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