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

zhptrd() void zhptrd ( char  uplo, int  n, doublecomplex  ap[], double  d[], double  e[], doublecomplex  tau[], int *  info  ) Reduces a complex Hermitian matrix stored in packed form to tridiagonal form Purpose This routine reduces a complex Hermitian matrix A stored in packed form to real symmetric tridiagonal form T by a unitary similarity transformation: Q^H * A * Q = T. Parameters [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,out] ap[] Array ap[lap] (lap >= n(n + 1)/2) [in] The upper or lower triangle of the symmetric matrix A, packed columnwise in a linear array. The j-th column of A is stored in the array ap[] as follows. uplo = 'U': ap[i + j*(j + 1)/2] = a[j][i] for 0 <= i <= j <= n - 1. uplo = 'L': ap[(i + j*(2*n - j - 1)/2] = a[j][i] for 0 <= j < = i <= n - 1. [out] If uplo = 'U', the diagonal and first superdiagonal of A are overwritten by the corresponding elements of the tridiagonal matrix T, and the elements above the first superdiagonal, with the array tau, represent the unitary matrix Q as a product of elementary reflectors. If uplo = 'L', the diagonal and first subdiagonal of A are overwritten by the corresponding elements of the tridiagonal matrix T, and the elements below the first subdiagonal, with the array tau, represent the unitary matrix Q as a product of elementary reflectors. See Further Details. [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'. [out] tau[] Array tau[ltau] (ltau >= n - 1) The scalar factors of the elementary reflectors (see Further Details). [out] info = 0: Successful exit. = -1: The argument uplo had an illegal value. (uplo != 'U' nor 'L') = -2: The argument n had an illegal value. (n < 0) Further Details If uplo = 'U', the matrix Q is represented as a product of elementary reflectors Q = H(n-1) . . . H(2) H(1). Each H(i) has the form H(i) = I - tau*v*v^T where tau is a complex scalar, and v is a complex vector with v(i+1〜n) = 0 and v(i) = 1. v(1〜i-1) is stored on exit in ap[], overwriting A(1〜i-1, i+1), and tau in tau[i-1]. If uplo = 'L', the matrix Q is represented as a product of elementary reflectors Q = H(1) H(2) . . . H(n-1). Each H(i) has the form H(i) = I - tau*v*v^T where tau is a complex scalar, and v is a complex vector with v(1〜i) = 0 and v(i+1) = 1; v(i+2〜n) is stored on exit in ap[], overwriting A(i+2〜n, i), and tau in tau[i-1]. Reference LAPACK