github.com/jingcheng-WU/gonum@v0.9.1-0.20210323123734-f1a2a11a8f7b/lapack/gonum/dpotrf.go (about)

     1  // Copyright ©2015 The Gonum Authors. All rights reserved.
     2  // Use of this source code is governed by a BSD-style
     3  // license that can be found in the LICENSE file.
     4  
     5  package gonum
     6  
     7  import (
     8  	"github.com/jingcheng-WU/gonum/blas"
     9  	"github.com/jingcheng-WU/gonum/blas/blas64"
    10  )
    11  
    12  // Dpotrf computes the Cholesky decomposition of the symmetric positive definite
    13  // matrix a. If ul == blas.Upper, then a is stored as an upper-triangular matrix,
    14  // and a = Uᵀ U is stored in place into a. If ul == blas.Lower, then a = L Lᵀ
    15  // is computed and stored in-place into a. If a is not positive definite, false
    16  // is returned. This is the blocked version of the algorithm.
    17  func (impl Implementation) Dpotrf(ul blas.Uplo, n int, a []float64, lda int) (ok bool) {
    18  	switch {
    19  	case ul != blas.Upper && ul != blas.Lower:
    20  		panic(badUplo)
    21  	case n < 0:
    22  		panic(nLT0)
    23  	case lda < max(1, n):
    24  		panic(badLdA)
    25  	}
    26  
    27  	// Quick return if possible.
    28  	if n == 0 {
    29  		return true
    30  	}
    31  
    32  	if len(a) < (n-1)*lda+n {
    33  		panic(shortA)
    34  	}
    35  
    36  	nb := impl.Ilaenv(1, "DPOTRF", string(ul), n, -1, -1, -1)
    37  	if nb <= 1 || n <= nb {
    38  		return impl.Dpotf2(ul, n, a, lda)
    39  	}
    40  	bi := blas64.Implementation()
    41  	if ul == blas.Upper {
    42  		for j := 0; j < n; j += nb {
    43  			jb := min(nb, n-j)
    44  			bi.Dsyrk(blas.Upper, blas.Trans, jb, j,
    45  				-1, a[j:], lda,
    46  				1, a[j*lda+j:], lda)
    47  			ok = impl.Dpotf2(blas.Upper, jb, a[j*lda+j:], lda)
    48  			if !ok {
    49  				return ok
    50  			}
    51  			if j+jb < n {
    52  				bi.Dgemm(blas.Trans, blas.NoTrans, jb, n-j-jb, j,
    53  					-1, a[j:], lda, a[j+jb:], lda,
    54  					1, a[j*lda+j+jb:], lda)
    55  				bi.Dtrsm(blas.Left, blas.Upper, blas.Trans, blas.NonUnit, jb, n-j-jb,
    56  					1, a[j*lda+j:], lda,
    57  					a[j*lda+j+jb:], lda)
    58  			}
    59  		}
    60  		return true
    61  	}
    62  	for j := 0; j < n; j += nb {
    63  		jb := min(nb, n-j)
    64  		bi.Dsyrk(blas.Lower, blas.NoTrans, jb, j,
    65  			-1, a[j*lda:], lda,
    66  			1, a[j*lda+j:], lda)
    67  		ok := impl.Dpotf2(blas.Lower, jb, a[j*lda+j:], lda)
    68  		if !ok {
    69  			return ok
    70  		}
    71  		if j+jb < n {
    72  			bi.Dgemm(blas.NoTrans, blas.Trans, n-j-jb, jb, j,
    73  				-1, a[(j+jb)*lda:], lda, a[j*lda:], lda,
    74  				1, a[(j+jb)*lda+j:], lda)
    75  			bi.Dtrsm(blas.Right, blas.Lower, blas.Trans, blas.NonUnit, n-j-jb, jb,
    76  				1, a[j*lda+j:], lda,
    77  				a[(j+jb)*lda+j:], lda)
    78  		}
    79  	}
    80  	return true
    81  }