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46 lines
1.5 KiB
Go
46 lines
1.5 KiB
Go
// Copyright ©2016 The gonum Authors. All rights reserved.
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// Use of this source code is governed by a BSD-style
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// license that can be found in the LICENSE file.
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package native
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import "github.com/gonum/blas"
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// Dgeql2 computes the QL factorization of the m×n matrix A. That is, Dgeql2
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// computes Q and L such that
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// A = Q * L
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// where Q is an m×m orthonormal matrix and L is a lower trapezoidal matrix.
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//
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// Q is represented as a product of elementary reflectors,
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// Q = H_{k-1} * ... * H_1 * H_0
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// where k = min(m,n) and each H_i has the form
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// H_i = I - tau[i] * v_i * v_i^T
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// 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
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// exit in A[0:m-k+i-1, n-k+i].
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//
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// tau must have length at least min(m,n), and Dgeql2 will panic otherwise.
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//
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// work is temporary memory storage and must have length at least n.
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//
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// Dgeql2 is an internal routine. It is exported for testing purposes.
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func (impl Implementation) Dgeql2(m, n int, a []float64, lda int, tau, work []float64) {
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checkMatrix(m, n, a, lda)
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if len(tau) < min(m, n) {
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panic(badTau)
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}
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if len(work) < n {
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panic(badWork)
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}
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k := min(m, n)
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var aii float64
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for i := k - 1; i >= 0; i-- {
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// Generate elementary reflector H_i to annihilate A[0:m-k+i-1, n-k+i].
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aii, tau[i] = impl.Dlarfg(m-k+i+1, a[(m-k+i)*lda+n-k+i], a[n-k+i:], lda)
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// Apply H_i to A[0:m-k+i, 0:n-k+i-1] from the left.
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a[(m-k+i)*lda+n-k+i] = 1
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impl.Dlarf(blas.Left, m-k+i+1, n-k+i, a[n-k+i:], lda, tau[i], a, lda, work)
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a[(m-k+i)*lda+n-k+i] = aii
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}
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}
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