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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 }