zgelqf zgeqp3 zgeqrf zunglq zungqr zunmlq zunmqr

zunmlq() void zunmlq ( char  side, char  trans, int  m, int  n, int  k, int  lda, doublecomplex  a[], doublecomplex  tau[], int  ldc, doublecomplex  c[], doublecomplex  work[], int  lwork, int *  info  ) Multiplies matrix by Q of LQ factorization of a complex matrix Purpose This routine overwrites the general complex m x n matrix C with side = 'L' side = 'R' trans = 'N': Q * C C * Q trans = 'C': Q^H * C C * Q^H where Q is a complex unitary matrix defined as the product of k elementary reflectors Q = H(k) . . . H(2) H(1) as returned by zgelqf. Q is of order m if side = 'L' and of order n if side = 'R'. 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 Number of columns of the matrix C. (n >= 0) (If n = 0, returns without computation) [in] k Number of elementary reflectors whose product defines the matrix Q. (m => k >= 0 if side = 'L', n >= k >= 0 if side = 'R') (if k = 0, returns without computation) [in] lda Leading dimension of the two dimensional array a[][]. (lda >= max(1, k)) [in] a[][] Array a[la][lda] (la >= m if side = 'L', la >= n if side = 'R') The i-th row must contain the vector which defines the elementary reflector H(i), for i = 1, 2, ..., k, as returned by zgelqf in the first k rows of its array argument a[][]. [in] tau[] Array tau[ltau] (ltau >= k) The scalar factors of the elementary reflectors H(i) as returned by zgelqf. [in] ldc Leading dimension of the two dimensional array c[][]. (ldc >= max(1, m)) [in,out] c[][] Array c[lc][ldc] (lc >= n) [in] 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 dimension of the array work[]. (lwork >= max(1, n) if side = 'L', lwork >= max(1, m) if side = 'R') For good performance lwork should genrally be larger. 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 != 'C' nor 'N') = -3: The argument m had an illegal value (m < 0) = -4: The argument n had an illegal value (n < 0) = -5: The argument k had an illegal value (k < 0 or k > m or n) = -6: The argument lda had an illegal value (lda < max(1, k)) = -9: The argument ldc had an illegal value (ldc < max(1, m)) = -12: The argument lwork had an illegal value (lwork too small) Reference LAPACK