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// Copyright ©2018 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"
)
// Dlauum computes the product
//
// U * Uᵀ if uplo is blas.Upper
// Lᵀ * L if uplo is blas.Lower
//
// where U or L is stored in the upper or lower triangular part of A.
// Only the upper or lower triangle of the result is stored, overwriting
// the corresponding factor in A.
func (impl Implementation) Dlauum(uplo blas.Uplo, n int, a []float64, lda int) {
switch {
case uplo != blas.Upper && uplo != blas.Lower:
panic(badUplo)
case n < 0:
panic(nLT0)
case lda < max(1, n):
panic(badLdA)
}
// Quick return if possible.
if n == 0 {
return
}
if len(a) < (n-1)*lda+n {
panic(shortA)
}
// Determine the block size.
opts := "U"
if uplo == blas.Lower {
opts = "L"
}
nb := impl.Ilaenv(1, "DLAUUM", opts, n, -1, -1, -1)
if nb <= 1 || n <= nb {
// Use unblocked code.
impl.Dlauu2(uplo, n, a, lda)
return
}
// Use blocked code.
bi := blas64.Implementation()
if uplo == blas.Upper {
// Compute the product U*Uᵀ.
for i := 0; i < n; i += nb {
ib := min(nb, n-i)
bi.Dtrmm(blas.Right, blas.Upper, blas.Trans, blas.NonUnit,
i, ib, 1, a[i*lda+i:], lda, a[i:], lda)
impl.Dlauu2(blas.Upper, ib, a[i*lda+i:], lda)
if n-i-ib > 0 {
bi.Dgemm(blas.NoTrans, blas.Trans, i, ib, n-i-ib,
1, a[i+ib:], lda, a[i*lda+i+ib:], lda, 1, a[i:], lda)
bi.Dsyrk(blas.Upper, blas.NoTrans, ib, n-i-ib,
1, a[i*lda+i+ib:], lda, 1, a[i*lda+i:], lda)
}
}
} else {
// Compute the product Lᵀ*L.
for i := 0; i < n; i += nb {
ib := min(nb, n-i)
bi.Dtrmm(blas.Left, blas.Lower, blas.Trans, blas.NonUnit,
ib, i, 1, a[i*lda+i:], lda, a[i*lda:], lda)
impl.Dlauu2(blas.Lower, ib, a[i*lda+i:], lda)
if n-i-ib > 0 {
bi.Dgemm(blas.Trans, blas.NoTrans, ib, i, n-i-ib,
1, a[(i+ib)*lda+i:], lda, a[(i+ib)*lda:], lda, 1, a[i*lda:], lda)
bi.Dsyrk(blas.Lower, blas.Trans, ib, n-i-ib,
1, a[(i+ib)*lda+i:], lda, 1, a[i*lda+i:], lda)
}
}
}
}
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