gonum.org/v1/gonum@v0.14.0/lapack/gonum/dgetf2.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  	"math"
     9  
    10  	"gonum.org/v1/gonum/blas/blas64"
    11  )
    12  
    13  // Dgetf2 computes the LU decomposition of the m×n matrix A.
    14  // The LU decomposition is a factorization of a into
    15  //
    16  //	A = P * L * U
    17  //
    18  // where P is a permutation matrix, L is a unit lower triangular matrix, and
    19  // U is a (usually) non-unit upper triangular matrix. On exit, L and U are stored
    20  // in place into a.
    21  //
    22  // ipiv is a permutation vector. It indicates that row i of the matrix was
    23  // changed with ipiv[i]. ipiv must have length at least min(m,n), and will panic
    24  // otherwise. ipiv is zero-indexed.
    25  //
    26  // Dgetf2 returns whether the matrix A is singular. The LU decomposition will
    27  // be computed regardless of the singularity of A, but division by zero
    28  // will occur if the false is returned and the result is used to solve a
    29  // system of equations.
    30  //
    31  // Dgetf2 is an internal routine. It is exported for testing purposes.
    32  func (Implementation) Dgetf2(m, n int, a []float64, lda int, ipiv []int) (ok bool) {
    33  	mn := min(m, n)
    34  	switch {
    35  	case m < 0:
    36  		panic(mLT0)
    37  	case n < 0:
    38  		panic(nLT0)
    39  	case lda < max(1, n):
    40  		panic(badLdA)
    41  	}
    42  
    43  	// Quick return if possible.
    44  	if mn == 0 {
    45  		return true
    46  	}
    47  
    48  	switch {
    49  	case len(a) < (m-1)*lda+n:
    50  		panic(shortA)
    51  	case len(ipiv) != mn:
    52  		panic(badLenIpiv)
    53  	}
    54  
    55  	bi := blas64.Implementation()
    56  
    57  	sfmin := dlamchS
    58  	ok = true
    59  	for j := 0; j < mn; j++ {
    60  		// Find a pivot and test for singularity.
    61  		jp := j + bi.Idamax(m-j, a[j*lda+j:], lda)
    62  		ipiv[j] = jp
    63  		if a[jp*lda+j] == 0 {
    64  			ok = false
    65  		} else {
    66  			// Swap the rows if necessary.
    67  			if jp != j {
    68  				bi.Dswap(n, a[j*lda:], 1, a[jp*lda:], 1)
    69  			}
    70  			if j < m-1 {
    71  				aj := a[j*lda+j]
    72  				if math.Abs(aj) >= sfmin {
    73  					bi.Dscal(m-j-1, 1/aj, a[(j+1)*lda+j:], lda)
    74  				} else {
    75  					for i := 0; i < m-j-1; i++ {
    76  						a[(j+1)*lda+j] = a[(j+1)*lda+j] / a[lda*j+j]
    77  					}
    78  				}
    79  			}
    80  		}
    81  		if j < mn-1 {
    82  			bi.Dger(m-j-1, n-j-1, -1, a[(j+1)*lda+j:], lda, a[j*lda+j+1:], 1, a[(j+1)*lda+j+1:], lda)
    83  		}
    84  	}
    85  	return ok
    86  }