github.com/jingcheng-WU/gonum@v0.9.1-0.20210323123734-f1a2a11a8f7b/lapack/gonum/dorgbr.go

// 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 "github.com/jingcheng-WU/gonum/lapack"

// Dorgbr generates one of the matrices Q or Pᵀ computed by Dgebrd
// computed from the decomposition Dgebrd. See Dgebd2 for the description of
// Q and Pᵀ.
//
// If vect == lapack.GenerateQ, then a is assumed to have been an m×k matrix and
// Q is of order m. If m >= k, then Dorgbr returns the first n columns of Q
// where m >= n >= k. If m < k, then Dorgbr returns Q as an m×m matrix.
//
// If vect == lapack.GeneratePT, then A is assumed to have been a k×n matrix, and
// Pᵀ is of order n. If k < n, then Dorgbr returns the first m rows of Pᵀ,
// where n >= m >= k. If k >= n, then Dorgbr returns Pᵀ as an n×n matrix.
//
// Dorgbr is an internal routine. It is exported for testing purposes.
func (impl Implementation) Dorgbr(vect lapack.GenOrtho, m, n, k int, a []float64, lda int, tau, work []float64, lwork int) {
	wantq := vect == lapack.GenerateQ
	mn := min(m, n)
	switch {
	case vect != lapack.GenerateQ && vect != lapack.GeneratePT:
		panic(badGenOrtho)
	case m < 0:
		panic(mLT0)
	case n < 0:
		panic(nLT0)
	case k < 0:
		panic(kLT0)
	case wantq && n > m:
		panic(nGTM)
	case wantq && n < min(m, k):
		panic("lapack: n < min(m,k)")
	case !wantq && m > n:
		panic(mGTN)
	case !wantq && m < min(n, k):
		panic("lapack: m < min(n,k)")
	case lda < max(1, n) && lwork != -1:
		// Normally, we follow the reference and require the leading
		// dimension to be always valid, even in case of workspace
		// queries. However, if a caller provided a placeholder value
		// for lda (and a) when doing a workspace query that didn't
		// fulfill the condition here, it would cause a panic. This is
		// exactly what Dgesvd does.
		panic(badLdA)
	case lwork < max(1, mn) && lwork != -1:
		panic(badLWork)
	case len(work) < max(1, lwork):
		panic(shortWork)
	}

	// Quick return if possible.
	work[0] = 1
	if m == 0 || n == 0 {
		return
	}

	if wantq {
		if m >= k {
			impl.Dorgqr(m, n, k, a, lda, tau, work, -1)
		} else if m > 1 {
			impl.Dorgqr(m-1, m-1, m-1, a[lda+1:], lda, tau, work, -1)
		}
	} else {
		if k < n {
			impl.Dorglq(m, n, k, a, lda, tau, work, -1)
		} else if n > 1 {
			impl.Dorglq(n-1, n-1, n-1, a[lda+1:], lda, tau, work, -1)
		}
	}
	lworkopt := int(work[0])
	lworkopt = max(lworkopt, mn)
	if lwork == -1 {
		work[0] = float64(lworkopt)
		return
	}

	switch {
	case len(a) < (m-1)*lda+n:
		panic(shortA)
	case wantq && len(tau) < min(m, k):
		panic(shortTau)
	case !wantq && len(tau) < min(n, k):
		panic(shortTau)
	}

	if wantq {
		// Form Q, determined by a call to Dgebrd to reduce an m×k matrix.
		if m >= k {
			impl.Dorgqr(m, n, k, a, lda, tau, work, lwork)
		} else {
			// Shift the vectors which define the elementary reflectors one
			// column to the right, and set the first row and column of Q to
			// those of the unit matrix.
			for j := m - 1; j >= 1; j-- {
				a[j] = 0
				for i := j + 1; i < m; i++ {
					a[i*lda+j] = a[i*lda+j-1]
				}
			}
			a[0] = 1
			for i := 1; i < m; i++ {
				a[i*lda] = 0
			}
			if m > 1 {
				// Form Q[1:m-1, 1:m-1]
				impl.Dorgqr(m-1, m-1, m-1, a[lda+1:], lda, tau, work, lwork)
			}
		}
	} else {
		// Form Pᵀ, determined by a call to Dgebrd to reduce a k×n matrix.
		if k < n {
			impl.Dorglq(m, n, k, a, lda, tau, work, lwork)
		} else {
			// Shift the vectors which define the elementary reflectors one
			// row downward, and set the first row and column of Pᵀ to
			// those of the unit matrix.
			a[0] = 1
			for i := 1; i < n; i++ {
				a[i*lda] = 0
			}
			for j := 1; j < n; j++ {
				for i := j - 1; i >= 1; i-- {
					a[i*lda+j] = a[(i-1)*lda+j]
				}
				a[j] = 0
			}
			if n > 1 {
				impl.Dorglq(n-1, n-1, n-1, a[lda+1:], lda, tau, work, lwork)
			}
		}
	}
	work[0] = float64(lworkopt)
}