| // 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 ( |
| "gonum.org/v1/gonum/blas" |
| "gonum.org/v1/gonum/lapack" |
| ) |
| |
| // Dgerqf computes an RQ factorization of the m×n matrix A, |
| // A = R * Q. |
| // On exit, if m <= n, the upper triangle of the subarray |
| // A[0:m, n-m:n] contains the m×m upper triangular matrix R. |
| // If m >= n, the elements on and above the (m-n)-th subdiagonal |
| // contain the m×n upper trapezoidal matrix R. |
| // The remaining elements, with tau, represent the |
| // orthogonal matrix Q as a product of min(m,n) elementary |
| // reflectors. |
| // |
| // The matrix Q is represented as a product of elementary reflectors |
| // Q = H_0 H_1 . . . H_{min(m,n)-1}. |
| // Each H(i) has the form |
| // H_i = I - tau_i * v * v^T |
| // where v is a vector with v[0:n-k+i-1] stored in A[m-k+i, 0:n-k+i-1], |
| // v[n-k+i:n] = 0 and v[n-k+i] = 1. |
| // |
| // tau must have length min(m,n), work must have length max(1, lwork), |
| // and lwork must be -1 or at least max(1, m), otherwise Dgerqf will panic. |
| // On exit, work[0] will contain the optimal length for work. |
| // |
| // Dgerqf is an internal routine. It is exported for testing purposes. |
| func (impl Implementation) Dgerqf(m, n int, a []float64, lda int, tau, work []float64, lwork int) { |
| checkMatrix(m, n, a, lda) |
| |
| if len(work) < max(1, lwork) { |
| panic(shortWork) |
| } |
| if lwork != -1 && lwork < max(1, m) { |
| panic(badWork) |
| } |
| |
| k := min(m, n) |
| if len(tau) != k { |
| panic(badTau) |
| } |
| |
| var nb, lwkopt int |
| if k == 0 { |
| lwkopt = 1 |
| } else { |
| nb = impl.Ilaenv(1, "DGERQF", " ", m, n, -1, -1) |
| lwkopt = m * nb |
| } |
| work[0] = float64(lwkopt) |
| |
| if lwork == -1 { |
| return |
| } |
| |
| // Return quickly if possible. |
| if k == 0 { |
| return |
| } |
| |
| nbmin := 2 |
| nx := 1 |
| iws := m |
| var ldwork int |
| if 1 < nb && nb < k { |
| // Determine when to cross over from blocked to unblocked code. |
| nx = max(0, impl.Ilaenv(3, "DGERQF", " ", m, n, -1, -1)) |
| if nx < k { |
| // Determine whether workspace is large enough for blocked code. |
| iws = m * nb |
| if lwork < iws { |
| // Not enough workspace to use optimal nb. Reduce |
| // nb and determine the minimum value of nb. |
| nb = lwork / m |
| nbmin = max(2, impl.Ilaenv(2, "DGERQF", " ", m, n, -1, -1)) |
| } |
| ldwork = nb |
| } |
| } |
| |
| var mu, nu int |
| if nbmin <= nb && nb < k && nx < k { |
| // Use blocked code initially. |
| // The last kk rows are handled by the block method. |
| ki := ((k - nx - 1) / nb) * nb |
| kk := min(k, ki+nb) |
| |
| var i int |
| for i = k - kk + ki; i >= k-kk; i -= nb { |
| ib := min(k-i, nb) |
| |
| // Compute the RQ factorization of the current block |
| // A[m-k+i:m-k+i+ib-1, 0:n-k+i+ib-1]. |
| impl.Dgerq2(ib, n-k+i+ib, a[(m-k+i)*lda:], lda, tau[i:], work) |
| if m-k+i > 0 { |
| // Form the triangular factor of the block reflector |
| // H = H_{i+ib-1} . . . H_{i+1} H_i. |
| impl.Dlarft(lapack.Backward, lapack.RowWise, |
| n-k+i+ib, ib, a[(m-k+i)*lda:], lda, tau[i:], |
| work, ldwork) |
| |
| // Apply H to A[0:m-k+i-1, 0:n-k+i+ib-1] from the right. |
| impl.Dlarfb(blas.Right, blas.NoTrans, lapack.Backward, lapack.RowWise, |
| m-k+i, n-k+i+ib, ib, a[(m-k+i)*lda:], lda, |
| work, ldwork, |
| a, lda, |
| work[ib*ldwork:], ldwork) |
| } |
| } |
| mu = m - k + i + nb |
| nu = n - k + i + nb |
| } else { |
| mu = m |
| nu = n |
| } |
| |
| // Use unblocked code to factor the last or only block. |
| if mu > 0 && nu > 0 { |
| impl.Dgerq2(mu, nu, a, lda, tau, work) |
| } |
| work[0] = float64(iws) |
| } |