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// Copyright ©2021 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"
)
// Dgesc2 solves a system of linear equations
//
// A * x = scale * b
//
// with a general n×n matrix A represented by the LU factorization with complete
// pivoting
//
// A = P * L * U * Q
//
// as computed by Dgetc2.
//
// On entry, rhs contains the right hand side vector b. On return, it is
// overwritten with the solution vector x.
//
// Dgesc2 returns a scale factor
//
// 0 <= scale <= 1
//
// chosen to prevent overflow in the solution.
//
// Dgesc2 is an internal routine. It is exported for testing purposes.
func (impl Implementation) Dgesc2(n int, a []float64, lda int, rhs []float64, ipiv, jpiv []int) (scale float64) {
switch {
case n < 0:
panic(nLT0)
case lda < max(1, n):
panic(badLdA)
}
// Quick return if possible.
if n == 0 {
return 0
}
switch {
case len(a) < (n-1)*lda+n:
panic(shortA)
case len(rhs) < n:
panic(shortRHS)
case len(ipiv) != n:
panic(badLenIpiv)
case len(jpiv) != n:
panic(badLenJpiv)
}
const smlnum = dlamchS / dlamchP
// Apply permutations ipiv to rhs.
impl.Dlaswp(1, rhs, 1, 0, n-1, ipiv[:n], 1)
// Solve for L part.
for i := 0; i < n-1; i++ {
for j := i + 1; j < n; j++ {
rhs[j] -= float64(a[j*lda+i] * rhs[i])
}
}
// Check for scaling.
scale = 1.0
bi := blas64.Implementation()
i := bi.Idamax(n, rhs, 1)
if 2*smlnum*math.Abs(rhs[i]) > math.Abs(a[(n-1)*lda+(n-1)]) {
temp := 0.5 / math.Abs(rhs[i])
bi.Dscal(n, temp, rhs, 1)
scale *= temp
}
// Solve for U part.
for i := n - 1; i >= 0; i-- {
temp := 1.0 / a[i*lda+i]
rhs[i] *= temp
for j := i + 1; j < n; j++ {
rhs[i] -= float64(rhs[j] * (a[i*lda+j] * temp))
}
}
// Apply permutations jpiv to the solution (rhs).
impl.Dlaswp(1, rhs, 1, 0, n-1, jpiv[:n], -1)
return scale
}
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