added new svd algorithm (Golub Kahan) and used by default for svd
This commit is contained in:
parent
19c1af1874
commit
89a5522144
@ -19,9 +19,9 @@ import org.ejml.sparse.csc.factory.DecompositionFactory_DSCC
|
|||||||
import org.ejml.sparse.csc.factory.DecompositionFactory_FSCC
|
import org.ejml.sparse.csc.factory.DecompositionFactory_FSCC
|
||||||
import org.ejml.sparse.csc.factory.LinearSolverFactory_DSCC
|
import org.ejml.sparse.csc.factory.LinearSolverFactory_DSCC
|
||||||
import org.ejml.sparse.csc.factory.LinearSolverFactory_FSCC
|
import org.ejml.sparse.csc.factory.LinearSolverFactory_FSCC
|
||||||
import space.kscience.kmath.UnstableKMathAPI
|
|
||||||
import space.kscience.kmath.linear.*
|
import space.kscience.kmath.linear.*
|
||||||
import space.kscience.kmath.linear.Matrix
|
import space.kscience.kmath.linear.Matrix
|
||||||
|
import space.kscience.kmath.UnstableKMathAPI
|
||||||
import space.kscience.kmath.nd.StructureFeature
|
import space.kscience.kmath.nd.StructureFeature
|
||||||
import space.kscience.kmath.operations.DoubleField
|
import space.kscience.kmath.operations.DoubleField
|
||||||
import space.kscience.kmath.operations.FloatField
|
import space.kscience.kmath.operations.FloatField
|
||||||
|
@ -706,7 +706,7 @@ public open class DoubleTensorAlgebra :
|
|||||||
override fun svd(
|
override fun svd(
|
||||||
structureND: StructureND<Double>,
|
structureND: StructureND<Double>,
|
||||||
): Triple<StructureND<Double>, StructureND<Double>, StructureND<Double>> =
|
): Triple<StructureND<Double>, StructureND<Double>, StructureND<Double>> =
|
||||||
svd(structureND = structureND, epsilon = 1e-10)
|
svdGolubKahan(structureND = structureND, epsilon = 1e-10)
|
||||||
|
|
||||||
override fun symEig(structureND: StructureND<Double>): Pair<DoubleTensor, DoubleTensor> =
|
override fun symEig(structureND: StructureND<Double>): Pair<DoubleTensor, DoubleTensor> =
|
||||||
symEigJacobi(structureND = structureND, maxIteration = 50, epsilon = 1e-15)
|
symEigJacobi(structureND = structureND, maxIteration = 50, epsilon = 1e-15)
|
||||||
|
@ -7,10 +7,7 @@ package space.kscience.kmath.tensors.core.internal
|
|||||||
|
|
||||||
import space.kscience.kmath.nd.*
|
import space.kscience.kmath.nd.*
|
||||||
import space.kscience.kmath.operations.invoke
|
import space.kscience.kmath.operations.invoke
|
||||||
import space.kscience.kmath.structures.DoubleBuffer
|
import space.kscience.kmath.structures.*
|
||||||
import space.kscience.kmath.structures.IntBuffer
|
|
||||||
import space.kscience.kmath.structures.asBuffer
|
|
||||||
import space.kscience.kmath.structures.indices
|
|
||||||
import space.kscience.kmath.tensors.core.*
|
import space.kscience.kmath.tensors.core.*
|
||||||
import space.kscience.kmath.tensors.core.BroadcastDoubleTensorAlgebra.div
|
import space.kscience.kmath.tensors.core.BroadcastDoubleTensorAlgebra.div
|
||||||
import space.kscience.kmath.tensors.core.BroadcastDoubleTensorAlgebra.dot
|
import space.kscience.kmath.tensors.core.BroadcastDoubleTensorAlgebra.dot
|
||||||
@ -316,6 +313,302 @@ internal fun DoubleTensorAlgebra.svdHelper(
|
|||||||
}
|
}
|
||||||
}
|
}
|
||||||
|
|
||||||
|
private fun pythag(a: Double, b: Double): Double {
|
||||||
|
val at: Double = abs(a)
|
||||||
|
val bt: Double = abs(b)
|
||||||
|
val ct: Double
|
||||||
|
val result: Double
|
||||||
|
if (at > bt) {
|
||||||
|
ct = bt / at
|
||||||
|
result = at * sqrt(1.0 + ct * ct)
|
||||||
|
} else if (bt > 0.0) {
|
||||||
|
ct = at / bt
|
||||||
|
result = bt * sqrt(1.0 + ct * ct)
|
||||||
|
} else result = 0.0
|
||||||
|
return result
|
||||||
|
}
|
||||||
|
|
||||||
|
private fun SIGN(a: Double, b: Double): Double {
|
||||||
|
if (b >= 0.0)
|
||||||
|
return abs(a)
|
||||||
|
else
|
||||||
|
return -abs(a)
|
||||||
|
}
|
||||||
|
|
||||||
|
internal fun MutableStructure2D<Double>.svdGolubKahanHelper(u: MutableStructure2D<Double>, w: BufferedTensor<Double>,
|
||||||
|
v: MutableStructure2D<Double>, iterations: Int, epsilon: Double) {
|
||||||
|
val shape = this.shape
|
||||||
|
val m = shape.component1()
|
||||||
|
val n = shape.component2()
|
||||||
|
var f = 0.0
|
||||||
|
val rv1 = DoubleArray(n)
|
||||||
|
var s = 0.0
|
||||||
|
var scale = 0.0
|
||||||
|
var anorm = 0.0
|
||||||
|
var g = 0.0
|
||||||
|
var l = 0
|
||||||
|
|
||||||
|
val wStart = 0
|
||||||
|
val wBuffer = w.source
|
||||||
|
|
||||||
|
for (i in 0 until n) {
|
||||||
|
/* left-hand reduction */
|
||||||
|
l = i + 1
|
||||||
|
rv1[i] = scale * g
|
||||||
|
g = 0.0
|
||||||
|
s = 0.0
|
||||||
|
scale = 0.0
|
||||||
|
if (i < m) {
|
||||||
|
for (k in i until m) {
|
||||||
|
scale += abs(this[k, i]);
|
||||||
|
}
|
||||||
|
if (abs(scale) > epsilon) {
|
||||||
|
for (k in i until m) {
|
||||||
|
this[k, i] = (this[k, i] / scale)
|
||||||
|
s += this[k, i] * this[k, i]
|
||||||
|
}
|
||||||
|
f = this[i, i]
|
||||||
|
if (f >= 0) {
|
||||||
|
g = (-1) * abs(sqrt(s))
|
||||||
|
} else {
|
||||||
|
g = abs(sqrt(s))
|
||||||
|
}
|
||||||
|
val h = f * g - s
|
||||||
|
this[i, i] = f - g
|
||||||
|
if (i != n - 1) {
|
||||||
|
for (j in l until n) {
|
||||||
|
s = 0.0
|
||||||
|
for (k in i until m) {
|
||||||
|
s += this[k, i] * this[k, j]
|
||||||
|
}
|
||||||
|
f = s / h
|
||||||
|
for (k in i until m) {
|
||||||
|
this[k, j] += f * this[k, i]
|
||||||
|
}
|
||||||
|
}
|
||||||
|
}
|
||||||
|
for (k in i until m) {
|
||||||
|
this[k, i] = this[k, i] * scale
|
||||||
|
}
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
wBuffer[wStart + i] = scale * g
|
||||||
|
/* right-hand reduction */
|
||||||
|
g = 0.0
|
||||||
|
s = 0.0
|
||||||
|
scale = 0.0
|
||||||
|
if (i < m && i != n - 1) {
|
||||||
|
for (k in l until n) {
|
||||||
|
scale += abs(this[i, k])
|
||||||
|
}
|
||||||
|
if (abs(scale) > epsilon) {
|
||||||
|
for (k in l until n) {
|
||||||
|
this[i, k] = this[i, k] / scale
|
||||||
|
s += this[i, k] * this[i, k]
|
||||||
|
}
|
||||||
|
f = this[i, l]
|
||||||
|
if (f >= 0) {
|
||||||
|
g = (-1) * abs(sqrt(s))
|
||||||
|
} else {
|
||||||
|
g = abs(sqrt(s))
|
||||||
|
}
|
||||||
|
val h = f * g - s
|
||||||
|
this[i, l] = f - g
|
||||||
|
for (k in l until n) {
|
||||||
|
rv1[k] = this[i, k] / h
|
||||||
|
}
|
||||||
|
if (i != m - 1) {
|
||||||
|
for (j in l until m) {
|
||||||
|
s = 0.0
|
||||||
|
for (k in l until n) {
|
||||||
|
s += this[j, k] * this[i, k]
|
||||||
|
}
|
||||||
|
for (k in l until n) {
|
||||||
|
this[j, k] += s * rv1[k]
|
||||||
|
}
|
||||||
|
}
|
||||||
|
}
|
||||||
|
for (k in l until n) {
|
||||||
|
this[i, k] = this[i, k] * scale
|
||||||
|
}
|
||||||
|
}
|
||||||
|
}
|
||||||
|
anorm = max(anorm, (abs(wBuffer[wStart + i]) + abs(rv1[i])));
|
||||||
|
}
|
||||||
|
|
||||||
|
for (i in n - 1 downTo 0) {
|
||||||
|
if (i < n - 1) {
|
||||||
|
if (abs(g) > epsilon) {
|
||||||
|
for (j in l until n) {
|
||||||
|
v[j, i] = (this[i, j] / this[i, l]) / g
|
||||||
|
}
|
||||||
|
for (j in l until n) {
|
||||||
|
s = 0.0
|
||||||
|
for (k in l until n)
|
||||||
|
s += this[i, k] * v[k, j]
|
||||||
|
for (k in l until n)
|
||||||
|
v[k, j] += s * v[k, i]
|
||||||
|
}
|
||||||
|
}
|
||||||
|
for (j in l until n) {
|
||||||
|
v[i, j] = 0.0
|
||||||
|
v[j, i] = 0.0
|
||||||
|
}
|
||||||
|
}
|
||||||
|
v[i, i] = 1.0
|
||||||
|
g = rv1[i]
|
||||||
|
l = i
|
||||||
|
}
|
||||||
|
|
||||||
|
for (i in min(n, m) - 1 downTo 0) {
|
||||||
|
l = i + 1
|
||||||
|
g = wBuffer[wStart + i]
|
||||||
|
for (j in l until n) {
|
||||||
|
this[i, j] = 0.0
|
||||||
|
}
|
||||||
|
if (abs(g) > epsilon) {
|
||||||
|
g = 1.0 / g
|
||||||
|
for (j in l until n) {
|
||||||
|
s = 0.0
|
||||||
|
for (k in l until m) {
|
||||||
|
s += this[k, i] * this[k, j]
|
||||||
|
}
|
||||||
|
f = (s / this[i, i]) * g
|
||||||
|
for (k in i until m) {
|
||||||
|
this[k, j] += f * this[k, i]
|
||||||
|
}
|
||||||
|
}
|
||||||
|
for (j in i until m) {
|
||||||
|
this[j, i] *= g
|
||||||
|
}
|
||||||
|
} else {
|
||||||
|
for (j in i until m) {
|
||||||
|
this[j, i] = 0.0
|
||||||
|
}
|
||||||
|
}
|
||||||
|
this[i, i] += 1.0
|
||||||
|
}
|
||||||
|
|
||||||
|
var flag = 0
|
||||||
|
var nm = 0
|
||||||
|
var c = 0.0
|
||||||
|
var h = 0.0
|
||||||
|
var y = 0.0
|
||||||
|
var z = 0.0
|
||||||
|
var x = 0.0
|
||||||
|
for (k in n - 1 downTo 0) {
|
||||||
|
for (its in 1 until iterations) {
|
||||||
|
flag = 1
|
||||||
|
for (newl in k downTo 0) {
|
||||||
|
nm = newl - 1
|
||||||
|
if (abs(rv1[newl]) + anorm == anorm) {
|
||||||
|
flag = 0
|
||||||
|
l = newl
|
||||||
|
break
|
||||||
|
}
|
||||||
|
if (abs(wBuffer[wStart + nm]) + anorm == anorm) {
|
||||||
|
l = newl
|
||||||
|
break
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
if (flag != 0) {
|
||||||
|
c = 0.0
|
||||||
|
s = 1.0
|
||||||
|
for (i in l until k + 1) {
|
||||||
|
f = s * rv1[i]
|
||||||
|
rv1[i] = c * rv1[i]
|
||||||
|
if (abs(f) + anorm == anorm) {
|
||||||
|
break
|
||||||
|
}
|
||||||
|
g = wBuffer[wStart + i]
|
||||||
|
h = pythag(f, g)
|
||||||
|
wBuffer[wStart + i] = h
|
||||||
|
h = 1.0 / h
|
||||||
|
c = g * h
|
||||||
|
s = (-f) * h
|
||||||
|
for (j in 0 until m) {
|
||||||
|
y = this[j, nm]
|
||||||
|
z = this[j, i]
|
||||||
|
this[j, nm] = y * c + z * s
|
||||||
|
this[j, i] = z * c - y * s
|
||||||
|
}
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
z = wBuffer[wStart + k]
|
||||||
|
if (l == k) {
|
||||||
|
if (z < 0.0) {
|
||||||
|
wBuffer[wStart + k] = -z
|
||||||
|
for (j in 0 until n)
|
||||||
|
v[j, k] = -v[j, k]
|
||||||
|
}
|
||||||
|
break
|
||||||
|
}
|
||||||
|
|
||||||
|
x = wBuffer[wStart + l]
|
||||||
|
nm = k - 1
|
||||||
|
y = wBuffer[wStart + nm]
|
||||||
|
g = rv1[nm]
|
||||||
|
h = rv1[k]
|
||||||
|
f = ((y - z) * (y + z) + (g - h) * (g + h)) / (2.0 * h * y)
|
||||||
|
g = pythag(f, 1.0)
|
||||||
|
f = ((x - z) * (x + z) + h * ((y / (f + SIGN(g, f))) - h)) / x
|
||||||
|
c = 1.0
|
||||||
|
s = 1.0
|
||||||
|
|
||||||
|
var i = 0
|
||||||
|
for (j in l until nm + 1) {
|
||||||
|
i = j + 1
|
||||||
|
g = rv1[i]
|
||||||
|
y = wBuffer[wStart + i]
|
||||||
|
h = s * g
|
||||||
|
g = c * g
|
||||||
|
z = pythag(f, h)
|
||||||
|
rv1[j] = z
|
||||||
|
c = f / z
|
||||||
|
s = h / z
|
||||||
|
f = x * c + g * s
|
||||||
|
g = g * c - x * s
|
||||||
|
h = y * s
|
||||||
|
y *= c
|
||||||
|
|
||||||
|
for (jj in 0 until n) {
|
||||||
|
x = v[jj, j];
|
||||||
|
z = v[jj, i];
|
||||||
|
v[jj, j] = x * c + z * s;
|
||||||
|
v[jj, i] = z * c - x * s;
|
||||||
|
}
|
||||||
|
z = pythag(f, h)
|
||||||
|
wBuffer[wStart + j] = z
|
||||||
|
if (abs(z) > epsilon) {
|
||||||
|
z = 1.0 / z
|
||||||
|
c = f * z
|
||||||
|
s = h * z
|
||||||
|
}
|
||||||
|
f = c * g + s * y
|
||||||
|
x = c * y - s * g
|
||||||
|
for (jj in 0 until m) {
|
||||||
|
y = this[jj, j]
|
||||||
|
z = this[jj, i]
|
||||||
|
this[jj, j] = y * c + z * s
|
||||||
|
this[jj, i] = z * c - y * s
|
||||||
|
}
|
||||||
|
}
|
||||||
|
rv1[l] = 0.0
|
||||||
|
rv1[k] = f
|
||||||
|
wBuffer[wStart + k] = x
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
for (i in 0 until n) {
|
||||||
|
for (j in 0 until m) {
|
||||||
|
u[j, i] = this[j, i]
|
||||||
|
}
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
data class LMSettings (
|
data class LMSettings (
|
||||||
var iteration:Int,
|
var iteration:Int,
|
||||||
var func_calls: Int,
|
var func_calls: Int,
|
||||||
|
@ -212,6 +212,36 @@ public fun DoubleTensorAlgebra.svd(
|
|||||||
return Triple(uTensor.transposed(), sTensor, vTensor.transposed())
|
return Triple(uTensor.transposed(), sTensor, vTensor.transposed())
|
||||||
}
|
}
|
||||||
|
|
||||||
|
public fun DoubleTensorAlgebra.svdGolubKahan(
|
||||||
|
structureND: StructureND<Double>,
|
||||||
|
iterations: Int = 30, epsilon: Double = 1e-10
|
||||||
|
): Triple<DoubleTensor, DoubleTensor, DoubleTensor> {
|
||||||
|
val size = structureND.dimension
|
||||||
|
val commonShape = structureND.shape.slice(0 until size - 2)
|
||||||
|
val (n, m) = structureND.shape.slice(size - 2 until size)
|
||||||
|
val uTensor = zeros(commonShape + intArrayOf(n, m))
|
||||||
|
val sTensor = zeros(commonShape + intArrayOf(m))
|
||||||
|
val vTensor = zeros(commonShape + intArrayOf(m, m))
|
||||||
|
|
||||||
|
val matrices = structureND.asDoubleTensor().matrices
|
||||||
|
val uTensors = uTensor.matrices
|
||||||
|
val sTensorVectors = sTensor.vectors
|
||||||
|
val vTensors = vTensor.matrices
|
||||||
|
|
||||||
|
for (index in matrices.indices) {
|
||||||
|
val matrix = matrices[index]
|
||||||
|
val matrixSize = matrix.shape.linearSize
|
||||||
|
val curMatrix = DoubleTensor(
|
||||||
|
matrix.shape,
|
||||||
|
matrix.source.view(0, matrixSize).copy()
|
||||||
|
)
|
||||||
|
curMatrix.as2D().svdGolubKahanHelper(uTensors[index].as2D(), sTensorVectors[index], vTensors[index].as2D(),
|
||||||
|
iterations, epsilon)
|
||||||
|
}
|
||||||
|
|
||||||
|
return Triple(uTensor, sTensor, vTensor)
|
||||||
|
}
|
||||||
|
|
||||||
/**
|
/**
|
||||||
* Returns eigenvalues and eigenvectors of a real symmetric matrix input or a batch of real symmetric matrices,
|
* Returns eigenvalues and eigenvectors of a real symmetric matrix input or a batch of real symmetric matrices,
|
||||||
* represented by a pair `eigenvalues to eigenvectors`.
|
* represented by a pair `eigenvalues to eigenvectors`.
|
||||||
|
Loading…
Reference in New Issue
Block a user