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[bytom/vapor.git] / vendor / gonum.org / v1 / gonum / lapack / gonum / dpbtf2.go

diff --git a/vendor/gonum.org/v1/gonum/lapack/gonum/dpbtf2.go b/vendor/gonum.org/v1/gonum/lapack/gonum/dpbtf2.go
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+// 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 = U^T * U if ul == blas.Upper
+//  A = L * L^T 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(ul blas.Uplo, n, kd int, ab []float64, ldab int) (ok bool) {
+       if ul != blas.Upper && ul != blas.Lower {
+               panic(badUplo)
+       }
+       checkSymBanded(ab, n, kd, ldab)
+       if n == 0 {
+               return
+       }
+       bi := blas64.Implementation()
+       kld := max(1, ldab-1)
+       if ul == blas.Upper {
+               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
+       }
+       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
+}