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zhegvx() void zhegvx ( int  itype, char  jobz, char  range, char  uplo, int  n, int  lda, doublecomplex  a[], int  ldb, doublecomplex  b[], double  vl, double  vu, int  il, int  iu, double  abstol, int *  m, double  w[], int  ldz, doublecomplex  z[], doublecomplex  work[], int  lwork, double  rwork[], int  iwork[], int  ifail[], int *  info  ) (Expert driver) Generalized eigenvalue problem of Hermitian matrices Purpose This routine computes selected eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem, of the form A*x = lambda*B*x, A*Bx = lambda*x, or B*A*x = lambda*x. Here A and B are assumed to be Hermitian and B is also positive definite. Eigenvalues and eigenvectors can be selected by specifying either a range of values or a range of indices for the desired eigenvalues. Parameters [in] itype Specifies the problem type to be solved: = 1: A*x = lambda*B*x. = 2: A*B*x = lambda*x. = 3: B*A*x = lambda*x. [in] jobz = 'N': Compute eigenvalues only. = 'V': Compute eigenvalues and eigenvectors. [in] range = 'A': All eigenvalues will be found. = 'V': All eigenvalues in the half-open interval (vl, vu] will be found. = 'I': The il-th through iu-th eigenvalues will be found. [in] uplo = 'U': Upper triangles of A and B are stored. = 'L': Lower triangles of A and B are stored. [in] n Order of the matrices A and B. (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] The Hermitian matrix A. If uplo = 'U', the leading n x n upper triangular part of a[][] contains the upper triangular part of the matrix A. If uplo = 'L', the leading n x n lower triangular part of a[][] contains the lower triangular part of the matrix A. [out] The upper triangle (if uplo='U') or the lower triangle (if uplo='L') of a[][], including the diagonal, is destroyed. [in] ldb Leading dimension of the two dimensional array b[][]. (ldb >= max(1, n)) [in,out] b[][] Array b[lb][ldb] (lb >= n) [in] The Hermitian positive definite matrix B. If uplo = 'U', the leading n x n upper triangular part of b[][] contains the upper triangular part of the matrix B. If uplo = 'L', the leading n x n lower triangular part of b[][] contains the lower triangular part of the matrix B. [out] If info <= n, the part of b[][] containing the matrix is overwritten by the triangular factor U or L from the Cholesky factorization B = U^H*U or B = L*L^H. [in] vl range = 'V': The lower bound of the interval to be searched for eigenvalues. (vl < vu) range = 'A' or 'I': Not referenced. [in] vu range = 'V': The upper bound of the interval to be searched for eigenvalues. (vl < vu) range = 'A' or 'I': Not referenced. [in] il range = 'I': The index of the smallest eigenvalue to be returned. (1 <= il <= iu <= n, if n > 0; il = 1 and iu = 0 if n = 0) range = 'A' or 'V': Not referenced. [in] iu range = 'I': The index of the largest eigenvalues to be returned. (1 <= il <= iu <= n, if n > 0; il = 1 and iu = 0 if n = 0) range = 'A' or 'V': Not referenced. [in] abstol The absolute error tolerance for the eigenvalues. An approximate eigenvalue is accepted as converged when it is determined to lie in an interval [a, b] of width less than or equal to abstol + eps * max(|a|, |b|), where eps is the machine precision. If abstol is less than or equal to zero, then eps*|T| will be used in its place, where |T| is the 1-norm of the tridiagonal matrix obtained by reducing C to tridiagonal form, where C is the symmetric matrix of the standard symmetric problem to which the generalized problem is transformed. Eigenvalues will be computed most accurately when abstol is set to twice the underflow threshold 2*dlamch('S'), not zero. If this routine returns with info > 0, indicating that some eigenvectors did not converge, try setting abstol to 2*dlamch('S'). [out] m The total number of eigenvalues found. (0 <= m <= n) If range = 'A', m = n, and if range = 'I', m = iu - il + 1. [out] w[] Array w[lw] (lw >= n) The first m elements contain the selected eigenvalues in ascending order. [in] ldz Leading dimension of the two dimensional array z[][]. (ldz >= 1 if jobz = 'N', ldz >= max(1, n) if jobz = 'V') [out] z[][] Array z[lz][ldz] (lz >= max(1, m)) jobz = 'V': If info = 0, the first m columns of z[][] contain the orthonormal eigenvectors of the matrix A corresponding to the selected eigenvalues, with the i-th column of z[][] holding the eigenvector associated with w[i].   The eigenvectors are normalized as follows:     itype = 1 or 2: Z^H*B*Z = I     itype = 3: Z^H*inv(B)*Z = I   If an eigenvector fails to converge, then that column of z[][] contains the latest approximation to the eigenvector, and the index of the eigenvector is returned in ifail[]. jobz = 'N': z[][] is not referenced. Note: The user must ensure that at least max(1, m) columns are supplied in the array z[][]; if range = 'V', the exact value of m is not known in advance and an upper bound must be used. [out] work[] Array work[lwork] Work array. On exit, if info = 0, work[0] returns the optimal lwork. [in] lwork The length of the array work[]. (lwork >= max(1, 2*n)) For optimal efficiency, lwork >= (nb + 1)*n, where nb is the optimal blocksize. 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] rwork[] Array rwork[lrwork] (lrwork >= 7*n) Work array. [out] iwork[] Array iwork[liwork] (liwork >= 5*n) Work array. [out] ifail[] Array ifail[lifail] (lifail >= n) jobz = 'V': If info = 0, the first m elements of ifail[] are zero. If info > 0, then ifail[] contains the indices of the eigenvectors that failed to converge. jobz = 'N': ifail[] is not referenced. [out] info = 0: Successful exit = -1: The argument itype had an illegal value (itype < 1 or itype > 3) = -2: The argument jobz had an illegal value (jobz != 'V' nor 'N') = -3: The argument range had an illegal value (range != 'A', 'V' nor 'I') = -4: The argument uplo had an illegal value (uplo != 'U' nor 'L') = -5: The argument n had an illegal value (n < 0) = -6: The argument lda had an illegal value (lda < max(1, n)) = -8: The argument ldb had an illegal value (ldb < max(1, n)) = -11: The argument vu had an illegal value (vu <= vl) = -12: The argument il had an illegal value (il < 1 or il > n) = -13: The argument iu had an illegal value (iu < min(n, il) or iu > n) = -17: The argument ldz had an illegal value (ldz too small) = -20: The argument lwork had an illegal value (lwork too small) = i (0 < i <= n): zheevx failed to converge; i eigenvectors failed to converge. Their indices are stored in array ifail[]. = i (i > n): The leading minor of order i-n of B is not positive definite. The factorization of B could not be completed and no eigenvalues or eigenvectors were computed Reference LAPACK