added svdGolabKahanHelper
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margarita0303
parent
a497a5df1a
commit
4ff3ab0100
@ -17,6 +17,7 @@ import space.kscience.kmath.tensors.core.DoubleTensor
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import space.kscience.kmath.tensors.core.DoubleTensorAlgebra
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import space.kscience.kmath.tensors.core.IntTensor
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import kotlin.math.abs
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import kotlin.math.max
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import kotlin.math.min
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import kotlin.math.sqrt
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@ -349,3 +350,298 @@ internal fun DoubleTensorAlgebra.svdHelper(
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matrixV.mutableBuffer.array()[matrixV.bufferStart + i] = vBuffer[i]
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}
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}
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internal fun pythag(a: Double, b: Double): Double {
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val at: Double = abs(a)
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val bt: Double = abs(b)
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val ct: Double
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val result: Double
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if (at > bt) {
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ct = bt / at
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result = at * sqrt(1.0 + ct * ct)
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} else if (bt > 0.0) {
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ct = at / bt
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result = bt * sqrt(1.0 + ct * ct)
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} else result = 0.0
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return result
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}
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internal fun SIGN(a: Double, b: Double): Double {
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if (b >= 0.0)
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return abs(a)
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else
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return -abs(a)
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}
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internal fun MutableStructure2D<Double>.svdGolabKahanHelper(u: MutableStructure2D<Double>, w: BufferedTensor<Double>, v: MutableStructure2D<Double>) {
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val shape = this.shape
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val m = shape.component1()
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val n = shape.component2()
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var f = 0.0
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val rv1 = DoubleArray(n)
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var s = 0.0
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var scale = 0.0
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var anorm = 0.0
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var g = 0.0
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var l = 0
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val epsilon = 1e-10
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for (i in 0 until n) {
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/* left-hand reduction */
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l = i + 1
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rv1[i] = scale * g
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g = 0.0
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s = 0.0
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scale = 0.0
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if (i < m) {
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for (k in i until m) {
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scale += abs(this[k, i]);
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}
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if (abs(scale) > epsilon) {
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for (k in i until m) {
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this[k, i] = (this[k, i] / scale)
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s += this[k, i] * this[k, i]
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}
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f = this[i, i]
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if (f >= 0) {
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g = (-1) * abs(sqrt(s))
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} else {
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g = abs(sqrt(s))
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}
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val h = f * g - s
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this[i, i] = f - g
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if (i != n - 1) {
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for (j in l until n) {
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s = 0.0
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for (k in i until m) {
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s += this[k, i] * this[k, j]
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}
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f = s / h
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for (k in i until m) {
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this[k, j] += f * this[k, i]
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}
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}
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}
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for (k in i until m) {
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this[k, i] = this[k, i] * scale
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}
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}
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}
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w.mutableBuffer.array()[w.bufferStart + i] = scale * g
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/* right-hand reduction */
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g = 0.0
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s = 0.0
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scale = 0.0
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if (i < m && i != n - 1) {
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for (k in l until n) {
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scale += abs(this[i, k])
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}
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if (abs(scale) > epsilon) {
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for (k in l until n) {
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this[i, k] = this[i, k] / scale
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s += this[i, k] * this[i, k]
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}
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f = this[i, l]
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if (f >= 0) {
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g = (-1) * abs(sqrt(s))
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} else {
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g = abs(sqrt(s))
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}
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val h = f * g - s
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this[i, l] = f - g
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for (k in l until n) {
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rv1[k] = this[i, k] / h
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}
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if (i != m - 1) {
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for (j in l until m) {
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s = 0.0
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for (k in l until n) {
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s += this[j, k] * this[i, k]
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}
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for (k in l until n) {
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this[j, k] += s * rv1[k]
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}
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}
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}
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for (k in l until n) {
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this[i, k] = this[i, k] * scale
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}
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}
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}
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anorm = max(anorm, (abs(w.mutableBuffer.array()[w.bufferStart + i]) + abs(rv1[i])));
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}
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for (i in n - 1 downTo 0) {
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if (i < n - 1) {
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if (abs(g) > epsilon) {
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for (j in l until n) {
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v[j, i] = (this[i, j] / this[i, l]) / g
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}
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for (j in l until n) {
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s = 0.0
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for (k in l until n)
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s += this[i, k] * v[k, j]
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for (k in l until n)
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v[k, j] += s * v[k, i]
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}
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}
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for (j in l until n) {
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v[i, j] = 0.0
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v[j, i] = 0.0
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}
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}
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v[i, i] = 1.0
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g = rv1[i]
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l = i
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}
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for (i in min(n, m) - 1 downTo 0) {
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l = i + 1
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g = w.mutableBuffer.array()[w.bufferStart + i]
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for (j in l until n) {
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this[i, j] = 0.0
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}
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if (abs(g) > epsilon) {
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g = 1.0 / g
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for (j in l until n) {
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s = 0.0
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for (k in l until m) {
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s += this[k, i] * this[k, j]
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}
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f = (s / this[i, i]) * g
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for (k in i until m) {
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this[k, j] += f * this[k, i]
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}
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}
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for (j in i until m) {
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this[j, i] *= g
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}
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} else {
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for (j in i until m) {
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this[j, i] = 0.0
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}
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}
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this[i, i] += 1.0
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}
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var flag = 0
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var nm = 0
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var c = 0.0
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var h = 0.0
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var y = 0.0
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var z = 0.0
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var x = 0.0
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for (k in n - 1 downTo 0) {
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for (its in 1 until 30) {
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flag = 1
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for (newl in k downTo 0) {
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nm = newl - 1
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if (abs(rv1[newl]) + anorm == anorm) {
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flag = 0
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l = newl
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break
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}
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if (abs(w.mutableBuffer.array()[w.bufferStart + nm]) + anorm == anorm) {
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l = newl
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break
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}
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}
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if (flag != 0) {
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c = 0.0
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s = 1.0
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for (i in l until k) {
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f = s * rv1[i]
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rv1[i] = c * rv1[i]
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if (abs(f) + anorm == anorm) {
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break
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}
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h = pythag(f, g)
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w.mutableBuffer.array()[w.bufferStart + i] = h
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h = 1.0 / h
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c = g * h
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s = (-f) * h
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for (j in 0 until m) {
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y = this[j, nm]
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z = this[j, i]
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this[j, nm] = y * c + z * s
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this[j, i] = z * c - y * s
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}
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}
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}
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z = w.mutableBuffer.array()[w.bufferStart + k]
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if (l == k) {
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if (z < 0.0) {
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w.mutableBuffer.array()[w.bufferStart + k] = -z
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for (j in 0 until n)
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v[j, k] = -v[j, k]
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}
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break
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}
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// надо придумать, что сделать - выкинуть ошибку?
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// if (its == 30) {
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// return
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// }
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x = w.mutableBuffer.array()[w.bufferStart + l]
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nm = k - 1
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y = w.mutableBuffer.array()[w.bufferStart + nm]
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g = rv1[nm]
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h = rv1[k]
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f = ((y - z) * (y + z) + (g - h) * (g + h)) / (2.0 * h * y)
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g = pythag(f, 1.0)
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f = ((x - z) * (x + z) + h * ((y / (f + SIGN(g, f))) - h)) / x
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c = 1.0
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s = 1.0
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var i = 0
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for (j in l until nm + 1) {
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i = j + 1
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g = rv1[i]
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y = w.mutableBuffer.array()[w.bufferStart + i]
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h = s * g
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g = c * g
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z = pythag(f, h)
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rv1[j] = z
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c = f / z
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s = h / z
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f = x * c + g * s
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g = g * c - x * s
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h = y * s
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y *= c
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for (jj in 0 until n) {
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x = v[jj, j];
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z = v[jj, i];
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v[jj, j] = x * c + z * s;
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v[jj, i] = z * c - x * s;
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}
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z = pythag(f, h)
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w.mutableBuffer.array()[w.bufferStart + j] = z
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if (abs(z) > epsilon) {
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z = 1.0 / z
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c = f * z
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s = h * z
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}
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f = c * g + s * y
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x = c * y - s * g
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for (jj in 0 until m) {
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y = this[jj, j]
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z = this[jj, i]
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this[jj, j] = y * c + z * s
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this[jj, i] = z * c - y * s
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}
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}
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rv1[l] = 0.0
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rv1[k] = f
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w.mutableBuffer.array()[w.bufferStart + k] = x
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}
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}
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for (i in 0 until m) {
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for (j in 0 until n) {
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u[j, i] = this[i, j]
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}
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}
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}
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