[Linear Algebra] Add det and slogdet (#604)

Author: Shashi456

Sources/TensorFlow/Operators/LinearAlgebra.swift

@@ -177,6 +177,31 @@ public func trace<T: TensorFlowNumeric>(_ matrix: Tensor<T>) -> Tensor<T> {
     return matrix.diagonalPart().sum(squeezingAxes: -1)
 }
 
+/// Computes the determinant of an optionally batched matrix.
+/// 
+/// - Parameter matrix: A tensor of shape `[..., M, M]`.
+/// - Returns: A tensor containing the determinants of all input submatrices.
+@inlinable 
+func det<T: TensorFlowFloatingPoint>(_ matrix: Tensor<T>) -> Tensor<T> {
+    _Raw.matrixDeterminant(matrix)
+}
+
+/// Computes the sign and the natural logarithm of the absolute value of the determinant of an
+/// optionally batched square matrix.
+///
+/// - Parameter matrix: A tensor of shape `[..., N, M, M]`.
+/// - Returns: 
+///   - sign: A tensor with shape `[N]`, representing the signs of the natural logarithms of the 
+///     determinants of input submatrices.
+///   - logAbsDeterminant: A tensor with shape `[N]`, representing the natural logarithms of the 
+///     absolute values of the determinants of input submatrices.
+@inlinable
+func slogdet<T: TensorFlowFloatingPoint>(_ matrix: Tensor<T>) -> (
+    sign: Tensor<T>, logAbsDeterminant: Tensor<T>
+) {
+    _Raw.logMatrixDeterminant(matrix)
+}
+
 /// Computes the natural logarithm of the determinant of a hermitian positive definite matrix.
 ///
 /// - Parameter matrix: A tensor of shape `[..., M, N]`.

Tests/TensorFlowTests/OperatorTests/LinearAlgebraTests.swift

@@ -115,6 +115,34 @@ final class LinearAlgebraTests: XCTestCase {
         assertEqual(computedGradient, expectedGradient, accuracy: 1e-16)
     }
 
+    func testDet() {
+        var matrix = Tensor<Float>(shape: [1, 4, 4], scalars: (0..<16).map(Float.init))
+        var computedDet = det(matrix)
+        var expectedDet = Tensor<Float>([0])
+        XCTAssertEqual(computedDet, expectedDet)
+
+        matrix = Tensor<Float>(shape: [2, 2, 2, 2], scalars: (0..<16).map(Float.init))
+        computedDet = det(matrix)
+        expectedDet = Tensor<Float>([[-2.0, -2.0], [-2.0, -2.0]])
+        assertEqual(computedDet, expectedDet, accuracy: 1e-5)
+    }
+
+    func testSlogdet() {
+        var input = Tensor<Float>(shape: [1, 2, 2], scalars: (0..<4).map(Float.init))
+        var expectedSigns = Tensor<Float>([-1])
+        var expectedLogs = Tensor<Float>([0.6931472])
+        var (computedSigns, computedLogs) = slogdet(input)
+        XCTAssertEqual(computedSigns, expectedSigns)
+        XCTAssertEqual(computedLogs, expectedLogs)
+        
+        input = Tensor<Float>(shape: [2, 2, 2, 2], scalars: (0..<16).map(Float.init))
+        expectedSigns = Tensor<Float>([[-1.0, -1.0], [-1.0, -1.0]])
+        expectedLogs = Tensor<Float>([[0.6931472, 0.6931462], [0.6931462, 0.6931435]])
+        (computedSigns, computedLogs) = slogdet(input)
+        XCTAssertEqual(computedSigns, expectedSigns)
+        XCTAssertEqual(computedLogs, expectedLogs)
+    }
+
     func testLogdet() {
         let input = Tensor<Float>([[[6.0, 4.0], [4.0, 6.0]], [[2.0, 6.0], [6.0, 20.0]]])
         let expected = Tensor<Float>([2.9957323, 1.3862934])
@@ -148,6 +176,8 @@ final class LinearAlgebraTests: XCTestCase {
         ("testSVD", testSVD),
         ("testTrace", testTrace),
         ("testTraceGradient", testTraceGradient),
+        ("testDet", testDet),
+        ("testSlogdet", testSlogdet),
         ("testLogdet", testLogdet),
         ("testLogdetGradient", testLogdetGradient)
     ]

Tests/TensorFlowTests/OperatorTests/MatrixTests.swift

@@ -15,7 +15,6 @@
 import XCTest
 @testable import TensorFlow
 
-
 final class MatrixTests: XCTestCase {
     func testDiagonalPart() {
         // Test on a matrix.