#include "blaswrap.h" #include "f2c.h" /* Subroutine */ int sgeqlf_(integer *m, integer *n, real *a, integer *lda, real *tau, real *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 ======= SGEQLF computes a QL factorization of a real M-by-N matrix A: A = Q * L. 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) REAL array, dimension (LDA,N) On entry, the M-by-N matrix A. On exit, if m >= n, the lower triangle of the subarray A(m-n+1:m,1:n) contains the N-by-N lower triangular matrix L; if m <= n, the elements on and below the (n-m)-th superdiagonal contain the M-by-N lower trapezoidal matrix L; the remaining elements, with the array TAU, represent the orthogonal 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) REAL array, dimension (min(M,N)) The scalar factors of the elementary reflectors (see Further Details). WORK (workspace/output) REAL 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,N). For optimum performance LWORK >= N*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 real scalar, and v is a real vector with v(m-k+i+1:m) = 0 and v(m-k+i) = 1; v(1:m-k+i-1) is stored on exit in A(1:m-k+i-1,n-k+i), 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 sgeql2_(integer *, integer *, real *, integer *, real *, real *, integer *); static integer ib, nb, ki, kk, mu, nu, nx; extern /* Subroutine */ int slarfb_(char *, char *, char *, char *, integer *, integer *, integer *, real *, integer *, real *, integer *, real *, integer *, real *, integer *), xerbla_(char *, integer *); extern integer ilaenv_(integer *, char *, char *, integer *, integer *, integer *, integer *, ftnlen, ftnlen); extern /* Subroutine */ int slarft_(char *, char *, integer *, integer *, real *, integer *, real *, real *, integer *); static integer ldwork, lwkopt; static logical lquery; static integer iws; #define a_ref(a_1,a_2) a[(a_2)*a_dim1 + a_1] a_dim1 = *lda; a_offset = 1 + a_dim1 * 1; a -= a_offset; --tau; --work; /* Function Body */ *info = 0; nb = ilaenv_(&c__1, "SGEQLF", " ", m, n, &c_n1, &c_n1, (ftnlen)6, (ftnlen) 1); lwkopt = *n * nb; work[1] = (real) lwkopt; 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,*n) && ! lquery) { *info = -7; } if (*info != 0) { i__1 = -(*info); xerbla_("SGEQLF", &i__1); return 0; } else if (lquery) { return 0; } /* Quick return if possible */ k = min(*m,*n); if (k == 0) { work[1] = 1.f; return 0; } nbmin = 2; nx = 1; iws = *n; 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, "SGEQLF", " ", 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 = *n; 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, "SGEQLF", " ", 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. The last kk columns are handled by the block method. */ ki = (k - nx - 1) / nb * nb; /* Computing MIN */ i__1 = k, i__2 = ki + nb; kk = min(i__1,i__2); i__1 = k - kk + 1; i__2 = -nb; for (i__ = k - kk + ki + 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 QL factorization of the current block A(1:m-k+i+ib-1,n-k+i:n-k+i+ib-1) */ i__3 = *m - k + i__ + ib - 1; sgeql2_(&i__3, &ib, &a_ref(1, *n - k + i__), lda, &tau[i__], & work[1], &iinfo); if (*n - k + i__ > 1) { /* Form the triangular factor of the block reflector H = H(i+ib-1) . . . H(i+1) H(i) */ i__3 = *m - k + i__ + ib - 1; slarft_("Backward", "Columnwise", &i__3, &ib, &a_ref(1, *n - k + i__), lda, &tau[i__], &work[1], &ldwork); /* Apply H' to A(1:m-k+i+ib-1,1:n-k+i-1) from the left */ i__3 = *m - k + i__ + ib - 1; i__4 = *n - k + i__ - 1; slarfb_("Left", "Transpose", "Backward", "Columnwise", &i__3, &i__4, &ib, &a_ref(1, *n - k + i__), lda, &work[1], & ldwork, &a[a_offset], lda, &work[ib + 1], &ldwork); } /* L10: */ } mu = *m - k + i__ + nb - 1; nu = *n - k + i__ + nb - 1; } else { mu = *m; nu = *n; } /* Use unblocked code to factor the last or only block */ if (mu > 0 && nu > 0) { sgeql2_(&mu, &nu, &a[a_offset], lda, &tau[1], &work[1], &iinfo); } work[1] = (real) iws; return 0; /* End of SGEQLF */ } /* sgeqlf_ */ #undef a_ref