#include "blaswrap.h" #include "f2c.h" /* Subroutine */ int dgerq2_(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 ======= DGERQ2 computes an RQ factorization of a real m by n matrix A: A = R * 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, if m <= n, the upper triangle of the subarray A(1:m,n-m+1:n) contains the m by m upper triangular matrix R; if m >= n, the elements on and above the (m-n)-th subdiagonal contain the m by n upper trapezoidal matrix R; 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) 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(1) H(2) . . . H(k), 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(n-k+i+1:n) = 0 and v(n-k+i) = 1; v(1:n-k+i-1) is stored on exit in A(m-k+i,1:n-k+i-1), and tau in TAU(i). ===================================================================== Test the input arguments Parameter adjustments */ /* System generated locals */ integer a_dim1, a_offset, i__1, i__2; /* 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_("DGERQ2", &i__1); return 0; } k = min(*m,*n); for (i__ = k; i__ >= 1; --i__) { /* Generate elementary reflector H(i) to annihilate A(m-k+i,1:n-k+i-1) */ i__1 = *n - k + i__; dlarfg_(&i__1, &a[*m - k + i__ + (*n - k + i__) * a_dim1], &a[*m - k + i__ + a_dim1], lda, &tau[i__]); /* Apply H(i) to A(1:m-k+i-1,1:n-k+i) from the right */ aii = a[*m - k + i__ + (*n - k + i__) * a_dim1]; a[*m - k + i__ + (*n - k + i__) * a_dim1] = 1.; i__1 = *m - k + i__ - 1; i__2 = *n - k + i__; dlarf_("Right", &i__1, &i__2, &a[*m - k + i__ + a_dim1], lda, &tau[ i__], &a[a_offset], lda, &work[1]); a[*m - k + i__ + (*n - k + i__) * a_dim1] = aii; /* L10: */ } return 0; /* End of DGERQ2 */ } /* dgerq2_ */