Skip to content
Permalink
Branch: master
Find file Copy path
Find file Copy path
Fetching contributors…
Cannot retrieve contributors at this time
416 lines (385 sloc) 11 KB
// 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 mat
import (
"gonum.org/v1/gonum/blas/blas64"
"gonum.org/v1/gonum/floats"
"gonum.org/v1/gonum/lapack"
"gonum.org/v1/gonum/lapack/lapack64"
)
// GSVDKind specifies the treatment of singular vectors during a GSVD
// factorization.
type GSVDKind int
const (
// GSVDNone specifies that no singular vectors should be computed during
// the decomposition.
GSVDNone GSVDKind = 0
// GSVDU specifies that the U singular vectors should be computed during
// the decomposition.
GSVDU GSVDKind = 1 << iota
// GSVDV specifies that the V singular vectors should be computed during
// the decomposition.
GSVDV
// GSVDQ specifies that the Q singular vectors should be computed during
// the decomposition.
GSVDQ
// GSVDAll is a convenience value for computing all of the singular vectors.
GSVDAll = GSVDU | GSVDV | GSVDQ
)
// GSVD is a type for creating and using the Generalized Singular Value Decomposition
// (GSVD) of a matrix.
//
// The factorization is a linear transformation of the data sets from the given
// variable×sample spaces to reduced and diagonalized "eigenvariable"×"eigensample"
// spaces.
type GSVD struct {
kind GSVDKind
r, p, c, k, l int
s1, s2 []float64
a, b, u, v, q blas64.General
work []float64
iwork []int
}
// succFact returns whether the receiver contains a successful factorization.
func (gsvd *GSVD) succFact() bool {
return gsvd.r != 0
}
// Factorize computes the generalized singular value decomposition (GSVD) of the input
// the r×c matrix A and the p×c matrix B. The singular values of A and B are computed
// in all cases, while the singular vectors are optionally computed depending on the
// input kind.
//
// The full singular value decomposition (kind == GSVDAll) deconstructs A and B as
// A = U * Σ₁ * [ 0 R ] * Qᵀ
//
// B = V * Σ₂ * [ 0 R ] * Qᵀ
// where Σ₁ and Σ₂ are r×(k+l) and p×(k+l) diagonal matrices of singular values, and
// U, V and Q are r×r, p×p and c×c orthogonal matrices of singular vectors. k+l is the
// effective numerical rank of the matrix [ Aᵀ Bᵀ ]ᵀ.
//
// It is frequently not necessary to compute the full GSVD. Computation time and
// storage costs can be reduced using the appropriate kind. Either only the singular
// values can be computed (kind == SVDNone), or in conjunction with specific singular
// vectors (kind bit set according to matrix.GSVDU, matrix.GSVDV and matrix.GSVDQ).
//
// Factorize returns whether the decomposition succeeded. If the decomposition
// failed, routines that require a successful factorization will panic.
func (gsvd *GSVD) Factorize(a, b Matrix, kind GSVDKind) (ok bool) {
// kill the previous decomposition
gsvd.r = 0
gsvd.kind = 0
r, c := a.Dims()
gsvd.r, gsvd.c = r, c
p, c := b.Dims()
gsvd.p = p
if gsvd.c != c {
panic(ErrShape)
}
var jobU, jobV, jobQ lapack.GSVDJob
switch {
default:
panic("gsvd: bad input kind")
case kind == GSVDNone:
jobU = lapack.GSVDNone
jobV = lapack.GSVDNone
jobQ = lapack.GSVDNone
case GSVDAll&kind != 0:
if GSVDU&kind != 0 {
jobU = lapack.GSVDU
gsvd.u = blas64.General{
Rows: r,
Cols: r,
Stride: r,
Data: use(gsvd.u.Data, r*r),
}
}
if GSVDV&kind != 0 {
jobV = lapack.GSVDV
gsvd.v = blas64.General{
Rows: p,
Cols: p,
Stride: p,
Data: use(gsvd.v.Data, p*p),
}
}
if GSVDQ&kind != 0 {
jobQ = lapack.GSVDQ
gsvd.q = blas64.General{
Rows: c,
Cols: c,
Stride: c,
Data: use(gsvd.q.Data, c*c),
}
}
}
// A and B are destroyed on call, so copy the matrices.
aCopy := DenseCopyOf(a)
bCopy := DenseCopyOf(b)
gsvd.s1 = use(gsvd.s1, c)
gsvd.s2 = use(gsvd.s2, c)
gsvd.iwork = useInt(gsvd.iwork, c)
gsvd.work = use(gsvd.work, 1)
lapack64.Ggsvd3(jobU, jobV, jobQ, aCopy.mat, bCopy.mat, gsvd.s1, gsvd.s2, gsvd.u, gsvd.v, gsvd.q, gsvd.work, -1, gsvd.iwork)
gsvd.work = use(gsvd.work, int(gsvd.work[0]))
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)
if ok {
gsvd.a = aCopy.mat
gsvd.b = bCopy.mat
gsvd.kind = kind
}
return ok
}
// Kind returns the GSVDKind of the decomposition. If no decomposition has been
// computed, Kind returns -1.
func (gsvd *GSVD) Kind() GSVDKind {
if !gsvd.succFact() {
return -1
}
return gsvd.kind
}
// Rank returns the k and l terms of the rank of [ Aᵀ Bᵀ ]ᵀ.
func (gsvd *GSVD) Rank() (k, l int) {
return gsvd.k, gsvd.l
}
// GeneralizedValues returns the generalized singular values of the factorized matrices.
// If the input slice is non-nil, the values will be stored in-place into the slice.
// In this case, the slice must have length min(r,c)-k, and GeneralizedValues will
// panic with matrix.ErrSliceLengthMismatch otherwise. If the input slice is nil,
// a new slice of the appropriate length will be allocated and returned.
//
// GeneralizedValues will panic if the receiver does not contain a successful factorization.
func (gsvd *GSVD) GeneralizedValues(v []float64) []float64 {
if !gsvd.succFact() {
panic(badFact)
}
r := gsvd.r
c := gsvd.c
k := gsvd.k
d := min(r, c)
if v == nil {
v = make([]float64, d-k)
}
if len(v) != d-k {
panic(ErrSliceLengthMismatch)
}
floats.DivTo(v, gsvd.s1[k:d], gsvd.s2[k:d])
return v
}
// ValuesA returns the singular values of the factorized A matrix.
// If the input slice is non-nil, the values will be stored in-place into the slice.
// In this case, the slice must have length min(r,c)-k, and ValuesA will panic with
// matrix.ErrSliceLengthMismatch otherwise. If the input slice is nil,
// a new slice of the appropriate length will be allocated and returned.
//
// ValuesA will panic if the receiver does not contain a successful factorization.
func (gsvd *GSVD) ValuesA(s []float64) []float64 {
if !gsvd.succFact() {
panic(badFact)
}
r := gsvd.r
c := gsvd.c
k := gsvd.k
d := min(r, c)
if s == nil {
s = make([]float64, d-k)
}
if len(s) != d-k {
panic(ErrSliceLengthMismatch)
}
copy(s, gsvd.s1[k:min(r, c)])
return s
}
// ValuesB returns the singular values of the factorized B matrix.
// If the input slice is non-nil, the values will be stored in-place into the slice.
// In this case, the slice must have length min(r,c)-k, and ValuesB will panic with
// matrix.ErrSliceLengthMismatch otherwise. If the input slice is nil,
// a new slice of the appropriate length will be allocated and returned.
//
// ValuesB will panic if the receiver does not contain a successful factorization.
func (gsvd *GSVD) ValuesB(s []float64) []float64 {
if !gsvd.succFact() {
panic(badFact)
}
r := gsvd.r
c := gsvd.c
k := gsvd.k
d := min(r, c)
if s == nil {
s = make([]float64, d-k)
}
if len(s) != d-k {
panic(ErrSliceLengthMismatch)
}
copy(s, gsvd.s2[k:d])
return s
}
// ZeroRTo extracts the matrix [ 0 R ] from the singular value decomposition, storing
// the result in-place into dst. [ 0 R ] is size (k+l)×c.
// If dst is nil, a new matrix is allocated. The resulting ZeroR matrix is returned.
//
// ZeroRTo will panic if the receiver does not contain a successful factorization.
func (gsvd *GSVD) ZeroRTo(dst *Dense) *Dense {
if !gsvd.succFact() {
panic(badFact)
}
r := gsvd.r
c := gsvd.c
k := gsvd.k
l := gsvd.l
h := min(k+l, r)
if dst == nil {
dst = NewDense(k+l, c, nil)
} else {
dst.reuseAsZeroed(k+l, c)
}
a := Dense{
mat: gsvd.a,
capRows: r,
capCols: c,
}
dst.Slice(0, h, c-k-l, c).(*Dense).
Copy(a.Slice(0, h, c-k-l, c))
if r < k+l {
b := Dense{
mat: gsvd.b,
capRows: gsvd.p,
capCols: c,
}
dst.Slice(r, k+l, c+r-k-l, c).(*Dense).
Copy(b.Slice(r-k, l, c+r-k-l, c))
}
return dst
}
// SigmaATo extracts the matrix Σ₁ from the singular value decomposition, storing
// the result in-place into dst. Σ₁ is size r×(k+l).
// If dst is nil, a new matrix is allocated. The resulting SigmaA matrix is returned.
//
// SigmaATo will panic if the receiver does not contain a successful factorization.
func (gsvd *GSVD) SigmaATo(dst *Dense) *Dense {
if !gsvd.succFact() {
panic(badFact)
}
r := gsvd.r
k := gsvd.k
l := gsvd.l
if dst == nil {
dst = NewDense(r, k+l, nil)
} else {
dst.reuseAsZeroed(r, k+l)
}
for i := 0; i < k; i++ {
dst.set(i, i, 1)
}
for i := k; i < min(r, k+l); i++ {
dst.set(i, i, gsvd.s1[i])
}
return dst
}
// SigmaBTo extracts the matrix Σ₂ from the singular value decomposition, storing
// the result in-place into dst. Σ₂ is size p×(k+l).
// If dst is nil, a new matrix is allocated. The resulting SigmaB matrix is returned.
//
// SigmaBTo will panic if the receiver does not contain a successful factorization.
func (gsvd *GSVD) SigmaBTo(dst *Dense) *Dense {
if !gsvd.succFact() {
panic(badFact)
}
r := gsvd.r
p := gsvd.p
k := gsvd.k
l := gsvd.l
if dst == nil {
dst = NewDense(p, k+l, nil)
} else {
dst.reuseAsZeroed(p, k+l)
}
for i := 0; i < min(l, r-k); i++ {
dst.set(i, i+k, gsvd.s2[k+i])
}
for i := r - k; i < l; i++ {
dst.set(i, i+k, 1)
}
return dst
}
// UTo extracts the matrix U from the singular value decomposition, storing
// the result in-place into dst. U is size r×r.
// If dst is nil, a new matrix is allocated. The resulting U matrix is returned.
//
// UTo will panic if the receiver does not contain a successful factorization.
func (gsvd *GSVD) UTo(dst *Dense) *Dense {
if !gsvd.succFact() {
panic(badFact)
}
if gsvd.kind&GSVDU == 0 {
panic("mat: improper GSVD kind")
}
r := gsvd.u.Rows
c := gsvd.u.Cols
if dst == nil {
dst = NewDense(r, c, nil)
} else {
dst.reuseAsNonZeroed(r, c)
}
tmp := &Dense{
mat: gsvd.u,
capRows: r,
capCols: c,
}
dst.Copy(tmp)
return dst
}
// VTo extracts the matrix V from the singular value decomposition, storing
// the result in-place into dst. V is size p×p.
// If dst is nil, a new matrix is allocated. The resulting V matrix is returned.
//
// VTo will panic if the receiver does not contain a successful factorization.
func (gsvd *GSVD) VTo(dst *Dense) *Dense {
if !gsvd.succFact() {
panic(badFact)
}
if gsvd.kind&GSVDV == 0 {
panic("mat: improper GSVD kind")
}
r := gsvd.v.Rows
c := gsvd.v.Cols
if dst == nil {
dst = NewDense(r, c, nil)
} else {
dst.reuseAsNonZeroed(r, c)
}
tmp := &Dense{
mat: gsvd.v,
capRows: r,
capCols: c,
}
dst.Copy(tmp)
return dst
}
// QTo extracts the matrix Q from the singular value decomposition, storing
// the result in-place into dst. Q is size c×c.
// If dst is nil, a new matrix is allocated. The resulting Q matrix is returned.
//
// QTo will panic if the receiver does not contain a successful factorization.
func (gsvd *GSVD) QTo(dst *Dense) *Dense {
if !gsvd.succFact() {
panic(badFact)
}
if gsvd.kind&GSVDQ == 0 {
panic("mat: improper GSVD kind")
}
r := gsvd.q.Rows
c := gsvd.q.Cols
if dst == nil {
dst = NewDense(r, c, nil)
} else {
dst.reuseAsNonZeroed(r, c)
}
tmp := &Dense{
mat: gsvd.q,
capRows: r,
capCols: c,
}
dst.Copy(tmp)
return dst
}
You can’t perform that action at this time.