Zgebak Zgebal Zgehrd Zhsein Zhseqr Ztrevc3 Ztrexc Ztrsen Ztrsna Ztrsyl Zunghr Zunmhr

Zunmhr() Sub Zunmhr ( Side As  String, Trans As  String, M As  Long, N As  Long, Ilo As  Long, Ihi As  Long, A() As  Complex, Tau() As  Complex, C() As  Complex, Info As  Long  ) Multiplies by a complex transform matrix to Hessenberg form Purpose This routine overwrites the general complex 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 orthogonal matrix of order nq, with nq = M if Side = "L" and nq = N if Side = "R". Q is defined as the product of Ihi-Ilo elementary reflectors, as returned by Zgehrd: Q = H(Ilo) H(Ilo+1) . . . H(Ihi-1). Parameters [in] Side = "L": Apply Q or Q~H from the Left. = "R": Apply Q or Q~H from the Right. [in] trans = "N": No transpose, apply Q. = "C": Conjugate transpose, apply Q~H. [in] M Number of rows of the matrix C. (M >= 0) (If M = 0, returns without computation) [in] N Order of the matrix A. (N >= 0) (If N = 0, returns without computation) [in] Ilo [in] Ihi Ilo and Ihi must have the same values as in the previous call of Zgehrd. Q is equal to the unit matrix except in the submatrix Q(Ilo+1〜Ihi, Ilo+1〜Ihi). Side = "L": 1 <= Ilo <= Ihi <= M (if M > 0), Ilo = 1 and Ihi = 0 (if M = 0). Side = "R": 1 <= Ilo <= Ihi <= N (if N > 0), Ilo = 1 and Ihi = 0 (if N = 0). [in] A() Array A(LA1 - 1, LA2 - 1) (LA1 >= M, LA2 >= M (if Side = "L"), LA1 >= N, LA2 >= N (if Side = "R")) The vectors which define the elementary reflectors, as returned by Zgehrd. [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 Zgehrd. [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 Trans had an illegal value. (Trans <> "N" nor "T") = -3: The argument M had an illegal value. (M < 0) = -4: The argument N had an illegal value. (N < 0) = -5: The argument Ilo had an illegal value. = -6: The argument Ihi had an illegal value. = -7: The argument A() is invalid. = -8: The argument Tau() is invalid. = -9: The argument C() is invalid. Reference LAPACK Example Program See examples of Zhsein.