#include "blaswrap.h" #include "f2c.h" /* Subroutine */ int cgeqr2_(integer *m, integer *n, complex *a, integer *lda, complex *tau, complex *work, integer *info) { /* -- LAPACK routine (version 3.1) -- Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. November 2006 Purpose ======= CGEQR2 computes a QR factorization of a complex m by n matrix A: A = Q * R. 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 above the diagonal of the array contain the min(m,n) by n upper trapezoidal matrix R (R is upper triangular if m >= n); the elements below 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) COMPLEX array, dimension (N) 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 complex scalar, and v is a complex vector with v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i), and tau in TAU(i). ===================================================================== Test the input arguments Parameter adjustments */ /* Table of constant values */ static integer c__1 = 1; /* System generated locals */ integer a_dim1, a_offset, i__1, i__2, i__3; complex q__1; /* Builtin functions */ void r_cnjg(complex *, complex *); /* Local variables */ static integer i__, k; static complex alpha; extern /* Subroutine */ int clarf_(char *, integer *, integer *, complex * , integer *, complex *, complex *, integer *, complex *), clarfg_(integer *, complex *, complex *, integer *, complex *), 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_("CGEQR2", &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+1:m,i) */ i__2 = *m - i__ + 1; /* Computing MIN */ i__3 = i__ + 1; clarfg_(&i__2, &a[i__ + i__ * a_dim1], &a[min(i__3,*m) + i__ * a_dim1] , &c__1, &tau[i__]); if (i__ < *n) { /* Apply H(i)' to A(i:m,i+1:n) from the left */ i__2 = i__ + i__ * a_dim1; alpha.r = a[i__2].r, alpha.i = a[i__2].i; i__2 = i__ + i__ * a_dim1; a[i__2].r = 1.f, a[i__2].i = 0.f; i__2 = *m - i__ + 1; i__3 = *n - i__; r_cnjg(&q__1, &tau[i__]); clarf_("Left", &i__2, &i__3, &a[i__ + i__ * a_dim1], &c__1, &q__1, &a[i__ + (i__ + 1) * a_dim1], lda, &work[1]); i__2 = i__ + i__ * a_dim1; a[i__2].r = alpha.r, a[i__2].i = alpha.i; } /* L10: */ } return 0; /* End of CGEQR2 */ } /* cgeqr2_ */