[Linear Algebra] Add det and slogdet

Sources/TensorFlow/Operators/LinearAlgebra.swift

@@ -143,6 +143,24 @@ public func trace<T: TensorFlowNumeric>(_ matrix: Tensor<T>) -> Tensor<T> {
     return matrix.diagonalPart().sum(squeezingAxes: -1)
 }
 
+/// Computes the determinant of one or more square matrices.
+/// 
+/// - 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 log of the absolute value of the determinant of
+/// one or more square matrices.
+///
+/// - Parameter matrix: A tensor of shape `[..., N, M, M]`.
+@inlinable
+func slogdet<T:TensorFlowFloatingPoint>(_ matrix: Tensor<T>) -> (Tensor<T>, 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

@@ -85,6 +85,22 @@ final class LinearAlgebraTests: XCTestCase {
         assertEqual(computedGradient, expectedGradient, accuracy: 1e-16)
     }
 
+    func testDet() {
+        let matrix = Tensor<Float>(shape: [1, 4, 4], scalars: (0..<16).map(Float.init))
+        let computedDet = det(matrix)
+        let expectedDet = Tensor<Float>([0])
+        XCTAssertEqual(computedDet, expectedDet)
+    }
+
+    func testSlogdet() {
+        let input = Tensor<Float>(shape: [1, 2, 2], scalars: (0..<4).map(Float.init))
+        let expectedSigns = Tensor<Float>([-1])
+        let expectedLogs = Tensor<Float>([0.6931472])
+        let (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])
@@ -117,6 +133,8 @@ final class LinearAlgebraTests: XCTestCase {
         ("testQRDecompositionApproximation", testQRDecompositionApproximation),
         ("testTrace", testTrace),
         ("testTraceGradient", testTraceGradient),
+        ("testDet", testDet),
+        ("testSlogdet", testSlogdet),
         ("testLogdet", testLogdet),
         ("testLogdetGradient", testLogdetGradient)
     ]

Tests/TensorFlowTests/OperatorTests/MatrixTests.swift

@@ -112,7 +112,7 @@ final class MatrixTests: XCTestCase {
         let expectedGrad = 2 * t3.bandPart(subdiagonalCount: 0, superdiagonalCount: -1)
         XCTAssertEqual(computedGrad, expectedGrad)
     }
-    
+
     static var allTests = [
         ("testDiagonalPart", testDiagonalPart),
         ("testDiagonal", testDiagonal),