custom-kube-scheduler/kubernetes/vendor/gonum.org/v1/gonum/lapack/gonum/dpbtf2.go

// Copyright ©2017 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"
)

// Dpbtf2 computes the Cholesky factorization of a symmetric positive banded
// matrix ab. The matrix ab is n×n with kd diagonal bands. The Cholesky
// factorization computed is
//  A = Uᵀ * U  if ul == blas.Upper
//  A = L * Lᵀ  if ul == blas.Lower
// ul also specifies the storage of ab. If ul == blas.Upper, then
// ab is stored as an upper-triangular banded matrix with kd super-diagonals,
// and if ul == blas.Lower, ab is stored as a lower-triangular banded matrix
// with kd sub-diagonals. On exit, the banded matrix U or L is stored in-place
// into ab depending on the value of ul. Dpbtf2 returns whether the factorization
// was successfully completed.
//
// The band storage scheme is illustrated below when n = 6, and kd = 2.
// The resulting Cholesky decomposition is stored in the same elements as the
// input band matrix (a11 becomes u11 or l11, etc.).
//
//  ul = blas.Upper
//  a11 a12 a13
//  a22 a23 a24
//  a33 a34 a35
//  a44 a45 a46
//  a55 a56  *
//  a66  *   *
//
//  ul = blas.Lower
//   *   *  a11
//   *  a21 a22
//  a31 a32 a33
//  a42 a43 a44
//  a53 a54 a55
//  a64 a65 a66
//
// Dpbtf2 is the unblocked version of the algorithm, see Dpbtrf for the blocked
// version.
//
// Dpbtf2 is an internal routine, exported for testing purposes.
func (Implementation) Dpbtf2(uplo blas.Uplo, n, kd int, ab []float64, ldab int) (ok bool) {
	switch {
	case uplo != blas.Upper && uplo != blas.Lower:
		panic(badUplo)
	case n < 0:
		panic(nLT0)
	case kd < 0:
		panic(kdLT0)
	case ldab < kd+1:
		panic(badLdA)
	}

	// Quick return if possible.
	if n == 0 {
		return true
	}

	if len(ab) < (n-1)*ldab+kd+1 {
		panic(shortAB)
	}

	bi := blas64.Implementation()

	kld := max(1, ldab-1)
	if uplo == blas.Upper {
		// Compute the Cholesky factorization A = Uᵀ * U.
		for j := 0; j < n; j++ {
			// Compute U(j,j) and test for non-positive-definiteness.
			ajj := ab[j*ldab]
			if ajj <= 0 {
				return false
			}
			ajj = math.Sqrt(ajj)
			ab[j*ldab] = ajj
			// Compute elements j+1:j+kn of row j and update the trailing submatrix
			// within the band.
			kn := min(kd, n-j-1)
			if kn > 0 {
				bi.Dscal(kn, 1/ajj, ab[j*ldab+1:], 1)
				bi.Dsyr(blas.Upper, kn, -1, ab[j*ldab+1:], 1, ab[(j+1)*ldab:], kld)
			}
		}
		return true
	}
	// Compute the Cholesky factorization A = L * Lᵀ.
	for j := 0; j < n; j++ {
		// Compute L(j,j) and test for non-positive-definiteness.
		ajj := ab[j*ldab+kd]
		if ajj <= 0 {
			return false
		}
		ajj = math.Sqrt(ajj)
		ab[j*ldab+kd] = ajj
		// Compute elements j+1:j+kn of column j and update the trailing submatrix
		// within the band.
		kn := min(kd, n-j-1)
		if kn > 0 {
			bi.Dscal(kn, 1/ajj, ab[(j+1)*ldab+kd-1:], kld)
			bi.Dsyr(blas.Lower, kn, -1, ab[(j+1)*ldab+kd-1:], kld, ab[(j+1)*ldab+kd:], kld)
		}
	}
	return true
}