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QuickStart Samples

# Accessing Matrix Components QuickStart Sample (IronPython)

Illustrates different ways of iterating through the rows and columns of a matrix using classes in the Extreme.Mathematics.LinearAlgebra namespace in IronPython.

View this sample in: C# Visual Basic F#

```Python import numerics # The Vector and Vector classes resides in the # Extreme.Mathematics.LinearAlgebra namespace. from Extreme.Mathematics import * from Extreme.Mathematics.LinearAlgebra import * from System import Array #/ Illustrates accessing matrix components and iterating #/ through the rows and columns of a matrix. Matrix classes #/ reside in the Extreme.Mathematics.LinearAlgebra namespace #/ of the Extreme Optimization Mathematics Library for .NET. # We'll work with this matrix: m = Matrix.Create(2, 3, \ Array[float]([ 1, 2, 3, 4, 5, 6 ]), \ MatrixElementOrder.ColumnMajor) # # Individual components # # The Matrix class has an indexer property that takes two arguments: # the row and column index. Both are zero based. print "m[1,1] =", m[1, 1] # # Rows and columns # # Indexed range access # The indexer property is overloaded to allow for direct indexed access # to complete or partial rows or columns. row1 = m[0, 1:3] # This prints "[3, 5]": print "row1 =", row1 # The special range : lets you access an entire row # or column without having to specify any details about the range. row2 = m[1, :] # This prints "[2, 4, 6]": print "2nd row =", row2 column1 = m[:, 0] # This prints "[1, 2]": print "column1 =", column1 # We can assign to rows and columns, too: m[:, 0] = row1 # This prints "[[3, 3, 5] [5, 4, 6]]" print "m =", m # GetRow and GetColumn provide an alternate mechanism # for achieving the same result. # Passing just one parameter retrieves the specified row or column: row1 = m.GetRow(1) # This prints "[2, 4, 6]": print "row1 =", row1 column1 = m.GetColumn(0) # This prints "[1, 2]": print "column1 =", column1 # You can also pass a start and end index: row2 = m.GetRow(0, 1, 2) # This prints "[3, 5]": print "row2 =", row2 # We can assign to rows and columns, too, using CopyTo: row2.CopyTo(m.GetColumn(0)) # This prints "[[3, 3, 5] [5, 4, 6]]" print "m =", m # Enumeration # The Rows and Columns methods allow you to enumerate over # the rows and columns of a matrix. # For example: this calculates the sum of the absolute values # of the components of the matrix m: sum = 0 for column in m.Columns: sum += column.OneNorm() # # Accessing diagonals # # Diagonals are retrieved using the GetDiagonal method: mainDiagonal = m.GetDiagonal() # An optional parameter specifies which diagonal: # n < 0 means subdiagonal # n > 0 means nth superdiagonal: superDiagonal = m.GetDiagonal(1) # # Accessing submatrices # # Indexed range access # A fourth overload of the indexer property lets you # extract a part of a matrix. Both parameters are Range # structures: a = Matrix.Create(10, 10) # Extract the 2nd to the 5th row of m: a1 = a[1:5, :] # Extract the odd columns: a2 = a[:, 1:10:2] # Extract the 4x4 leading submatrix of m: a3 = a[0:4, 0:4] # You can also assign to submatrices: identity5 = DenseMatrix.GetIdentity(5) a[0:5, 5:10] = identity5 a[5:10, 0:5] = identity5 # The same results can be achieved with the GetSubmatrix method. # Extract the 2nd to the 5th row of m. # Start and end columns are supplied manually. a4 = a.GetSubmatrix(1, 4, 0, 9) # Extract the odd columns: # Here we need to supply the transpose parameter. a5 = a.GetSubmatrix(0, 9, 1, 1, 9, 2, TransposeOperation.None) # Extract the 4x4 leading submatrix of m. # And let's get its transpose, just because we can. # We need to specify the row and column stride: a6 = a.GetSubmatrix(0, 3, 1, 0, 3, 1, TransposeOperation.Transpose) # You can still assign to submatrices, using the # CopyTo method: identity5.CopyTo(a.GetSubmatrix(0, 4, 5, 9)) identity5.CopyTo(a.GetSubmatrix(5, 9, 0, 4)) ```

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