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zhegvd() void zhegvd ( int  itype, char  jobz, char  uplo, int  n, int  lda, doublecomplex  a[], int  ldb, doublecomplex  b[], double  w[], doublecomplex  work[], int  lwork, double  rwork[], int  lrwork, int  iwork[], int  liwork, int *  info  ) (Divide and conquer driver) Generalized eigenvalue problem of Hermitian matrices Purpose This routine computes all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem, of the form A*x = lambda*B*x, A*B*x = lambda*x, or B*A*x = lambda*x. Here A and B are assumed to be Hermitian and B is also positive definite. If eigenvectors are desired, it uses a divide and conquer algorithm. 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] 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] jobz = 'V': If info = 0, a[][] contains the matrix Z of eigenvectors. The eigenvectors are normalized as follows:     itype = 1 or 2: Z^H*B*Z = I     itype = 3: Z^H*inv(B)*Z = I   jobz = 'N': 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. [out] w[] Array w[lw] (lw >= n) If info = 0, the eigenvalues in ascending order. [out] work[] Array work[lwork] Complex work array On exit, if info = 0, work[0] returns the optimal lwork. [in] lwork The size of work[]. (lwork >= 1 (if n <= 1), n + 1 (if jobz = 'N'), n^2 + 2*n (if jobz = 'V')) If lwork = -1, then a workspace query is assumed. The routine only calculates the optimal size of the work[], rwork[] and iwork[] arrays, and returns these values in work[0], rwork[0] and iwork[0]. [out] rwork[] Array rwork[lrwork] Work array. On exit, if info = 0, rwork[0] returns the optimal lwork. [in] lrwork The size of rwork[]. (lrwork >= 1 (if n <= 1), n (if jobz = 'N'), 2*n^2 + 5*n + 1 (if jobz = 'V')) If lrwork = -1, then a workspace query is assumed. The routine only calculates the optimal size of the work[], rwork[] and iwork[] arrays, and returns these values in work[0], rwork[0] and iwork[0]. [out] iwork[] Array iwork[liwork] Integer work array. On exit, if info = 0, iwork[0] returns the optimal liwork. [in] liwork The size of iwork[]. (liwork >= 1 (if n <= 1), 1 (if jobz = 'N'), 5*n + 3 (if jobz = 'V')) If liwork = -1, then a workspace query is assumed. The routine only calculates the optimal size of the work[], rwork[] and iwork[] arrays, and returns these values in work[0], rwork[0] and iwork[0]. [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 uplo had an illegal value (uplo != 'U' nor 'L') = -4: The argument n had an illegal value (n < 0) = -5: The argument lda had an illegal value (lda < max(1, n)) = -7: The argument ldb had an illegal value (ldb < max(1, n)) = -11: The argument lwork had an illegal value (lwork too small) = -13: The argument lrwork had an illegal value (lrwork too small) = -15: The argument liwork had an illegal value (liwork too small) = i (0 < i <= n): If jobz = 'N', then the algorithm failed to converge; i off-diagonal elements of an intermediate tridiagonal form did not converge to zero. If jobz = 'V', then the algorithm failed to compute an eigenvalue while working on the submatrix lying in rows and columns i/(n + 1) through mod(i, n + 1). = 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