85 lines
2.1 KiB
Go
85 lines
2.1 KiB
Go
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// 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 gonum
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import (
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"math"
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"gonum.org/v1/gonum/blas/blas64"
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)
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// Dgetf2 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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// Dgetf2 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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//
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// Dgetf2 is an internal routine. It is exported for testing purposes.
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func (Implementation) Dgetf2(m, n int, a []float64, lda int, ipiv []int) (ok bool) {
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mn := min(m, n)
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switch {
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case m < 0:
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panic(mLT0)
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case n < 0:
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panic(nLT0)
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case lda < max(1, n):
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panic(badLdA)
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}
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// Quick return if possible.
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if mn == 0 {
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return true
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}
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switch {
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case len(a) < (m-1)*lda+n:
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panic(shortA)
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case len(ipiv) != mn:
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panic(badLenIpiv)
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}
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bi := blas64.Implementation()
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sfmin := dlamchS
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ok = true
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for j := 0; j < mn; j++ {
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// Find a pivot and test for singularity.
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jp := j + bi.Idamax(m-j, a[j*lda+j:], lda)
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ipiv[j] = jp
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if a[jp*lda+j] == 0 {
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ok = false
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} else {
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// Swap the rows if necessary.
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if jp != j {
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bi.Dswap(n, a[j*lda:], 1, a[jp*lda:], 1)
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}
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if j < m-1 {
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aj := a[j*lda+j]
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if math.Abs(aj) >= sfmin {
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bi.Dscal(m-j-1, 1/aj, a[(j+1)*lda+j:], lda)
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} else {
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for i := 0; i < m-j-1; i++ {
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a[(j+1)*lda+j] = a[(j+1)*lda+j] / a[lda*j+j]
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}
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}
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}
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}
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if j < mn-1 {
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bi.Dger(m-j-1, n-j-1, -1, a[(j+1)*lda+j:], lda, a[j*lda+j+1:], 1, a[(j+1)*lda+j+1:], lda)
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}
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}
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return ok
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}
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