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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 (
"math"
"gonum.org/v1/gonum/blas"
"gonum.org/v1/gonum/blas/blas64"
)
// Dpotf2 computes the Cholesky decomposition of the symmetric positive definite
// matrix a. If ul == blas.Upper, then a is stored as an upper-triangular matrix,
// and a = Uᵀ U is stored in place into a. If ul == blas.Lower, then a = L Lᵀ
// is computed and stored in-place into a. If a is not positive definite, false
// is returned. This is the unblocked version of the algorithm.
//
// Dpotf2 is an internal routine. It is exported for testing purposes.
func (Implementation) Dpotf2(ul blas.Uplo, n int, a []float64, lda int) (ok bool) {
switch {
case ul != blas.Upper && ul != blas.Lower:
panic(badUplo)
case n < 0:
panic(nLT0)
case lda < max(1, n):
panic(badLdA)
}
// Quick return if possible.
if n == 0 {
return true
}
if len(a) < (n-1)*lda+n {
panic(shortA)
}
bi := blas64.Implementation()
if ul == blas.Upper {
for j := 0; j < n; j++ {
ajj := a[j*lda+j]
if j != 0 {
ajj -= bi.Ddot(j, a[j:], lda, a[j:], lda)
}
if ajj <= 0 || math.IsNaN(ajj) {
a[j*lda+j] = ajj
return false
}
ajj = math.Sqrt(ajj)
a[j*lda+j] = ajj
if j < n-1 {
bi.Dgemv(blas.Trans, j, n-j-1,
-1, a[j+1:], lda, a[j:], lda,
1, a[j*lda+j+1:], 1)
bi.Dscal(n-j-1, 1/ajj, a[j*lda+j+1:], 1)
}
}
return true
}
for j := 0; j < n; j++ {
ajj := a[j*lda+j]
if j != 0 {
ajj -= bi.Ddot(j, a[j*lda:], 1, a[j*lda:], 1)
}
if ajj <= 0 || math.IsNaN(ajj) {
a[j*lda+j] = ajj
return false
}
ajj = math.Sqrt(ajj)
a[j*lda+j] = ajj
if j < n-1 {
bi.Dgemv(blas.NoTrans, n-j-1, j,
-1, a[(j+1)*lda:], lda, a[j*lda:], 1,
1, a[(j+1)*lda+j:], lda)
bi.Dscal(n-j-1, 1/ajj, a[(j+1)*lda+j:], lda)
}
}
return true
}