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93 lines
2.6 KiB
Go
93 lines
2.6 KiB
Go
// Copyright ©2015 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 native
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import (
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"gonum.org/v1/gonum/blas"
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"gonum.org/v1/gonum/blas/blas64"
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)
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// Dgetri computes the inverse of the matrix A using the LU factorization computed
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// by Dgetrf. On entry, a contains the PLU decomposition of A as computed by
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// Dgetrf and on exit contains the reciprocal of the original matrix.
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//
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// Dgetri will not perform the inversion if the matrix is singular, and returns
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// a boolean indicating whether the inversion was successful.
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//
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// work is temporary storage, and lwork specifies the usable memory length.
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// At minimum, lwork >= n and this function will panic otherwise.
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// Dgetri is a blocked inversion, but the block size is limited
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// by the temporary space available. If lwork == -1, instead of performing Dgetri,
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// the optimal work length will be stored into work[0].
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func (impl Implementation) Dgetri(n int, a []float64, lda int, ipiv []int, work []float64, lwork int) (ok bool) {
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checkMatrix(n, n, a, lda)
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if len(ipiv) < n {
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panic(badIpiv)
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}
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nb := impl.Ilaenv(1, "DGETRI", " ", n, -1, -1, -1)
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if lwork == -1 {
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work[0] = float64(n * nb)
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return true
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}
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if lwork < n {
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panic(badWork)
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}
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if len(work) < lwork {
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panic(badWork)
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}
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if n == 0 {
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return true
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}
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ok = impl.Dtrtri(blas.Upper, blas.NonUnit, n, a, lda)
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if !ok {
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return false
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}
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nbmin := 2
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ldwork := nb
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if nb > 1 && nb < n {
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iws := max(ldwork*n, 1)
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if lwork < iws {
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nb = lwork / ldwork
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nbmin = max(2, impl.Ilaenv(2, "DGETRI", " ", n, -1, -1, -1))
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}
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}
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bi := blas64.Implementation()
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// TODO(btracey): Replace this with a more row-major oriented algorithm.
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if nb < nbmin || nb >= n {
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// Unblocked code.
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for j := n - 1; j >= 0; j-- {
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for i := j + 1; i < n; i++ {
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work[i*ldwork] = a[i*lda+j]
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a[i*lda+j] = 0
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}
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if j < n {
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bi.Dgemv(blas.NoTrans, n, n-j-1, -1, a[(j+1):], lda, work[(j+1)*ldwork:], ldwork, 1, a[j:], lda)
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}
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}
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} else {
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nn := ((n - 1) / nb) * nb
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for j := nn; j >= 0; j -= nb {
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jb := min(nb, n-j)
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for jj := j; jj < j+jb-1; jj++ {
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for i := jj + 1; i < n; i++ {
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work[i*ldwork+(jj-j)] = a[i*lda+jj]
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a[i*lda+jj] = 0
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}
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}
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if j+jb < n {
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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)
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bi.Dtrsm(blas.Right, blas.Lower, blas.NoTrans, blas.Unit, n, jb, 1, work[j*ldwork:], ldwork, a[j:], lda)
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}
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}
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}
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for j := n - 2; j >= 0; j-- {
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jp := ipiv[j]
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if jp != j {
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bi.Dswap(n, a[j:], lda, a[jp:], lda)
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}
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}
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return true
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}
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