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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"
)
// Dgetri computes the inverse of the matrix A using the LU factorization computed
// by Dgetrf. On entry, a contains the PLU decomposition of A as computed by
// Dgetrf and on exit contains the reciprocal of the original matrix.
//
// Dgetri will not perform the inversion if the matrix is singular, and returns
// a boolean indicating whether the inversion was successful.
//
// work is temporary storage, and lwork specifies the usable memory length.
// At minimum, lwork >= n and this function will panic otherwise.
// Dgetri is a blocked inversion, but the block size is limited
// by the temporary space available. If lwork == -1, instead of performing Dgetri,
// the optimal work length will be stored into work[0].
func (impl Implementation) Dgetri(n int, a []float64, lda int, ipiv []int, work []float64, lwork int) (ok bool) {
iws := max(1, n)
switch {
case n < 0:
panic(nLT0)
case lda < max(1, n):
panic(badLdA)
case lwork < iws && lwork != -1:
panic(badLWork)
case len(work) < max(1, lwork):
panic(shortWork)
}
if n == 0 {
work[0] = 1
return true
}
nb := impl.Ilaenv(1, "DGETRI", " ", n, -1, -1, -1)
if lwork == -1 {
work[0] = float64(n * nb)
return true
}
switch {
case len(a) < (n-1)*lda+n:
panic(shortA)
case len(ipiv) != n:
panic(badLenIpiv)
}
// Form inv(U).
ok = impl.Dtrtri(blas.Upper, blas.NonUnit, n, a, lda)
if !ok {
return false
}
nbmin := 2
if 1 < nb && nb < n {
iws = max(n*nb, 1)
if lwork < iws {
nb = lwork / n
nbmin = max(2, impl.Ilaenv(2, "DGETRI", " ", n, -1, -1, -1))
}
}
ldwork := nb
bi := blas64.Implementation()
// Solve the equation inv(A)*L = inv(U) for inv(A).
// TODO(btracey): Replace this with a more row-major oriented algorithm.
if nb < nbmin || n <= nb {
// Unblocked code.
for j := n - 1; j >= 0; j-- {
for i := j + 1; i < n; i++ {
// Copy current column of L to work and replace with zeros.
work[i] = a[i*lda+j]
a[i*lda+j] = 0
}
// Compute current column of inv(A).
if j < n-1 {
bi.Dgemv(blas.NoTrans, n, n-j-1, -1, a[(j+1):], lda, work[(j+1):], 1, 1, a[j:], lda)
}
}
} else {
// Blocked code.
nn := ((n - 1) / nb) * nb
for j := nn; j >= 0; j -= nb {
jb := min(nb, n-j)
// Copy current block column of L to work and replace
// with zeros.
for jj := j; jj < j+jb; jj++ {
for i := jj + 1; i < n; i++ {
work[i*ldwork+(jj-j)] = a[i*lda+jj]
a[i*lda+jj] = 0
}
}
// Compute current block column of inv(A).
if j+jb < n {
bi.Dgemm(blas.NoTrans, blas.NoTrans, n, jb, n-j-jb, -1, a[(j+jb):], lda, work[(j+jb)*ldwork:], ldwork, 1, a[j:], lda)
}
bi.Dtrsm(blas.Right, blas.Lower, blas.NoTrans, blas.Unit, n, jb, 1, work[j*ldwork:], ldwork, a[j:], lda)
}
}
// Apply column interchanges.
for j := n - 2; j >= 0; j-- {
jp := ipiv[j]
if jp != j {
bi.Dswap(n, a[j:], lda, a[jp:], lda)
}
}
work[0] = float64(iws)
return true
}