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triangular.go
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triangular.go
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package mat64
import (
"math"
"github.com/gonum/blas"
"github.com/gonum/blas/blas64"
"github.com/gonum/lapack/lapack64"
"github.com/gonum/matrix"
)
var (
triDense *TriDense
_ Matrix = triDense
_ Triangular = triDense
_ RawTriangular = triDense
)
const badTriCap = "mat64: bad capacity for TriDense"
// TriDense represents an upper or lower triangular matrix in dense storage
// format.
type TriDense struct {
mat blas64.Triangular
cap int
}
type Triangular interface {
Matrix
// Triangular returns the number of rows/columns in the matrix and its
// orientation.
Triangle() (n int, kind matrix.TriKind)
// TTri is the equivalent of the T() method in the Matrix interface but
// guarantees the transpose is of triangular type.
TTri() Triangular
}
type RawTriangular interface {
RawTriangular() blas64.Triangular
}
var (
_ Matrix = TransposeTri{}
_ Triangular = TransposeTri{}
_ UntransposeTrier = TransposeTri{}
)
// TransposeTri is a type for performing an implicit transpose of a Triangular
// matrix. It implements the Triangular interface, returning values from the
// transpose of the matrix within.
type TransposeTri struct {
Triangular Triangular
}
// At returns the value of the element at row i and column j of the transposed
// matrix, that is, row j and column i of the Triangular field.
func (t TransposeTri) At(i, j int) float64 {
return t.Triangular.At(j, i)
}
// Dims returns the dimensions of the transposed matrix. Triangular matrices are
// square and thus this is the same size as the original Triangular.
func (t TransposeTri) Dims() (r, c int) {
c, r = t.Triangular.Dims()
return r, c
}
// T performs an implicit transpose by returning the Triangular field.
func (t TransposeTri) T() Matrix {
return t.Triangular
}
// Triangle returns the number of rows/columns in the matrix and its orientation.
func (t TransposeTri) Triangle() (int, matrix.TriKind) {
n, upper := t.Triangular.Triangle()
return n, !upper
}
// TTri performs an implicit transpose by returning the Triangular field.
func (t TransposeTri) TTri() Triangular {
return t.Triangular
}
// Untranspose returns the Triangular field.
func (t TransposeTri) Untranspose() Matrix {
return t.Triangular
}
func (t TransposeTri) UntransposeTri() Triangular {
return t.Triangular
}
// NewTriDense creates a new Triangular matrix with n rows and columns. If data == nil,
// a new slice is allocated for the backing slice. If len(data) == n*n, data is
// used as the backing slice, and changes to the elements of the returned TriDense
// will be reflected in data. If neither of these is true, NewTriDense will panic.
//
// The data must be arranged in row-major order, i.e. the (i*c + j)-th
// element in the data slice is the {i, j}-th element in the matrix.
// Only the values in the triangular portion corresponding to kind are used.
func NewTriDense(n int, kind matrix.TriKind, data []float64) *TriDense {
if n < 0 {
panic("mat64: negative dimension")
}
if data != nil && len(data) != n*n {
panic(matrix.ErrShape)
}
if data == nil {
data = make([]float64, n*n)
}
uplo := blas.Lower
if kind == matrix.Upper {
uplo = blas.Upper
}
return &TriDense{
mat: blas64.Triangular{
N: n,
Stride: n,
Data: data,
Uplo: uplo,
Diag: blas.NonUnit,
},
cap: n,
}
}
func (t *TriDense) Dims() (r, c int) {
return t.mat.N, t.mat.N
}
// Triangle returns the dimension of t and its orientation. The returned
// orientation is only valid when n is not zero.
func (t *TriDense) Triangle() (n int, kind matrix.TriKind) {
return t.mat.N, matrix.TriKind(!t.isZero()) && t.triKind()
}
func (t *TriDense) isUpper() bool {
return isUpperUplo(t.mat.Uplo)
}
func (t *TriDense) triKind() matrix.TriKind {
return matrix.TriKind(isUpperUplo(t.mat.Uplo))
}
func isUpperUplo(u blas.Uplo) bool {
switch u {
case blas.Upper:
return true
case blas.Lower:
return false
default:
panic(badTriangle)
}
}
// asSymBlas returns the receiver restructured as a blas64.Symmetric with the
// same backing memory. Panics if the receiver is unit.
// This returns a blas64.Symmetric and not a *SymDense because SymDense can only
// be upper triangular.
func (t *TriDense) asSymBlas() blas64.Symmetric {
if t.mat.Diag == blas.Unit {
panic("mat64: cannot convert unit TriDense into blas64.Symmetric")
}
return blas64.Symmetric{
N: t.mat.N,
Stride: t.mat.Stride,
Data: t.mat.Data,
Uplo: t.mat.Uplo,
}
}
// T performs an implicit transpose by returning the receiver inside a Transpose.
func (t *TriDense) T() Matrix {
return Transpose{t}
}
// TTri performs an implicit transpose by returning the receiver inside a TransposeTri.
func (t *TriDense) TTri() Triangular {
return TransposeTri{t}
}
func (t *TriDense) RawTriangular() blas64.Triangular {
return t.mat
}
// Reset zeros the dimensions of the matrix so that it can be reused as the
// receiver of a dimensionally restricted operation.
//
// See the Reseter interface for more information.
func (t *TriDense) Reset() {
// N and Stride must be zeroed in unison.
t.mat.N, t.mat.Stride = 0, 0
// Defensively zero Uplo to ensure
// it is set correctly later.
t.mat.Uplo = 0
t.mat.Data = t.mat.Data[:0]
}
func (t *TriDense) isZero() bool {
// It must be the case that t.Dims() returns
// zeros in this case. See comment in Reset().
return t.mat.Stride == 0
}
// untranspose untransposes a matrix if applicable. If a is an Untransposer, then
// untranspose returns the underlying matrix and true. If it is not, then it returns
// the input matrix and false.
func untransposeTri(a Triangular) (Triangular, bool) {
if ut, ok := a.(UntransposeTrier); ok {
return ut.UntransposeTri(), true
}
return a, false
}
// reuseAs resizes a zero receiver to an n×n triangular matrix with the given
// orientation. If the receiver is non-zero, reuseAs checks that the receiver
// is the correct size and orientation.
func (t *TriDense) reuseAs(n int, kind matrix.TriKind) {
ul := blas.Lower
if kind == matrix.Upper {
ul = blas.Upper
}
if t.mat.N > t.cap {
panic(badTriCap)
}
if t.isZero() {
t.mat = blas64.Triangular{
N: n,
Stride: n,
Diag: blas.NonUnit,
Data: use(t.mat.Data, n*n),
Uplo: ul,
}
t.cap = n
return
}
if t.mat.N != n {
panic(matrix.ErrShape)
}
if t.mat.Uplo != ul {
panic(matrix.ErrTriangle)
}
}
// isolatedWorkspace returns a new TriDense matrix w with the size of a and
// returns a callback to defer which performs cleanup at the return of the call.
// This should be used when a method receiver is the same pointer as an input argument.
func (t *TriDense) isolatedWorkspace(a Triangular) (w *TriDense, restore func()) {
n, kind := a.Triangle()
if n == 0 {
panic("zero size")
}
w = getWorkspaceTri(n, kind, false)
return w, func() {
t.Copy(w)
putWorkspaceTri(w)
}
}
// Copy makes a copy of elements of a into the receiver. It is similar to the
// built-in copy; it copies as much as the overlap between the two matrices and
// returns the number of rows and columns it copied. Only elements within the
// receiver's non-zero triangle are set.
//
// See the Copier interface for more information.
func (t *TriDense) Copy(a Matrix) (r, c int) {
r, c = a.Dims()
r = min(r, t.mat.N)
c = min(c, t.mat.N)
if r == 0 || c == 0 {
return 0, 0
}
switch a := a.(type) {
case RawMatrixer:
amat := a.RawMatrix()
if t.isUpper() {
for i := 0; i < r; i++ {
copy(t.mat.Data[i*t.mat.Stride+i:i*t.mat.Stride+c], amat.Data[i*amat.Stride+i:i*amat.Stride+c])
}
} else {
for i := 0; i < r; i++ {
copy(t.mat.Data[i*t.mat.Stride:i*t.mat.Stride+i+1], amat.Data[i*amat.Stride:i*amat.Stride+i+1])
}
}
case RawTriangular:
amat := a.RawTriangular()
aIsUpper := isUpperUplo(amat.Uplo)
tIsUpper := t.isUpper()
switch {
case tIsUpper && aIsUpper:
for i := 0; i < r; i++ {
copy(t.mat.Data[i*t.mat.Stride+i:i*t.mat.Stride+c], amat.Data[i*amat.Stride+i:i*amat.Stride+c])
}
case !tIsUpper && !aIsUpper:
for i := 0; i < r; i++ {
copy(t.mat.Data[i*t.mat.Stride:i*t.mat.Stride+i+1], amat.Data[i*amat.Stride:i*amat.Stride+i+1])
}
default:
for i := 0; i < r; i++ {
t.set(i, i, amat.Data[i*amat.Stride+i])
}
}
default:
isUpper := t.isUpper()
for i := 0; i < r; i++ {
if isUpper {
for j := i; j < c; j++ {
t.set(i, j, a.At(i, j))
}
} else {
for j := 0; j <= i; j++ {
t.set(i, j, a.At(i, j))
}
}
}
}
return r, c
}
// InverseTri computes the inverse of the triangular matrix a, storing the result
// into the receiver. If a is ill-conditioned, a Condition error will be returned.
// Note that matrix inversion is numerically unstable, and should generally be
// avoided where possible, for example by using the Solve routines.
func (t *TriDense) InverseTri(a Triangular) error {
if rt, ok := a.(RawTriangular); ok {
t.checkOverlap(rt.RawTriangular())
}
n, _ := a.Triangle()
t.reuseAs(a.Triangle())
t.Copy(a)
work := make([]float64, 3*n)
iwork := make([]int, n)
cond := lapack64.Trcon(matrix.CondNorm, t.mat, work, iwork)
if math.IsInf(cond, 1) {
return matrix.Condition(cond)
}
ok := lapack64.Trtri(t.mat)
if !ok {
return matrix.Condition(math.Inf(1))
}
if cond > matrix.ConditionTolerance {
return matrix.Condition(cond)
}
return nil
}
// MulTri takes the product of triangular matrices a and b and places the result
// in the receiver. The size of a and b must match, and they both must have the
// same TriKind, or Mul will panic.
func (t *TriDense) MulTri(a, b Triangular) {
n, kind := a.Triangle()
nb, kindb := b.Triangle()
if n != nb {
panic(matrix.ErrShape)
}
if kind != kindb {
panic(matrix.ErrTriangle)
}
aU, _ := untransposeTri(a)
bU, _ := untransposeTri(b)
t.reuseAs(n, kind)
var restore func()
if t == aU {
t, restore = t.isolatedWorkspace(aU)
defer restore()
} else if t == bU {
t, restore = t.isolatedWorkspace(bU)
defer restore()
}
// TODO(btracey): Improve the set of fast-paths.
if kind == matrix.Upper {
for i := 0; i < n; i++ {
for j := i; j < n; j++ {
var v float64
for k := i; k <= j; k++ {
v += a.At(i, k) * b.At(k, j)
}
t.SetTri(i, j, v)
}
}
return
}
for i := 0; i < n; i++ {
for j := 0; j <= i; j++ {
var v float64
for k := j; k <= i; k++ {
v += a.At(i, k) * b.At(k, j)
}
t.SetTri(i, j, v)
}
}
}
// copySymIntoTriangle copies a symmetric matrix into a TriDense
func copySymIntoTriangle(t *TriDense, s Symmetric) {
n, upper := t.Triangle()
ns := s.Symmetric()
if n != ns {
panic("mat64: triangle size mismatch")
}
ts := t.mat.Stride
if rs, ok := s.(RawSymmetricer); ok {
sd := rs.RawSymmetric()
ss := sd.Stride
if upper {
if sd.Uplo == blas.Upper {
for i := 0; i < n; i++ {
copy(t.mat.Data[i*ts+i:i*ts+n], sd.Data[i*ss+i:i*ss+n])
}
return
}
for i := 0; i < n; i++ {
for j := i; j < n; j++ {
t.mat.Data[i*ts+j] = sd.Data[j*ss+i]
}
return
}
}
if sd.Uplo == blas.Upper {
for i := 0; i < n; i++ {
for j := 0; j <= i; j++ {
t.mat.Data[i*ts+j] = sd.Data[j*ss+i]
}
}
return
}
for i := 0; i < n; i++ {
copy(t.mat.Data[i*ts:i*ts+i+1], sd.Data[i*ss:i*ss+i+1])
}
return
}
if upper {
for i := 0; i < n; i++ {
for j := i; j < n; j++ {
t.mat.Data[i*ts+j] = s.At(i, j)
}
}
return
}
for i := 0; i < n; i++ {
for j := 0; j <= i; j++ {
t.mat.Data[i*ts+j] = s.At(i, j)
}
}
}