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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"
)
// Dtrtri computes the inverse of a triangular matrix, storing the result in place
// into a. This is the BLAS level 3 version of the algorithm which builds upon
// Dtrti2 to operate on matrix blocks instead of only individual columns.
//
// Dtrtri will not perform the inversion if the matrix is singular, and returns
// a boolean indicating whether the inversion was successful.
func (impl Implementation) Dtrtri(uplo blas.Uplo, diag blas.Diag, n int, a []float64, lda int) (ok bool) {
switch {
case uplo != blas.Upper && uplo != blas.Lower:
panic(badUplo)
case diag != blas.NonUnit && diag != blas.Unit:
panic(badDiag)
case n < 0:
panic(nLT0)
case lda < max(1, n):
panic(badLdA)
}
if n == 0 {
return true
}
if len(a) < (n-1)*lda+n {
panic(shortA)
}
if diag == blas.NonUnit {
for i := 0; i < n; i++ {
if a[i*lda+i] == 0 {
return false
}
}
}
bi := blas64.Implementation()
nb := impl.Ilaenv(1, "DTRTRI", "UD", n, -1, -1, -1)
if nb <= 1 || nb > n {
impl.Dtrti2(uplo, diag, n, a, lda)
return true
}
if uplo == blas.Upper {
for j := 0; j < n; j += nb {
jb := min(nb, n-j)
bi.Dtrmm(blas.Left, blas.Upper, blas.NoTrans, diag, j, jb, 1, a, lda, a[j:], lda)
bi.Dtrsm(blas.Right, blas.Upper, blas.NoTrans, diag, j, jb, -1, a[j*lda+j:], lda, a[j:], lda)
impl.Dtrti2(blas.Upper, diag, jb, a[j*lda+j:], lda)
}
return true
}
nn := ((n - 1) / nb) * nb
for j := nn; j >= 0; j -= nb {
jb := min(nb, n-j)
if j+jb <= n-1 {
bi.Dtrmm(blas.Left, blas.Lower, blas.NoTrans, diag, n-j-jb, jb, 1, a[(j+jb)*lda+j+jb:], lda, a[(j+jb)*lda+j:], lda)
bi.Dtrsm(blas.Right, blas.Lower, blas.NoTrans, diag, n-j-jb, jb, -1, a[j*lda+j:], lda, a[(j+jb)*lda+j:], lda)
}
impl.Dtrti2(blas.Lower, diag, jb, a[j*lda+j:], lda)
}
return true
}