| // Copyright ©2015 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/blas/blas64" |
| ) |
| |
| // Dgetrf computes the LU decomposition of the m×n matrix A. |
| // The LU decomposition is a factorization of A into |
| // A = P * L * U |
| // where P is a permutation matrix, L is a unit lower triangular matrix, and |
| // U is a (usually) non-unit upper triangular matrix. On exit, L and U are stored |
| // in place into a. |
| // |
| // ipiv is a permutation vector. It indicates that row i of the matrix was |
| // changed with ipiv[i]. ipiv must have length at least min(m,n), and will panic |
| // otherwise. ipiv is zero-indexed. |
| // |
| // Dgetrf is the blocked version of the algorithm. |
| // |
| // Dgetrf returns whether the matrix A is singular. The LU decomposition will |
| // be computed regardless of the singularity of A, but division by zero |
| // will occur if the false is returned and the result is used to solve a |
| // system of equations. |
| func (impl Implementation) Dgetrf(m, n int, a []float64, lda int, ipiv []int) (ok bool) { |
| mn := min(m, n) |
| checkMatrix(m, n, a, lda) |
| if len(ipiv) < mn { |
| panic(badIpiv) |
| } |
| if m == 0 || n == 0 { |
| return false |
| } |
| bi := blas64.Implementation() |
| nb := impl.Ilaenv(1, "DGETRF", " ", m, n, -1, -1) |
| if nb <= 1 || nb >= min(m, n) { |
| // Use the unblocked algorithm. |
| return impl.Dgetf2(m, n, a, lda, ipiv) |
| } |
| ok = true |
| for j := 0; j < mn; j += nb { |
| jb := min(mn-j, nb) |
| blockOk := impl.Dgetf2(m-j, jb, a[j*lda+j:], lda, ipiv[j:]) |
| if !blockOk { |
| ok = false |
| } |
| for i := j; i <= min(m-1, j+jb-1); i++ { |
| ipiv[i] = j + ipiv[i] |
| } |
| impl.Dlaswp(j, a, lda, j, j+jb-1, ipiv[:j+jb], 1) |
| if j+jb < n { |
| impl.Dlaswp(n-j-jb, a[j+jb:], lda, j, j+jb-1, ipiv[:j+jb], 1) |
| bi.Dtrsm(blas.Left, blas.Lower, blas.NoTrans, blas.Unit, |
| jb, n-j-jb, 1, |
| a[j*lda+j:], lda, |
| a[j*lda+j+jb:], lda) |
| if j+jb < m { |
| bi.Dgemm(blas.NoTrans, blas.NoTrans, m-j-jb, n-j-jb, jb, -1, |
| a[(j+jb)*lda+j:], lda, |
| a[j*lda+j+jb:], lda, |
| 1, a[(j+jb)*lda+j+jb:], lda) |
| } |
| } |
| } |
| return ok |
| } |