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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 (
"gonum.org/v1/gonum/blas"
"gonum.org/v1/gonum/blas/blas64"
)
// Dgetrs solves a system of equations using an LU factorization.
// The system of equations solved is
// A * X = B if trans == blas.Trans
// Aᵀ * X = B if trans == blas.NoTrans
// A is a general n×n matrix with stride lda. B is a general matrix of size n×nrhs.
//
// On entry b contains the elements of the matrix B. On exit, b contains the
// elements of X, the solution to the system of equations.
//
// a and ipiv contain the LU factorization of A and the permutation indices as
// computed by Dgetrf. ipiv is zero-indexed.
func (impl Implementation) Dgetrs(trans blas.Transpose, n, nrhs int, a []float64, lda int, ipiv []int, b []float64, ldb int) {
switch {
case trans != blas.NoTrans && trans != blas.Trans && trans != blas.ConjTrans:
panic(badTrans)
case n < 0:
panic(nLT0)
case nrhs < 0:
panic(nrhsLT0)
case lda < max(1, n):
panic(badLdA)
case ldb < max(1, nrhs):
panic(badLdB)
}
// Quick return if possible.
if n == 0 || nrhs == 0 {
return
}
switch {
case len(a) < (n-1)*lda+n:
panic(shortA)
case len(b) < (n-1)*ldb+nrhs:
panic(shortB)
case len(ipiv) != n:
panic(badLenIpiv)
}
bi := blas64.Implementation()
if trans == blas.NoTrans {
// Solve A * X = B.
impl.Dlaswp(nrhs, b, ldb, 0, n-1, ipiv, 1)
// Solve L * X = B, updating b.
bi.Dtrsm(blas.Left, blas.Lower, blas.NoTrans, blas.Unit,
n, nrhs, 1, a, lda, b, ldb)
// Solve U * X = B, updating b.
bi.Dtrsm(blas.Left, blas.Upper, blas.NoTrans, blas.NonUnit,
n, nrhs, 1, a, lda, b, ldb)
return
}
// Solve Aᵀ * X = B.
// Solve Uᵀ * X = B, updating b.
bi.Dtrsm(blas.Left, blas.Upper, blas.Trans, blas.NonUnit,
n, nrhs, 1, a, lda, b, ldb)
// Solve Lᵀ * X = B, updating b.
bi.Dtrsm(blas.Left, blas.Lower, blas.Trans, blas.Unit,
n, nrhs, 1, a, lda, b, ldb)
impl.Dlaswp(nrhs, b, ldb, 0, n-1, ipiv, -1)
}