github.com/jingcheng-WU/gonum@v0.9.1-0.20210323123734-f1a2a11a8f7b/lapack/gonum/dorg2r.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  // Dorg2r generates an m×n matrix Q with orthonormal columns defined by the
    13  // product of elementary reflectors as computed by Dgeqrf.
    14  //  Q = H_0 * H_1 * ... * H_{k-1}
    15  // len(tau) >= k, 0 <= k <= n, 0 <= n <= m, len(work) >= n.
    16  // Dorg2r will panic if these conditions are not met.
    17  //
    18  // Dorg2r is an internal routine. It is exported for testing purposes.
    19  func (impl Implementation) Dorg2r(m, n, k int, a []float64, lda int, tau []float64, work []float64) {
    20  	switch {
    21  	case m < 0:
    22  		panic(mLT0)
    23  	case n < 0:
    24  		panic(nLT0)
    25  	case n > m:
    26  		panic(nGTM)
    27  	case k < 0:
    28  		panic(kLT0)
    29  	case k > n:
    30  		panic(kGTN)
    31  	case lda < max(1, n):
    32  		panic(badLdA)
    33  	}
    34  
    35  	if n == 0 {
    36  		return
    37  	}
    38  
    39  	switch {
    40  	case len(a) < (m-1)*lda+n:
    41  		panic(shortA)
    42  	case len(tau) < k:
    43  		panic(shortTau)
    44  	case len(work) < n:
    45  		panic(shortWork)
    46  	}
    47  
    48  	bi := blas64.Implementation()
    49  
    50  	// Initialize columns k+1:n to columns of the unit matrix.
    51  	for l := 0; l < m; l++ {
    52  		for j := k; j < n; j++ {
    53  			a[l*lda+j] = 0
    54  		}
    55  	}
    56  	for j := k; j < n; j++ {
    57  		a[j*lda+j] = 1
    58  	}
    59  	for i := k - 1; i >= 0; i-- {
    60  		for i := range work {
    61  			work[i] = 0
    62  		}
    63  		if i < n-1 {
    64  			a[i*lda+i] = 1
    65  			impl.Dlarf(blas.Left, m-i, n-i-1, a[i*lda+i:], lda, tau[i], a[i*lda+i+1:], lda, work)
    66  		}
    67  		if i < m-1 {
    68  			bi.Dscal(m-i-1, -tau[i], a[(i+1)*lda+i:], lda)
    69  		}
    70  		a[i*lda+i] = 1 - tau[i]
    71  		for l := 0; l < i; l++ {
    72  			a[l*lda+i] = 0
    73  		}
    74  	}
    75  }