Laboratoire de l'Informatique et du Parallélisme » Pobyso

def slz_compute_scaled_function(functionSa, \

                                      variableNameSa, \

                                      lowerBoundSa, \

                                      upperBoundSa, \

                                      floatingPointPrecSa):

    """

    From a function, compute the scaled function whose domain

    is included in [1, 2) and whose image is also included in [1,2).

    Return a tuple: 

    [0]: the scaled function

    [1]: the scaled domain lower bound

    [2]: the scaled domain upper bound

    [3]: the scaled image lower bound

    [4]: the scaled image upper bound

    """

    x = var(variableNameSa)

    # Scalling the domain -> [1,2[.

    boundsIntervalRifSa = RealIntervalField(floatingPointPrecSa)

    domainBoundsIntervalSa = boundsIntervalRifSa(lowerBoundSa, upperBoundSa)

    (domainScalingExpressionSa, invDomainScalingExpressionSa) = \

        slz_interval_scaling_expression(domainBoundsIntervalSa, variableNameSa)

    print "domainScalingExpression for argument :", domainScalingExpressionSa

    print "f: ", f

    ff = f.subs({x : domainScalingExpressionSa})

    #ff = f.subs_expr(x==domainScalingExpressionSa)

    scaledLowerBoundSa = invDomainScalingExpressionSa(lowerBoundSa).n()

    scaledUpperBoundSa = invDomainScalingExpressionSa(upperBoundSa).n()

    print 'ff:', ff, "- Domain:", scaledLowerBoundSa, scaledUpperBoundSa

    #

    # Scalling the image -> [1,2[.

    flbSa = f(lowerBoundSa).n()

    fubSa = f(upperBoundSa).n()

    if flbSa <= fubSa: # Increasing

        imageBinadeBottomSa = floor(flbSa.log2())

    else: # Decreasing

        imageBinadeBottomSa = floor(fubSa.log2())

    print 'ff:', ff, '- Image:', flbSa, fubSa, imageBinadeBottomSa

    imageBoundsIntervalSa = boundsIntervalRifSa(flbSa, fubSa)

    (imageScalingExpressionSa, invImageScalingExpressionSa) = \

        slz_interval_scaling_expression(imageBoundsIntervalSa, variableNameSa)

    iis = invImageScalingExpressionSa.function(x)

    fff = iis.subs({x:ff})

    print "fff:", fff,

    print " - Image:", fff(scaledLowerBoundSa), fff(scaledUpperBoundSa)

    return([fff, scaledLowerBoundSa, scaledUpperBoundSa, \

            fff(scaledLowerBoundSa), fff(scaledUpperBoundSa)])

    - a first polynomial (without the changed variable f(x) = p(x-x0));

    - a second polynomila (with a changed variable f(x) = q(x))

    - the center, x0, of the interval;

    """

    Compute the Sage version of the Taylor polynomial and it's

    companion data (interval, center...)

    The input parameter is a five elements tuple:

    - [0]: the polyomial (without variable change);

    - [1]: the polyomial (with variable change done in Sollya);

    - [2]: the interval (as Sollya range);

    - [3]: the interval center;

    - [4]: the approximation error. 

    The function return a 5 elements tuple: formed with all the 

    input elements converted into their Sollya counterpart.

    """