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// Copyright ©2015 The Gonum Authors. All rights reserved.
// Use of this source code is governed by a BSD-style
// license that can be found in the LICENSE file.
package gonum
import "gonum.org/v1/gonum/blas"
// Dgebd2 reduces an m×n matrix A to upper or lower bidiagonal form by an orthogonal
// transformation.
// Qᵀ * A * P = B
// if m >= n, B is upper diagonal, otherwise B is lower bidiagonal.
// d is the diagonal, len = min(m,n)
// e is the off-diagonal len = min(m,n)-1
//
// Dgebd2 is an internal routine. It is exported for testing purposes.
func (impl Implementation) Dgebd2(m, n int, a []float64, lda int, d, e, tauQ, tauP, work []float64) {
switch {
case m < 0:
panic(mLT0)
case n < 0:
panic(nLT0)
case lda < max(1, n):
panic(badLdA)
}
// Quick return if possible.
minmn := min(m, n)
if minmn == 0 {
return
}
switch {
case len(d) < minmn:
panic(shortD)
case len(e) < minmn-1:
panic(shortE)
case len(tauQ) < minmn:
panic(shortTauQ)
case len(tauP) < minmn:
panic(shortTauP)
case len(work) < max(m, n):
panic(shortWork)
}
if m >= n {
for i := 0; i < n; i++ {
a[i*lda+i], tauQ[i] = impl.Dlarfg(m-i, a[i*lda+i], a[min(i+1, m-1)*lda+i:], lda)
d[i] = a[i*lda+i]
a[i*lda+i] = 1
// Apply H_i to A[i:m, i+1:n] from the left.
if i < n-1 {
impl.Dlarf(blas.Left, m-i, n-i-1, a[i*lda+i:], lda, tauQ[i], a[i*lda+i+1:], lda, work)
}
a[i*lda+i] = d[i]
if i < n-1 {
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)
e[i] = a[i*lda+i+1]
a[i*lda+i+1] = 1
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)
a[i*lda+i+1] = e[i]
} else {
tauP[i] = 0
}
}
return
}
for i := 0; i < m; i++ {
a[i*lda+i], tauP[i] = impl.Dlarfg(n-i, a[i*lda+i], a[i*lda+min(i+1, n-1):], 1)
d[i] = a[i*lda+i]
a[i*lda+i] = 1
if i < m-1 {
impl.Dlarf(blas.Right, m-i-1, n-i, a[i*lda+i:], 1, tauP[i], a[(i+1)*lda+i:], lda, work)
}
a[i*lda+i] = d[i]
if i < m-1 {
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)
e[i] = a[(i+1)*lda+i]
a[(i+1)*lda+i] = 1
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)
a[(i+1)*lda+i] = e[i]
} else {
tauQ[i] = 0
}
}
}