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Basic matrix inversion

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This commit is contained in:
Alexander Nozik 2018-10-12 10:49:11 +03:00
parent 0cde0cfea5
commit f894175897
2 changed files with 92 additions and 36 deletions
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113
kmath-core/src/commonMain/kotlin/scientifik/kmath/linear/LinearAlgrebra.kt
View File

@ -55,6 +55,26 @@ abstract class MatrixSpace<T : Any>(val rows: Int, val columns: Int, val field:
(0 until a.columns).asSequence().map { k -> field.multiply(a[i, k], b[k, j]) }.reduce { first, second -> field.add(first, second) }
}
}
override fun equals(other: Any?): Boolean {
if (this === other) return true
if (other !is MatrixSpace<*>) return false
if (rows != other.rows) return false
if (columns != other.columns) return false
if (field != other.field) return false
return true
}
override fun hashCode(): Int {
var result = rows
result = 31 * result + columns
result = 31 * result + field.hashCode()
return result
}
}
infix fun <T : Any> Matrix<T>.dot(b: Matrix<T>): Matrix<T> = this.context.multiply(this, b)
@ -90,8 +110,38 @@ interface Matrix<T : Any> : SpaceElement<Matrix<T>, MatrixSpace<T>> {
}
companion object {
fun <T : Any> one(rows: Int, columns: Int, field: Field<T>): Matrix<T> {
return matrix(rows, columns, field) { i, j -> if (i == j) field.one else field.zero }
/**
* Create [ArrayMatrix] with custom field
*/
fun <T : Any> of(rows: Int, columns: Int, field: Field<T>, initializer: (Int, Int) -> T) =
ArrayMatrix(ArrayMatrixSpace(rows, columns, field), initializer)
/**
* Create [ArrayMatrix] of doubles. The implementation in general should be faster than generic one due to boxing.
*/
fun ofReal(rows: Int, columns: Int, initializer: (Int, Int) -> Double) =
ArrayMatrix(ArrayMatrixSpace(rows, columns, DoubleField, realNDFieldFactory), initializer)
/**
* Create a diagonal value matrix. By default value equals [Field.one].
*/
fun <T : Any> diagonal(rows: Int, columns: Int, field: Field<T>, values: (Int) -> T = { field.one }): Matrix<T> {
return of(rows, columns, field) { i, j -> if (i == j) values(i) else field.zero }
}
/**
* Equality check on two generic matrices
*/
fun equals(mat1: Matrix<*>, mat2: Matrix<*>): Boolean {
if (mat1 === mat2) return true
if (mat1.context != mat2.context) return false
for (i in 0 until mat1.rows) {
for (j in 0 until mat2.columns) {
if (mat1[i, j] != mat2[i, j]) return false
}
}
return true
}
}
}
@ -117,6 +167,30 @@ interface Vector<T : Any> : SpaceElement<Vector<T>, VectorSpace<T>> {
get() = context.size
operator fun get(i: Int): T
companion object {
/**
* Create vector with custom field
*/
fun <T : Any> of(size: Int, field: Field<T>, initializer: (Int) -> T) =
ArrayVector(ArrayVectorSpace(size, field), initializer)
/**
* Create vector of [Double]
*/
fun ofReal(size: Int, initializer: (Int) -> Double) =
ArrayVector(ArrayVectorSpace(size, DoubleField, realNDFieldFactory), initializer)
fun equals(v1: Vector<*>, v2: Vector<*>): Boolean {
if (v1 === v2) return true
if (v1.context != v2.context) return false
for (i in 0 until v2.size) {
if (v1[i] != v2[i]) return false
}
return true
}
}
}
@ -195,40 +269,15 @@ class ArrayVector<T : Any> internal constructor(override val context: ArrayVecto
interface LinearSolver<T : Any> {
fun solve(a: Matrix<T>, b: Matrix<T>): Matrix<T>
fun solve(a: Matrix<T>, b: Vector<T>): Vector<T> = solve(a, b.toMatrix()).toVector()
fun inverse(a: Matrix<T>): Matrix<T> = solve(a, Matrix.one(a.rows, a.columns, a.context.field))
fun inverse(a: Matrix<T>): Matrix<T> = solve(a, Matrix.diagonal(a.rows, a.columns, a.context.field))
}
/**
* Create vector with custom field
*/
fun <T : Any> vector(size: Int, field: Field<T>, initializer: (Int) -> T) =
ArrayVector(ArrayVectorSpace(size, field), initializer)
/**
* Create vector of [Double]
*/
fun realVector(size: Int, initializer: (Int) -> Double) =
ArrayVector(ArrayVectorSpace(size, DoubleField, realNDFieldFactory), initializer)
/**
* Convert vector to array (copying content of array)
*/
fun <T : Any> Array<T>.asVector(field: Field<T>) = vector(size, field) { this[it] }
fun DoubleArray.asVector() = realVector(this.size) { this[it] }
/**
* Create [ArrayMatrix] with custom field
*/
fun <T : Any> matrix(rows: Int, columns: Int, field: Field<T>, initializer: (Int, Int) -> T) =
ArrayMatrix(ArrayMatrixSpace(rows, columns, field), initializer)
/**
* Create [ArrayMatrix] of doubles.
*/
fun realMatrix(rows: Int, columns: Int, initializer: (Int, Int) -> Double) =
ArrayMatrix(ArrayMatrixSpace(rows, columns, DoubleField, realNDFieldFactory), initializer)
fun <T : Any> Array<T>.toVector(field: Field<T>) = Vector.of(size, field) { this[it] }
fun DoubleArray.toVector() = Vector.ofReal(this.size) { this[it] }
/**
* Convert matrix to vector if it is possible
@ -243,7 +292,7 @@ fun <T : Any> Matrix<T>.toVector(): Vector<T> {
// //Generic vector
// vector(rows, context.field) { get(it, 0) }
// }
vector(rows, context.field) { get(it, 0) }
Vector.of(rows, context.field) { get(it, 0) }
}
else -> error("Can't convert matrix with more than one column to vector")
}
@ -257,6 +306,6 @@ fun <T : Any> Vector<T>.toMatrix(): Matrix<T> {
// //Generic vector
// matrix(size, 1, context.field) { i, j -> get(i) }
// }
return matrix(size, 1, context.field) { i, j -> get(i) }
return Matrix.of(size, 1, context.field) { i, j -> get(i) }
}

15
kmath-core/src/commonTest/kotlin/scientifik/kmath/linear/RealLUSolverTest.kt
View File

@ -2,13 +2,20 @@ package scientifik.kmath.linear
import scientifik.kmath.operations.DoubleField
import kotlin.test.Test
import kotlin.test.assertEquals
import kotlin.test.assertTrue
class RealLUSolverTest {
@Test
fun testInvert() {
val matrix = Matrix.one(2, 2, DoubleField)
fun testInvertOne() {
val matrix = Matrix.diagonal(2, 2, DoubleField)
val inverted = RealLUSolver.inverse(matrix)
assertEquals(1.0, inverted[0, 0])
assertTrue { Matrix.equals(matrix,inverted) }
}
// @Test
// fun testInvert() {
// val matrix = realMatrix(2,2){}
// val inverted = RealLUSolver.inverse(matrix)
// assertTrue { Matrix.equals(matrix,inverted) }
// }
}