#include "blaswrap.h" #include "f2c.h" /* Subroutine */ int dgelq2_(integer *m, integer *n, doublereal *a, integer * lda, doublereal *tau, doublereal *work, integer *info) { /* -- LAPACK routine (version 3.1) -- Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. November 2006 Purpose ======= DGELQ2 computes an LQ factorization of a real 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) DOUBLE PRECISION 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 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) DOUBLE PRECISION array, dimension (min(M,N)) The scalar factors of the elementary reflectors (see Further Details). WORK (workspace) DOUBLE PRECISION array, dimension (M) 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(1:i-1) = 0 and v(i) = 1; 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 */ /* System generated locals */ integer a_dim1, a_offset, i__1, i__2, i__3; /* Local variables */ static integer i__, k; static doublereal aii; extern /* Subroutine */ int dlarf_(char *, integer *, integer *, doublereal *, integer *, doublereal *, doublereal *, integer *, doublereal *), dlarfg_(integer *, doublereal *, doublereal *, integer *, doublereal *), xerbla_(char *, integer *); a_dim1 = *lda; a_offset = 1 + a_dim1; a -= a_offset; --tau; --work; /* Function Body */ *info = 0; if (*m < 0) { *info = -1; } else if (*n < 0) { *info = -2; } else if (*lda < max(1,*m)) { *info = -4; } if (*info != 0) { i__1 = -(*info); xerbla_("DGELQ2", &i__1); return 0; } k = min(*m,*n); i__1 = k; for (i__ = 1; i__ <= i__1; ++i__) { /* Generate elementary reflector H(i) to annihilate A(i,i+1:n) */ i__2 = *n - i__ + 1; /* Computing MIN */ i__3 = i__ + 1; dlarfg_(&i__2, &a[i__ + i__ * a_dim1], &a[i__ + min(i__3,*n) * a_dim1] , lda, &tau[i__]); if (i__ < *m) { /* Apply H(i) to A(i+1:m,i:n) from the right */ aii = a[i__ + i__ * a_dim1]; a[i__ + i__ * a_dim1] = 1.; i__2 = *m - i__; i__3 = *n - i__ + 1; dlarf_("Right", &i__2, &i__3, &a[i__ + i__ * a_dim1], lda, &tau[ i__], &a[i__ + 1 + i__ * a_dim1], lda, &work[1]); a[i__ + i__ * a_dim1] = aii; } /* L10: */ } return 0; /* End of DGELQ2 */ } /* dgelq2_ */