Vector

#include \(<\tilde{}\)/matrix/Vector.h\(>\)

class Vector:

The Vector class provides the vector abstraction. A vector of order size is an ordered 1d array of size numbers. For example a vector of order 5:

\(x = [x_0\) \(x_1\) \(x_2\) \(x_3\) \(x_4]\)

In the Vector class the data is stored in a 1d double array of length equal to the order of the Vector. At present time none of the methods are declared as being virtual. THIS MAY CHANGE FOR PARALLEL.

To construct a Vector of order \(0\).

To construct a Vector of order size. The constructor creates an array to store the data and zeroes this array. If not enough memory is available a warning message is printed and a Vector of order \(0\) is returned. The Zero() method is invoked on the new Vector before it is returned.

To construct a Vector of order size whose data will be stored in the array pointed to by data. The array pointed to by data is not set to zero by the constructor. Note that delete will not be called on this array in the destructor. It is up to the user to ensure that the array pointed to by data is at least as large as size, if this is not the case erroneous results or a segmentation fault may occur.

To construct a Vector using another Vector. The new Vector will be identical to the Vector other. The constructor creates an array to store the data and zeroes this array. If not enough memory is available a warning message is printed and a Vector of order \(0\) is returned. The contents of the array are then set equal to the contents of other.

Will delete any space allocated in the constructors. If the array is passed in the constructor, the space is not deallocated.

Returns the order of the Vector, size.

Zeros out the Vector, i.e. sets all the components of the Vector to \(0\).

Assembles into the current Vector the Vector V. The contents of the current Vector at location (loc(i)) is set equal to the current value plus fact times the value of the Vector V at location (i). returns \(0\) if successful. A warning message is printed for each invalid location in the current Vector or V and a \(-1\) is returned.

To add a factor fact times the Vector other to the current Vector. returns \(0\) if successful. An error message is printed and \(-1\) is returned if Vectors are not of the same size. Checks are made to see if the number of operations can be reduced if fact is \(0\) or \(1\).

To add a factor fact times the Vector formed by the product of the matrix m and the Vector v to the current Vector. No temporary Vector is created. Returns \(0\) if successful. Prints a warning message and returns \(-1\) if sizes are incompatible. Checks are made to see if the number of operations can be reduced if fact is \(0\) or \(1\).

Returns the 2 norm of the Vector. Returns the sqrt() of the result of invoking the \(\hat{ }\) operator on the current Vector with the current Vector as the argument.

Returns the data at location x in the Vector. Assumes (x) is a valid location in the Vector, i.e. \(0 <= x\) order, a segmentation fault or erroneous results can occur if this is not the case.

Used to set the data at location(x) in the Vector. Assumes (x) is a valid location in the Vector, i.e. \(0 <= x <\) order, a segmentation fault or erroneous results can occur if this is not the case.

To safely return the data at location x in the Vector. Checks to ensure x is a valid location, i.e. \(0 <= x\) order. If x is not a valid location a warning message is printed and VECTOR_NOT_VALID_ENTRY (a static class variable) is returned. This is a slower but safer version of () const.

Used to safely set the data at location(x) in the Vector. Checks to ensure x is a valid location, i.e. \(0 <= x\) order. If x is not a valid location a warning message is printed and VECTOR_NOT_VALID_ENTRY (a static class variable) is modified. This is a slower but safer version of ().

Returns a Vector of order loc.Size(). The contents of the new Vector are given by the contents of the current Vector at the locations given by the loc. For example the contents of the new Vector at location \(i\) are equal to the contents of the current Vector at location loc(i). Creates a new Vector, copies the data from the current Vector and returns the new Vector. For each invalid location specified in loc for the current Vector, a warning message is printed.

Sets the current Vector to be equal to the Vector given by other. If the Vectors are of different sizes, the current data, if allocated in a constructor, is deallocated and more space allocated before the contents are copied. If not enough memory is available a warning message is printed and the order of the current Vector is set to \(0\).

A method to add fact to each component of the current Vector.

A method to subtract fact from each component of the current Vector.

A method to multiply each component of the current Vector by fact.

A method which will divide each component of the current Vector by fact. If fact is equal to zero an warning message is printed and the components of the Vector are set to VECTOR_VERY_LARGE_VALUE (defined in \(<\)Vector.h\(>\)).

A method to return a new Vector whose components are equal to the components of the current Vector plus the value fact. A new Vector is constructed using the current Vector as an argument to the constructor; before the new matrix is returned, the += operator is invoked on the matrix with fact. If the new Vector and current Vector are of different size, i.e. constructor fails to get enough memory, a warning message is printed.

A method to return a new Vector whose components are equal to the components of the current Vector minus the value fact. A new Vector is constructed using the current Vector as an argument to the constructor; before the new matrix is returned, the -= operator is invoked on the matrix with fact. If the new Vector and current Vector are of different size, i.e. constructor fails to get enough memory, a warning message is printed.

A method to return a new Vector whose components are equal to the components of the current Vector times the value fact. A new Vector is constructed using the current Vector as an argument to the constructor; before the new matrix is returned, the = operator is invoked on the matrix with fact. If the new Vector and current Vector are of different sizes, a warning message is printed.

A method to return a new Vector whose components are equal to the components of the current Vector divided the value fact. A new Vector is constructed using the current Vector as an argument to the constructor; before the new matrix is returned, the /= operator is invoked on the matrix with fact. Warning messages are printed if fact is equal to \(0\) or if the new Vector and current Vector are of different sizes.

A method to add the contents of the Vector V to the current Vector. If Vectors are not of same order a warning message is printed and nothing is done.

A method to subtract the contents of the Vector V from the current Vector. If Vectors are not of same order a warning message is printed and nothing is done.

A method to return a new Vector which is equal to the sum of the the current Vector and the Vector V. A new Vector is constructed using the current Vector as an argument to the constructor; before the new matrix is returned, the += operator is invoked on the matrix with V. If the current Vector and V are not of the same size, a warning message is printed and a copy of the current Vector is returned. A warning message is also returned if the new Vector is not of the correct size, i.e. ran out of memory.

A method to return a new Vector which is equal to the the current Vector minus the Vector V. A new Vector is constructed using the current Vector as an argument to the constructor; before the new matrix is returned, the -= operator is invoked on the matrix with V. If the current Vector and V are not of the same size, a warning message is printed and a copy of the current Vector is returned. A warning message is also returned if the new Vector is not of the correct size, i.e. ran out of memory.

A method to return the dot product of the current Vector and the Vector V. If the current Vector and V are not of the same size, a warning message is printed and \(0\) returned.

A method to return a new Vector, \(x\), equal to the solution of the matrix equation \(Mx=\) the current Vector. A new Vector is created for the return of size M.noRows(). A new Matrix is created of order M.noRows() x M.noRows() and set equal to M if M is square, or \(M^tM\) if M is not square. The new Vector is then set equal to the result of invoking Solve(\*this) on the new Matrix.

friend OPS_Stream &operator$<<$(OPS_Stream &s, const Vector &V);

A function to print out the contents of the Vector V to the output stream s. prints out the contents of the Vector in the stream and then prints the newline character.

friend istream &operator$>>$(istream &s, const Vector &V);

A function to read the contents of the Vector V from the input stream s. Sets the components of V equal to the next V.Size() entries in the stream.