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60 lines
1.9 KiB
Go
60 lines
1.9 KiB
Go
// Copyright ©2015 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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// Dgeqr2 computes a QR factorization of the m×n matrix A.
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//
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// In a QR factorization, Q is an m×m orthonormal matrix, and R is an
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// upper triangular m×n matrix.
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//
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// A is modified to contain the information to construct Q and R.
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// The upper triangle of a contains the matrix R. The lower triangular elements
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// (not including the diagonal) contain the elementary reflectors. tau is modified
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// to contain the reflector scales. tau must have length at least min(m,n), and
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// this function will panic otherwise.
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//
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// The ith elementary reflector can be explicitly constructed by first extracting
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// the
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// v[j] = 0 j < i
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// v[j] = 1 j == i
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// v[j] = a[j*lda+i] j > i
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// and computing H_i = I - tau[i] * v * v^T.
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//
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// The orthonormal matrix Q can be constructed from a product of these elementary
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// reflectors, Q = H_0 * H_1 * ... * H_{k-1}, where k = min(m,n).
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//
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// work is temporary storage of length at least n and this function will panic otherwise.
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//
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// Dgeqr2 is an internal routine. It is exported for testing purposes.
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func (impl Implementation) Dgeqr2(m, n int, a []float64, lda int, tau, work []float64) {
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// TODO(btracey): This is oriented such that columns of a are eliminated.
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// This likely could be re-arranged to take better advantage of row-major
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// storage.
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checkMatrix(m, n, a, lda)
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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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if len(tau) < k {
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panic(badTau)
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}
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for i := 0; i < k; i++ {
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// Generate elementary reflector H_i.
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a[i*lda+i], tau[i] = impl.Dlarfg(m-i, a[i*lda+i], a[min((i+1), m-1)*lda+i:], lda)
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if i < n-1 {
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aii := a[i*lda+i]
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a[i*lda+i] = 1
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impl.Dlarf(blas.Left, m-i, n-i-1,
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a[i*lda+i:], lda,
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tau[i],
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a[i*lda+i+1:], lda,
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work)
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a[i*lda+i] = aii
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}
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}
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}
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