Accord.Tests.Math.SingularValueDecompositionTest.SingularValueDecompositionConstructorTest3 C# (CSharp) Method

        public void SingularValueDecompositionConstructorTest3()
        {
            // Test using SVD assumption auto-correction feature.

            // Test for m-x-n matrices where m < n. The available SVD
            // routine was not meant to be used in this case.

            double[,] value = new double[,]
             { 
                 { 1, 2 },
                 { 3, 4 },
                 { 5, 6 },
                 { 7, 8 }
             }.Transpose(); // value is 2x4, having less rows than columns.

            var target = new SingularValueDecomposition(value, true, true, true);

            double[,] actual = Matrix.Multiply(Matrix.Multiply(target.LeftSingularVectors, 
                Matrix.Diagonal(target.Diagonal)), target.RightSingularVectors.Transpose());

            // Checking the decomposition
            Assert.IsTrue(Matrix.IsEqual(actual, value, 0.01));
            Assert.IsTrue(Matrix.IsEqual(target.Reverse(), value, 1e-2));
            
            // Checking values
            double[,] U =
            {
                { 0.641423027995072, -0.767187395072177 },
                { 0.767187395072177,  0.641423027995072 },
            };

            // U should be equal despite some sign changes
            Assert.IsTrue(Matrix.IsEqual(target.LeftSingularVectors, U, 0.001));


            double[,] V = // economy svd
            {
                {  0.152483233310201,  0.822647472225661,  },
                {  0.349918371807964,  0.421375287684580,  },
                {  0.547353510305727,  0.0201031031435023, },
                {  0.744788648803490, -0.381169081397574,  },
            };

            // V can be different, but for the economy SVD it is often equal
            Assert.IsTrue(Matrix.IsEqual(target.RightSingularVectors, V, 0.0001));


            double[,] S = 
            {
                { 14.2690954992615, 0.000000000000000 },
                {  0.0000000000000,	0.626828232417543 },
            };

            // The diagonal values should be equal
            Assert.IsTrue(Matrix.IsEqual(target.Diagonal, Matrix.Diagonal(S), 0.001));
        }