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ec100cf00f
Improved function documentation Fixed dlarfb and dlarft and added full tests Added dgelq2 Working Dgels Fix many comments and tests Many PR comment responses Responded to more PR comments Many PR comments
45 lines
1.4 KiB
Go
45 lines
1.4 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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// Dgelq2 computes the LQ factorization of the m×n matrix a.
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//
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// During Dgelq2, a is modified to contain the information to construct Q and L.
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// The lower triangle of a contains the matrix L. The upper 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 of at least k = min(m,n)
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// and this function will panic otherwise.
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//
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// See Dgeqr2 for a description of the elementary reflectors and orthonormal
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// matrix Q. Q is constructed as a product of these elementary reflectors,
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// Q = H_k ... H_2*H_1.
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//
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// Work is temporary storage of length at least m and this function will panic otherwise.
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func (impl Implementation) Dgelq2(m, n int, a []float64, lda int, tau, work []float64) {
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checkMatrix(m, n, a, lda)
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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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if len(work) < m {
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panic(badWork)
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}
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for i := 0; i < k; i++ {
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a[i*lda+i], tau[i] = impl.Dlarfg(n-i, a[i*lda+i], a[i*lda+min(i+1, n-1):], 1)
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if i < m-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.Right, m-i-1, n-i,
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a[i*lda+i:], 1,
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tau[i],
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a[(i+1)*lda+i:], 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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