source: anuga_work/development/shallow_water_1d/quantity_domain.py @ 5316

"""Class Quantity - Implements values at each triangular element

To create:

   Quantity(domain, vertex_values)

   domain: Associated domain structure. Required.

   vertex_values: N x 3 array of values at each vertex for each element.
                  Default None

   If vertex_values are None Create array of zeros compatible with domain.
   Otherwise check that it is compatible with dimenions of domain.
   Otherwise raise an exception
"""


class Quantity:

    def __init__(self, domain, vertex_values=None):

        from domain_t2 import Domain
        from Numeric import array, zeros, Float

        if vertex_values is None:
            N = domain.number_of_elements
            self.vertex_values = zeros((N, 2), Float)
        else:
            self.vertex_values = array(vertex_values).astype(Float)

            N, V = self.vertex_values.shape
            assert V == 2,\
                   'Two vertex values per element must be specified'


            msg = 'Number of vertex values (%d) must be consistent with'\
                  %N
            msg += 'number of elements in specified domain (%d).'\
                   %domain.number_of_elements

            assert N == domain.number_of_elements, msg

        self.domain = domain

        #Allocate space for other quantities
        self.centroid_values = zeros(N, Float)

        #Intialise centroid values
        self.interpolate()



    #Methods for operator overloading
    def __len__(self):
        return self.centroid_values.shape[0]


    def __neg__(self):
        """Negate all values in this quantity giving meaning to the
        expression -Q where Q is an instance of class Quantity
        """

        Q = Quantity(self.domain)
        Q.set_values(-self.vertex_values)
        return Q


    def __add__(self, other):
        """Add to self anything that could populate a quantity

        E.g other can be a constant, an array, a function, another quantity
        (except for a filename or points, attributes (for now))
        - see set_values for details
        """

        Q = Quantity(self.domain)
        Q.set_values(other)

        result = Quantity(self.domain)
        result.set_values(self.vertex_values + Q.vertex_values)
        return result

    def __radd__(self, other):
        """Handle cases like 7+Q, where Q is an instance of class Quantity
        """
        return self + other


    def __sub__(self, other):
        return self + -other  #Invoke __neg__

    def __mul__(self, other):
        """Multiply self with anything that could populate a quantity

        E.g other can be a constant, an array, a function, another quantity
        (except for a filename or points, attributes (for now))
        - see set_values for details

        Note that if two quantitites q1 and q2 are multiplied,
        vertex values are multiplied entry by entry
        while centroid and edge values are re-interpolated.
        Hence they won't be the product of centroid or edge values
        from q1 and q2.
        """

        Q = Quantity(self.domain)
        Q.set_values(other)

        result = Quantity(self.domain)
        result.set_values(self.vertex_values * Q.vertex_values)
        return result

    def __rmul__(self, other):
        """Handle cases like 3*Q, where Q is an instance of class Quantity
        """
        return self * other

    def __pow__(self, other):
        """Raise quantity to (numerical) power

        As with __mul__ vertex values are processed entry by entry
        while centroid and edge values are re-interpolated.

        Example using __pow__:
          Q = (Q1**2 + Q2**2)**0.5

        """

        result = Quantity(self.domain)
        result.set_values(self.vertex_values**other)
        return result



    def interpolate(self):
        """Compute interpolated values at edges and centroid
        Pre-condition: vertex_values have been set
        """

        N = self.vertex_values.shape[0]
        for i in range(N):
            v0 = self.vertex_values[i, 0]
            v1 = self.vertex_values[i, 1]

            self.centroid_values[i] = (v0 + v1)/2.0


    def set_values(self, X, location='vertices'):
        """Set values for quantity

        X: Compatible list, Numeric array (see below), constant or function
        location: Where values are to be stored.
                  Permissible options are: vertices, centroid
                  Default is "vertices"

        In case of location == 'centroid' the dimension values must
        be a list of a Numerical array of length N, N being the number
        of elements in the mesh. Otherwise it must be of dimension Nx3

        The values will be stored in elements following their
        internal ordering.

        If values are described a function, it will be evaluated at specified points

        If selected location is vertices, values for centroid and edges
        will be assigned interpolated values.
        In any other case, only values for the specified locations
        will be assigned and the others will be left undefined.
        """

        if location not in ['vertices', 'centroids']:
            msg = 'Invalid location: %s, (possible choices vertices, centroids)' %location
            raise msg

        if X is None:
            msg = 'Given values are None'
            raise msg

        import types

        if callable(X):
            #Use function specific method
            self.set_function_values(X, location)
        elif type(X) in [types.FloatType, types.IntType, types.LongType]:
            if location == 'centroids':
                self.centroid_values[:] = X
            else:
                self.vertex_values[:] = X

        else:
            #Use array specific method
            self.set_array_values(X, location)

        if location == 'vertices':
            #Intialise centroid values
            self.interpolate()




    def set_function_values(self, f, location='vertices'):
        """Set values for quantity using specified function

        f: x -> z Function where x and z are arrays
        location: Where values are to be stored.
                  Permissible options are: vertices, centroid
                  Default is "vertices"
        """
        
        if location == 'centroids':
            
            P = self.domain.centroids
            self.set_values(f(P), location)
        else:
            #Vertices
            P = self.domain.get_vertices()
            
            for i in range(2):
                self.vertex_values[:,i] = f(P[:,i])        

    def set_array_values(self, values, location='vertices'):
        """Set values for quantity

        values: Numeric array
        location: Where values are to be stored.
                  Permissible options are: vertices, centroid, edges
                  Default is "vertices"

        In case of location == 'centroid' the dimension values must
        be a list of a Numerical array of length N, N being the number
        of elements in the mesh. Otherwise it must be of dimension Nx2

        The values will be stored in elements following their
        internal ordering.

        If selected location is vertices, values for centroid
        will be assigned interpolated values.
        In any other case, only values for the specified locations
        will be assigned and the others will be left undefined.
        """

        from Numeric import array, Float

        values = array(values).astype(Float)

        N = self.centroid_values.shape[0]

        msg = 'Number of values must match number of elements'
        assert values.shape[0] == N, msg

        if location == 'centroids':
            assert len(values.shape) == 1, 'Values array must be 1d'
            self.centroid_values = values
        else:
            assert len(values.shape) == 2, 'Values array must be 2d'
            msg = 'Array must be N x 2'
            assert values.shape[1] == 2, msg

            self.vertex_values = values
  

    def extrapolate_first_order(self):
        """Extrapolate conserved quantities from centroid to
        vertices for each volume using
        first order scheme.
        """

        qc = self.centroid_values
        qv = self.vertex_values

        for i in range(2):
            qv[:,i] = qc


    def get_integral(self):
        """Compute the integral of quantity across entire domain
        """
        integral = 0
        for k in range(self.domain.number_of_elements):
            area = self.domain.areas[k]
            qc = self.centroid_values[k]
            integral += qc*area

        return integral




class Conserved_quantity(Quantity):
    """Class conserved quantity adds to Quantity:

    boundary values, storage and method for updating, and
    methods for (second order) extrapolation from centroid to vertices inluding
    gradients and limiters
    """

    def __init__(self, domain, vertex_values=None):
        Quantity.__init__(self, domain, vertex_values)

        from Numeric import zeros, Float

        #Allocate space for boundary values
        L = len(domain.boundary)
        self.boundary_values = zeros(L, Float)

        #Allocate space for updates of conserved quantities by
        #flux calculations and forcing functions

        N = domain.number_of_elements
        self.gradients = zeros(N, Float)
        self.explicit_update = zeros(N, Float )
        self.semi_implicit_update = zeros(N, Float )


    def update(self, timestep):
        #Call correct module function
        #(either from this module or C-extension)
        return update(self, timestep)


    def compute_gradients(self):
        #Call correct module function
        #(either from this module or C-extension)
        return compute_gradients(self)


    def limit(self):
        #Call correct module function
        #(either from this module or C-extension)
        limit(self)


    def extrapolate_second_order(self):
        #Call correct module function
        #(either from this module or C-extension)
        extrapolate_second_order(self)


def update(quantity, timestep):
    """Update centroid values based on values stored in
    explicit_update and semi_implicit_update as well as given timestep

    Function implementing forcing terms must take on argument
    which is the domain and they must update either explicit
    or implicit updates, e,g,:

    def gravity(domain):
        ....
        domain.quantities['xmomentum'].explicit_update = ...
        domain.quantities['ymomentum'].explicit_update = ...



    Explicit terms must have the form

        G(q, t)

    and explicit scheme is

       q^{(n+1}) = q^{(n)} + delta_t G(q^{n}, n delta_t)


    Semi implicit forcing terms are assumed to have the form

       G(q, t) = H(q, t) q

    and the semi implicit scheme will then be

      q^{(n+1}) = q^{(n)} + delta_t H(q^{n}, n delta_t) q^{(n+1})


    """

    from Numeric import sum, equal, ones, exp, Float

    N = quantity.centroid_values.shape[0]


    #Divide H by conserved quantity to obtain G (see docstring above)


    for k in range(N):
        x = quantity.centroid_values[k]
        if x == 0.0:
            #FIXME: Is this right
            quantity.semi_implicit_update[k] = 0.0
        else:
            quantity.semi_implicit_update[k] /= x


    #Semi implicit updates
    denominator = ones(N, Float)-timestep*quantity.semi_implicit_update

    if sum(equal(denominator, 0.0)) > 0.0:
        msg = 'Zero division in semi implicit update. Call Stephen :-)'
        raise msg
    else:
        #Update conserved_quantities from semi implicit updates
        quantity.centroid_values /= denominator

#    quantity.centroid_values = exp(timestep*quantity.semi_implicit_update)*quantity.centroid_values


    #Explicit updates
    quantity.centroid_values += timestep*quantity.explicit_update

def extrapolate_second_order(quantity):
    """Extrapolate conserved quantities from centroid to
    vertices for each volume using
    second order scheme.
    """

    quantity.compute_gradients()
    a = quantity.gradients

    X = quantity.domain.vertices
    qc = quantity.centroid_values
    qv = quantity.vertex_values

    #Check each triangle
    for k in range(quantity.domain.number_of_elements):
        #Centroid coordinates
        x = quantity.domain.centroids[k]

        #vertex coordinates
        x0, x1 = X[k,:]

        #Extrapolate
        qv[k,0] = qc[k] + a[k]*(x0-x)
        qv[k,1] = qc[k] + a[k]*(x1-x)
    
    quantity.limit()

def compute_gradients(self):
        """Compute gradients of piecewise linear function defined by centroids of
        neighbouring volumes.
        """


        from Numeric import array, zeros, Float

        N = self.centroid_values.shape[0]


        G = self.gradients
        Q = self.centroid_values
        X = self.domain.centroids

        for k in range(N):

            # first and last elements have boundaries

            if k == 0:

                #Get data
                k0 = k
                k1 = k+1

                q0 = Q[k0]
                q1 = Q[k1]

                x0 = X[k0] #V0 centroid
                x1 = X[k1] #V1 centroid

                #Gradient
                G[k] = (q1 - q0)/(x1 - x0)

            elif k == N-1:

                #Get data
                k0 = k
                k1 = k-1

                q0 = Q[k0]
                q1 = Q[k1]

                x0 = X[k0] #V0 centroid
                x1 = X[k1] #V1 centroid

                #Gradient
                G[k] = (q1 - q0)/(x1 - x0)

            else:
                #Interior Volume (2 neighbours)

                #Get data
                k0 = k-1
                k2 = k+1

                q0 = Q[k0]
                q1 = Q[k]
                q2 = Q[k2]

                x0 = X[k0] #V0 centroid
                x1 = X[k]  #V1 centroid (Self)
                x2 = X[k2] #V2 centroid

                #Gradient
                #G[k] = (q2-q0)/(x2-x0)
                G[k] = ((q0-q1)/(x0-x1)*(x2-x1) - (q2-q1)/(x2-x1)*(x0-x1))/(x2-x0)

def limit(quantity):
    """Limit slopes for each volume to eliminate artificial variance
    introduced by e.g. second order extrapolator

    This is an unsophisticated limiter as it does not take into
    account dependencies among quantities.

    precondition:
    vertex values are estimated from gradient
    postcondition:
    vertex values are updated
    """

    from Numeric import zeros, Float

    N = quantity.domain.number_of_elements

    beta = quantity.domain.beta

    qc = quantity.centroid_values
    qv = quantity.vertex_values

    #Find min and max of this and neighbour's centroid values
    qmax = zeros(qc.shape, Float)
    qmin = zeros(qc.shape, Float)

    for k in range(N):
        qmax[k] = qmin[k] = qc[k]
        for i in range(2):
            n = quantity.domain.neighbours[k,i]
            if n >= 0:
                qn = qc[n] #Neighbour's centroid value

                qmin[k] = min(qmin[k], qn)
                qmax[k] = max(qmax[k], qn)

    #Diffences between centroids and maxima/minima
    dqmax = qmax - qc
    dqmin = qmin - qc

    #Deltas between vertex and centroid values
    dq = zeros(qv.shape, Float)
    for i in range(2):
        dq[:,i] = qv[:,i] - qc

    #Phi limiter
    for k in range(N):

        #Find the gradient limiter (phi) across vertices
        phi = 1.0
        for i in range(2):
            r = 1.0
            if (dq[k,i] > 0): r = dqmax[k]/dq[k,i]
            if (dq[k,i] < 0): r = dqmin[k]/dq[k,i]

            phi = min( min(r*beta, 1), phi )

        #Then update using phi limiter
        for i in range(2):
            qv[k,i] = qc[k] + phi*dq[k,i]