Add dependencies for code generator

vendor/gonum.org/v1/gonum/lapack/gonum/dgeqr2.go

@@ -0,0 +1,76 @@
+// Copyright ©2015 The Gonum Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package gonum
+
+import "gonum.org/v1/gonum/blas"
+
+// Dgeqr2 computes a QR factorization of the m×n matrix A.
+//
+// In a QR factorization, Q is an m×m orthonormal matrix, and R is an
+// upper triangular m×n matrix.
+//
+// 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 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] = 1           j == i
+//  v[j] = a[j*lda+i]  j > i
+// and computing H_i = I - tau[i] * v * v^T.
+//
+// The orthonormal matrix Q can be constructed from a product of these elementary
+// reflectors, Q = H_0 * H_1 * ... * H_{k-1}, where k = min(m,n).
+//
+// work is temporary storage of length at least n and this function will panic otherwise.
+//
+// Dgeqr2 is an internal routine. It is exported for testing purposes.
+func (impl Implementation) Dgeqr2(m, n int, a []float64, lda int, tau, work []float64) {
+	// TODO(btracey): This is oriented such that columns of a are eliminated.
+	// This likely could be re-arranged to take better advantage of row-major
+	// storage.
+
+	switch {
+	case m < 0:
+		panic(mLT0)
+	case n < 0:
+		panic(nLT0)
+	case lda < max(1, n):
+		panic(badLdA)
+	case len(work) < n:
+		panic(shortWork)
+	}
+
+	// Quick return if possible.
+	k := min(m, n)
+	if k == 0 {
+		return
+	}
+
+	switch {
+	case len(a) < (m-1)*lda+n:
+		panic(shortA)
+	case len(tau) < k:
+		panic(shortTau)
+	}
+
+	for i := 0; i < k; i++ {
+		// Generate elementary reflector H_i.
+		a[i*lda+i], tau[i] = impl.Dlarfg(m-i, a[i*lda+i], a[min((i+1), m-1)*lda+i:], lda)
+		if i < n-1 {
+			aii := a[i*lda+i]
+			a[i*lda+i] = 1
+			impl.Dlarf(blas.Left, m-i, n-i-1,
+				a[i*lda+i:], lda,
+				tau[i],
+				a[i*lda+i+1:], lda,
+				work)
+			a[i*lda+i] = aii
+		}
+	}
+}