - vl[j+1][*]*i.   Each eigenvector is scaled so the largest component has |real part| + |imaginary part| = 1. jobvl = 'N': Not referenced. [in] ldvr Leading dimension of the two dimensional array vr[][]. (ldvr >= 1 if jobvr = 'N', ldvr >= n if jobvr = 'V') [out] vr[][] Array vr[lvr][ldvr] (lvr >= n) jobvr = 'V': The right eigenvectors v(j) are stored one after another in the columns of vr[][] in the same order as their eigenvalues.   If the j-th eigenvalue is real, then v(j) = vr[j][*], the j-th column of vr[][].   If j-th and (j+1)-th eigenvalues form a complex conjugate pair, then v(j) = vr[j][*] + vr[j+1][*]*i and v(j+1) = vr[j][*] - vr[j+1][*]*i.   Each eigenvector is scaled so the largest component has |real part| + |imag. part| = 1. jobvr = 'N': Not referenced. [out] work[] Array work[lwork] Work array. On exit, if info = 0, work[0] returns the optimal lwork. [in] lwork The dimension of the array work[]. (lwork >= max(1, 8*n)) For good performance, lwork must generally be larger. If lwork = -1, then a workspace query is assumed. The routine only calculates the optimal size of the work[] array, and returns the value in work[0]. [out] info = 0: Successful exit = -1: The argument jobvl had an illegal value (jobvl != 'V' nor 'N') = -2: The argument jobvr had an illegal value (jobvr != 'V' nor 'N') = -3: The argument n had an illegal value (n < 0) = -4: The argument lda had an illegal value (lda < max(1, n)) = -6: The argument ldb had an illegal value (ldb < max(1, n)) = -11: The argument ldvl had an illegal value (ldvl too small) = -13: The argument ldvr had an illegal value (ldvr too small) = -16: The argument lwork had an illegal value (lwork too small) = i (0 < i <= n): The QZ iteration failed. No eigenvectors have been calculated, but alphar[j], alphai[j], and beta[j] should be correct for j = i, ..., n-1. = n+1: Other than QZ iteration failed in dhgeqz = n+2: Error return from dtgevc Reference LAPACK