github.com/gonum/lapack@v0.0.0-20181123203213-e4cdc5a0bff9/native/dgeqrf.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 native
     6  
     7  import (
     8  	"github.com/gonum/blas"
     9  	"github.com/gonum/lapack"
    10  )
    11  
    12  // Dgeqrf computes the QR factorization of the m×n matrix A using a blocked
    13  // algorithm. See the documentation for Dgeqr2 for a description of the
    14  // parameters at entry and exit.
    15  //
    16  // work is temporary storage, and lwork specifies the usable memory length.
    17  // The length of work must be at least max(1, lwork) and lwork must be -1
    18  // or at least n, otherwise this function will panic.
    19  // Dgeqrf is a blocked QR factorization, but the block size is limited
    20  // by the temporary space available. If lwork == -1, instead of performing Dgeqrf,
    21  // the optimal work length will be stored into work[0].
    22  //
    23  // tau must have length at least min(m,n), and this function will panic otherwise.
    24  func (impl Implementation) Dgeqrf(m, n int, a []float64, lda int, tau, work []float64, lwork int) {
    25  	if len(work) < max(1, lwork) {
    26  		panic(shortWork)
    27  	}
    28  	// nb is the optimal blocksize, i.e. the number of columns transformed at a time.
    29  	nb := impl.Ilaenv(1, "DGEQRF", " ", m, n, -1, -1)
    30  	lworkopt := n * max(nb, 1)
    31  	lworkopt = max(n, lworkopt)
    32  	if lwork == -1 {
    33  		work[0] = float64(lworkopt)
    34  		return
    35  	}
    36  	checkMatrix(m, n, a, lda)
    37  	if lwork < n {
    38  		panic(badWork)
    39  	}
    40  	k := min(m, n)
    41  	if len(tau) < k {
    42  		panic(badTau)
    43  	}
    44  	if k == 0 {
    45  		work[0] = float64(lworkopt)
    46  		return
    47  	}
    48  	nbmin := 2 // Minimal block size.
    49  	var nx int // Use unblocked (unless changed in the next for loop)
    50  	iws := n
    51  	ldwork := nb
    52  	// Only consider blocked if the suggested block size is > 1 and the
    53  	// number of rows or columns is sufficiently large.
    54  	if 1 < nb && nb < k {
    55  		// nx is the block size at which the code switches from blocked
    56  		// to unblocked.
    57  		nx = max(0, impl.Ilaenv(3, "DGEQRF", " ", m, n, -1, -1))
    58  		if k > nx {
    59  			iws = ldwork * n
    60  			if lwork < iws {
    61  				// Not enough workspace to use the optimal block
    62  				// size. Get the minimum block size instead.
    63  				nb = lwork / n
    64  				nbmin = max(2, impl.Ilaenv(2, "DGEQRF", " ", m, n, -1, -1))
    65  			}
    66  		}
    67  	}
    68  	for i := range work {
    69  		work[i] = 0
    70  	}
    71  	// Compute QR using a blocked algorithm.
    72  	var i int
    73  	if nbmin <= nb && nb < k && nx < k {
    74  		for i = 0; i < k-nx; i += nb {
    75  			ib := min(k-i, nb)
    76  			// Compute the QR factorization of the current block.
    77  			impl.Dgeqr2(m-i, ib, a[i*lda+i:], lda, tau[i:], work)
    78  			if i+ib < n {
    79  				// Form the triangular factor of the block reflector and apply H^T
    80  				// In Dlarft, work becomes the T matrix.
    81  				impl.Dlarft(lapack.Forward, lapack.ColumnWise, m-i, ib,
    82  					a[i*lda+i:], lda,
    83  					tau[i:],
    84  					work, ldwork)
    85  				impl.Dlarfb(blas.Left, blas.Trans, lapack.Forward, lapack.ColumnWise,
    86  					m-i, n-i-ib, ib,
    87  					a[i*lda+i:], lda,
    88  					work, ldwork,
    89  					a[i*lda+i+ib:], lda,
    90  					work[ib*ldwork:], ldwork)
    91  			}
    92  		}
    93  	}
    94  	// Call unblocked code on the remaining columns.
    95  	if i < k {
    96  		impl.Dgeqr2(m-i, n-i, a[i*lda+i:], lda, tau[i:], work)
    97  	}
    98  	work[0] = float64(lworkopt)
    99  }