# Vector Operations in IronPython QuickStart Sample

Illustrates how to perform operations on Vector objects, including construction, element access, arithmetic operations in IronPython.

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```Python import numerics from math import exp # The Vector class resides in the Extreme.Mathematics # namespace. from Extreme.Mathematics.LinearAlgebra import * # The delegate class resides in the Extreme.Mathematics # namespace. from Extreme.Mathematics import * # Illustrates operations on Vector objects from the # Extreme.Mathematics.LinearAlgebra namespace of Numerics.NET. # For details on the basic workings of Vector # objects, including constructing, copying and # cloning vectors, see the BasicVectors QuickStart # Sample. # # Let's create some vectors to work with. v1 = Vector([1, 2, 3, 4, 5]) v2 = Vector([1, -2, 3, -4, 5]) v3 = Vector([3, 2, 1, 0, -1]) # # Vector Arithmetic # # The Vector class defines overloaded addition, # subtraction, and multiplication and division # operators: print "v1 =", v1 print "v2 =", v2 print "Basic arithmetic:" v = -v1 print "-v1 =", v v = v1 + v2 print "v1 + v2 =", v v = v1 - v2 print "v1 - v2 =", v # Vectors can only be multiplied or divided by # a real number. For dot products, see the # DotProduct method. v = 5 * v1 print "5 * v1 =", v v = v1 * 5 print "v1 * 5 =", v v = v1 / 5 print "v1 / 5 =", v # For each operator, there is a corresponding # static method. For example: v1 + v2 is # equivalent to: v = Vector.Add(v1, v2) # v1 - v2 corresponds to: v = Vector.Subtract(v1, v2) # You can also apply these methods to Vector objects. # In this case, they change the first operand. print "v3 =", v3 v3.Add(v1) # Note that this is different from the += operator! # The += operator creates a Vector.Create object, # whereas the Add method above does not. print "v3+v1 -> v3 =", v3 # This method is overloaded so you can directly # add a scaled vector: v3.Add(-2, v1) print "v3-2v1 -> v3 =", v3 # Corresponding to the * operator, we have the # scale method: v3.Multiply(3) print "3v3 -> v3 =", v3 print # # Norms, dot products, etc. # print "Norms, dot products, etc." # The dot product is calculated in one of two ways: # Using the static DotProduct method: a = Vector.DotProduct(v1, v2) # Or using the DotProduct method on one of the two # vectors: b = v1.DotProduct.Overloads[DenseVector](v2) print "DotProduct(v1, v2) = {0} = {1}".format(a, b) # The Norm method returns the standard two norm # of a Vector: a = v1.Norm() print "|v1| =", a # .the Norm method is overloaded to allow other norms, # including the one-norm: a = v1.Norm(1) print "one norm(v1) =", a # ...the positive infinity norm, which returns the # absolute value of the largest component: a = v1.Norm(float.PositiveInfinity) print "+inf norm(v1) =", a # ...the negative infinity norm, which returns the # absolute value of the smallest component: a = v1.Norm(float.NegativeInfinity) print "-inf norm(v1) =", a # ...and even the zero norm, which simply returns # the number of components of the vector: a = v1.Norm(0) print "zero-norm(v1) =", a # You can get the square of the two norm with the # NormSquared method. a = v1.NormSquared() print "|v1|^2 =", a print # # Largest and smallest elements # # The Vector class defines methods to find the # largest or smallest element or its index. print "v2 =", v2 # The Max method returns the largest element: print "Max(v2) =", v2.Max() # The AbsoluteMax method returns the element with # the largest absolute value. print "Absolute max(v2) =", v2.AbsoluteMax() # The Min method returns the smallest element: print "Min(v2) =", v2.Min() # The AbsoluteMin method returns the element with # the smallest absolute value. print "Absolute min(v2) =", v2.AbsoluteMin() # Each of these methods has an equivalent method # that returns the zero-based index of the element # instead of its value, for example: print "Index of Min(v2) =", v2.MinIndex() # Finally, the Apply method lets you apply # an arbitrary function to each element of the # vector: v1.Apply(exp) print "Exp(v1) =", v1 # There is also a static method that returns a # Vector.Create object: v = Vector.Apply(exp, v2) ```