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QuickStart Samples

# Basic Matrices QuickStart Sample (IronPython)

Illustrates the basic use of the Matrix class for working with matrices in IronPython.

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import numerics from System import Array from Extreme.Mathematics import * # The DenseMatrix class resides in the Extreme.Mathematics.LinearAlgebra # namespace. from Extreme.Mathematics.LinearAlgebra import * #/ Illustrates the use of the DenseMatrix class in the #/ Extreme.Mathematics.LinearAlgebra namespace of the Extreme Optimization #/ Mathematics Library for .NET. # # Constructing matrices # # Option #1: specify number of rows and columns. # The following constructs a matrix with 3 rows # and 5 columns: m1 = Matrix.Create(3, 5) print "m1 =", m1 # Option #2: specify a rank 2 double array. # By default, elements are taken in column-major # order. Therefore, the following creates a matrix # with 3 rows and 4 columns: m2 = Matrix([[1, 2, 3], [2, 3, 4], [3, 4, 5], [4, 5, 6]]) print "m2 =", m2 m3 = m2 # Option #4: Specify component array, and number # of rows and columns. The elements are listed # in column-major order. The following matrix # is identical to m3: components = Array[float]([ 1, 2, 3, 2, 3, 4, 3, 4, 5, 4, 5, 6 ]) m4 = Matrix.Create(3, 4, components, MatrixElementOrder.ColumnMajor) print "m4 =", m4 # Option #5: same as above, but specify element # order. The following matrix is identical to m4: m5 = Matrix.Create(4, 3, components, MatrixElementOrder.RowMajor) print "m5 =", m5 # Option #6: same as #4, but specify whether to copy # the matrix components, or use the specified array # as internal storage. m6 = Matrix.Create(3, 4, components, MatrixElementOrder.ColumnMajor, False) # Option #7: same as #5, but specify whether to copy # the matrix components, or use the specified array # as internal storage. m7 = Matrix.Create(4, 3, components, MatrixElementOrder.RowMajor, False) # In addition, you can also create an identity # matrix by calling the static GetIdentity method. # The following constructs a 4x4 identity matrix: m8 = DenseMatrix.GetIdentity(4) print "m8 =", m8 # # DenseMatrix properties # # The RowCount and ColumnCount properties give the # number of rows and columns, respectively: print "m1.RowCount =", m1.RowCount print "m1.ColumnCount =", m1.ColumnCount # The ToArray method returns a one-dimensional # double array that contains the components of the # vector. By default, elements are returned in # column major order. This is always a copy: components = m3.ToArray() print "Components:" print "components[3] =", components[3] components[3] = 1 print "m3[0,1] =", m3[0,1] # The ToArray method is overloaded, so you can # choose whether you want the elements in row major # or in column major order. The order parameter is # of type MatrixElementOrder: components = m3.ToArray(MatrixElementOrder.RowMajor) print "In row major order:" print "components[3] =", components[3] # # Accessing matrix elements # # The DenseMatrix class defines an indexer property # that takes zero-based row and column indices. print "Assigning with private storage:" print "m1[0,2] =", m1[0,2] # You can assign to this property: m1[0,2] = 7 print "m1[0,2] =", m1[0,2] # The matrices m6 and m7 had the copy parameter in # the constructor set to false. As a result, they # share their component storage. Changing one vector # also changes the other: print "Assigning with shared storage:" print "m6[0,0] =", m6[0,0] m7[0,0] = 3 print "m6[0,0] =", m6[0,0] # # Copying and cloning matrices # # A shallow copy of a matrix constructs a matrix # that shares the component storage with the original. # This is done using the ShallowCopy method. Note # that we have to cast the return value since it is # of type Matrix, the abstract base type of all # the matrix classes: print "Shallow copy vs. clone:" m10 = m2.ShallowCopy() # The clone method creates a full copy. m11 = m2.Clone() # When we change m2, m10 changes, but m11 is left # unchanged: print "m2[1,1] =", m2[1,1] m2[1,1] = -2 print "m10[1,1] =", m10[1,1] print "m11[1,1] =", m11[1,1] # We can give a matrix its own component storage # by calling the CloneData method: print "CloneData:" m11.CloneData() # Now, changing the original v2 no longer changes v7: m2[1,1] = 4 print "m11[1,1] =", m11[1,1]

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