zgebak zgebal zgehrd zhsein zhseqr ztrevc3 ztrexc ztrsen ztrsna ztrsyl zunghr zunmhr

zunmhr() void zunmhr ( char  side, char  trans, int  m, int  n, int  ilo, int  ihi, int  lda, doublecomplex  a[], doublecomplex  tau[], int  ldc, doublecomplex  c[], doublecomplex  work[], int  lwork, int *  info  ) 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 unitary 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). If side = 'L', then 1 <= ilo <= ihi <= m, if m > 0, and ilo = 1 and ihi = 0, if m = 0. if side = 'R', then 1 <= ilo <= ihi <= n, if n > 0, and ilo = 1 and ihi = 0, if n = 0. [in] lda Leading dimension of the two dimensional array a[][]. (lda >= max(1, m) if side = 'L', lda >= max(1, n) if side = 'R') [in] a[][] Array a[la][lda] (la >= m if side = 'L', la >= n if side = 'R') The vectors which define the elementary reflectors, as returned by zgehrd. [in] tau[] Array tau[ltau] (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] ldc Leading dimension of the two dimensional array c[][]. (ldc >= max(1, m)) [in,out] c[][] Array c[lc][ldc] (lc >= 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] work[] Array work[lwork] Work array. On exit, if info = 0, work[0] returns the optimal lwork. [in] lwork The size of work[]. (lwork >= max(1, n) if side = 'L', lwork >= max(1, m) if side = 'R') For optimum performance lwork >= n*nb if side = 'L', and lwork >= m*nb if side = 'R', where nb is the optimal blocksize. If lwork = -1, then a workspace query is assumed. The routine only calculates the optimal size of the work[] array, and returns the value in work[0]. [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 (ilo < 1 or (ilo > m if side = 'L', ilo > n if side = 'R')) = -6: The argument ihi had an illegal value ((ihi < min(ilo, m) or ihi > m if side = 'L'), (ihi < min(ilo, n) or ihi > n if side = 'R')) = -7: The argument lda had an illegal value. (lda < max(1, m) if side = 'L', lda < max(1, n) if side = 'R') = -10: The argument ldc had an illegal value. (ldc < max(1, m)) = -13: The argument lwork had an illegal value (lwork too small) Reference LAPACK