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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 an m×n matrix A using partial
// pivoting with row interchanges.
//
// The LU decomposition is a factorization of A into
//
// A = P * L * U
//
// where P is a permutation matrix, L is a lower triangular with unit diagonal
// elements (lower trapezoidal if m > n), and U is upper triangular (upper
// trapezoidal if m < n).
//
// On entry, a contains the matrix A. On return, L and U are stored in place
// into a, and P is represented by ipiv.
//
// ipiv contains a sequence of row interchanges. It indicates that row i of the
// matrix was interchanged with ipiv[i]. ipiv must have length min(m,n), and
// Dgetf2 will panic otherwise. ipiv is zero-indexed.
//
// Dgetf2 returns whether the matrix A is nonsingular. The LU decomposition will
// be computed regardless of the singularity of A, but the result should not be
// used to solve a system of equation.
//
// 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
}
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