+++ /dev/null
-// Copyright ©2017 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 (
- "math"
-
- "gonum.org/v1/gonum/blas"
- "gonum.org/v1/gonum/blas/blas64"
-)
-
-// Dlaqp2 computes a QR factorization with column pivoting of the block A[offset:m, 0:n]
-// of the m×n matrix A. The block A[0:offset, 0:n] is accordingly pivoted, but not factorized.
-//
-// On exit, the upper triangle of block A[offset:m, 0:n] is the triangular factor obtained.
-// The elements in block A[offset:m, 0:n] below the diagonal, together with tau, represent
-// the orthogonal matrix Q as a product of elementary reflectors.
-//
-// offset is number of rows of the matrix A that must be pivoted but not factorized.
-// offset must not be negative otherwise Dlaqp2 will panic.
-//
-// On exit, jpvt holds the permutation that was applied; the jth column of A*P was the
-// jpvt[j] column of A. jpvt must have length n, otherwise Dlaqp2 will panic.
-//
-// On exit tau holds the scalar factors of the elementary reflectors. It must have length
-// at least min(m-offset, n) otherwise Dlaqp2 will panic.
-//
-// vn1 and vn2 hold the partial and complete column norms respectively. They must have length n,
-// otherwise Dlaqp2 will panic.
-//
-// work must have length n, otherwise Dlaqp2 will panic.
-//
-// Dlaqp2 is an internal routine. It is exported for testing purposes.
-func (impl Implementation) Dlaqp2(m, n, offset int, a []float64, lda int, jpvt []int, tau, vn1, vn2, work []float64) {
- checkMatrix(m, n, a, lda)
- if len(jpvt) != n {
- panic(badIpiv)
- }
- mn := min(m-offset, n)
- if len(tau) < mn {
- panic(badTau)
- }
- if len(vn1) < n {
- panic(badVn1)
- }
- if len(vn2) < n {
- panic(badVn2)
- }
- if len(work) < n {
- panic(badWork)
- }
-
- tol3z := math.Sqrt(dlamchE)
-
- bi := blas64.Implementation()
-
- // Compute factorization.
- for i := 0; i < mn; i++ {
- offpi := offset + i
-
- // Determine ith pivot column and swap if necessary.
- p := i + bi.Idamax(n-i, vn1[i:], 1)
- if p != i {
- bi.Dswap(m, a[p:], lda, a[i:], lda)
- jpvt[p], jpvt[i] = jpvt[i], jpvt[p]
- vn1[p] = vn1[i]
- vn2[p] = vn2[i]
- }
-
- // Generate elementary reflector H_i.
- if offpi < m-1 {
- a[offpi*lda+i], tau[i] = impl.Dlarfg(m-offpi, a[offpi*lda+i], a[(offpi+1)*lda+i:], lda)
- } else {
- tau[i] = 0
- }
-
- if i < n-1 {
- // Apply H_i^T to A[offset+i:m, i:n] from the left.
- aii := a[offpi*lda+i]
- a[offpi*lda+i] = 1
- impl.Dlarf(blas.Left, m-offpi, n-i-1, a[offpi*lda+i:], lda, tau[i], a[offpi*lda+i+1:], lda, work)
- a[offpi*lda+i] = aii
- }
-
- // Update partial column norms.
- for j := i + 1; j < n; j++ {
- if vn1[j] == 0 {
- continue
- }
-
- // The following marked lines follow from the
- // analysis in Lapack Working Note 176.
- r := math.Abs(a[offpi*lda+j]) / vn1[j] // *
- temp := math.Max(0, 1-r*r) // *
- r = vn1[j] / vn2[j] // *
- temp2 := temp * r * r // *
- if temp2 < tol3z {
- var v float64
- if offpi < m-1 {
- v = bi.Dnrm2(m-offpi-1, a[(offpi+1)*lda+j:], lda)
- }
- vn1[j] = v
- vn2[j] = v
- } else {
- vn1[j] *= math.Sqrt(temp) // *
- }
- }
- }
-}
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