Zhbtrd Zhetrd Zhptrd Zpteqr Zstedc Zstein Zstemr Zsteqr Zungtr Zunmtr Zupgtr Zupmtr

Zupmtr() Sub Zupmtr ( Side As  String, Uplo As  String, Trans As  String, M As  Long, N As  Long, Ap() As  Complex, Tau() As  Complex, C() As  Complex, Info As  Long  ) Multiplies by a transform matrix from a real symmetric matrix in packed form to tridiagonal form Purpose This routine overwrites the general real M x N matrix C with Side = "L" Side = "R" Trans = "N": Q * C C * Q Trans = "T": Q^H * C C * Q^H where Q is a complex unitary matrix of order Nq, with Nq = M if Side = "L" and Nq = N if Side = "R". Q is defined as the product of Nq - 1 elementary reflectors, as returned by Zhptrd: If Uplo = "U", Q = H(Nq-1) . . . H(2) H(1), If Uplo = "L", Q = H(1) H(2) . . . H(Nq-1). Parameters [in] Side = "L": Apply Q or Q^H from the Left. = "R": Apply Q or Q^H from the Right. [in] Uplo = "U": Upper triangular packed storage used in previous call to Zhptrd. = "L": Lower triangular packed storage used in previous call to Zhptrd. [in] Trans = "N": No transpose, apply Q. = "T": Transpose, apply Q^H. [in] M Number of rows of the matrix C. (M >= 0) (If M = 0, returns without computation) [in] N Number of columns of the matrix C. (N >= 0) (If N = 0, returns without computation) [in] Ap() Array Ap(LAp - 1) (LAp >= M(M + 1)/2 if Side ="L", LAp >= N(N + 1)/2 if Side ="R") The vectors which define the elementary reflectors, as returned by Zhptrd. Ap() is modified by the routine but restored on exit. [in] Tau() Array Tau(LTau - 1) (LTau >= M - 1 if Side = "L", LTau >= N - 1 if Side = "R") Tau(i) must contain the scalar factor of the elementary reflector H(i), as returned by Zhptrd. [in,out] C() Array C(LC1 - 1, LC2 - 1) (LC1 >= M, LC2 >= N) [in] The M x N matrix C. [out] C is overwritten by Q*C or Q^H*C or C*Q^H or C*Q. [out] Info = 0: Successful exit. = -1: The argument Side had an illegal value. (Side <> "L" nor "R") = -2: The argument Uplo had an illegal value (Uplo != "U" nor "L") = -3: The argument Trans had an illegal value. (Trans <> "T" nor "N") = -4: The argument M had an illegal value. (M < 0) = -5: The argument N had an illegal value. (N < 0) = -6: The argument Ap() is invalid. = -7: The argument Tau() is invalid. = -8: The argument C() is invalid. Reference LAPACK