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|
package tensor
import (
"math"
"github.com/chewxy/math32"
"github.com/pkg/errors"
)
func (t *Dense) multiSVDNorm(rowAxis, colAxis int) (retVal *Dense, err error) {
if rowAxis > colAxis {
rowAxis--
}
dims := t.Dims()
if retVal, err = t.RollAxis(colAxis, dims, true); err != nil {
return
}
if retVal, err = retVal.RollAxis(rowAxis, dims, true); err != nil {
return
}
// manual, since SVD only works on matrices. In the future, this needs to be fixed when gonum's lapack works for float32
// TODO: SVDFuture
switch dims {
case 2:
retVal, _, _, err = retVal.SVD(false, false)
case 3:
toStack := make([]*Dense, retVal.Shape()[0])
for i := 0; i < retVal.Shape()[0]; i++ {
var sliced, ithS *Dense
if sliced, err = sliceDense(retVal, ss(i)); err != nil {
return
}
if ithS, _, _, err = sliced.SVD(false, false); err != nil {
return
}
toStack[i] = ithS
}
retVal, err = toStack[0].Stack(0, toStack[1:]...)
return
default:
err = errors.Errorf("multiSVDNorm for dimensions greater than 3")
}
return
}
// Norm returns the p-ordered norm of the *Dense, given the axes.
//
// This implementation is directly adapted from Numpy, which is licenced under a BSD-like licence, and can be found here: https://docs.scipy.org/doc/numpy-1.9.1/license.html
func (t *Dense) Norm(ord NormOrder, axes ...int) (retVal *Dense, err error) {
var ret Tensor
var ok bool
var abs, norm0, normN interface{}
var oneOverOrd interface{}
switch t.t {
case Float64:
abs = math.Abs
norm0 = func(x float64) float64 {
if x != 0 {
return 1
}
return 0
}
normN = func(x float64) float64 {
return math.Pow(math.Abs(x), float64(ord))
}
oneOverOrd = float64(1) / float64(ord)
case Float32:
abs = math32.Abs
norm0 = func(x float32) float32 {
if x != 0 {
return 1
}
return 0
}
normN = func(x float32) float32 {
return math32.Pow(math32.Abs(x), float32(ord))
}
oneOverOrd = float32(1) / float32(ord)
default:
err = errors.Errorf("Norms only works on float types")
return
}
dims := t.Dims()
// simple case
if len(axes) == 0 {
if ord.IsUnordered() || (ord.IsFrobenius() && dims == 2) || (ord == Norm(2) && dims == 1) {
backup := t.AP
ap := makeAP(1)
defer ap.zero()
ap.unlock()
ap.SetShape(t.Size())
ap.lock()
t.AP = ap
if ret, err = Dot(t, t); err != nil { // returns a scalar
err = errors.Wrapf(err, opFail, "Norm-0")
return
}
if retVal, ok = ret.(*Dense); !ok {
return nil, errors.Errorf(opFail, "Norm-0")
}
switch t.t {
case Float64:
retVal.SetF64(0, math.Sqrt(retVal.GetF64(0)))
case Float32:
retVal.SetF32(0, math32.Sqrt(retVal.GetF32(0)))
}
t.AP = backup
return
}
axes = make([]int, dims)
for i := range axes {
axes[i] = i
}
}
switch len(axes) {
case 1:
cloned := t.Clone().(*Dense)
switch {
case ord.IsUnordered() || ord == Norm(2):
if ret, err = Square(cloned); err != nil {
return
}
if retVal, ok = ret.(*Dense); !ok {
return nil, errors.Errorf(opFail, "UnorderedNorm-1")
}
if retVal, err = retVal.Sum(axes...); err != nil {
return
}
if ret, err = Sqrt(retVal); err != nil {
return
}
return assertDense(ret)
case ord.IsInf(1):
if ret, err = cloned.Apply(abs); err != nil {
return
}
if retVal, ok = ret.(*Dense); !ok {
return nil, errors.Errorf(opFail, "InfNorm-1")
}
return retVal.Max(axes...)
case ord.IsInf(-1):
if ret, err = cloned.Apply(abs); err != nil {
return
}
if retVal, ok = ret.(*Dense); !ok {
return nil, errors.Errorf(opFail, "-InfNorm-1")
}
return retVal.Min(axes...)
case ord == Norm(0):
if ret, err = cloned.Apply(norm0); err != nil {
return
}
if retVal, ok = ret.(*Dense); !ok {
return nil, errors.Errorf(opFail, "Norm-0")
}
return retVal.Sum(axes...)
case ord == Norm(1):
if ret, err = cloned.Apply(abs); err != nil {
return
}
if retVal, ok = ret.(*Dense); !ok {
return nil, errors.Errorf(opFail, "Norm-1")
}
return retVal.Sum(axes...)
default:
if ret, err = cloned.Apply(normN); err != nil {
return
}
if retVal, ok = ret.(*Dense); !ok {
return nil, errors.Errorf(opFail, "Norm-N")
}
if retVal, err = retVal.Sum(axes...); err != nil {
return
}
return retVal.PowScalar(oneOverOrd, true)
}
case 2:
rowAxis := axes[0]
colAxis := axes[1]
// checks
if rowAxis < 0 {
return nil, errors.Errorf("Row Axis %d is < 0", rowAxis)
}
if colAxis < 0 {
return nil, errors.Errorf("Col Axis %d is < 0", colAxis)
}
if rowAxis == colAxis {
return nil, errors.Errorf("Duplicate axes found. Row Axis: %d, Col Axis %d", rowAxis, colAxis)
}
cloned := t.Clone().(*Dense)
switch {
case ord == Norm(2):
// svd norm
if retVal, err = t.multiSVDNorm(rowAxis, colAxis); err != nil {
return nil, errors.Wrapf(err, opFail, "MultiSVDNorm, case 2 with Ord == Norm(2)")
}
dims := retVal.Dims()
return retVal.Max(dims - 1)
case ord == Norm(-2):
// svd norm
if retVal, err = t.multiSVDNorm(rowAxis, colAxis); err != nil {
return nil, errors.Wrapf(err, opFail, "MultiSVDNorm, case 2 with Ord == Norm(-2)")
}
dims := retVal.Dims()
return retVal.Min(dims - 1)
case ord == Norm(1):
if colAxis > rowAxis {
colAxis--
}
if ret, err = cloned.Apply(abs); err != nil {
return nil, errors.Wrapf(err, opFail, "Apply abs in Norm. ord == Norm(1")
}
if retVal, err = assertDense(ret); err != nil {
return nil, errors.Wrapf(err, opFail, "Norm-1, axis=2")
}
if retVal, err = retVal.Sum(rowAxis); err != nil {
return
}
return retVal.Max(colAxis)
case ord == Norm(-1):
if colAxis > rowAxis {
colAxis--
}
if ret, err = cloned.Apply(abs); err != nil {
return
}
if retVal, err = assertDense(ret); err != nil {
return nil, errors.Wrapf(err, opFail, "Norm-(-1), axis=2")
}
if retVal, err = retVal.Sum(rowAxis); err != nil {
return
}
return retVal.Min(colAxis)
case ord == Norm(0):
return nil, errors.Errorf("Norm of order 0 undefined for matrices")
case ord.IsInf(1):
if rowAxis > colAxis {
rowAxis--
}
if ret, err = cloned.Apply(abs); err != nil {
return
}
if retVal, err = assertDense(ret); err != nil {
return nil, errors.Wrapf(err, opFail, "InfNorm, axis=2")
}
if retVal, err = retVal.Sum(colAxis); err != nil {
return nil, errors.Wrapf(err, "Sum in infNorm")
}
return retVal.Max(rowAxis)
case ord.IsInf(-1):
if rowAxis > colAxis {
rowAxis--
}
if ret, err = cloned.Apply(abs); err != nil {
return
}
if retVal, err = assertDense(ret); err != nil {
return nil, errors.Wrapf(err, opFail, "-InfNorm, axis=2")
}
if retVal, err = retVal.Sum(colAxis); err != nil {
return nil, errors.Wrapf(err, opFail, "Sum with InfNorm")
}
return retVal.Min(rowAxis)
case ord.IsUnordered() || ord.IsFrobenius():
if ret, err = cloned.Apply(abs); err != nil {
return
}
if retVal, ok = ret.(*Dense); !ok {
return nil, errors.Errorf(opFail, "Frobenius Norm, axis = 2")
}
if ret, err = Square(retVal); err != nil {
return
}
if retVal, err = assertDense(ret); err != nil {
return nil, errors.Wrapf(err, opFail, "Norm-0, axis=2")
}
if retVal, err = retVal.Sum(axes...); err != nil {
return
}
if ret, err = Sqrt(retVal); err != nil {
return
}
return assertDense(ret)
case ord.IsNuclear():
// svd norm
if retVal, err = t.multiSVDNorm(rowAxis, colAxis); err != nil {
return
}
return retVal.Sum(len(t.Shape()) - 1)
case ord == Norm(0):
err = errors.Errorf("Norm order 0 undefined for matrices")
return
default:
return nil, errors.Errorf("Not yet implemented: Norm for Axes %v, ord %v", axes, ord)
}
default:
err = errors.Errorf(dimMismatch, 2, len(axes))
return
}
panic("Unreachable")
}
|
