Feature/tensors performance #497
@ -1,325 +0,0 @@
|
||||
package space.kscience.kmath.tensors
|
||||
|
||||
import space.kscience.kmath.nd.*
|
||||
import kotlin.math.abs
|
||||
import kotlin.math.max
|
||||
import kotlin.math.min
|
||||
import kotlin.math.sqrt
|
||||
|
||||
/*
|
||||
* Copyright 2018-2021 KMath contributors.
|
||||
* Use of this source code is governed by the Apache 2.0 license that can be found in the license/LICENSE.txt file.
|
||||
*/
|
||||
|
||||
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
|
||||
}
|
||||
|
||||
fun SIGN(a: Double, b: Double): Double {
|
||||
if (b >= 0.0)
|
||||
return abs(a)
|
||||
else
|
||||
return -abs(a)
|
||||
}
|
||||
|
||||
// matrix v is not transposed at the output
|
||||
|
||||
internal fun MutableStructure2D<Double>.svdGolabKahan(v: MutableStructure2D<Double>, w: MutableStructure2D<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
|
||||
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 (scale != 0.0) {
|
||||
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
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
w[i, 0] = 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 (scale != 0.0) {
|
||||
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(w[i, 0]) + abs(rv1[i])));
|
||||
}
|
||||
|
||||
for (i in n - 1 downTo 0) {
|
||||
if (i < n - 1) {
|
||||
if (g != 0.0) {
|
||||
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
|
||||
}
|
||||
|
||||
// до этого момента все правильно считается
|
||||
// дальше - нет
|
||||
|
||||
for (i in min(n, m) - 1 downTo 0) {
|
||||
l = i + 1
|
||||
g = w[i, 0]
|
||||
for (j in l until n) {
|
||||
this[i, j] = 0.0
|
||||
}
|
||||
if (g != 0.0) {
|
||||
// !!!!! вот тут деление на почти ноль
|
||||
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
|
||||
}
|
||||
|
||||
// println("matrix")
|
||||
// this.print()
|
||||
// тут матрица должна выглядеть так:
|
||||
// 0.134840 -0.762770 0.522117
|
||||
// -0.269680 -0.476731 -0.245388
|
||||
// -0.404520 -0.190693 -0.527383
|
||||
// -0.539360 0.095346 -0.297540
|
||||
// -0.674200 0.381385 0.548193
|
||||
|
||||
this[0, 2] = 0.522117
|
||||
this[1, 2] = -0.245388
|
||||
this[2, 2] = -0.527383
|
||||
this[3, 2] = -0.297540
|
||||
this[4, 2] = 0.548193
|
||||
|
||||
// задала правильные значения, чтобы проверить правильность кода дальше
|
||||
// дальше - все корректно
|
||||
|
||||
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 30) {
|
||||
flag = 1
|
||||
for (newl in k downTo 0) {
|
||||
nm = newl - 1
|
||||
if (abs(rv1[newl]) + anorm == anorm) {
|
||||
flag = 0
|
||||
l = newl
|
||||
break
|
||||
}
|
||||
if (abs(w[nm, 0]) + anorm == anorm) {
|
||||
l = newl
|
||||
break
|
||||
}
|
||||
}
|
||||
|
||||
if (flag != 0) {
|
||||
c = 0.0
|
||||
s = 1.0
|
||||
for (i in l until k) {
|
||||
f = s * rv1[i]
|
||||
rv1[i] = c * rv1[i]
|
||||
if (abs(f) + anorm == anorm) {
|
||||
break
|
||||
}
|
||||
h = pythag(f, g)
|
||||
w[i, 0] = 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 = w[k, 0]
|
||||
if (l == k) {
|
||||
if (z < 0.0) {
|
||||
w[k, 0] = -z
|
||||
for (j in 0 until n)
|
||||
v[j, k] = -v[j, k]
|
||||
}
|
||||
break
|
||||
}
|
||||
|
||||
// надо придумать, что сделать - выкинуть ошибку?
|
||||
// if (its == 30) {
|
||||
// return
|
||||
// }
|
||||
|
||||
x = w[l, 0]
|
||||
nm = k - 1
|
||||
y = w[nm, 0]
|
||||
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 = w[i, 0]
|
||||
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)
|
||||
w[j, 0] = z
|
||||
if (z != 0.0) {
|
||||
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
|
||||
w[k, 0] = x
|
||||
}
|
||||
}
|
||||
}
|
Loading…
Reference in New Issue
Block a user