925 lines
25 KiB
Swift
925 lines
25 KiB
Swift
// Copyright © 2014-2018 the Surge contributors
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//
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// Permission is hereby granted, free of charge, to any person obtaining a copy
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// of this software and associated documentation files (the "Software"), to deal
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// in the Software without restriction, including without limitation the rights
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// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
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// copies of the Software, and to permit persons to whom the Software is
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// furnished to do so, subject to the following conditions:
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//
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// The above copyright notice and this permission notice shall be included in
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// all copies or substantial portions of the Software.
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//
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// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
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// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
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// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
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// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
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// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
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// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
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// THE SOFTWARE.
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@testable import Surge
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import XCTest
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// swiftlint:disable nesting type_body_length
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class MatrixTests: XCTestCase {
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func test_init_rows_columns_repeatedValue() {
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typealias Scalar = Double
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let actual: Matrix<Scalar> = Matrix(rows: 2, columns: 3, repeatedValue: 42.0)
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let expected: Matrix<Scalar> = [
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[42.0, 42.0, 42.0],
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[42.0, 42.0, 42.0],
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]
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XCTAssertEqual(actual, expected)
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}
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func test_init_contents() {
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typealias Scalar = Double
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let contents: [[Scalar]] = [
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[1, 2, 3, 4],
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[5, 6, 7, 8],
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[9, 10, 11, 12],
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]
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let actual: Matrix<Scalar> = Matrix(contents)
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let expected: Matrix<Scalar> = [
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[1, 2, 3, 4],
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[5, 6, 7, 8],
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[9, 10, 11, 12],
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]
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XCTAssertEqual(actual, expected)
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}
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func test_init_row() {
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typealias Scalar = Double
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let row: [Scalar] = [1, 2, 3, 4]
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let actual: Matrix<Scalar> = Matrix(row: row)
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let expected: Matrix<Scalar> = [
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[1, 2, 3, 4],
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]
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XCTAssertEqual(actual, expected)
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}
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func test_init_column() {
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typealias Scalar = Double
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let column: [Scalar] = [1, 2, 3, 4]
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let actual: Matrix<Scalar> = Matrix(column: column)
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let expected: Matrix<Scalar> = [
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[1],
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[2],
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[3],
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[4],
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]
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XCTAssertEqual(actual, expected)
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}
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func test_init_rows_columns_grid() {
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typealias Scalar = Double
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let grid: [Scalar] = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12]
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let actual: Matrix<Scalar> = Matrix(rows: 3, columns: 4, grid: grid)
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let expected: Matrix<Scalar> = [
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[1, 2, 3, 4],
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[5, 6, 7, 8],
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[9, 10, 11, 12],
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]
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XCTAssertEqual(actual, expected)
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}
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func test_grid() {
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typealias Scalar = Double
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let contents: [[Scalar]] = [
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[1, 2, 3, 4],
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[5, 6, 7, 8],
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[9, 10, 11, 12],
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]
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let matrix: Matrix<Scalar> = Matrix(contents)
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let actual = matrix.grid
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let expected: [Scalar] = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12]
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XCTAssertEqual(actual, expected)
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}
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func test_init_identity() {
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let actual: Matrix<Double> = Matrix.identity(size: 3)
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let expected: Matrix<Double> = [
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[1.0, 0.0, 0.0],
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[0.0, 1.0, 0.0],
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[0.0, 0.0, 1.0],
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]
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XCTAssertEqual(actual, expected)
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}
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func test_init_eye() {
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let actual_2x3: Matrix<Double> = Matrix.eye(rows: 2, columns: 3)
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let expected_2x3: Matrix<Double> = [
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[1.0, 0.0, 0.0],
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[0.0, 1.0, 0.0],
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]
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XCTAssertEqual(actual_2x3, expected_2x3)
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let actual_3x2: Matrix<Double> = Matrix.eye(rows: 3, columns: 2)
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let expected_3x2: Matrix<Double> = [
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[1.0, 0.0],
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[0.0, 1.0],
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[0.0, 0.0],
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]
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XCTAssertEqual(actual_3x2, expected_3x2)
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let actual_3x3: Matrix<Double> = Matrix.eye(rows: 3, columns: 3)
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let expected_3x3: Matrix<Double> = [
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[1.0, 0.0, 0.0],
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[0.0, 1.0, 0.0],
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[0.0, 0.0, 1.0],
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]
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XCTAssertEqual(actual_3x3, expected_3x3)
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}
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func test_init_diagonal_repeatedValue() {
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let actual_2x3: Matrix<Double> = Matrix.diagonal(rows: 2, columns: 3, repeatedValue: 42.0)
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let expected_2x3: Matrix<Double> = [
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[42.0, 0.0, 0.0],
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[0.0, 42.0, 0.0],
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]
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XCTAssertEqual(actual_2x3, expected_2x3)
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let actual_3x2: Matrix<Double> = Matrix.diagonal(rows: 3, columns: 2, repeatedValue: 42.0)
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let expected_3x2: Matrix<Double> = [
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[42.0, 0.0],
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[0.0, 42.0],
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[0.0, 0.0],
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]
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XCTAssertEqual(actual_3x2, expected_3x2)
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let actual_3x3: Matrix<Double> = Matrix.diagonal(rows: 3, columns: 3, repeatedValue: 42.0)
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let expected_3x3: Matrix<Double> = [
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[42.0, 0.0, 0.0],
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[0.0, 42.0, 0.0],
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[0.0, 0.0, 42.0],
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]
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XCTAssertEqual(actual_3x3, expected_3x3)
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}
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func test_init_diagonal_scalars() {
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let actual_2x3: Matrix<Double> = Matrix.diagonal(rows: 2, columns: 3, scalars: [1, 2])
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let expected_2x3: Matrix<Double> = [
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[1.0, 0.0, 0.0],
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[0.0, 2.0, 0.0],
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]
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XCTAssertEqual(actual_2x3, expected_2x3)
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let actual_3x2: Matrix<Double> = Matrix.diagonal(rows: 3, columns: 2, scalars: [1, 2])
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let expected_3x2: Matrix<Double> = [
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[1.0, 0.0],
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[0.0, 2.0],
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[0.0, 0.0],
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]
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XCTAssertEqual(actual_3x2, expected_3x2)
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let actual_3x3: Matrix<Double> = Matrix.diagonal(rows: 3, columns: 3, scalars: [1, 2, 3])
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let expected_3x3: Matrix<Double> = [
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[1.0, 0.0, 0.0],
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[0.0, 2.0, 0.0],
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[0.0, 0.0, 3.0],
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]
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XCTAssertEqual(actual_3x3, expected_3x3)
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}
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func test_subscript_row_get() {
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typealias Scalar = Double
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let matrix: Matrix<Scalar> = [
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[1, 2, 3, 4],
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[5, 6, 7, 8],
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[9, 10, 11, 12],
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]
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XCTAssertEqual(matrix[row: 0], [1, 2, 3, 4])
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XCTAssertEqual(matrix[row: 1], [5, 6, 7, 8])
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}
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func test_subscript_column_get() {
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typealias Scalar = Double
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let matrix: Matrix<Scalar> = [
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[1, 2, 3, 4],
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[5, 6, 7, 8],
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[9, 10, 11, 12],
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]
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XCTAssertEqual(matrix[column: 0], [1, 5, 9])
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XCTAssertEqual(matrix[column: 1], [2, 6, 10])
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}
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func test_subscript_row_set() {
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typealias Scalar = Double
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var matrix: Matrix<Scalar> = [
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[1, 2, 3, 4],
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[5, 6, 7, 8],
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[9, 10, 11, 12],
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]
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matrix[row: 0] = [13.0, 14.0, 15.0, 16.0]
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let expected: Matrix<Scalar> = [
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[13, 14, 15, 16],
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[5, 6, 7, 8],
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[9, 10, 11, 12],
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]
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XCTAssertEqual(matrix, expected)
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}
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func test_subscript_column_set() {
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typealias Scalar = Double
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var matrix: Matrix<Scalar> = [
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[1, 2, 3, 4],
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[5, 6, 7, 8],
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[9, 10, 11, 12],
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]
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matrix[column: 0] = [20, 30, 40]
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let expected: Matrix<Scalar> = [
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[20, 2, 3, 4],
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[30, 6, 7, 8],
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[40, 10, 11, 12],
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]
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XCTAssertEqual(matrix, expected)
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}
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func test_add_matrix_matrix_float() {
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typealias Scalar = Float
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let matrix: Matrix<Scalar> = [
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[1, 2, 3, 4],
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[5, 6, 7, 8],
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[9, 10, 11, 12],
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]
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let actual = matrix + matrix
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let expected: Matrix<Float> = [
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[2, 4, 6, 8],
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[10, 12, 14, 16],
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[18, 20, 22, 24],
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]
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XCTAssertEqual(actual, expected)
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}
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func test_add_matrix_matrix_double() {
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typealias Scalar = Double
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let matrix: Matrix<Scalar> = [
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[1, 2, 3, 4],
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[5, 6, 7, 8],
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[9, 10, 11, 12],
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]
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let actual = matrix + matrix
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let expected: Matrix<Scalar> = [
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[2, 4, 6, 8],
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[10, 12, 14, 16],
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[18, 20, 22, 24],
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]
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XCTAssertEqual(actual, expected)
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}
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func test_sub_matrix_matrix_float() {
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typealias Scalar = Float
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let matrix: Matrix<Scalar> = [
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[1, 2, 3, 4],
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[5, 6, 7, 8],
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[9, 10, 11, 12],
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]
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let actual = matrix - matrix
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let expected: Matrix<Float> = [
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[0, 0, 0, 0],
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[0, 0, 0, 0],
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[0, 0, 0, 0],
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]
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XCTAssertEqual(actual, expected)
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}
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func test_sub_matrix_matrix_double() {
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typealias Scalar = Double
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let matrix: Matrix<Scalar> = [
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[1, 2, 3, 4],
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[5, 6, 7, 8],
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[9, 10, 11, 12],
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]
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let actual = matrix - matrix
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let expected: Matrix<Scalar> = [
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[0, 0, 0, 0],
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[0, 0, 0, 0],
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[0, 0, 0, 0],
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]
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XCTAssertEqual(actual, expected)
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}
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func test_mul_scalar_matrix_float() {
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typealias Scalar = Float
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let lhs: Scalar = 2
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let rhs: Matrix<Scalar> = [
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[2, 4, 6],
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[10, 12, 14],
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]
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let actual = lhs * rhs
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let expected: Matrix<Scalar> = [
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[4, 8, 12],
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[20, 24, 28],
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]
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XCTAssertEqual(actual, expected)
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}
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func test_mul_scalar_matrix_double() {
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typealias Scalar = Double
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let lhs: Scalar = 2
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let rhs: Matrix<Scalar> = [
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[2, 4, 6],
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[10, 12, 14],
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]
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let actual = lhs * rhs
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let expected: Matrix<Scalar> = [
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[4, 8, 12],
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[20, 24, 28],
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]
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XCTAssertEqual(actual, expected)
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}
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func test_mul_matrix_matrix_float() {
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typealias Scalar = Float
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let lhs: Matrix<Scalar> = [
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[2, 4],
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[10, 12],
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[18, 20],
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]
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let rhs: Matrix<Scalar> = [
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[2, 4, 6],
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[10, 12, 14],
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]
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let actual = lhs * rhs
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let expected: Matrix<Scalar> = [
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[44, 56, 68],
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[140, 184, 228],
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[236, 312, 388],
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]
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XCTAssertEqual(actual, expected)
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}
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func test_mul_matrix_matrix_double() {
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typealias Scalar = Double
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let lhs: Matrix<Scalar> = [
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[2, 4],
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[10, 12],
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[18, 20],
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]
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let rhs: Matrix<Scalar> = [
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[2, 4, 6],
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[10, 12, 14],
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]
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let actual = lhs * rhs
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let expected: Matrix<Scalar> = [
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[44, 56, 68],
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[140, 184, 228],
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[236, 312, 388],
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]
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XCTAssertEqual(actual, expected)
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}
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func test_mul_matrix_vector_float() {
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typealias Scalar = Float
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let lhs: Matrix<Scalar> = [
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[1, 2, 3],
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[4, 5, 6],
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]
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let rhs: Vector<Scalar> = [1, 2, 4]
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let actual = lhs * rhs
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let expected: Vector<Scalar> = [17, 38]
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XCTAssertEqual(actual, expected)
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}
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func test_mul_matrix_vector_double() {
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typealias Scalar = Double
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let lhs: Matrix<Scalar> = [
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[1, 2, 3],
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[4, 5, 6],
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]
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let rhs: Vector<Scalar> = [1, 2, 4]
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let actual = lhs * rhs
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let expected: Vector<Scalar> = [17, 38]
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XCTAssertEqual(actual, expected)
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}
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func test_div_matrix_scalar_float() {
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typealias Scalar = Float
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let lhs: Matrix<Scalar> = [
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[2, 4, 6],
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[10, 12, 14],
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]
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let rhs: Scalar = 2
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let actual = lhs / rhs
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let expected: Matrix<Scalar> = [
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[1, 2, 3],
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[5, 6, 7],
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]
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XCTAssertEqual(actual, expected, accuracy: 1e-6)
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}
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func test_div_matrix_scalar_double() {
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typealias Scalar = Double
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let lhs: Matrix<Scalar> = [
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[2, 4, 6],
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[10, 12, 14],
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]
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let rhs: Scalar = 2
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let actual = lhs / rhs
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let expected: Matrix<Scalar> = [
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[1, 2, 3],
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[5, 6, 7],
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]
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XCTAssertEqual(actual, expected, accuracy: 1e-8)
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}
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func test_div_matrix_matrix_float() {
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typealias Scalar = Float
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let lhs: Matrix<Scalar> = [
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[2, 3],
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[2, 2],
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]
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let rhs: Matrix<Scalar> = [
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[-1, 3/2],
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[1, -1],
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]
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let actual = lhs / rhs
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let expected: Matrix<Scalar> = [
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[10, 12],
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[8, 10],
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]
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XCTAssertEqual(actual, expected, accuracy: 1e-5)
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}
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func test_div_matrix_matrix_double() {
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typealias Scalar = Double
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let lhs: Matrix<Scalar> = [
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[2, 3],
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[2, 2],
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]
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let rhs: Matrix<Scalar> = [
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[-1, 3/2],
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[1, -1],
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]
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let actual = lhs / rhs
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let expected: Matrix<Scalar> = [
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[10, 12],
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[8, 10],
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]
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XCTAssertEqual(actual, expected, accuracy: 1e-8)
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}
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func test_pow_matrix_scalar_float() {
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typealias Scalar = Float
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let lhs: Matrix<Scalar> = [
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[1, 2, 3],
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[4, 5, 6],
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]
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let rhs: Scalar = 2
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let actual = pow(lhs, rhs)
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let expected: Matrix<Scalar> = .init(
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lhs.map { row in
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row.map { pow($0, rhs) }
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}
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)
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XCTAssertEqual(actual, expected, accuracy: 1e-5)
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}
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func test_pow_matrix_scalar_double() {
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typealias Scalar = Double
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let lhs: Matrix<Scalar> = [
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[1, 2, 3],
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[4, 5, 6],
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]
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let rhs: Scalar = 2
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let actual = pow(lhs, rhs)
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let expected: Matrix<Scalar> = .init(
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lhs.map { row in
|
|
row.map { pow($0, rhs) }
|
|
}
|
|
)
|
|
|
|
XCTAssertEqual(actual, expected, accuracy: 1e-8)
|
|
}
|
|
|
|
func test_exp_matrix_float() {
|
|
typealias Scalar = Float
|
|
|
|
let lhs: Matrix<Scalar> = [
|
|
[1, 2, 3],
|
|
[4, 5, 6],
|
|
]
|
|
|
|
let actual = exp(lhs)
|
|
let expected: Matrix<Scalar> = .init(
|
|
lhs.map { row in
|
|
row.map { exp($0) }
|
|
}
|
|
)
|
|
|
|
XCTAssertEqual(actual, expected, accuracy: 1e-3)
|
|
}
|
|
|
|
func test_exp_matrix_double() {
|
|
typealias Scalar = Double
|
|
|
|
let lhs: Matrix<Scalar> = [
|
|
[1, 2, 3],
|
|
[4, 5, 6],
|
|
]
|
|
|
|
let actual = exp(lhs)
|
|
let expected: Matrix<Scalar> = .init(
|
|
lhs.map { row in
|
|
row.map { exp($0) }
|
|
}
|
|
)
|
|
|
|
XCTAssertEqual(actual, expected, accuracy: 1e-8)
|
|
}
|
|
|
|
func test_sum_matrix_rows_double() {
|
|
typealias Scalar = Double
|
|
|
|
let lhs: Matrix<Scalar> = [
|
|
[1, 2, 3],
|
|
[4, 5, 6],
|
|
]
|
|
|
|
let actual = sum(lhs, axies: .row)
|
|
let expected: Matrix<Scalar> = [
|
|
[6],
|
|
[15],
|
|
]
|
|
|
|
XCTAssertEqual(actual, expected, accuracy: 1e-5)
|
|
}
|
|
|
|
func test_sum_matrix_rows_float() {
|
|
typealias Scalar = Float
|
|
|
|
let lhs: Matrix<Scalar> = [
|
|
[1, 2, 3],
|
|
[4, 5, 6],
|
|
]
|
|
|
|
let actual = sum(lhs, axies: .row)
|
|
let expected: Matrix<Scalar> = [
|
|
[6],
|
|
[15],
|
|
]
|
|
|
|
XCTAssertEqual(actual, expected, accuracy: 1e-5)
|
|
}
|
|
|
|
func test_sum_matrix_columns_double() {
|
|
typealias Scalar = Double
|
|
|
|
let lhs: Matrix<Scalar> = [
|
|
[1, 2, 3],
|
|
[4, 5, 6],
|
|
]
|
|
|
|
let actual = sum(lhs, axies: .column)
|
|
let expected: Matrix<Scalar> = [
|
|
[5, 7, 9],
|
|
]
|
|
|
|
XCTAssertEqual(actual, expected, accuracy: 1e-5)
|
|
}
|
|
|
|
func test_sum_matrix_columns_float() {
|
|
typealias Scalar = Float
|
|
|
|
let lhs: Matrix<Scalar> = [
|
|
[1, 2, 3],
|
|
[4, 5, 6],
|
|
]
|
|
|
|
let actual = sum(lhs, axies: .column)
|
|
let expected: Matrix<Scalar> = [
|
|
[5, 7, 9],
|
|
]
|
|
|
|
XCTAssertEqual(actual, expected, accuracy: 1e-5)
|
|
}
|
|
|
|
func test_inv_matrix_double() {
|
|
typealias Scalar = Double
|
|
|
|
let lhs: Matrix<Scalar> = [
|
|
[2, 3],
|
|
[2, 2],
|
|
]
|
|
|
|
let actual = inv(lhs)
|
|
let expected: Matrix<Scalar> = [
|
|
[-1, 1.5],
|
|
[1, -1],
|
|
]
|
|
|
|
XCTAssertEqual(actual, expected, accuracy: 1e-8)
|
|
}
|
|
|
|
func test_inv_matrix_float() {
|
|
typealias Scalar = Float
|
|
|
|
let lhs: Matrix<Scalar> = [
|
|
[2, 3],
|
|
[2, 2],
|
|
]
|
|
|
|
let actual = inv(lhs)
|
|
let expected: Matrix<Scalar> = [
|
|
[-1, 1.5],
|
|
[1, -1],
|
|
]
|
|
|
|
XCTAssertEqual(actual, expected, accuracy: 1e-6)
|
|
}
|
|
|
|
func test_tranpose_matrix_double() {
|
|
typealias Scalar = Double
|
|
|
|
let lhs: Matrix<Scalar> = [
|
|
[1, 2, 3],
|
|
[4, 5, 6],
|
|
]
|
|
|
|
let actual = transpose(lhs)
|
|
let expected: Matrix<Scalar> = [
|
|
[1, 4],
|
|
[2, 5],
|
|
[3, 6],
|
|
]
|
|
|
|
XCTAssertEqual(actual, expected)
|
|
}
|
|
|
|
func test_tranpose_matrix_float() {
|
|
typealias Scalar = Float
|
|
|
|
let lhs: Matrix<Scalar> = [
|
|
[1, 2, 3],
|
|
[4, 5, 6],
|
|
]
|
|
|
|
let actual = transpose(lhs)
|
|
let expected: Matrix<Scalar> = [
|
|
[1, 4],
|
|
[2, 5],
|
|
[3, 6],
|
|
]
|
|
|
|
XCTAssertEqual(actual, expected)
|
|
}
|
|
|
|
func test_det_matrix_double() {
|
|
typealias Scalar = Double
|
|
|
|
let lhs: Matrix<Scalar> = [
|
|
[1, 2],
|
|
[5, 6],
|
|
]
|
|
|
|
let actual = det(lhs)
|
|
let expected: Scalar = 6 - 10
|
|
|
|
XCTAssertEqual(actual, expected)
|
|
}
|
|
|
|
func test_det_matrix_float() {
|
|
typealias Scalar = Float
|
|
|
|
let lhs: Matrix<Scalar> = [
|
|
[1, 2],
|
|
[5, 6],
|
|
]
|
|
|
|
let actual = det(lhs)
|
|
let expected: Scalar = 6 - 10
|
|
|
|
XCTAssertEqual(actual, expected)
|
|
}
|
|
|
|
func test_mul_empty_float() {
|
|
typealias Scalar = Float
|
|
|
|
let lhs: Matrix<Scalar> = [
|
|
[1]
|
|
]
|
|
let rhs: Matrix<Scalar> = [
|
|
[]
|
|
]
|
|
|
|
let result = lhs * rhs
|
|
|
|
XCTAssertEqual(result.rows, 1)
|
|
XCTAssertEqual(result.columns, 0)
|
|
}
|
|
|
|
func complexVectorMatches<T: FloatingPoint>(_ a: [(T, T)], _ b: [(T, T)], accuracy: T) -> Bool {
|
|
guard a.count == b.count else {
|
|
return false
|
|
}
|
|
return (zip(a, b).first { a, e -> Bool in
|
|
!(abs(a.0 - e.0) < accuracy && abs(a.1 - e.1) < accuracy)
|
|
}) == nil
|
|
}
|
|
|
|
func eigen_decomposition_trivial_generic<T: FloatingPoint & ExpressibleByFloatLiteral>(defaultAccuracy: T, eigendecompostionFn: ((Matrix<T>) throws -> MatrixEigenDecompositionResult<T>)) throws {
|
|
let matrix = Matrix<T>([
|
|
[1, 0, 0],
|
|
[0, 2, 0],
|
|
[0, 0, 3],
|
|
])
|
|
let ed = try eigendecompostionFn(matrix)
|
|
|
|
let expectedEigenValues: [(T, T)] = [(1, 0), (2, 0), (3, 0)]
|
|
XCTAssertTrue(complexVectorMatches(ed.eigenValues, expectedEigenValues, accuracy: defaultAccuracy))
|
|
|
|
let expectedEigenVector: [(T, T)] = [(1, 0), (0, 0), (0, 0), (0, 0), (1, 0), (0, 0), (0, 0), (0, 0), (1, 0)]
|
|
let flatLeft = ed.leftEigenVectors.flatMap { $0 }
|
|
XCTAssertTrue(complexVectorMatches(flatLeft, expectedEigenVector, accuracy: defaultAccuracy))
|
|
|
|
let flatRight = ed.rightEigenVectors.flatMap { $0 }
|
|
XCTAssertTrue(complexVectorMatches(flatRight, expectedEigenVector, accuracy: defaultAccuracy))
|
|
}
|
|
|
|
func test_eigen_decomposition_trivial() throws {
|
|
try eigen_decomposition_trivial_generic(defaultAccuracy: 1e-11) { (m: Matrix<Double>) throws -> MatrixEigenDecompositionResult<Double> in
|
|
try eigenDecompose(m)
|
|
}
|
|
try eigen_decomposition_trivial_generic(defaultAccuracy: 1e-8) { (m: Matrix<Float>) throws -> MatrixEigenDecompositionResult<Float> in
|
|
try eigenDecompose(m)
|
|
}
|
|
}
|
|
|
|
// Example from https://docs.scipy.org/doc/numpy/reference/generated/numpy.linalg.eig.html
|
|
func eigen_decomposition_complex_results_numpy_example_generic<T: FloatingPoint & ExpressibleByFloatLiteral>(defaultAccuracy: T, eigendecompostionFn: ((Matrix<T>) throws -> MatrixEigenDecompositionResult<T>)) throws {
|
|
let matrix = Matrix<T>([
|
|
[1, -1],
|
|
[1, 1],
|
|
])
|
|
let ed = try eigendecompostionFn(matrix)
|
|
|
|
let expectedEigenValues: [(T, T)] = [(1, 1), (1, -1)]
|
|
XCTAssertTrue(complexVectorMatches(ed.eigenValues, expectedEigenValues, accuracy: defaultAccuracy))
|
|
|
|
let expectedEigenVector: [(T, T)] = [(0.707_106_78, 0), (0.707_106_78, 0), (0, -0.707_106_78), (0, 0.707_106_78)]
|
|
|
|
// Numpy only gives the right eigenvector
|
|
let flatRight = ed.rightEigenVectors.flatMap { $0 }
|
|
XCTAssertTrue(complexVectorMatches(flatRight, expectedEigenVector, accuracy: 0.000_001))
|
|
}
|
|
|
|
func test_eigen_decomposition_complex_results_numpy_example() throws {
|
|
try eigen_decomposition_complex_results_numpy_example_generic(defaultAccuracy: 1e-11) { (m: Matrix<Double>) throws -> MatrixEigenDecompositionResult<Double> in
|
|
try eigenDecompose(m)
|
|
}
|
|
try eigen_decomposition_complex_results_numpy_example_generic(defaultAccuracy: 1e-8) { (m: Matrix<Float>) throws -> MatrixEigenDecompositionResult<Float> in
|
|
try eigenDecompose(m)
|
|
}
|
|
}
|
|
|
|
// Example from Intel's DGEEV documentation
|
|
// https://software.intel.com/sites/products/documentation/doclib/mkl_sa/11/mkl_lapack_examples/dgeev.htm
|
|
func eigen_decomposition_complex_results_dgeev_example_generic<T: FloatingPoint & ExpressibleByFloatLiteral>(defaultAccuracy: T, eigendecompostionFn: ((Matrix<T>) throws -> MatrixEigenDecompositionResult<T>)) throws {
|
|
let matrix = Matrix<T>(rows: 5, columns: 5, grid: [
|
|
-1.01, 0.86, -4.60, 3.31, -4.81,
|
|
3.98, 0.53, -7.04, 5.29, 3.55,
|
|
3.30, 8.26, -3.89, 8.20, -1.51,
|
|
4.43, 4.96, -7.66, -7.33, 6.18,
|
|
7.31, -6.43, -6.16, 2.47, 5.58
|
|
])
|
|
let ed = try eigendecompostionFn(matrix)
|
|
|
|
let expectedEigenValues: [(T, T)] = [(2.86, 10.76), (2.86, -10.76), (-0.69, 4.70), (-0.69, -4.70), (-10.46, 0)]
|
|
XCTAssertTrue(complexVectorMatches(ed.eigenValues, expectedEigenValues, accuracy: 0.02))
|
|
|
|
let expectedLeftEigenVectors: [[(T, T)]] = [
|
|
[(0.04, 0.29), (0.04, -0.29), (-0.13, -0.33), (-0.13, 0.33), (0.04, 0)],
|
|
[(0.62, 0.00), (0.62, 0.00), (0.69, 0.00), (0.69, 0.00), (0.56, 0)],
|
|
[(-0.04, -0.58), (-0.04, 0.58), (-0.39, -0.07), (-0.39, 0.07), (-0.13, 0)],
|
|
[(0.28, 0.01), (0.28, -0.01), (-0.02, -0.19), (-0.02, 0.19), (-0.80, 0)],
|
|
[(-0.04, 0.34), (-0.04, -0.34), (-0.40, 0.22), (-0.40, -0.22), (0.18, 0)],
|
|
]
|
|
XCTAssertEqual(ed.leftEigenVectors.count, expectedLeftEigenVectors.count)
|
|
for i in 0..<ed.leftEigenVectors.count {
|
|
XCTAssertTrue(complexVectorMatches(ed.leftEigenVectors[i], expectedLeftEigenVectors[i], accuracy: 0.02))
|
|
}
|
|
|
|
let expectedRightEigenVectors: [[(T, T)]] = [
|
|
[(0.11, 0.17), (0.11, -0.17), (0.73, 0.00), (0.73, 0.00), (0.46, 0.0)],
|
|
[(0.41, -0.26), (0.41, 0.26), (-0.03, -0.02), (-0.03, 0.02), (0.34, 0.0)],
|
|
[(0.10, -0.51), (0.10, 0.51), (0.19, -0.29), (0.19, 0.29), (0.31, 0.0)],
|
|
[(0.40, -0.09), (0.40, 0.09), (-0.08, -0.08), (-0.08, 0.08), (-0.74, 0.0)],
|
|
[(0.54, 0.00), (0.54, 0.00), (-0.29, -0.49), (-0.29, 0.49), (0.16, 0.0)],
|
|
]
|
|
XCTAssertEqual(ed.rightEigenVectors.count, expectedRightEigenVectors.count)
|
|
for i in 0..<ed.rightEigenVectors.count {
|
|
XCTAssertTrue(complexVectorMatches(ed.rightEigenVectors[i], expectedRightEigenVectors[i], accuracy: 0.02))
|
|
}
|
|
}
|
|
|
|
func test_eigen_decomposition_complex_results_dgeev_example() throws {
|
|
try eigen_decomposition_complex_results_dgeev_example_generic(defaultAccuracy: 1e-11) { (m: Matrix<Double>) throws -> MatrixEigenDecompositionResult<Double> in
|
|
try eigenDecompose(m)
|
|
}
|
|
try eigen_decomposition_complex_results_dgeev_example_generic(defaultAccuracy: 1e-8) { (m: Matrix<Float>) throws -> MatrixEigenDecompositionResult<Float> in
|
|
try eigenDecompose(m)
|
|
}
|
|
}
|
|
|
|
func test_eigen_decompose_throws_when_not_square() throws {
|
|
let matrix = Matrix<Double>([
|
|
[1, 0, 0],
|
|
[0, 2, 0],
|
|
])
|
|
|
|
XCTAssertThrowsError(try eigenDecompose(matrix), "not square") { e in
|
|
XCTAssertEqual(e as? EigenDecompositionError, EigenDecompositionError.matrixNotSquare)
|
|
}
|
|
}
|
|
}
|