gonum.org/v1/gonum@v0.14.0/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  	"gonum.org/v1/gonum/blas"
     9  	"gonum.org/v1/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  //
    15  //	Q = H_0 * H_1 * ... * H_{k-1}
    16  //
    17  // len(tau) >= k, 0 <= k <= n, 0 <= n <= m, len(work) >= n.
    18  // Dorg2r will panic if these conditions are not met.
    19  //
    20  // Dorg2r is an internal routine. It is exported for testing purposes.
    21  func (impl Implementation) Dorg2r(m, n, k int, a []float64, lda int, tau []float64, work []float64) {
    22  	switch {
    23  	case m < 0:
    24  		panic(mLT0)
    25  	case n < 0:
    26  		panic(nLT0)
    27  	case n > m:
    28  		panic(nGTM)
    29  	case k < 0:
    30  		panic(kLT0)
    31  	case k > n:
    32  		panic(kGTN)
    33  	case lda < max(1, n):
    34  		panic(badLdA)
    35  	}
    36  
    37  	if n == 0 {
    38  		return
    39  	}
    40  
    41  	switch {
    42  	case len(a) < (m-1)*lda+n:
    43  		panic(shortA)
    44  	case len(tau) < k:
    45  		panic(shortTau)
    46  	case len(work) < n:
    47  		panic(shortWork)
    48  	}
    49  
    50  	bi := blas64.Implementation()
    51  
    52  	// Initialize columns k+1:n to columns of the unit matrix.
    53  	for l := 0; l < m; l++ {
    54  		for j := k; j < n; j++ {
    55  			a[l*lda+j] = 0
    56  		}
    57  	}
    58  	for j := k; j < n; j++ {
    59  		a[j*lda+j] = 1
    60  	}
    61  	for i := k - 1; i >= 0; i-- {
    62  		for i := range work {
    63  			work[i] = 0
    64  		}
    65  		if i < n-1 {
    66  			a[i*lda+i] = 1
    67  			impl.Dlarf(blas.Left, m-i, n-i-1, a[i*lda+i:], lda, tau[i], a[i*lda+i+1:], lda, work)
    68  		}
    69  		if i < m-1 {
    70  			bi.Dscal(m-i-1, -tau[i], a[(i+1)*lda+i:], lda)
    71  		}
    72  		a[i*lda+i] = 1 - tau[i]
    73  		for l := 0; l < i; l++ {
    74  			a[l*lda+i] = 0
    75  		}
    76  	}
    77  }