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

zhbtrd() void zhbtrd ( char  vect, char  uplo, int  n, int  kd, int  ldab, doublecomplex  ab[], double  d[], double  e[], int  ldq, doublecomplex  q[], doublecomplex  work[], int *  info  ) Reduces a complex Hermitian band matrix to tridiagonal form Purpose This routine reduces a complex Hermitian band matrix A to real symmetric tridiagonal form T by a unitary similarity transformation: Q^H * A * Q = T. Parameters [in] vect = 'N': Do not form Q. = 'V': Form Q. = 'U': Update a matrix X, by forming X*Q. [in] uplo = 'U': Upper triangle of A is stored. = 'L': Lower triangle of A is stored. [in] n Order of the matrix A. (n >= 0) (If n = 0, returns without computation) [in] kd Number of superdiagonals of the matrix A if uplo = 'U' or number of subdiagonals if uplo = 'L'. (kd >= 0) [in] ldab Leading dimension of the two dimensional array ab[][]. (ldab >= kd + 1) [in,out] ab[][] Array ab[lab][ldab] (lab >= n) [in] The upper or lower triangle of the Hermitian band matrix A, stored in the first kd+1 columns of the array. The j-th column of A is stored in the j-th row of the array ab as follows. uplo = 'U': ab[j][kd + i - j] = A(i, j) for max(0, j - kd - 1) <= i <= j <= n - 1. uplo = 'L': ab[j][i - j] = A(i, j) for 0 <= j <= i <= min(n - 1, j + kd - 1). [out] The diagonal elements of ab are overwritten by the diagonal elements of the tridiagonal matrix T. If kd > 0, the elements on the first superdiagonal (if uplo = 'U') or the first subdiagonal (if uplo = 'L') are overwritten by the off-diagonal elements of T. The rest of ab is overwritten by values generated during the reduction. [out] d[] Array d[ld] (ld >= n) The diagonal elements of the tridiagonal matrix T: d[i] = a[i][i]. [out] e[] Array e[le] (le >= n - 1) The off-diagonal elements of the tridiagonal matrix T: e[i] = a[i+1][i] if uplo = 'U', e[i] = a[i][i+1] if uplo = 'L'. [in] ldq Leading dimension of the two dimensional array q[][]. (ldq >= 1 if vect = 'N'. ldq >= n if vect = 'V' or 'U'.) [in,out] q[][] Array q[lq][ldq] (lq >= n) [in] If vect = 'U', then q must contain an n x n matrix X. If vect = 'N' or 'V', then q need not be set. [out] If vect = 'V', q contains the n x n unitary matrix Q. If vect = 'U', q contains the product X*Q. If vect = 'N', the array q is not referenced. [out] work[] Array work[lwork] (lwork >= n) Work array. [out] info = 0: Successful exit. = -1: The argument vect had an illegal value. (vect != 'N', 'V' nor 'U') = -2: The argument uplo had an illegal value. (uplo != 'U' nor 'L') = -3: The argument n had an illegal value. (n < 0) = -4: The argument kd had an illegal value. (kd < 0) = -5: The argument ldab had an illegal value (ldab < kd + 1) = -9: The argument ldz had an illegal value (ldq too small) Reference LAPACK