github.com/gonum/lapack@v0.0.0-20181123203213-e4cdc5a0bff9/native/dgebd2.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 "github.com/gonum/blas"
     8  
     9  // Dgebd2 reduces an m×n matrix A to upper or lower bidiagonal form by an orthogonal
    10  // transformation.
    11  //  Q^T * A * P = B
    12  // if m >= n, B is upper diagonal, otherwise B is lower bidiagonal.
    13  // d is the diagonal, len = min(m,n)
    14  // e is the off-diagonal len = min(m,n)-1
    15  //
    16  // Dgebd2 is an internal routine. It is exported for testing purposes.
    17  func (impl Implementation) Dgebd2(m, n int, a []float64, lda int, d, e, tauQ, tauP, work []float64) {
    18  	checkMatrix(m, n, a, lda)
    19  	if len(d) < min(m, n) {
    20  		panic(badD)
    21  	}
    22  	if len(e) < min(m, n)-1 {
    23  		panic(badE)
    24  	}
    25  	if len(tauQ) < min(m, n) {
    26  		panic(badTauQ)
    27  	}
    28  	if len(tauP) < min(m, n) {
    29  		panic(badTauP)
    30  	}
    31  	if len(work) < max(m, n) {
    32  		panic(badWork)
    33  	}
    34  	if m >= n {
    35  		for i := 0; i < n; i++ {
    36  			a[i*lda+i], tauQ[i] = impl.Dlarfg(m-i, a[i*lda+i], a[min(i+1, m-1)*lda+i:], lda)
    37  			d[i] = a[i*lda+i]
    38  			a[i*lda+i] = 1
    39  			// Apply H_i to A[i:m, i+1:n] from the left.
    40  			if i < n-1 {
    41  				impl.Dlarf(blas.Left, m-i, n-i-1, a[i*lda+i:], lda, tauQ[i], a[i*lda+i+1:], lda, work)
    42  			}
    43  			a[i*lda+i] = d[i]
    44  			if i < n-1 {
    45  				a[i*lda+i+1], tauP[i] = impl.Dlarfg(n-i-1, a[i*lda+i+1], a[i*lda+min(i+2, n-1):], 1)
    46  				e[i] = a[i*lda+i+1]
    47  				a[i*lda+i+1] = 1
    48  				impl.Dlarf(blas.Right, m-i-1, n-i-1, a[i*lda+i+1:], 1, tauP[i], a[(i+1)*lda+i+1:], lda, work)
    49  				a[i*lda+i+1] = e[i]
    50  			} else {
    51  				tauP[i] = 0
    52  			}
    53  		}
    54  		return
    55  	}
    56  	for i := 0; i < m; i++ {
    57  		a[i*lda+i], tauP[i] = impl.Dlarfg(n-i, a[i*lda+i], a[i*lda+min(i+1, n-1):], 1)
    58  		d[i] = a[i*lda+i]
    59  		a[i*lda+i] = 1
    60  		if i < m-1 {
    61  			impl.Dlarf(blas.Right, m-i-1, n-i, a[i*lda+i:], 1, tauP[i], a[(i+1)*lda+i:], lda, work)
    62  		}
    63  		a[i*lda+i] = d[i]
    64  		if i < m-1 {
    65  			a[(i+1)*lda+i], tauQ[i] = impl.Dlarfg(m-i-1, a[(i+1)*lda+i], a[min(i+2, m-1)*lda+i:], lda)
    66  			e[i] = a[(i+1)*lda+i]
    67  			a[(i+1)*lda+i] = 1
    68  			impl.Dlarf(blas.Left, m-i-1, n-i-1, a[(i+1)*lda+i:], lda, tauQ[i], a[(i+1)*lda+i+1:], lda, work)
    69  			a[(i+1)*lda+i] = e[i]
    70  		} else {
    71  			tauQ[i] = 0
    72  		}
    73  	}
    74  }