C# DenseMatrix.Append方法代码示例

        public DenseMatrix createMatrix(Model model)
        {
            int numConstraints = model.Constraints.Count;
            int numDecisionVars = model.Goal.Coefficients.Length;
            int varCounter = numDecisionVars;
            //  matrix(rows, columns)
            DenseMatrix coefficients = new DenseMatrix(numConstraints, numDecisionVars);
            DenseMatrix artificialVars = new DenseMatrix(numConstraints, 1);
            var constraintCounter = 0;
            this.rhsValues = new DenseVector(numConstraints);
            this.basics = new List<int>();
            this.artificialRows = new List<int>();
            foreach (var constraint in model.Constraints) {
                rhsValues[constraintCounter] = constraint.Value;

                // if the constraint RHS is negative, invert the coefficients and flip the inequality sign
                if (constraint.Value < 0)
                {
                    for (int i = 0; i< model.Goal.Coefficients.Length; i++) {
                        model.Goal.Coefficients[i] = model.Goal.Coefficients[i] * -1;
                    }
                    if (constraint.Relationship == Relationship.LessThanOrEquals)
                    {
                        constraint.Relationship = Relationship.GreaterThanOrEquals;
                    }
                    else if (constraint.Relationship == Relationship.GreaterThanOrEquals)
                    {
                        constraint.Relationship = Relationship.LessThanOrEquals;
                    }
                    // also flip the rhs value which we already put in the array for the simplex setup
                    rhsValues[constraintCounter] = rhsValues[constraintCounter] * -1;
                }

                coefficients.SetRow(constraintCounter, 0, constraint.Coefficients.Length, new DenseVector(constraint.Coefficients));
                // if it's a less than, add a slack column to the coefs matrix
                if (constraint.Relationship == Relationship.LessThanOrEquals)
                {
                    DenseVector slack = DenseVector.Create(model.Constraints.Count, delegate(int s) { return 0; });
                    slack.At(constraintCounter, 1);
                    coefficients = (DenseMatrix)coefficients.Append(slack.ToColumnMatrix());

                    this.basics.Add(varCounter);
                }
                else
                {
                    // Need to add an artificial variable for >= and = constraints

                    DenseVector surplus = DenseVector.Create(model.Constraints.Count, delegate(int s) { return 0; });
                    surplus.At(constraintCounter, -1);
                    coefficients = (DenseMatrix)coefficients.Append(surplus.ToColumnMatrix());

                    DenseVector artificial = DenseVector.Create(model.Constraints.Count, delegate(int s) { return 0; });
                    artificial.At(constraintCounter, 1);
                    artificialVars = (DenseMatrix)artificialVars.Append(artificial.ToColumnMatrix());

                    // Keeps track of the rows with artificial variable, for setting w
                    artificialRows.Add(constraintCounter);
                }
                varCounter++;
                constraintCounter++;
            }

            // put the constraints and stuff into the matrix
            if (artificialVars.ColumnCount > 1)
            {
                artificialVars = (DenseMatrix)artificialVars.SubMatrix(0, artificialVars.RowCount, 1, artificialVars.ColumnCount - 1);

                for (int i = coefficients.ColumnCount; i < coefficients.ColumnCount + artificialVars.ColumnCount; i++)
                {
                    this.basics.Add(i);
                }

                coefficients = (DenseMatrix)coefficients.Append(artificialVars);

                numArtificial = artificialVars.ColumnCount;
            }
            else
            {
                numArtificial = 0;
            }

            return coefficients;
        }

        /// <summary>
        /// Run example
        /// </summary>
        public void Run()
        {
            // Format matrix output to console
            var formatProvider = (CultureInfo)CultureInfo.InvariantCulture.Clone();
            formatProvider.TextInfo.ListSeparator = " ";
            
            // Create square matrix
            var matrix = new DenseMatrix(5);
            var k = 0;
            for (var i = 0; i < matrix.RowCount; i++)
            {
                for (var j = 0; j < matrix.ColumnCount; j++)
                {
                    matrix[i, j] = k++;
                }
            }

            Console.WriteLine(@"Initial matrix");
            Console.WriteLine(matrix.ToString("#0.00\t", formatProvider));
            Console.WriteLine();

            // Create vector
            var vector = new DenseVector(new[] { 50.0, 51.0, 52.0, 53.0, 54.0 });
            Console.WriteLine(@"Sample vector");
            Console.WriteLine(vector.ToString("#0.00\t", formatProvider));
            Console.WriteLine();

            // 1. Insert new column
            var result = matrix.InsertColumn(3, vector);
            Console.WriteLine(@"1. Insert new column");
            Console.WriteLine(result.ToString("#0.00\t", formatProvider));
            Console.WriteLine();

            // 2. Insert new row
            result = matrix.InsertRow(3, vector);
            Console.WriteLine(@"2. Insert new row");
            Console.WriteLine(result.ToString("#0.00\t", formatProvider));
            Console.WriteLine();

            // 3. Set column values
            matrix.SetColumn(2, (Vector)vector);
            Console.WriteLine(@"3. Set column values");
            Console.WriteLine(matrix.ToString("#0.00\t", formatProvider));
            Console.WriteLine();

            // 4. Set row values. 
            matrix.SetRow(3, (double[])vector);
            Console.WriteLine(@"4. Set row values");
            Console.WriteLine(matrix.ToString("#0.00\t", formatProvider));
            Console.WriteLine();

            // 5. Set diagonal values. SetRow/SetColumn/SetDiagonal accepts Vector and double[] as input parameter
            matrix.SetDiagonal(new[] { 5.0, 4.0, 3.0, 2.0, 1.0 });
            Console.WriteLine(@"5. Set diagonal values");
            Console.WriteLine(matrix.ToString("#0.00\t", formatProvider));
            Console.WriteLine();

            // 6. Set submatrix values
            matrix.SetSubMatrix(1, 3, 1, 3, DenseMatrix.Identity(3));
            Console.WriteLine(@"6. Set submatrix values");
            Console.WriteLine(matrix.ToString("#0.00\t", formatProvider));
            Console.WriteLine();

            // Permutations. 
            // Initialize a new instance of the Permutation class. An array represents where each integer is permuted too: 
            // indices[i] represents that integer "i" is permuted to location indices[i]
            var permutations = new Permutation(new[] { 0, 1, 3, 2, 4 });
            
            // 7. Permute rows 3 and 4
            matrix.PermuteRows(permutations);
            Console.WriteLine(@"7. Permute rows 3 and 4");
            Console.WriteLine(matrix.ToString("#0.00\t", formatProvider));
            Console.WriteLine();

            // 8. Permute columns 1 and 2, 3 and 5
            permutations = new Permutation(new[] { 1, 0, 4, 3, 2 });
            matrix.PermuteColumns(permutations);
            Console.WriteLine(@"8. Permute columns 1 and 2, 3 and 5");
            Console.WriteLine(matrix.ToString("#0.00\t", formatProvider));
            Console.WriteLine();

            // 9. Concatenate the matrix with the given matrix
            var append = matrix.Append(matrix);

            // Concatenate into result matrix
            matrix.Append(matrix, append);
            Console.WriteLine(@"9. Append matrix to matrix");
            Console.WriteLine(append.ToString("#0.00\t", formatProvider));
            Console.WriteLine();

             // 10. Stack the matrix on top of the given matrix matrix
            var stack = matrix.Stack(matrix);

            // Stack into result matrix
            matrix.Stack(matrix, stack);
            Console.WriteLine(@"10. Stack the matrix on top of the given matrix matrix");
            Console.WriteLine(stack.ToString("#0.00\t", formatProvider));
//.........这里部分代码省略.........

        private void optimize(DenseMatrix coefficients, DenseVector objFunValues, bool artifical)
        {
            //for calculations on the optimal solution row
            int cCounter,
                width = coefficients.ColumnCount;
            DenseVector cBVect = new DenseVector(basics.Count);

            //Sets up the b matrix
            DenseMatrix b = new DenseMatrix(basics.Count, 1);

            //basics will have values greater than coefficients.ColumnCount - 1 if there are still artificial variables
            //or if Nathan is bad and didn't get rid of them correctly
            foreach (int index in basics)
            {
                b = (DenseMatrix)b.Append(DenseVector.OfVector(coefficients.Column(index)).ToColumnMatrix());
            }
            // removes the first column
            b = (DenseMatrix)b.SubMatrix(0, b.RowCount, 1, b.ColumnCount - 1);

            double[] cPrimes = new double[width];
            double[] rhsOverPPrime;
            DenseMatrix[] pPrimes = new DenseMatrix[width];
            DenseMatrix bInverse;

            int newEntering, exitingRow;

            bool optimal = false;

            if(artifical)
            {
                rhsOverPPrime = new double[numConstraints + 1];
            }
            else
            {
                rhsOverPPrime = new double[numConstraints];
            }

            while (!optimal)
            {
                //calculates the inverse of b for this iteration
                bInverse = (DenseMatrix)b.Inverse();

                //updates the C vector with the most recent basic variables
                cCounter = 0;
                foreach (int index in basics)
                {
                    cBVect[cCounter++] = objFunValues.At(index);
                }

                //calculates the pPrimes and cPrimes
                for (int i = 0; i < coefficients.ColumnCount; i++)
                {
                    if (!basics.Contains(i))
                    {
                        pPrimes[i] = (DenseMatrix)bInverse.Multiply((DenseMatrix)coefficients.Column(i).ToColumnMatrix());

                        //c' = objFunVals - cB * P'n
                        //At(0) to turn it into a double
                        cPrimes[i] = objFunValues.At(i) - (pPrimes[i].LeftMultiply(cBVect)).At(0);
                    }
                    else
                    {
                        pPrimes[i] = null;
                    }
                }

                //RHS'
                xPrime = (DenseMatrix)bInverse.Multiply((DenseMatrix)rhsValues.ToColumnMatrix());

                //Starts newEntering as the first nonbasic
                newEntering = -1;
                int iter = 0;
                while(newEntering == -1)
                {
                    if(!basics.Contains(iter))
                    {
                        newEntering = iter;
                    }

                    iter++;
                }

                //new entering becomes the small cPrime that corresponds to a non-basic value
                for (int i = 0; i < cPrimes.Length; i++)
                {
                    if (cPrimes[i] < cPrimes[newEntering] && !basics.Contains(i))
                    {
                        newEntering = i;
                    }
                }

                //if the smallest cPrime is >= 0, ie they are all positive
                if (cPrimes[newEntering] >= 0)
                {
                    optimal = true;
                }
                else
                {
                    //fix me to deal with if all these values are negative
                    exitingRow = 0;
//.........这里部分代码省略.........

        public static void TestPosePrimitives()
        {
            DenseVector poseQuat = new DenseVector(new double[] {1, 0, 0, 0});
            DenseVector posePosition = new DenseVector(new double[] {0, 0, 1});
            DenseMatrix inverseCalibration = (DenseMatrix)Pose3D.CreateCalibrationMatrix(525, 320, 240).Inverse();
            DenseMatrix dPixels = new DenseMatrix(3, 1);
            dPixels[0, 0] = 320;
            dPixels[1, 0] = 240;
            dPixels[2, 0] = 1;

            dPixels = (DenseMatrix)dPixels.Append(dPixels);

            Console.WriteLine("New: Using calibration Matrix");
            Console.WriteLine(Pose3D.DPixelToWorld(poseQuat, posePosition, inverseCalibration, dPixels, new DenseMatrix(1, dPixels.ColumnCount, 1.0)).ToString("0.0"));
            //Console.WriteLine("Old: Using calibration Matrix");
            //Console.WriteLine(Pose3D.DPixelToWorld_Old(poseQuat, posePosition, inverseCalibration, dPixels).ToString("0.0"));

            Console.WriteLine("New: No calibration Matrix");
            Console.WriteLine(Pose3D.DPixelToWorld(poseQuat, posePosition, DenseMatrix.Identity(3), dPixels, new DenseMatrix(1, dPixels.ColumnCount, 1.0)).ToString("0.0"));
            //Console.WriteLine("Old: No calibration Matrix");
            //Console.WriteLine(Pose3D.DPixelToWorld_Old(poseQuat, posePosition, DenseMatrix.Identity(4), dPixels).ToString("0.0"));
        }