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