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// Copyright ©2017 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"
// Dgerq2 computes an RQ factorization of the m×n matrix A,
//
// A = R * Q.
//
// On exit, if m <= n, the upper triangle of the subarray
// A[0:m, n-m:n] contains the m×m upper triangular matrix R.
// If m >= n, the elements on and above the (m-n)-th subdiagonal
// contain the m×n upper trapezoidal matrix R.
// The remaining elements, with tau, represent the
// orthogonal matrix Q as a product of min(m,n) elementary
// reflectors.
//
// The matrix Q is represented as a product of elementary reflectors
//
// Q = H_0 H_1 . . . H_{min(m,n)-1}.
//
// Each H(i) has the form
//
// H_i = I - tau_i * v * vᵀ
//
// where v is a vector with v[0:n-k+i-1] stored in A[m-k+i, 0:n-k+i-1],
// v[n-k+i:n] = 0 and v[n-k+i] = 1.
//
// tau must have length min(m,n) and work must have length m, otherwise
// Dgerq2 will panic.
//
// Dgerq2 is an internal routine. It is exported for testing purposes.
func (impl Implementation) Dgerq2(m, n int, a []float64, lda int, tau, work []float64) {
switch {
case m < 0:
panic(mLT0)
case n < 0:
panic(nLT0)
case lda < max(1, n):
panic(badLdA)
case len(work) < m:
panic(shortWork)
}
// Quick return if possible.
k := min(m, n)
if k == 0 {
return
}
switch {
case len(a) < (m-1)*lda+n:
panic(shortA)
case len(tau) < k:
panic(shortTau)
}
for i := k - 1; i >= 0; i-- {
// Generate elementary reflector H[i] to annihilate
// A[m-k+i, 0:n-k+i-1].
mki := m - k + i
nki := n - k + i
var aii float64
aii, tau[i] = impl.Dlarfg(nki+1, a[mki*lda+nki], a[mki*lda:], 1)
// Apply H[i] to A[0:m-k+i-1, 0:n-k+i] from the right.
a[mki*lda+nki] = 1
impl.Dlarf(blas.Right, mki, nki+1, a[mki*lda:], 1, tau[i], a, lda, work)
a[mki*lda+nki] = aii
}
}
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