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71 lines
2.1 KiB
Go
71 lines
2.1 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 (
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"gonum.org/v1/gonum/blas"
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"gonum.org/v1/gonum/blas/blas64"
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)
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// Dgetrf computes the LU decomposition of the m×n matrix A.
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// The LU decomposition is a factorization of A into
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// A = P * L * U
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// where P is a permutation matrix, L is a unit lower triangular matrix, and
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// U is a (usually) non-unit upper triangular matrix. On exit, L and U are stored
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// in place into a.
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//
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// ipiv is a permutation vector. It indicates that row i of the matrix was
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// changed with ipiv[i]. ipiv must have length at least min(m,n), and will panic
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// otherwise. ipiv is zero-indexed.
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//
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// Dgetrf is the blocked version of the algorithm.
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//
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// Dgetrf returns whether the matrix A is singular. The LU decomposition will
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// be computed regardless of the singularity of A, but division by zero
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// will occur if the false is returned and the result is used to solve a
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// system of equations.
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func (impl Implementation) Dgetrf(m, n int, a []float64, lda int, ipiv []int) (ok bool) {
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mn := min(m, n)
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checkMatrix(m, n, a, lda)
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if len(ipiv) < mn {
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panic(badIpiv)
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}
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if m == 0 || n == 0 {
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return false
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}
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bi := blas64.Implementation()
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nb := impl.Ilaenv(1, "DGETRF", " ", m, n, -1, -1)
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if nb <= 1 || nb >= min(m, n) {
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// Use the unblocked algorithm.
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return impl.Dgetf2(m, n, a, lda, ipiv)
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}
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ok = true
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for j := 0; j < mn; j += nb {
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jb := min(mn-j, nb)
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blockOk := impl.Dgetf2(m-j, jb, a[j*lda+j:], lda, ipiv[j:])
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if !blockOk {
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ok = false
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}
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for i := j; i <= min(m-1, j+jb-1); i++ {
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ipiv[i] = j + ipiv[i]
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}
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impl.Dlaswp(j, a, lda, j, j+jb-1, ipiv[:j+jb], 1)
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if j+jb < n {
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impl.Dlaswp(n-j-jb, a[j+jb:], lda, j, j+jb-1, ipiv[:j+jb], 1)
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bi.Dtrsm(blas.Left, blas.Lower, blas.NoTrans, blas.Unit,
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jb, n-j-jb, 1,
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a[j*lda+j:], lda,
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a[j*lda+j+jb:], lda)
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if j+jb < m {
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bi.Dgemm(blas.NoTrans, blas.NoTrans, m-j-jb, n-j-jb, jb, -1,
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a[(j+jb)*lda+j:], lda,
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a[j*lda+j+jb:], lda,
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1, a[(j+jb)*lda+j+jb:], lda)
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}
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}
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}
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return ok
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}
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