gonum.org/v1/gonum@v0.15.1-0.20240517103525-f853624cb1bb/lapack/gonum/dorgl2.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  	"gonum.org/v1/gonum/blas"
     9  	"gonum.org/v1/gonum/blas/blas64"
    10  )
    11  
    12  // Dorgl2 generates an m×n matrix Q with orthonormal rows defined as the first m
    13  // rows of a product of k elementary reflectors of order n
    14  //
    15  //	Q = H_{k-1} * ... * H_0
    16  //
    17  // as returned by Dgelqf.
    18  //
    19  // On entry, tau and the first k rows of A must contain the scalar factors and
    20  // the vectors, respectively, which define the elementary reflectors H_i,
    21  // i=0,...,k-1, as returned by Dgelqf. On return, A contains the matrix Q.
    22  //
    23  // tau must have length at least k, work must have length at least m, and it
    24  // must hold that 0 <= k <= m <= n, otherwise Dorgl2 will panic.
    25  //
    26  // Dorgl2 is an internal routine. It is exported for testing purposes.
    27  func (impl Implementation) Dorgl2(m, n, k int, a []float64, lda int, tau, work []float64) {
    28  	switch {
    29  	case m < 0:
    30  		panic(mLT0)
    31  	case n < m:
    32  		panic(nLTM)
    33  	case k < 0:
    34  		panic(kLT0)
    35  	case k > m:
    36  		panic(kGTM)
    37  	case lda < max(1, n):
    38  		panic(badLdA)
    39  	}
    40  
    41  	if m == 0 {
    42  		return
    43  	}
    44  
    45  	switch {
    46  	case len(a) < (m-1)*lda+n:
    47  		panic(shortA)
    48  	case len(tau) < k:
    49  		panic(shortTau)
    50  	case len(work) < m:
    51  		panic(shortWork)
    52  	}
    53  
    54  	bi := blas64.Implementation()
    55  
    56  	if k < m {
    57  		for i := k; i < m; i++ {
    58  			for j := 0; j < n; j++ {
    59  				a[i*lda+j] = 0
    60  			}
    61  		}
    62  		for j := k; j < m; j++ {
    63  			a[j*lda+j] = 1
    64  		}
    65  	}
    66  	for i := k - 1; i >= 0; i-- {
    67  		if i < n-1 {
    68  			if i < m-1 {
    69  				a[i*lda+i] = 1
    70  				impl.Dlarf(blas.Right, m-i-1, n-i, a[i*lda+i:], 1, tau[i], a[(i+1)*lda+i:], lda, work)
    71  			}
    72  			bi.Dscal(n-i-1, -tau[i], a[i*lda+i+1:], 1)
    73  		}
    74  		a[i*lda+i] = 1 - tau[i]
    75  		for l := 0; l < i; l++ {
    76  			a[i*lda+l] = 0
    77  		}
    78  	}
    79  }