zhbtrd zhetrd zhptrd zpteqr zstedc zstein zstemr zsteqr zungtr zunmtr zupgtr zupmtr

zstedc() void zstedc ( char  compz, int  n, double  d[], double  e[], int  ldz, doublecomplex  z[], doublecomplex  work[], int  lwork, double  rwork[], int  lrwork, int  iwork[], int  liwork, int *  info  ) Eigenvalues and eigenvectors of symmetric tridiagonal matrix to which a Hermitian matrix was reduced (Divide and conquer method) Purpose This routine computes all eigenvalues and, optionally, eigenvectors of a symmetric tridiagonal matrix to which a Hermitian matrix was reduced using the divide and conquer method. The eigenvectors of a full or band complex Hermitian matrix can also be found if zhetrd or zhptrd or zhbtrd has been used to reduce this matrix to tridiagonal form. Parameters [in] compz = 'N': Compute eigenvalues only. = 'I': Compute eigenvalues and eigenvectors of the tridiagonal matrix. = 'V': Compute eigenvalues and eigenvectors of the original Hermitian matrix. On entry, z[][] must contain the unitary matrix used to reduce the original matrix to tridiagonal form. [in] n Order of the matrix. (n >= 0) (If n = 0, returns without computation) [in,out] d[] Array d[ld] (ld >= n) [in] The diagonal elements of the tridiagonal matrix. [out] If info = 0, the eigenvalues in ascending order. [in,out] e[] Array e[le] (le >= n - 1) [in] The (n - 1) subdiagonal elements of the tridiagonal matrix. [out] e[] has been destroyed. [in] ldz Leading dimension of the two dimensional array z[][]. (ldz >= 1 if compz = 'N', ldz >= max(1, n) if compz = 'V' or 'I') [in,out] z[][] Array z[lz][ldz] (lz >= n) [in] If compz = 'V', then z[][] contains the unitary matrix used in the reduction to tridiagonal form. [out] If info = 0, then if compz = 'V', z[][] contains the orthonormal eigenvectors of the original Hermitian matrix, and if compz = 'I', z[][] contains the orthonormal eigenvectors of the symmetric tridiagonal matrix. If compz = 'N', then z[][] is not referenced. [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 compz = 'N' or 'I' or n <= 1, lwork >= n^2 if compz = 'V' and n > 1) Note that for compz = 'V', then if n is less than or equal to the minimum divide size, usually 25, then lwork need only be 1. If lwork = -1, then a workspace query is assumed. The routine only calculates the optimal sizes 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 lrwork. [in] lrwork The size of rwork[]. (lrwork >= 1 if compz = 'N' or n <= 1, lrwork >= 1 + 3*n + 2*n*lg(n) + 4*n^2 if compz = 'V' and n > 1 (where lg(n) = smallest integer k such that 2^k >= n), lrwork >= 1 + 4*n + 2*n^2 if compz = 'I' and n > 1) Note that for compz = 'I' or 'V', then if n is less than or equal to the minimum divide size, usually 25, then liwork need only be max(1, 2*(n-1)). If lrwork = -1, then a workspace query is assumed. The routine only calculates the optimal sizes 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 compz = 'N' or n <= 1, liwork >= 6 + 6*n + 5*n*lg(n) if compz = 'V' and n > 1 (where lg(n) = smallest integer k such that 2^k >= n), liwork >= 3 + 5*n if compz = 'I' and n > 1) Note that for compz = 'I' or 'V', then if n is less than or equal to the minimum divide size, usually 25, then liwork need only be 1. If liwork = -1, then a workspace query is assumed. The routine only calculates the optimal sizes 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 compz an illegal value. (compz != 'N', 'I' nor 'V') = -2: The argument n had an illegal value. (n < 0) = -5: The argument ldz had an illegal value. (ldz < 1 or (compz = 'V' or 'I' and ldz < max(1, n))) = -8: The argument lwork had an illegal value. (lwork too small) = -10: The argument lrwork had an illegal value. (lrwork too small) = -12: The argument liwork had an illegal value. (liwork too small) = i > 0: The algorithm has failed to compute an eigenvalue while working on the submatrix lying in rows and columns i/(n + 1) through mod(i, n + 1). Reference LAPACK