The first section of the exhibition is devoted to Fortuny’s formative years in Rome and includes works that reveal his precocious maturity, evident in his pencil, chalk and charcoal life studies, his watercolours (Il contino) and his oils (Odalisque). These precious objects, some of them now housed in the world’s leading archaeology museums, reveal Fortuny’s interest in careful observation and explain his extremely refined ability to capture texture, colour and light in his own creations as well as the remarkable virtuosity of his work, which rapidly extended his fame among Europe and America’s leading collectors. In addition, visitors can appreciate works from the artist’s remarkable collection of antiques that he had in his atelier. While Mariano Fortuny has long been celebrated in the specialist literature and through the numerous exhibitions and different initiatives of varying quality and importance that have been devoted to him in recent decades, his stature as an artist and his profound roots in the most authentic tradition of the great Spanish School justify a focus on the part of the Prado of the same level of ambition and importance as those which the Museum has dedicated to the most important artists represented in its collection.Ĭurated by Javier Barón, Chief Curator of 19th-century Painting, the exhibition is structured as a chronological survey of Fortuny’s contributions as a painter, watercolourist, draughtsman and printmaker. Devoted to one of the 19th-century Spanish artists who has enjoyed the most sustained reputation and greatest international fame, and a notable figure within Spanish art of all periods, the exhibition is on display in Rooms A and B of the Jerónimos Building from 21 November 2017 to 18 March 2018. Continuing the Museo del Prado ’s strategy, launched some years ago, of reassessing the great masters of 19th-century Spanish painting, the Museum is now presenting the major exhibition Fortuny (1838-1874), sponsored by Fundación AXA and with the special collaboration of the Museo Fortuny in Venice and the Museu Nacional d’Art de Catalunya. Saint Petersburg, The State Hermitage Museum, 2017. Mariano Fortuny y Marsal, Opium Smoker, 1869.
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Instead we arrange for this information to be contained in a VBA module.Īs far as possible we want this module to contain only user-specified information with a minimum of other code cluttering it up.Ba S, Myers WR, Brenneman WA (2015) Optimal sliced Latin hypercube designs. For a project like this such an approach would be too difficult to implement. Commercial packages use specially designed “random” worksheet functions entered into cells to identify the cells concerned and to specify the distribution to be used. Having written functions to generate ‘latin hypercube’ arrays and some inverse distribution functions, we can now put the two together to generate the uncorrelated sample arrays (tomorrow’s post will explain how to make them correlated).įirstly, we need a way for the user to specify the input variables. ' which is a uniformly distributed on the range (i - 1)/n 0 ' Returns an array of n random numbers in ascending order, the ith member of Public Function unifun(ByVal n As Long) As Double() The code to implement the function goes something like this: Will have the cumulative distribution function \(F_ & 0 0Īnd the remaining values using a for loop from 2 to n. In symbols, if \(U\) is uniformly distributed on the interval (0, 1) then the random variable \(X\), defined by The inverse transform method is based on the idea that if you take a random variable that is uniformly distributed on the interval (0, 1) and put it into the inverse distribution function of a desired distribution, the resulting random variable will have that distribution. Consequently, this is the method I have chosen to use in this project. This is exactly what we need for ‘latin hypercube’ sampling. The two most general methods, in the sense that they can be made to return distributions with any possible functional form, are the acceptance-rejection method and the inverse transform method, the latter has the further advantage that it can easily be made to return values from equal-probability subdivisions of the range of our desired random variable. Other methods are more general and can produce random numbers conforming to many different distributions. Most of them are specific to particular distributions with, as you might expect, the normal having the most. We want to convert a random variable that is uniformly distributed on the range [0, 1), as supplied by VBA’s Rnd() function, into a random variable distributed according to any desired distribution. Ways of generating non-uniform random variables As we are trying to develop a tool that is of fairly general applicability, we need a method that will generate samples distributed according to any distribution we may choose. Out there ‘in the wild’ random variables occur in all shapes and sizes, not just the standard ones. Excel and many other applications natively provide a random function that returns values that are uniformly distributed on the range [0, 1). The object of the exercise is to generate an array of random numbers that are distributed according to a given frequency distribution. Today’s post describes how to generate random numbers according to arbitrarily chosen probability distributions using the inverse transform method. It follows on from yesterday’s, where I gave an overview of the problem and how I propose to tackle it. Welcome back! This is number two in a series of five blog posts that describe how to construct a Monte Carlo risk analysis application in Excel VBA. 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