#include "blaswrap.h" #include "f2c.h" /* Subroutine */ int cgelqf_(integer *m, integer *n, complex *a, integer *lda, complex *tau, complex *work, integer *lwork, integer *info) { /* -- LAPACK routine (version 3.0) -- Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., Courant Institute, Argonne National Lab, and Rice University June 30, 1999 Purpose ======= CGELQF computes an LQ factorization of a complex M-by-N matrix A: A = L * Q. Arguments ========= M (input) INTEGER The number of rows of the matrix A. M >= 0. N (input) INTEGER The number of columns of the matrix A. N >= 0. A (input/output) COMPLEX array, dimension (LDA,N) On entry, the M-by-N matrix A. On exit, the elements on and below the diagonal of the array contain the m-by-min(m,n) lower trapezoidal matrix L (L is lower triangular if m <= n); the elements above the diagonal, with the array TAU, represent the unitary matrix Q as a product of elementary reflectors (see Further Details). LDA (input) INTEGER The leading dimension of the array A. LDA >= max(1,M). TAU (output) COMPLEX array, dimension (min(M,N)) The scalar factors of the elementary reflectors (see Further Details). WORK (workspace/output) COMPLEX array, dimension (LWORK) On exit, if INFO = 0, WORK(1) returns the optimal LWORK. LWORK (input) INTEGER The dimension of the array WORK. LWORK >= max(1,M). For optimum performance LWORK >= M*NB, 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, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued by XERBLA. INFO (output) INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value Further Details =============== The matrix Q is represented as a product of elementary reflectors Q = H(k)' . . . H(2)' H(1)', where k = min(m,n). Each H(i) has the form H(i) = I - tau * v * v' where tau is a complex scalar, and v is a complex vector with v(1:i-1) = 0 and v(i) = 1; conjg(v(i+1:n)) is stored on exit in A(i,i+1:n), and tau in TAU(i). ===================================================================== Test the input arguments Parameter adjustments */ /* Table of constant values */ static integer c__1 = 1; static integer c_n1 = -1; static integer c__3 = 3; static integer c__2 = 2; /* System generated locals */ integer a_dim1, a_offset, i__1, i__2, i__3, i__4; /* Local variables */ static integer i__, k, nbmin, iinfo; extern /* Subroutine */ int cgelq2_(integer *, integer *, complex *, integer *, complex *, complex *, integer *); static integer ib, nb; extern /* Subroutine */ int clarfb_(char *, char *, char *, char *, integer *, integer *, integer *, complex *, integer *, complex *, integer *, complex *, integer *, complex *, integer *); static integer nx; extern /* Subroutine */ int clarft_(char *, char *, integer *, integer *, complex *, integer *, complex *, complex *, integer *), xerbla_(char *, integer *); extern integer ilaenv_(integer *, char *, char *, integer *, integer *, integer *, integer *, ftnlen, ftnlen); static integer ldwork, lwkopt; static logical lquery; static integer iws; #define a_subscr(a_1,a_2) (a_2)*a_dim1 + a_1 #define a_ref(a_1,a_2) a[a_subscr(a_1,a_2)] a_dim1 = *lda; a_offset = 1 + a_dim1 * 1; a -= a_offset; --tau; --work; /* Function Body */ *info = 0; nb = ilaenv_(&c__1, "CGELQF", " ", m, n, &c_n1, &c_n1, (ftnlen)6, (ftnlen) 1); lwkopt = *m * nb; work[1].r = (real) lwkopt, work[1].i = 0.f; lquery = *lwork == -1; if (*m < 0) { *info = -1; } else if (*n < 0) { *info = -2; } else if (*lda < max(1,*m)) { *info = -4; } else if (*lwork < max(1,*m) && ! lquery) { *info = -7; } if (*info != 0) { i__1 = -(*info); xerbla_("CGELQF", &i__1); return 0; } else if (lquery) { return 0; } /* Quick return if possible */ k = min(*m,*n); if (k == 0) { work[1].r = 1.f, work[1].i = 0.f; return 0; } nbmin = 2; nx = 0; iws = *m; if (nb > 1 && nb < k) { /* Determine when to cross over from blocked to unblocked code. Computing MAX */ i__1 = 0, i__2 = ilaenv_(&c__3, "CGELQF", " ", m, n, &c_n1, &c_n1, ( ftnlen)6, (ftnlen)1); nx = max(i__1,i__2); if (nx < k) { /* Determine if workspace is large enough for blocked code. */ ldwork = *m; iws = ldwork * nb; if (*lwork < iws) { /* Not enough workspace to use optimal NB: reduce NB and determine the minimum value of NB. */ nb = *lwork / ldwork; /* Computing MAX */ i__1 = 2, i__2 = ilaenv_(&c__2, "CGELQF", " ", m, n, &c_n1, & c_n1, (ftnlen)6, (ftnlen)1); nbmin = max(i__1,i__2); } } } if (nb >= nbmin && nb < k && nx < k) { /* Use blocked code initially */ i__1 = k - nx; i__2 = nb; for (i__ = 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) { /* Computing MIN */ i__3 = k - i__ + 1; ib = min(i__3,nb); /* Compute the LQ factorization of the current block A(i:i+ib-1,i:n) */ i__3 = *n - i__ + 1; cgelq2_(&ib, &i__3, &a_ref(i__, i__), lda, &tau[i__], &work[1], & iinfo); if (i__ + ib <= *m) { /* Form the triangular factor of the block reflector H = H(i) H(i+1) . . . H(i+ib-1) */ i__3 = *n - i__ + 1; clarft_("Forward", "Rowwise", &i__3, &ib, &a_ref(i__, i__), lda, &tau[i__], &work[1], &ldwork); /* Apply H to A(i+ib:m,i:n) from the right */ i__3 = *m - i__ - ib + 1; i__4 = *n - i__ + 1; clarfb_("Right", "No transpose", "Forward", "Rowwise", &i__3, &i__4, &ib, &a_ref(i__, i__), lda, &work[1], &ldwork, &a_ref(i__ + ib, i__), lda, &work[ib + 1], &ldwork); } /* L10: */ } } else { i__ = 1; } /* Use unblocked code to factor the last or only block. */ if (i__ <= k) { i__2 = *m - i__ + 1; i__1 = *n - i__ + 1; cgelq2_(&i__2, &i__1, &a_ref(i__, i__), lda, &tau[i__], &work[1], & iinfo); } work[1].r = (real) iws, work[1].i = 0.f; return 0; /* End of CGELQF */ } /* cgelqf_ */ #undef a_ref #undef a_subscr