Add QR factorization to lapack64 interface.

lapack64/lapack64.go

@@ -47,3 +47,29 @@ func Potrf(a blas64.Symmetric) (t blas64.Triangular, ok bool) {
 	t.Diag = blas.NonUnit
 	return
 }
+
+// Geqrf computes the QR factorization of the m×n matrix A using a blocked
+// algorithm. During Dgeqr2, A is modified to contain the information to construct Q and R.
+// The upper triangle of a contains the matrix R. The lower triangular elements
+// (not including the diagonal) contain the elementary reflectors. Tau is modified
+// to contain the reflector scales. Tau must have length at least k = min(m,n), and
+// this function will panic otherwise.
+//
+// The ith elementary reflector can be explicitly constructed by first extracting
+// the
+//  v[j] = 0           j < i
+//  v[j] = i           j == i
+//  v[j] = a[i*lda+j]  j > i
+// and computing h_i = I - tau[i] * v * v^T.
+//
+// The orthonormal matrix Q can be constucted from a product of these elementary
+// reflectors, Q = H_1*H_2 ... H_k, where k = min(m,n).
+//
+// Work is temporary storage, and lwork specifies the usable memory length.
+// At minimum, lwork >= m and this function will panic otherwise.
+// Dgeqrf is a blocked LQ factorization, but the block size is limited
+// by the temporary space available. If lwork == -1, instead of performing Dgelqf,
+// the optimal work length will be stored into work[0].
+func Geqrf(a blas64.General, tau, work []float64, lwork int) {
+	lapack64.Dgeqrf(a.Rows, a.Cols, a.Data, a.Stride, tau, work, lwork)
+}