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 // 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 // Dorghr generates an n×n orthogonal matrix Q which is defined as the product // of ihi-ilo elementary reflectors: // Q = H_{ilo} H_{ilo+1} ... H_{ihi-1}. // // a and lda represent an n×n matrix that contains the elementary reflectors, as // returned by Dgehrd. On return, a is overwritten by the n×n orthogonal matrix // Q. Q will be equal to the identity matrix except in the submatrix // Q[ilo+1:ihi+1,ilo+1:ihi+1]. // // ilo and ihi must have the same values as in the previous call of Dgehrd. It // must hold that // 0 <= ilo <= ihi < n if n > 0, // ilo = 0, ihi = -1 if n == 0. // // tau contains the scalar factors of the elementary reflectors, as returned by // Dgehrd. tau must have length n-1. // // work must have length at least max(1,lwork) and lwork must be at least // ihi-ilo. For optimum performance lwork must be at least (ihi-ilo)*nb where nb // is the optimal blocksize. On return, work[0] will contain the optimal value // of lwork. // // If lwork == -1, instead of performing Dorghr, only the optimal value of lwork // will be stored into work[0]. // // If any requirement on input sizes is not met, Dorghr will panic. // // Dorghr is an internal routine. It is exported for testing purposes. func (impl Implementation) Dorghr(n, ilo, ihi int, a []float64, lda int, tau, work []float64, lwork int) { nh := ihi - ilo switch { case ilo < 0 || max(1, n) <= ilo: panic(badIlo) case ihi < min(ilo, n-1) || n <= ihi: panic(badIhi) case lda < max(1, n): panic(badLdA) case lwork < max(1, nh) && lwork != -1: panic(badLWork) case len(work) < max(1, lwork): panic(shortWork) } // Quick return if possible. if n == 0 { work[0] = 1 return } lwkopt := max(1, nh) * impl.Ilaenv(1, "DORGQR", " ", nh, nh, nh, -1) if lwork == -1 { work[0] = float64(lwkopt) return } switch { case len(a) < (n-1)*lda+n: panic(shortA) case len(tau) < n-1: panic(shortTau) } // Shift the vectors which define the elementary reflectors one column // to the right. for i := ilo + 2; i < ihi+1; i++ { copy(a[i*lda+ilo+1:i*lda+i], a[i*lda+ilo:i*lda+i-1]) } // Set the first ilo+1 and the last n-ihi-1 rows and columns to those of // the identity matrix. for i := 0; i < ilo+1; i++ { for j := 0; j < n; j++ { a[i*lda+j] = 0 } a[i*lda+i] = 1 } for i := ilo + 1; i < ihi+1; i++ { for j := 0; j <= ilo; j++ { a[i*lda+j] = 0 } for j := i; j < n; j++ { a[i*lda+j] = 0 } } for i := ihi + 1; i < n; i++ { for j := 0; j < n; j++ { a[i*lda+j] = 0 } a[i*lda+i] = 1 } if nh > 0 { // Generate Q[ilo+1:ihi+1,ilo+1:ihi+1]. impl.Dorgqr(nh, nh, nh, a[(ilo+1)*lda+ilo+1:], lda, tau[ilo:ihi], work, lwork) } work[0] = float64(lwkopt) }