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

zsteqr() void zsteqr ( char  compz, int  n, double  d[], double  e[], int  ldz, doublecomplex  z[], double  work[], int *  info  ) Eigenvalues and eigenvectors of symmetric tridiagonal matrix to which a Hermitian matrix was reduced (QL or QR method) Purpose This routine computes all eigenvalues and, optionally, eigenvectors of a symmetric tridiagonal matrix to which a Hermitian matrix was reduced using the implicit QL or QR 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. = '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. = 'I': Compute eigenvalues and eigenvectors of the tridiagonal matrix. z[][] is initialized to the identity matrix. [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] (lwork >= max(1, 2*n - 2)) Work array. If compz = 'N', then work is not referenced. [out] info = 0: Successful exit. = -1: The argument compz an illegal value. (compz != 'N', 'V' nor 'I') = -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))) = i > 0: The algorithm has failed to find all the eigenvalues in a total of 30*n iterations. i elements of e have not converged to zero. On exit, d and e contain the elements of a symmetric tridiagonal matrix which is unitarily similar to the original matrix. Reference LAPACK