fix commands

[bytom/shuttle.git] / vendor / github.com / bytom / vendor / gonum.org / v1 / gonum / lapack / gonum / dgeql2.go

diff --git a/vendor/github.com/bytom/vendor/gonum.org/v1/gonum/lapack/gonum/dgeql2.go b/vendor/github.com/bytom/vendor/gonum.org/v1/gonum/lapack/gonum/dgeql2.go
new file mode 100644 (file)
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--- /dev/null
+++ b/vendor/github.com/bytom/vendor/gonum.org/v1/gonum/lapack/gonum/dgeql2.go
@@ -0,0 +1,45 @@
+// Copyright ©2016 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"
+
+// Dgeql2 computes the QL factorization of the m×n matrix A. That is, Dgeql2
+// computes Q and L such that
+//  A = Q * L
+// where Q is an m×m orthonormal matrix and L is a lower trapezoidal matrix.
+//
+// Q is represented as a product of elementary reflectors,
+//  Q = H_{k-1} * ... * H_1 * H_0
+// where k = min(m,n) and each H_i has the form
+//  H_i = I - tau[i] * v_i * v_i^T
+// Vector v_i has v[m-k+i+1:m] = 0, v[m-k+i] = 1, and v[:m-k+i+1] is stored on
+// exit in A[0:m-k+i-1, n-k+i].
+//
+// tau must have length at least min(m,n), and Dgeql2 will panic otherwise.
+//
+// work is temporary memory storage and must have length at least n.
+//
+// Dgeql2 is an internal routine. It is exported for testing purposes.
+func (impl Implementation) Dgeql2(m, n int, a []float64, lda int, tau, work []float64) {
+       checkMatrix(m, n, a, lda)
+       if len(tau) < min(m, n) {
+               panic(badTau)
+       }
+       if len(work) < n {
+               panic(badWork)
+       }
+       k := min(m, n)
+       var aii float64
+       for i := k - 1; i >= 0; i-- {
+               // Generate elementary reflector H_i to annihilate A[0:m-k+i-1, n-k+i].
+               aii, tau[i] = impl.Dlarfg(m-k+i+1, a[(m-k+i)*lda+n-k+i], a[n-k+i:], lda)
+
+               // Apply H_i to A[0:m-k+i, 0:n-k+i-1] from the left.
+               a[(m-k+i)*lda+n-k+i] = 1
+               impl.Dlarf(blas.Left, m-k+i+1, n-k+i, a[n-k+i:], lda, tau[i], a, lda, work)
+               a[(m-k+i)*lda+n-k+i] = aii
+       }
+}