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416 lines
11 KiB
Go
416 lines
11 KiB
Go
// Copyright ©2017 The Gonum Authors. All rights reserved.
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// Use of this source code is governed by a BSD-style
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// license that can be found in the LICENSE file.
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package mat
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import (
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"gonum.org/v1/gonum/blas/blas64"
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"gonum.org/v1/gonum/floats"
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"gonum.org/v1/gonum/lapack"
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"gonum.org/v1/gonum/lapack/lapack64"
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)
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// GSVDKind specifies the treatment of singular vectors during a GSVD
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// factorization.
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type GSVDKind int
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const (
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// GSVDNone specifies that no singular vectors should be computed during
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// the decomposition.
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GSVDNone GSVDKind = 0
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// GSVDU specifies that the U singular vectors should be computed during
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// the decomposition.
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GSVDU GSVDKind = 1 << iota
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// GSVDV specifies that the V singular vectors should be computed during
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// the decomposition.
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GSVDV
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// GSVDQ specifies that the Q singular vectors should be computed during
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// the decomposition.
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GSVDQ
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// GSVDAll is a convenience value for computing all of the singular vectors.
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GSVDAll = GSVDU | GSVDV | GSVDQ
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)
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// GSVD is a type for creating and using the Generalized Singular Value Decomposition
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// (GSVD) of a matrix.
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//
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// The factorization is a linear transformation of the data sets from the given
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// variable×sample spaces to reduced and diagonalized "eigenvariable"×"eigensample"
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// spaces.
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type GSVD struct {
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kind GSVDKind
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r, p, c, k, l int
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s1, s2 []float64
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a, b, u, v, q blas64.General
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work []float64
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iwork []int
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}
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// succFact returns whether the receiver contains a successful factorization.
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func (gsvd *GSVD) succFact() bool {
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return gsvd.r != 0
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}
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// Factorize computes the generalized singular value decomposition (GSVD) of the input
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// the r×c matrix A and the p×c matrix B. The singular values of A and B are computed
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// in all cases, while the singular vectors are optionally computed depending on the
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// input kind.
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//
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// The full singular value decomposition (kind == GSVDAll) deconstructs A and B as
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// A = U * Σ₁ * [ 0 R ] * Q^T
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//
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// B = V * Σ₂ * [ 0 R ] * Q^T
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// where Σ₁ and Σ₂ are r×(k+l) and p×(k+l) diagonal matrices of singular values, and
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// U, V and Q are r×r, p×p and c×c orthogonal matrices of singular vectors. k+l is the
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// effective numerical rank of the matrix [ A^T B^T ]^T.
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//
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// It is frequently not necessary to compute the full GSVD. Computation time and
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// storage costs can be reduced using the appropriate kind. Either only the singular
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// values can be computed (kind == SVDNone), or in conjunction with specific singular
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// vectors (kind bit set according to matrix.GSVDU, matrix.GSVDV and matrix.GSVDQ).
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//
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// Factorize returns whether the decomposition succeeded. If the decomposition
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// failed, routines that require a successful factorization will panic.
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func (gsvd *GSVD) Factorize(a, b Matrix, kind GSVDKind) (ok bool) {
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// kill the previous decomposition
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gsvd.r = 0
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gsvd.kind = 0
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r, c := a.Dims()
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gsvd.r, gsvd.c = r, c
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p, c := b.Dims()
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gsvd.p = p
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if gsvd.c != c {
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panic(ErrShape)
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}
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var jobU, jobV, jobQ lapack.GSVDJob
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switch {
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default:
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panic("gsvd: bad input kind")
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case kind == GSVDNone:
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jobU = lapack.GSVDNone
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jobV = lapack.GSVDNone
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jobQ = lapack.GSVDNone
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case GSVDAll&kind != 0:
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if GSVDU&kind != 0 {
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jobU = lapack.GSVDU
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gsvd.u = blas64.General{
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Rows: r,
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Cols: r,
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Stride: r,
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Data: use(gsvd.u.Data, r*r),
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}
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}
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if GSVDV&kind != 0 {
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jobV = lapack.GSVDV
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gsvd.v = blas64.General{
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Rows: p,
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Cols: p,
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Stride: p,
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Data: use(gsvd.v.Data, p*p),
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}
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}
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if GSVDQ&kind != 0 {
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jobQ = lapack.GSVDQ
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gsvd.q = blas64.General{
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Rows: c,
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Cols: c,
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Stride: c,
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Data: use(gsvd.q.Data, c*c),
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}
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}
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}
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// A and B are destroyed on call, so copy the matrices.
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aCopy := DenseCopyOf(a)
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bCopy := DenseCopyOf(b)
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gsvd.s1 = use(gsvd.s1, c)
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gsvd.s2 = use(gsvd.s2, c)
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gsvd.iwork = useInt(gsvd.iwork, c)
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gsvd.work = use(gsvd.work, 1)
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lapack64.Ggsvd3(jobU, jobV, jobQ, aCopy.mat, bCopy.mat, gsvd.s1, gsvd.s2, gsvd.u, gsvd.v, gsvd.q, gsvd.work, -1, gsvd.iwork)
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gsvd.work = use(gsvd.work, int(gsvd.work[0]))
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gsvd.k, gsvd.l, ok = lapack64.Ggsvd3(jobU, jobV, jobQ, aCopy.mat, bCopy.mat, gsvd.s1, gsvd.s2, gsvd.u, gsvd.v, gsvd.q, gsvd.work, len(gsvd.work), gsvd.iwork)
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if ok {
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gsvd.a = aCopy.mat
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gsvd.b = bCopy.mat
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gsvd.kind = kind
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}
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return ok
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}
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// Kind returns the GSVDKind of the decomposition. If no decomposition has been
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// computed, Kind returns -1.
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func (gsvd *GSVD) Kind() GSVDKind {
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if !gsvd.succFact() {
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return -1
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}
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return gsvd.kind
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}
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// Rank returns the k and l terms of the rank of [ A^T B^T ]^T.
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func (gsvd *GSVD) Rank() (k, l int) {
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return gsvd.k, gsvd.l
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}
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// GeneralizedValues returns the generalized singular values of the factorized matrices.
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// If the input slice is non-nil, the values will be stored in-place into the slice.
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// In this case, the slice must have length min(r,c)-k, and GeneralizedValues will
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// panic with matrix.ErrSliceLengthMismatch otherwise. If the input slice is nil,
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// a new slice of the appropriate length will be allocated and returned.
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//
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// GeneralizedValues will panic if the receiver does not contain a successful factorization.
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func (gsvd *GSVD) GeneralizedValues(v []float64) []float64 {
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if !gsvd.succFact() {
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panic(badFact)
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}
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r := gsvd.r
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c := gsvd.c
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k := gsvd.k
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d := min(r, c)
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if v == nil {
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v = make([]float64, d-k)
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}
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if len(v) != d-k {
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panic(ErrSliceLengthMismatch)
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}
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floats.DivTo(v, gsvd.s1[k:d], gsvd.s2[k:d])
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return v
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}
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// ValuesA returns the singular values of the factorized A matrix.
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// If the input slice is non-nil, the values will be stored in-place into the slice.
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// In this case, the slice must have length min(r,c)-k, and ValuesA will panic with
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// matrix.ErrSliceLengthMismatch otherwise. If the input slice is nil,
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// a new slice of the appropriate length will be allocated and returned.
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//
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// ValuesA will panic if the receiver does not contain a successful factorization.
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func (gsvd *GSVD) ValuesA(s []float64) []float64 {
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if !gsvd.succFact() {
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panic(badFact)
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}
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r := gsvd.r
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c := gsvd.c
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k := gsvd.k
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d := min(r, c)
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if s == nil {
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s = make([]float64, d-k)
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}
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if len(s) != d-k {
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panic(ErrSliceLengthMismatch)
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}
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copy(s, gsvd.s1[k:min(r, c)])
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return s
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}
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// ValuesB returns the singular values of the factorized B matrix.
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// If the input slice is non-nil, the values will be stored in-place into the slice.
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// In this case, the slice must have length min(r,c)-k, and ValuesB will panic with
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// matrix.ErrSliceLengthMismatch otherwise. If the input slice is nil,
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// a new slice of the appropriate length will be allocated and returned.
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//
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// ValuesB will panic if the receiver does not contain a successful factorization.
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func (gsvd *GSVD) ValuesB(s []float64) []float64 {
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if !gsvd.succFact() {
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panic(badFact)
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}
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r := gsvd.r
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c := gsvd.c
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k := gsvd.k
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d := min(r, c)
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if s == nil {
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s = make([]float64, d-k)
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}
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if len(s) != d-k {
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panic(ErrSliceLengthMismatch)
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}
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copy(s, gsvd.s2[k:d])
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return s
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}
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// ZeroRTo extracts the matrix [ 0 R ] from the singular value decomposition, storing
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// the result in-place into dst. [ 0 R ] is size (k+l)×c.
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// If dst is nil, a new matrix is allocated. The resulting ZeroR matrix is returned.
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//
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// ZeroRTo will panic if the receiver does not contain a successful factorization.
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func (gsvd *GSVD) ZeroRTo(dst *Dense) *Dense {
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if !gsvd.succFact() {
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panic(badFact)
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}
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r := gsvd.r
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c := gsvd.c
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k := gsvd.k
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l := gsvd.l
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h := min(k+l, r)
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if dst == nil {
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dst = NewDense(k+l, c, nil)
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} else {
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dst.reuseAsZeroed(k+l, c)
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}
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a := Dense{
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mat: gsvd.a,
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capRows: r,
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capCols: c,
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}
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dst.Slice(0, h, c-k-l, c).(*Dense).
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Copy(a.Slice(0, h, c-k-l, c))
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if r < k+l {
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b := Dense{
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mat: gsvd.b,
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capRows: gsvd.p,
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capCols: c,
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}
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dst.Slice(r, k+l, c+r-k-l, c).(*Dense).
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Copy(b.Slice(r-k, l, c+r-k-l, c))
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}
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return dst
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}
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// SigmaATo extracts the matrix Σ₁ from the singular value decomposition, storing
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// the result in-place into dst. Σ₁ is size r×(k+l).
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// If dst is nil, a new matrix is allocated. The resulting SigmaA matrix is returned.
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//
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// SigmaATo will panic if the receiver does not contain a successful factorization.
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func (gsvd *GSVD) SigmaATo(dst *Dense) *Dense {
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if !gsvd.succFact() {
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panic(badFact)
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}
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r := gsvd.r
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k := gsvd.k
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l := gsvd.l
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if dst == nil {
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dst = NewDense(r, k+l, nil)
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} else {
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dst.reuseAsZeroed(r, k+l)
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}
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for i := 0; i < k; i++ {
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dst.set(i, i, 1)
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}
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for i := k; i < min(r, k+l); i++ {
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dst.set(i, i, gsvd.s1[i])
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}
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return dst
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}
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// SigmaBTo extracts the matrix Σ₂ from the singular value decomposition, storing
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// the result in-place into dst. Σ₂ is size p×(k+l).
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// If dst is nil, a new matrix is allocated. The resulting SigmaB matrix is returned.
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//
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// SigmaBTo will panic if the receiver does not contain a successful factorization.
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func (gsvd *GSVD) SigmaBTo(dst *Dense) *Dense {
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if !gsvd.succFact() {
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panic(badFact)
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}
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r := gsvd.r
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p := gsvd.p
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k := gsvd.k
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l := gsvd.l
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if dst == nil {
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dst = NewDense(p, k+l, nil)
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} else {
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dst.reuseAsZeroed(p, k+l)
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}
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for i := 0; i < min(l, r-k); i++ {
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dst.set(i, i+k, gsvd.s2[k+i])
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}
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for i := r - k; i < l; i++ {
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dst.set(i, i+k, 1)
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}
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return dst
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}
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// UTo extracts the matrix U from the singular value decomposition, storing
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// the result in-place into dst. U is size r×r.
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// If dst is nil, a new matrix is allocated. The resulting U matrix is returned.
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//
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// UTo will panic if the receiver does not contain a successful factorization.
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func (gsvd *GSVD) UTo(dst *Dense) *Dense {
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if !gsvd.succFact() {
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panic(badFact)
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}
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if gsvd.kind&GSVDU == 0 {
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panic("mat: improper GSVD kind")
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}
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r := gsvd.u.Rows
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c := gsvd.u.Cols
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if dst == nil {
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dst = NewDense(r, c, nil)
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} else {
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dst.reuseAs(r, c)
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}
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tmp := &Dense{
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mat: gsvd.u,
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capRows: r,
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capCols: c,
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}
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dst.Copy(tmp)
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return dst
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}
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// VTo extracts the matrix V from the singular value decomposition, storing
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// the result in-place into dst. V is size p×p.
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// If dst is nil, a new matrix is allocated. The resulting V matrix is returned.
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//
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// VTo will panic if the receiver does not contain a successful factorization.
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func (gsvd *GSVD) VTo(dst *Dense) *Dense {
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if !gsvd.succFact() {
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panic(badFact)
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}
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if gsvd.kind&GSVDV == 0 {
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panic("mat: improper GSVD kind")
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}
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r := gsvd.v.Rows
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c := gsvd.v.Cols
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if dst == nil {
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dst = NewDense(r, c, nil)
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} else {
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dst.reuseAs(r, c)
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}
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tmp := &Dense{
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mat: gsvd.v,
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capRows: r,
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capCols: c,
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}
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dst.Copy(tmp)
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return dst
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}
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// QTo extracts the matrix Q from the singular value decomposition, storing
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// the result in-place into dst. Q is size c×c.
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// If dst is nil, a new matrix is allocated. The resulting Q matrix is returned.
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//
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// QTo will panic if the receiver does not contain a successful factorization.
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func (gsvd *GSVD) QTo(dst *Dense) *Dense {
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if !gsvd.succFact() {
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panic(badFact)
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}
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if gsvd.kind&GSVDQ == 0 {
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panic("mat: improper GSVD kind")
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}
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r := gsvd.q.Rows
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c := gsvd.q.Cols
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if dst == nil {
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dst = NewDense(r, c, nil)
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} else {
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dst.reuseAs(r, c)
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}
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tmp := &Dense{
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mat: gsvd.q,
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capRows: r,
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capCols: c,
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}
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dst.Copy(tmp)
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return dst
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}
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