A new algorithm for computing moments of complex non-central Wishart distributionsE. Di Nardo*elvira.dinardo@unito.ithttps://www.elviradinardo.it Tel: +390116702862 Fax: +390116702878G. Guarino**giuseppe.guarino@aspbasilicata.it * Dipartimento di Matematica "G.Peano", Universit\303\240 di Torino,Via Carlo Alberto 10, Torino, Italy** Local Health Authority of Potenza, via Torraca 2, Potenza, Italy JSFH
<Text-field style="Heading 1" layout="Heading 1">Introduction</Text-field>Abstract: We provide a new algorithm for computing joint moments of complex non-central Wishart distributions, based on a symbolic method that is particularly well suited for implementation with multivariate statistical distributions. The joint moments we compute are of the form 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 with 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 a multi-index of non-negative integers and 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 complex matrices. A classical method for computing joint moments (1) rely on multivariable derivatives of the moment generating function of the complex non-central Wishart distribution, which has the following rather complicated expression 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 with LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2JS1GLDYmUSJJRicvJSdpdGFsaWNHUSV0cnVlRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRidGNy9GO1Enbm9ybWFsRidGK0Y3Rj0= identity matrix, LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2JS1GLDYmUScmIzkzMTtGJy8lJ2l0YWxpY0dRJmZhbHNlRicvJStleGVjdXRhYmxlR0Y2LyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJ0Y3RjlGK0Y3Rjk= the covariance matrix and LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2JS1GLDYmUScmIzkzNztGJy8lJ2l0YWxpY0dRJmZhbHNlRicvJStleGVjdXRhYmxlR0Y2LyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJ0Y3RjlGK0Y3Rjk= the non-centrality matrix. Since the non-central Wishart random matrix can be expressed as the convolution of two different random matrices 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, where one corresponds to the central distribution and the other involves formal variables [1], the main idea of the new algorithm is to apply a suitable binomial expansion using multiset subdivisions, and then to substitute the moments of these two random matrices, computed in a separate procedure. Multiset subdivisions are again employed to compute these separated moments. In particular, the moments of the associated central Wishart distribution are constructed using a combinatorial device, the necklace, which exploits the cyclic property of the trace. In this worksheet, in addition to the algorithm based on the aforementioned binomial expansion, we present an algorithm for computing the moments in (1) using the moment generating function (2). A comparison of computation times shows the greater efficiency of the first algorithm. The present worksheet constitutes an updated version of a previously published worksheet on the same algorithm. The authors wish to express their gratitude to Raymond Kan [5] for his constructive comments on the earlier version. Application Areas/Subject: Combinatorics & algebraic methodsKeywords: Convolution, multiset subdivision, necklace, joint moment, traceSee Also: Background on multiset subdivisions and multivariate Fa\303\240 di Bruno's formula, see [2,3].
<Text-field style="Heading 1" layout="Heading 1">Initialization</Text-field> LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JFEocmVzdGFydEYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi9RIjtGJy8lJ2l0YWxpY0dRJmZhbHNlRicvRjBRJ25vcm1hbEYnLyUmZmVuY2VHRjgvJSpzZXBhcmF0b3JHUSV0cnVlRicvJSlzdHJldGNoeUdGOC8lKnN5bW1ldHJpY0dGOC8lKGxhcmdlb3BHRjgvJS5tb3ZhYmxlbGltaXRzR0Y4LyUnYWNjZW50R0Y4LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSllcXVhbGl0eUdGOEY2LyUrZXhlY3V0YWJsZUdGOEY5 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 NyVJKnBhcnRpdGlvbkc2IkksbXVsdGlub21pYWxHRiRJKHBlcm11dGVHRiQ= NyRJKlRyYW5zcG9zZUc2IkkoRmxhdHRlbkdGJA==
<Text-field style="Heading 1" layout="Heading 1">Multiset subdivisions </Text-field> The function makeTab has been thoroughly described in [2]. The procedure generates multiset subdivisions, i.e., partitions of a multiset (see examples below). The list of all partitions of a set with 3 blocks is: 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,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, 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 , LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkobWZlbmNlZEdGJDYmLUYjNiYtRiw2Ji1GIzYkLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEoJmFscGhhO0YnLyUnaXRhbGljR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictRiM2JC1JI21uR0YkNiRRIjFGJ0Y+Rj4vJS9zdWJzY3JpcHRzaGlmdEdRIjBGJ0Y+Rj4vJSVvcGVuR1EifGZyRicvJSZjbG9zZUdRInxockYnLUkjbW9HRiQ2LlEiLEYnRj4vJSZmZW5jZUdGPS8lKnNlcGFyYXRvckdRJXRydWVGJy8lKXN0cmV0Y2h5R0Y9LyUqc3ltbWV0cmljR0Y9LyUobGFyZ2VvcEdGPS8lLm1vdmFibGVsaW1pdHNHRj0vJSdhY2NlbnRHRj0vJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR1EsMC4zMzMzMzMzZW1GJy8lKWVxdWFsaXR5R0Y9LUYsNiYtRiM2Ji1GNTYlRjctRiM2JC1GRDYkUSIyRidGPkY+RkdGUC1GNTYlRjctRiM2JC1GRDYkUSIzRidGPkY+RkdGPkY+RkpGTUY+Rj5GSkZNRj4=, 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.Setting 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 we obtain: 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Compacting the previous output we obtain: 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http://www.maplesoft.com/applications/view.aspx?SID=33039
<Text-field style="Heading 2" layout="Heading 2">The Maple routines and examples</Text-field>
<Text-field style="Text" bold="true" size="14" family="Serif" layout="Heading 3"><Font size="14" bold="true" family="Serif"> The Maple routines</Font></Text-field> 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<Text-field style="Heading 3" layout="Heading 3">Examples</Text-field> In (3.1.2.1) the multiset 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 is considered with LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2JS1JJW1zdWJHRiQ2JS1GLDYmUScmIzk0NTtGJy8lJ2l0YWxpY0dRJmZhbHNlRicvJStleGVjdXRhYmxlR0Y5LyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1GIzYlLUkjbW5HRiQ2JVEiMUYnRjpGPEY6RjwvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJ0Y6RjxGK0Y6Rjw= having multiplicity 2. The subdivisions are:LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2J0YrLUYjNictSShtZmVuY2VkR0YkNictRiM2JS1JJW1zdWJHRiQ2JS1GLDYmUScmIzk0NTtGJy8lJ2l0YWxpY0dRJmZhbHNlRicvJStleGVjdXRhYmxlR0ZALyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1GIzYlLUkjbW5HRiQ2JVEiMUYnRkFGQ0ZBRkMvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJ0ZBRkNGQUZDLyUlb3BlbkdRInxmckYnLyUmY2xvc2VHUSJ8aHJGJy1JI21vR0YkNi9RIixGJ0ZBRkMvJSZmZW5jZUdGQC8lKnNlcGFyYXRvckdRJXRydWVGJy8lKXN0cmV0Y2h5R0ZALyUqc3ltbWV0cmljR0ZALyUobGFyZ2VvcEdGQC8lLm1vdmFibGVsaW1pdHNHRkAvJSdhY2NlbnRHRkAvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR1EsMC4zMzMzMzMzZW1GJy8lKWVxdWFsaXR5R0ZARjNGQUZDRitGQUZDRitGQUZD, denoted in the output with 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 denoted in the output with LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2JS1JKG1mZW5jZWRHRiQ2Jy1GIzYnLUYyNictRiM2J0YrLUYjNiUtSShtc3Vic3VwR0YkNictRiw2JlEnJiM5NDU7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUrZXhlY3V0YWJsZUdGRC8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictRiM2JS1JI21uR0YkNiVRIjFGJ0ZFRkdGRUZHLUZNNiVRIjJGJ0ZFRkcvJTFzdXBlcnNjcmlwdHNoaWZ0R1EiMEYnLyUvc3Vic2NyaXB0c2hpZnRHRlVGRUZHRitGRUZHRkVGRy8lJW9wZW5HUSJbRicvJSZjbG9zZUdRIl1GJy1JI21vR0YkNi9RIixGJ0ZFRkcvJSZmZW5jZUdGRC8lKnNlcGFyYXRvckdRJXRydWVGJy8lKXN0cmV0Y2h5R0ZELyUqc3ltbWV0cmljR0ZELyUobGFyZ2VvcEdGRC8lLm1vdmFibGVsaW1pdHNHRkQvJSdhY2NlbnRHRkQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR1EsMC4zMzMzMzMzZW1GJy8lKWVxdWFsaXR5R0ZERkxGRUZHRkVGR0ZYRmVuRkVGR0YrRkVGRw== 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 NyQ3JDckJkkmYWxwaGFHNiI2IyIiIkYlRik3JDcjKiRGJSIiI0Yp In (3.1.2.2) the multiset LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2JS1JKG1mZW5jZWRHRiQ2Jy1GIzYnLUklbXN1YkdGJDYlLUYsNiZRJyYjOTQ1O0YnLyUnaXRhbGljR1EmZmFsc2VGJy8lK2V4ZWN1dGFibGVHRj4vJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLUYjNiUtSSNtbkdGJDYlUSIxRidGP0ZBRj9GQS8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYnLUkjbW9HRiQ2L1EiLEYnRj9GQS8lJmZlbmNlR0Y+LyUqc2VwYXJhdG9yR1EldHJ1ZUYnLyUpc3RyZXRjaHlHRj4vJSpzeW1tZXRyaWNHRj4vJShsYXJnZW9wR0Y+LyUubW92YWJsZWxpbWl0c0dGPi8lJ2FjY2VudEdGPi8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHUSwwLjMzMzMzMzNlbUYnLyUpZXF1YWxpdHlHRj4tRjc2JUY5LUYjNiUtRkc2JVEiMkYnRj9GQUY/RkFGSkY/RkFGP0ZBLyUlb3BlbkdRInxmckYnLyUmY2xvc2VHUSJ8aHJGJ0Y/RkFGK0Y/RkE= is considered with LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2JS1JJW1zdWJHRiQ2JS1GLDYmUScmIzk0NTtGJy8lJ2l0YWxpY0dRJmZhbHNlRicvJStleGVjdXRhYmxlR0Y5LyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1GIzYlLUkjbW5HRiQ2JVEiMUYnRjpGPEY6RjwvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJ0Y6RjxGK0Y6Rjw= having multiplicity 1 and LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2I1EhRictRiM2Ji1JJW1zdWJHRiQ2JS1GLDYmUScmIzk0NTtGJy8lJ2l0YWxpY0dRJmZhbHNlRicvJStleGVjdXRhYmxlR0Y5LyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1GIzYmLUkjbW5HRiQ2JVEiMkYnRjpGPEY6LyUwZm9udF9zdHlsZV9uYW1lR1EpMkR+SW5wdXRGJ0Y8LyUvc3Vic2NyaXB0c2hpZnRHUSIwRidGOkZFRjxGK0Y6RkVGPA== having multiplicity 1. The subdivisions are: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, denoted in the output with 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, denoted in the output with 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 NyQ3JDcjKiYmSSZhbHBoYUc2IjYjIiIiRiomRic2IyIiI0YqRio3JDckRiZGK0Yq In (3.1.2.3) the 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 is considered with LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2JS1JJW1zdWJHRiQ2JS1GLDYmUScmIzk0NTtGJy8lJ2l0YWxpY0dRJmZhbHNlRicvJStleGVjdXRhYmxlR0Y5LyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1GIzYlLUkjbW5HRiQ2JVEiMUYnRjpGPEY6RjwvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJ0Y6RjxGK0Y6Rjw= having multiplicity 2 and LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2JS1JJW1zdWJHRiQ2JS1GLDYmUScmIzk0NTtGJy8lJ2l0YWxpY0dRJmZhbHNlRicvJStleGVjdXRhYmxlR0Y5LyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1GIzYlLUkjbW5HRiQ2JVEiMkYnRjpGPEY6RjwvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJ0Y6RjxGK0Y6Rjw= having multiplicity 1. The subdivisions are: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, denoted in the output with 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denoted in the output with 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, denoted in the output with 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JSFH 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 NyY3JDckKiYmSSZhbHBoYUc2IjYjIiIiRiomRic2IyIiI0YqRiZGLTckNyVGJkYmRitGKjckNyMqJkYmRi1GK0YqRio3JDckKiRGJkYtRitGKg==
<Text-field style="Heading 1" layout="Heading 1">MFB Function</Text-field>The procedure MFB computes the moments of the complex central Wishart distribution and of the matrix LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JlEiQUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnL0Y2USdub3JtYWxGJw==, whose entries are suitable formal variables. In [1], these moments correspond to formulae (37) and (38), respectively. Here, we simply note that in order to compute the i-th coefficient of the composition of two multivariable formal power series, the function MFB does not rely on nested partial derivatives, but instead makes use of the procedure makeTab. The following functions are provided and discussed in detail in the MAPLE worksheet [3]. (https://www.maplesoft.com/Applications/Detail.aspx?id=101396).
<Text-field style="Heading 3" layout="Heading 3">The Code</Text-field> 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
<Text-field style="Heading 3" layout="Heading 3">Examples</Text-field> In (4.2.1) the coefficient of order 2 of 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 LCYqJiZJImZHNiI2IyIiIyIiIiZJImdHRiY2I0YpRihGKSomJkYlRixGKSZGK0YnRilGKQ== In (4.2.2) the coefficient of order 2 of 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JSFH 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 LCYqKCZJImZHNiI2IyIiIyIiIiZJImdHRiY2JCIiIUYpRikmRis2JEYpRi1GKUYpKiYmRiU2I0YpRikmRis2JEYpRilGKUYp In (4.2.3) the coefficient of order 2 of 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 LCwqKiZJImZHNiI2IyIiJCIiIiZJImdHRiY2JSIiIUYtRilGKSZGKzYlRi1GKUYtRikmRis2JUYpRi1GLUYpRikqKCZGJTYjIiIjRilGKkYpJkYrNiVGKUYpRi1GKUYpKihGM0YpRi5GKSZGKzYlRilGLUYpRilGKSooRjNGKSZGKzYlRi1GKUYpRilGMEYpRikqJiZGJTYjRilGKSZGKzYlRilGKUYpRilGKQ== 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 LCYqLEkjZjFHNiIiIiJJI2YyR0YlIiIjJkkjZzFHRiU2JEYmIiIhRiYmSSNnMkdGJTYkRixGJkYmJkYuRitGJkYoKipGJEYmRidGJkYpRiYmRi42JEYmRiZGJkYo LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JFEmam9pbnRGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSShtZmVuY2VkR0YkNiUtRiM2KC1GMzYnLUYjNiYtSSNtbkdGJDYlUSIxRicvJSdpdGFsaWNHUSZmYWxzZUYnL0YwUSdub3JtYWxGJy1JI21vR0YkNi9RIixGJ0Y/RkIvJSZmZW5jZUdGQS8lKnNlcGFyYXRvckdRJXRydWVGJy8lKXN0cmV0Y2h5R0ZBLyUqc3ltbWV0cmljR0ZBLyUobGFyZ2VvcEdGQS8lLm1vdmFibGVsaW1pdHNHRkEvJSdhY2NlbnRHRkEvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR1EsMC4zMzMzMzMzZW1GJy8lKWVxdWFsaXR5R0ZBLUY8NiVRIjBGJ0Y/RkJGL0Y/RkIvJSVvcGVuR1EiW0YnLyUmY2xvc2VHUSJdRidGRC1GMzYnLUYjNiZGO0ZERjtGL0Y/RkJGXG9GX29GRC1GMzYnLUYjNiZGaW5GREY7Ri9GP0ZCRlxvRl9vRi9GP0ZCLUZFNi9RIjtGJ0Y/RkJGSEZKRk1GT0ZRRlNGVUZXL0ZlblEsMC4yNzc3Nzc4ZW1GJ0ZnbkY/LyUrZXhlY3V0YWJsZUdGQUZC LCYqMEkjZjFHNiIiIiJJI2YyR0YlIiIjSSNmM0dGJUYmJkkjZzFHRiU2JEYmIiIhRiYmSSNnMkdGJTYkRi1GJkYmJkYvRixGJiZJI2czR0YlRjBGJiIiJSouRiRGJkYnRiZGKUYmRipGJiZGLzYkRiZGJkYmRjJGJkY0 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 NiY3JDckIiIiRiU3JCIiIUYnNyRGJkYkNyQ3JEYlRic3JEYnRiU3JEYrRio= The print is in vertical mode 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 NyQ3JCIiIkYkNyRGJCIiIQ== NyQ3JCIiIiIiITckRiRGJA== NyQ3JCIiIyIiIjckIiIhRic= NyQ3JCIiIUYkNyQiIiMiIiI= NyQ3JCIiIyIiITckRiUiIiI= NyQ3JCIiISIiIjckIiIjRiQ= 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 Univariate with Univariate 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 we have the same result of MFB function. 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<Text-field style="Heading 1" layout="Heading 1">Algorithm for computing joint moments of complex non-central Wishart distributions</Text-field>In this section, we introduce the Maple algorithm for the symbolic computation of the joint moments (1). The computation is divided into several procedures, which are explained in detail below.
<Text-field style="Heading 2" layout="Heading 2">The leftShift function</Text-field>Left shift of a vector: each element of the output vector is obtained by shifting the corresponding element of the input vector (given in arg1) one position to the left.
<Text-field style="Heading 3" layout="Heading 3">The Code</Text-field>
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 LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSpsZWZ0U2hpZnRHRihmKjYjSSJ2R0YoRig2JEkpb3BlcmF0b3JHRihJJmFycm93R0YoRig3JC1JI29wR0YmNiMmOSQ2IzsiIiMhIiImRjk2IyIiIkYoRihGKDcjRi4=
<Text-field style="Heading 3" layout="Heading 3">Example</Text-field>In (5.2.2) the vector [1,2,3,4] is shifted in [2,3,4,1].
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 NyYiIiMiIiQiIiUiIiI=
<Text-field style="Heading 2" layout="Heading 2">The Mnecklaces function</Text-field>Let us consider the multiset MFNWtKUb<ob<R=MDLCdNrqRLKb:bFCGSE[JnrC_b;_drOugieu_aMYyyyyFhjRNhgfmfFaL?wnPaMijh?ahfiMG^OfpB?y`@cCwbWp_<oc_@_tNq\\X[KOd[fkM@s_PftfrcgbPXsPNs\\hf\\oxon`YxupXtsiiuqfnHg@psuIyrAy=yfUYywQiwpuIyxeiytwuK>`FVBHVCDOZMZ:hMHR\\uNVqRs=U:]nkHjw@JxpMjdwSms=MP=lLATQ[mrmXsXqpRuYveQMXJfTKZlJpMPctpviog\\qMPORtUZ]ln=Xj=Xyatv@weqvUUqfdxt=v\\IKl@rl@JYuK>PxNTw_pjGHPUyxOToT=UxAncTNo<NYIKqluWyqCYv@LQbAoqhjP<n`FpkY\\chfsXatwp;ikgV_qyvnVr=NgSYelysribxvmdYveqkOgBaf:KV_;gVGfwqHYGw^?sJYvsiYlYhykX`arWeF;mreaw;sH;kB=weTSXfegnGf\\YTkEyG;hbaw^[ucgbN=h@QyD?rL?B=GRIeB]SdOKGJSvHYvDMIA]VpmuaWRJOwrcX_CWZ=S:GR;OdtaBO=C\\wTv_WbaLuTu:Hy:\\N;pshlPfLYYh]:Al<>pMBfaJ:<uC>P<:;yaUBSysamVEdPRTQ@mMJ<MZ=pvUnfAMmTy_pJTUV^Il\\TyHQJvlMY=tDaw;lT><MV\\xjPUELtkAyDqT`TMn`w:<NhaZ:>uCBpMJ::>U<L=<lY=yVUKoLqihWU<xAPxR@j]QM;xLP=WE=Ub=m;]kkaq^ilVDySYWpdprayC`pqLWDiW?xXc<uWDv;TsnITLHUtds\\PLLtS^`tcHoqpL`hP\\uxwQMZuPOdJpXqvELBDUNplD\\Tu<LpMXT=NBeJuDWVuwliwcxsudLQPlwuNq@p_mUv=n^dtcIWBYQOTmLhmOXURMWcilvIua]lUxjBljAlkrEoBUrUxlV`rsDugyle\\Qp@Um=xSMtMumk=whpu;XvXLOBls`inaAXmiuqyurHXVqVv<nYyLZdokDKEpjXlqgHnpHRJLS^plwXjHdSoxUb=n\\<vA=WEtu=tVMysfMMeDx:]RUxmmIQ;DQqatN\\Ut]TOETUQKmUw^LsBqrhyRL]V\\mxeltZYKOIUMXmxAwOYsTqTHttXAoY\\OfaSYeRXHqA<qa\\JN]KF=pb<woELkpkcLUVIsvEKGeUspsfYqKTt:ENAEsOmQs]UYqsYaZc@a@g\\<punfpnWcZhi<okLPofNiXwuHymHXlL?]mncXN_iOZNY\\<N`Tqdegi`Pb_Is?vsR@pji_uwh]imEX]<xpi>dWF`Uou^`hWOtTiexqyIHdQGsghe`Wh`VsIniHQptp_QxyUX`mih_GeEatoXp_NnnVndfv\\ywow_ENaP`ZSXtlGkfggGxpbIiphcqpwq@gHHgCyqYikEfy_GrrFsrylN@kBQqTynWnkxnvoaZ\\^ncHbGicKhhuFxiNygXinfcGqlva[Bvh<yg;praai=?oT`gFnhCghH?ksXjUXp<fkJNrqOrfQyUIny`yx?tKwgNAsfPljWfX_skpxGwZWgcN`^v>_;ioOylIHpVw[tOc>hmg^jehcE^qfwnKQbxgkiw`mYudqw^aqTiabycwh[XqwHWgjotLyjLpmJa^^@aaHsDvfEHyJNvuWnwGx`hohYgVxtTHr[Vu=p]G_uZYsOPsCQiNOgLYn`Gby^lQihVYh`wy^Xwuwc`o`lpqRQpmWixHq[pgAP]WQvn@l]VpUIshxsFvkAX^h^ju^c<OcpPdjX]mXrIhx>_n?@aZhv^FtA_wJ_`oHbqvay_yNQumWxL^`IGupQyooepYtrW^O^s@O`SgbMGeXOd@wpS`uxayxgoo?juQlkQpVGtTI_OxibAatGaIwvGhejPmBab>pnlw]pFbH?yc>``qlEFuygeriadVoyohlV_hx]ynkVw\\rhrf_fthsIfvaYrMqiBfkXA`WOr]OajVvSIywGqy^rVFuZ_nfFmVhnnxvTGwqwdL>km^]`wiIY_C?mOge`Ofb`ruaoE`eNprRWf`?nZF^gifoYae?[qoqq?mEpvMOkKgepaZTO`AAdXXgC>qE`bBWgX_f@H]MyhYHf<HyP@jG@smIZQIcVpiSIo:HxHhcqFqeggy?i>NhmXpxfwRiZGvymowVOglou[ycV?odalNxwZ`ngyqcH\\VnvHYn`W^x^vD`jliwbP_Dglkv`Tvsiy]jPwBxiR>_DGxBFdsAvTfrFqrRondvn^Hb\\V_nWad>[c@oSnbMvbmiqtW^kvnSqfHp]yA]SpkDQrfOkEhnk`cGos=Gjl@hUXwV@fuwpfVlR`ciIwLyeBXaspmpwhr_j`OZ;p_DIjWhuo@yZym=HxoxyUIc`OdjIfxGrrOcq^uqY];x_[qgDnaRy_Fvc[O[YNyJI[avp\\ipfGtg^rLo_XnuCYfvwnHikVHm<_fAYskxdpOj_?\\Zp^FW^VfuIxtYxkxwd;YsS@lUxtcp_RA^<peDvfJFjYWjrfhOFyFVtsobDaikNmEy]Ngk_IygyyNA\\hIhCFj_wl`PlJPgLOZOFj?>mQ?lrObdGdQGxNHp<arBGjQhaVax\\Ibkpy<HgvIp`oseNroq\\QV]=ohko[c_p:pi:^ciNaDXxBptVih`wp_yf;afYfm@Fa=wVYWU]t=Mi:YHT;Y]GxKCD[EhSgSG]b^Awe]rPmYwgfKowa_bVCscoyYKSmouM?CCsxewum?vxwuB[YCShXyTYyIy]xBmHsYtnAY]GxKCv[EhSeSJES>]rGKF]wvMCfLyYXuElUw\\wh_aG]mIFaUYSgcUGmUg\\Swv=SVmXoyYtisHwd]iy>KBciyaGXIsU@wsYMRw_t^etagbfwuU?YkUhGyrVgSwqEI]Ei;uZ[iQGeqISnwSM]DHAFvwgoQT>Wt<mFKaeQcSQEvu]ehoVlCTYwU\\OXbXkjds?yth\\tGyXXHNi<uRhqoiLflUiyP<dT]tQ_MQUMMlyRAIvhpRlDtnynsLQvYTodnyXPpXtgmNVuqJUjkmyKEqQtPYiQFPuyxPYAWIwjcNhYxZ>?kxvwVAw[F^Nx[`>\\]aengjyFqmYbCIwff^ih`@PvTnj\\gatfmb@v_I`gY_MYfO`raN_gPxj^\\Qw[;?iofre?\\RhdL@`jgb>afFGxdpt=oqfAkkgso`cZnunGtgivdVyX>hKPt;@]qQ\\E>_\\^Zg^sTxfBgiWFpG@l<aslQ_^a[gyoIwovImNa[WHt\\Wkj`jQWdFqZcWyDfb>qfFGpdptSWdjWaWHn_OqfolH@^`nxm^]bVn?Fdiq\\x@\\pOt=nnO`^Lf[V>`\\QhJ?`wId\\GkHXbiqp:_x[@qLVZex]_irPikPndGGhU^jXOhe?rD@kIAm\\idgiesGfS^ZcasS`oc>lBhyF>[DGxlq_\\v`lH^gFf@h[KNwmw`tXkkx[B@dSXqKybfF_CWyf>]anb;ajOWdVqZKGmeQwm^x@a\\ePgfqflGdg^ZcW_CYsBnnZ@kOpvWF`e@kLIaFooAXjSatl`mLO_UNfMAksw[bf]=AgbWkGgnlxZQQcjfkRhx:PtCfkZ>pbhn?hnNG\\PivBPsHqH_hGyGp_ck[CrICmkea[wkiCiKfpERVkFcQgMwUvCdk[Ihag;wIN]F>cHqeClmFFMTLWth?U\\UwBCiCMd=AgBmumowqOf`Ir]ufNafOCf;KWKqWrWRS]v[kf<[YLyrgUuUgTA_urGtI_GterHASoWCH?i]Ce^qh[kGgkX]Cv^qXAgWGYt_yBqMrBMCw_GnKTwKuKYxJmVoSVrWHNgR_[emIXBkY]IhMiWtOdBCHSuIqiDwqDLKRQehXAi?aXvyYs[cJoTSOWDGWEMxpAuX?ynYB>SRWQHt=WoEcpovnOwAiF?GuCEv;[rsEwQwhGyTaygNEdPUHlctawFgixTqEyav=shGeb_qrbMgCYSjMeWgSeOYF=vDgD`iikUwo[tP_xmkvtOS=_e_AGOSFfkbxUrUYWiMvMKE>SXtgvNmregCeWb??UnOglOd<yuMOrpWIies<eWCWivWW;OinyFOohAOUvMH`sbhWVwGXgGwrEEKOY?eY;Cgk?XQmr]ww=cY<KfpgV>ECyYINkHxqVvQDESRoysPsdjqgs[imUEYOejMyTEG==y^ahDWEckFY_u\\_bJAHEKsBQHB[xqacTqesITfGgJ[RtQVt;u_qcHkcEiEP_Gn[TQgDfcD^YCkKf?gtlmt`YHquxsMeB]V[]I\\]u<AfewcFkCtAY@wWEacV;UTSH[;gTSWyGr;IVcWry_GFsIUMv@IVJ=ChYgPuUicTPKrLgyRcVxwtSWg;me`OfhWGT;eqEd@EEtcR`AeugVawuFESHcSByDdyRFOtoqHMAT`UIHuR>[g;qc?my__IssxfqeWEBQAc\\?gDgUhIbmeXXEVLYw<wG>KWTWT^iWEshuEgqsgasUsGTJUGFQt]MWcmrCmwmwC_etFusPAvSwgq_T<abJ_UPwgpmXWUhTqrRccL?v\\?U>Oh[WtK_EE[UpMGq?GLWDDKg?eSZgcQMHcItVyVYohSwu;AcwSgkOEl_yjoi`qwSAVYAb^kYDWBVSI<EVgiIVwtssgpGe=oEBQeVoyRIuHYyeWfqiDMAFoCHpWEsws;?Y[Qb\\qbDateuficewsvdmx\\oFwkFjyFgosD_RYubgsdbWtWUR]ewFec`kSR_cKyTyQw@AUPUBm_rEWyV;ib[UQQg[IYseXWeTcmt_?Ua?tVaf:UC?yd<cftSIFWft[BLUB]Uw?iY>WGDoIF=TPgdnmHDitF?UQoeNXW?XkxpWXtlXqsleQ:=udaoAHtMuMFhvN@XEeMI`VGeXn=XDyL:AS=uYhPkayu_etOdrMuV^HTTYtVuYxdwlHsYxtX=uuIOXMpfHuw]nheRVYtWlxRdk[Tq>XL;PtXpQQXyR]OmExlmm<H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procedure Mnecklaces outputs all necklaces that can be constructed by permuting the elements of the multiset passed as LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYpLUkjbWlHRiQ2JVElYXJnMUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi5RIi5GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGTC8lKWVxdWFsaXR5R0Y9LUY2Ni5RIn5GJ0Y5RjtGPkZARkJGREZGRkhGSkZNRk9GUUYvLyUrZXhlY3V0YWJsZUdGPUYyIn combinatorics, an m-ary necklace of length n is an equivalence class of n-character strings over an alphabet of size m. Here n is equal to 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. Given the lexicographically smallest string, called the representative, all other elements of the necklace can be obtained by circular rotations of the representative. A necklace represents a structure of n circularly connected beads, each of up to m different colors.Depending on the value assigned to arg2, the following outputs are performed:0: Print only the cardinalities of the necklaces, grouping and enumerating those with the same cardinality. 1: Print only the cardinalities of the necklaces as a list. 2: Print both the cardinality and the representative of each necklace. 3: Print all elements of all necklaces; the first element of each is the representative. 4: Print only the total number of necklaces.Example: The four necklaces that can be formed with 3 red beads and 3 blue beads are as follows: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 can obtain the same result by using: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Instead 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 generates: [6, [1, 1, 1, 2, 2, 2]] [6, [1, 1, 2, 1, 2, 2]] [6, [1, 1, 2, 2, 1, 2]] [2, [1, 2, 1, 2, 1, 2]]or using 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 generates: [6, [red, red, red, blue, blue, blue]] [6, [red, red, blue, red, blue, blue]] [6, [red, red, blue, blue, red, blue]] [2, [red, blue, red, blue, red, blue]]
<Text-field style="Heading 3" layout="Heading 3">The Code</Text-field> 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
<Text-field style="Heading 3" layout="Heading 3">Example</Text-field> In the following, necklaces that can be made with 4 beads, labelled with 1, and 2 beads, labelled with 2. 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 NyQ3JCIiJCIiIjckIiInIiIj The function is executed setting the second parameter from 0 to 4 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 NiQvSSRQYXJHNiIiIiEvSSdPdXRwdXRHRiU3JDckIiIjIiIiNyQiIiciIiQ= NiQvSSRQYXJHNiIiIiIvSSdPdXRwdXRHRiU3JiIiIyIiJ0YrRis= NiQvSSRQYXJHNiIiIiMvSSdPdXRwdXRHRiU3JjckIiInNygiIiJGLUYtRiZGJkYmNyRGKzcoRi1GLUYmRi1GJkYmNyRGKzcoRi1GLUYmRiZGLUYmNyRGJjcoRi1GJkYtRiZGLUYm NiQvSSRQYXJHNiIiIiQvSSdPdXRwdXRHRiU3JjcoNygiIiJGLEYsIiIjRi1GLTcoRixGLEYtRi1GLUYsNyhGLEYtRi1GLUYsRiw3KEYtRi1GLUYsRixGLDcoRi1GLUYsRixGLEYtNyhGLUYsRixGLEYtRi03KDcoRixGLEYtRixGLUYtNyhGLEYtRixGLUYtRiw3KEYtRixGLUYtRixGLDcoRixGLUYtRixGLEYtNyhGLUYtRixGLEYtRiw3KEYtRixGLEYtRixGLTcoNyhGLEYsRi1GLUYsRi03KEYsRi1GLUYsRi1GLDcoRi1GLUYsRi1GLEYsNyhGLUYsRi1GLEYsRi03KEYsRi1GLEYsRi1GLTcoRi1GLEYsRi1GLUYsNyQ3KEYsRi1GLEYtRixGLTcoRi1GLEYtRixGLUYs NiQvSSRQYXJHNiIiIiUvSSdPdXRwdXRHRiVGJg== A different output can be obtained by using the following colors: 3 red and 3 blue beads. 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<Text-field style="Heading 2" layout="Heading 2">The m2v function</Text-field>The routine m2v converts a multiset (arg1) into a list, inserting parentheses between different symbols, to group equal characters for the next processing step
<Text-field style="Heading 3" layout="Heading 3">The code</Text-field> LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzZndy1JI21pR0YkNiRRJG0ydkYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi9RIn5GJy8lJ2l0YWxpY0dRJmZhbHNlRicvRjBRJ25vcm1hbEYnLyUmZmVuY2VHRjgvJSpzZXBhcmF0b3JHRjgvJSlzdHJldGNoeUdGOC8lKnN5bW1ldHJpY0dGOC8lKGxhcmdlb3BHRjgvJS5tb3ZhYmxlbGltaXRzR0Y4LyUnYWNjZW50R0Y4LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGSy8lKWVxdWFsaXR5R0Y4LUYzNi9RKiZjb2xvbmVxO0YnRjZGOUY7Rj1GP0ZBRkNGRUZHL0ZKUSwwLjI3Nzc3NzhlbUYnL0ZNRlRGTkYyLUYzNjFRJXByb2NGJy8lJWJvbGRHUSV0cnVlRidGNi9GMFElYm9sZEYnLyUrZm9udHdlaWdodEdGZ25GO0Y9Rj9GQUZDRkVGR0ZJRkxGTi1JKG1mZW5jZWRHRiQ2JS1GIzYmLUYsNiRRIlZGJ0YvRjYvJStleGVjdXRhYmxlR0Y4RjlGNkY5LUYsNiNRIUYnLUknbXNwYWNlR0YkNiYvJSdoZWlnaHRHUSYwLjBleEYnLyUmd2lkdGhHRksvJSZkZXB0aEdGXHAvJSpsaW5lYnJlYWtHUShuZXdsaW5lRidGMkYyRjJGMi1GMzYxUSZsb2NhbEYnRllGNkZmbkZobkY7Rj1GP0ZBRkNGRUZHRklGTEZORjItRiw2JFEidUYnRi8tRjM2L1EiLEYnRjZGOUY7L0Y+RmVuRj9GQUZDRkVGR0ZJL0ZNUSwwLjMzMzMzMzNlbUYnRk4tRiw2JFEiVUYnRi9GanAtRiw2JFEidkYnRi9GanAtRiw2JFEiaUYnRi8tRjM2L1EiO0YnRjZGOUY7Rl1xRj9GQUZDRkVGR0ZJRlVGTkYyRmdwRlAtRltvNictRiM2JkZkb0Y2RmJvRjlGNkY5LyUlb3BlbkdRIltGJy8lJmNsb3NlR1EiXUYnRmlxRjJGYHFGUEZcckZpcUZnb0YyRjJGMkYyRmNxRlAtSSVtc3ViR0YkNiVGX28tRiM2JC1JI21uR0YkNiVRIjFGJ0Y2RjlGLy8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYnRmlxRmdvRjJGMkYyRjItRjM2MVEkZm9yRidGWUY2RmZuRmhuRjtGPUY/RkFGQ0ZFRkdGSUZMRk5GMkZmcUYyLUYzNjFRJWZyb21GJ0ZZRjZGZm5GaG5GO0Y9Rj9GQUZDRkVGR0ZJRkxGTkYyRltzRjItRjM2MVEjdG9GJ0ZZRjZGZm5GaG5GO0Y9Rj9GQUZDRkVGR0ZJRkxGTkYyLUYsNiRRJW5vcHNGJ0YvRmpuRjItRjM2MVEjZG9GJ0ZZRjZGZm5GaG5GO0Y9Rj9GQUZDRkVGR0ZJRkxGTkZnb0YyRjJGMkYyRjJGMkYyLUYzNjFRI2lmRidGWUY2RmZuRmhuRjtGPUY/RkFGQ0ZFRkdGSUZMRk5GMi1GZ3I2JUZfby1GIzYkRmZxRi9GX3MtRjM2L1EiPUYnRjZGOUY7Rj1GP0ZBRkNGRUZHRlNGVUZORmNxRjItRjM2MVEldGhlbkYnRllGNkZmbkZobkY7Rj1GP0ZBRkNGRUZHRklGTEZORjJGZ3BGUC1GW282Jy1GIzYpLUYsNiRRI29wRidGLy1GW282JS1GIzYmRmdwRjZGYm9GOUY2RjlGanBGZHRGNkZib0Y5RjZGOUZgckZjckZpcUZnb0YyRjJGMkYyRjJGMkYyRjJGMkYyRjJGMkYyRjJGMkYyRjJGMkYyRjJGMi1GMzYxUSVlbHNlRidGWUY2RmZuRmhuRjtGPUY/RkFGQ0ZFRkdGSUZMRk5GMkZjcUZQRmR0RmlxRmdvRjJGMkYyRjJGMkYyRjJGMkYyRjJGMkYyRjJGMkYyRjJGMkYyRjJGMkYyRjJGMkYyRjJGMkYyRmBxRlAtRltvNictRiM2KUZidS1GW282JS1GIzYmRmBxRjZGYm9GOUY2RjlGanBGZ3BGNkZib0Y5RjZGOUZgckZjckZpcUZnb0YyRjJGMkYyRjJGMkYyRjJGMkYyRjJGMkYyRjJGMkYyRjJGMkYyRjJGMkYyRjJGMkYyRjJGMkZncEZQLUZbbzYnLUYjNiZGY3FGNkZib0Y5RjZGOUZgckZjckZpcUZnb0YyRjJGMkYyRjJGMkYyLUYzNjFRI2ZpRidGWUY2RmZuRmhuRjtGPUY/RkFGQ0ZFRkdGSUZMRk5GaXFGZ29GMkYyRjJGMi1GMzYxUSNvZEYnRllGNkZmbkZobkY7Rj1GP0ZBRkNGRUZHRklGTEZORmlxRmdvRjJGMkYyRjJGXHZGaXFGZ28tRmhvNiZGam9GXXBGX3AvRmJwUSVhdXRvRictRjM2MVEkZW5kRidGWUY2RmZuRmhuRjtGPUY/RkFGQ0ZFRkdGSUZMRk4tRjM2L1EiOkYnRjZGOUY7Rj1GP0ZBRkNGRUZHRlNGVUZORjZGYm9GOQ==
<Text-field style="Heading 3" layout="Heading 3">Example</Text-field> In (5.4.2.1), the input multiset [2,2,1,1,1,2,1] is transformed into the list [2, 2],[1, 1, 1],[2],[1] This function is subsequently called by cn and cno, which construct the matrix trace structure. For instance [2, 2],[1, 1, 1],[2],[1] can be processed to yield 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 LUkjVHJHNiI2JiokJkkiQkdGJDYjIiIjRioqJCZGKDYjIiIiIiIkRidGLA== 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 NyY3JCIiI0YkNyUiIiJGJkYmNyNGJDcjRiY=
<Text-field style="Heading 2" layout="Heading 2">Some useful sub-functions</Text-field>cn functionCn receives the output of m2v and maps each block to a product of matrices with the same indexes; blocks of cardinality >1 correspond to matrix powers.cno functionCno performs the same operation as Cn, but for multiple lists. Different lists correspond to different elements in a summation. conv & convo functionThe procedures conv and convo make use of cn and cno with input lists produced by the procedure Mnecklaces.
<Text-field style="Heading 3" layout="Heading 3">The Codes</Text-field> 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
<Text-field style="Heading 3" layout="Heading 3">Examples</Text-field> The steps are: 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 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JFEjY25GJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSShtZmVuY2VkR0YkNiUtRiM2KC1GMzYnLUYjNjItSSNtbkdGJDYlUSIxRicvJSdpdGFsaWNHUSZmYWxzZUYnL0YwUSdub3JtYWxGJy1JI21vR0YkNi9RIixGJ0Y/RkIvJSZmZW5jZUdGQS8lKnNlcGFyYXRvckdRJXRydWVGJy8lKXN0cmV0Y2h5R0ZBLyUqc3ltbWV0cmljR0ZBLyUobGFyZ2VvcEdGQS8lLm1vdmFibGVsaW1pdHNHRkEvJSdhY2NlbnRHRkEvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR1EsMC4zMzMzMzMzZW1GJy8lKWVxdWFsaXR5R0ZBRjtGREY7RkQtRjw2JVEiMkYnRj9GQkZERmluRkRGO0ZERmluRj8vJStleGVjdXRhYmxlR0ZBRkJGP0ZCLyUlb3BlbkdRIltGJy8lJmNsb3NlR1EiXUYnRkQtRjw2JVEiNkYnRj9GQkY/RlxvRkJGP0ZCLUZFNi9RIjtGJ0Y/RkJGSEZKRk1GT0ZRRlNGVUZXL0ZlblEsMC4yNzc3Nzc4ZW1GJ0ZnbkY/RlxvRkI= LCQtSSNUckc2IjYmKiQmSSJCR0YlNiMiIiIiIiQqJCZGKTYjIiIjRjBGKEYuIiIn The steps are: 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 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JFEkY25vRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYlLUYjNiYtRjM2Jy1GIzYoLUYzNictRiM2Mi1JI21uR0YkNiVRIjFGJy8lJ2l0YWxpY0dRJmZhbHNlRicvRjBRJ25vcm1hbEYnLUkjbW9HRiQ2L1EiLEYnRkNGRi8lJmZlbmNlR0ZFLyUqc2VwYXJhdG9yR1EldHJ1ZUYnLyUpc3RyZXRjaHlHRkUvJSpzeW1tZXRyaWNHRkUvJShsYXJnZW9wR0ZFLyUubW92YWJsZWxpbWl0c0dGRS8lJ2FjY2VudEdGRS8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHUSwwLjMzMzMzMzNlbUYnLyUpZXF1YWxpdHlHRkVGP0ZIRj9GSC1GQDYlUSIyRidGQ0ZGRkhGXW9GSEY/RkhGXW9GQy8lK2V4ZWN1dGFibGVHRkVGRkZDRkYvJSVvcGVuR1EiW0YnLyUmY2xvc2VHUSJdRidGSC1GMzYnLUYjNjJGP0ZIRj9GSEZdb0ZIRl1vRkhGXW9GSEY/RkhGXW9GQ0Zgb0ZGRkNGRkZib0Zlb0ZDRmBvRkZGQ0ZGRmJvRmVvRkNGYG9GRkZDRkZGQ0Zgb0ZG LCYtSSNUckc2IjYnSSZPbWVnYUdGJSokJkkiQkdGJTYjIiIiIiIkKiQmRio2IyIiI0YxRilGL0YsLUYkNidGJyokRilGMSokRi9GLUYpRi9GLA== The input multiset is LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2JS1JKG1mZW5jZWRHRiQ2Jy1GIzYpLUkjbW5HRiQ2JVEiMUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLUkjbW9HRiQ2L1EiLEYnRjpGPS8lJmZlbmNlR0Y8LyUqc2VwYXJhdG9yR1EldHJ1ZUYnLyUpc3RyZXRjaHlHRjwvJSpzeW1tZXRyaWNHRjwvJShsYXJnZW9wR0Y8LyUubW92YWJsZWxpbWl0c0dGPC8lJ2FjY2VudEdGPC8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHUSwwLjMzMzMzMzNlbUYnLyUpZXF1YWxpdHlHRjwtRjc2JVEiMkYnRjpGPUZALUY3NiVRIjNGJ0Y6Rj1GOkY9RjpGPS8lJW9wZW5HUSJbRicvJSZjbG9zZUdRIl1GJ0Y6Rj1GK0Y6Rj0=. The generated necklaces are LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2JS1JKG1mZW5jZWRHRiQ2Jy1GIzYlLUkjbW5HRiQ2JVEkMTIzRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRidGOkY9RjpGPS8lJW9wZW5HUSJbRicvJSZjbG9zZUdRIl1GJ0Y6Rj1GK0Y6Rj0= and LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2JS1JKG1mZW5jZWRHRiQ2Jy1GIzYlLUkjbW5HRiQ2JVEkMTMyRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRidGOkY9RjpGPS8lJW9wZW5HUSJbRicvJSZjbG9zZUdRIl1GJ0Y6Rj1GK0Y6Rj0=. For each necklace, the trace of the product of matrices corresponding to the indexes LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2JS1JKG1mZW5jZWRHRiQ2Jy1GIzYlLUkjbW5HRiQ2JVEkMTIzRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRidGOkY9RjpGPS8lJW9wZW5HUSJbRicvJSZjbG9zZUdRIl1GJ0Y6Rj1GK0Y6Rj0=and LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2JS1JKG1mZW5jZWRHRiQ2Jy1GIzYlLUkjbW5HRiQ2JVEkMTMyRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRidGOkY9RjpGPS8lJW9wZW5HUSJbRicvJSZjbG9zZUdRIl1GJ0Y6Rj1GK0Y6Rj0= is is constructed. The same procedure is applied by convo, but with the non-centrality matrix LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2JS1GLDYmUScmIzkzNztGJy8lJ2l0YWxpY0dRJmZhbHNlRicvJStleGVjdXRhYmxlR0Y2LyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJ0Y3RjlGK0Y3Rjk= inserted in the first position. 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 LCYtSSNUckc2IjYlJkkiQkdGJTYjIiIiJkYoNiMiIiMmRig2IyIiJEYwLUYkNiVGJ0YuRitGMA== 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 LC4tSSNUckc2IjYmSSZPbWVnYUdGJSZJIkJHRiU2IyIiIiZGKTYjIiIjJkYpNiMiIiRGKy1GJDYmRidGLEYvRihGKy1GJDYmRidGL0YoRixGKy1GJDYmRidGKEYvRixGKy1GJDYmRidGL0YsRihGKy1GJDYmRidGLEYoRi9GKw== If the multiset is empty, the output is 0. 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 IiIh 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 IiIh Format the Tr argument with a dot separator LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzZeby1JI21pR0YkNiRRJGZUckYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi9RKiZjb2xvbmVxO0YnLyUnaXRhbGljR1EmZmFsc2VGJy9GMFEnbm9ybWFsRicvJSZmZW5jZUdGOC8lKnNlcGFyYXRvckdGOC8lKXN0cmV0Y2h5R0Y4LyUqc3ltbWV0cmljR0Y4LyUobGFyZ2VvcEdGOC8lLm1vdmFibGVsaW1pdHNHRjgvJSdhY2NlbnRHRjgvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZLLyUpZXF1YWxpdHlHRjgtRjM2MVElcHJvY0YnLyUlYm9sZEdRJXRydWVGJ0Y2L0YwUSVib2xkRicvJStmb250d2VpZ2h0R0ZXRjtGPUY/RkFGQ0ZFRkcvRkpRJjAuMGVtRicvRk1GZW5GTi1JKG1mZW5jZWRHRiQ2JS1GIzYmLUYsNiNRIUYnRjYvJStleGVjdXRhYmxlR0Y4RjlGNkY5RlxvLUknbXNwYWNlR0YkNiYvJSdoZWlnaHRHUSYwLjBleEYnLyUmd2lkdGhHRmVuLyUmZGVwdGhHRmZvLyUqbGluZWJyZWFrR1EobmV3bGluZUYnLUYzNi9RIn5GJ0Y2RjlGO0Y9Rj9GQUZDRkVGR0ZaRmZuRk5GXnAtRjM2MVEmbG9jYWxGJ0ZTRjZGVkZYRjtGPUY/RkFGQ0ZFRkdGWkZmbkZORl5wLUYsNiRRInZGJ0YvRjItRmhuNictRiM2Ji1GLDYkUSVhcmdzRidGL0Y2Rl9vRjlGNkY5LyUlb3BlbkdRIltGJy8lJmNsb3NlR1EiXUYnLUYzNi9RIixGJ0Y2RjlGOy9GPkZVRj9GQUZDRkVGR0ZaL0ZNUSwwLjMzMzMzMzNlbUYnRk4tRiw2JFEiaUYnRi9GZHEtRiw2JFEldk91dEYnRi8tRjM2L1EiO0YnRjZGOUY7RmdxRj9GQUZDRkVGR0ZaRkxGTkZhb0ZecEZecEZdckYyRmRwLUZobjYnLUYjNiYtSSNtbkdGJDYlUSIxRidGNkY5RjZGX29GOUY2RjlGXnFGYXFGYHJGYW9GXnBGXnAtRjM2MVEkZm9yRidGU0Y2RlZGWEY7Rj1GP0ZBRkNGRUZHRlpGZm5GTkZecEZqcUZecC1GMzYxUSVmcm9tRidGU0Y2RlZGWEY7Rj1GP0ZBRkNGRUZHRlpGZm5GTkZecC1GaHI2JVEiMkYnRjZGOUZecC1GMzYxUSN0b0YnRlNGNkZWRlhGO0Y9Rj9GQUZDRkVGR0ZaRmZuRk5GXnAtRiw2JFEmbmFyZ3NGJ0YvRl5wLUYzNjFRI2RvRidGU0Y2RlZGWEY7Rj1GP0ZBRkNGRUZHRlpGZm5GTkZecEZdckYyRl1yLUYzNi9RKSZtaWRkb3Q7RidGNkY5RjtGPUY/RkFGQ0ZFRkcvRkpRLDAuMTY2NjY2N2VtRicvRk1GYXRGTkZkcC1GaG42Jy1GIzYmRmpxRjZGX29GOUY2RjlGXnFGYXFGYHJGXnAtRjM2MVEjb2RGJ0ZTRjZGVkZYRjtGPUY/RkFGQ0ZFRkdGWkZmbkZORmByRmFvRl5wRl5wLUYsNiRRJWBUcmBGJ0YvLUZobjYlLUYjNiZGXXJGNkZfb0Y5RjZGOUZgckZhby1GYm82JkZkb0Znb0Zpby9GXHBRJWF1dG9GJy1GMzYxUSRlbmRGJ0ZTRjZGVkZYRjtGPUY/RkFGQ0ZFRkdGWkZmbkZOLUYzNi9RIjpGJ0Y2RjlGO0Y9Rj9GQUZDRkVGR0ZJRkxGTkY2Rl9vRjk= 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 LUkjVHJHNiI2Iy1JIi5HNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiQ2KUkmT21lZ2FHRiRJJlNpZ21hR0YkJkkiSEdGJDYjIiIjRi0mRi82IyIiIkYtRi4= 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 LUkjVHJHNiI2Iy1JIi5HNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiQ2KUkmT21lZ2FHRiRJJlNpZ21hR0YkJkkiSEdGJDYjIiIjRi0mRi82IyIiIkYtRi4=
<Text-field style="Heading 2" layout="Heading 2">The nCWishart function</Text-field>The procedure nCWishart computes moments of a complex non-central Wishart distribution (formula (36) in [1]). It uses mkT for the binomial expansion, Mnecklaces to generate all necklaces from the multiset with molteplicity given by the multi-index i, and conv/convo to convert necklaces into traces of matrix products. These traces are combined with the central Wishart moments (37) and the formal variable matrix moments (38), forming the convolution LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2J0YrLUYjNictRiw2JlEjV2NGJy8lJ2l0YWxpY0dRJXRydWVGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi9RIitGJ0Y5L0Y9USdub3JtYWxGJy8lJmZlbmNlR0Y7LyUqc2VwYXJhdG9yR0Y7LyUpc3RyZXRjaHlHRjsvJSpzeW1tZXRyaWNHRjsvJShsYXJnZW9wR0Y7LyUubW92YWJsZWxpbWl0c0dGOy8lJ2FjY2VudEdGOy8lJ2xzcGFjZUdRLDAuMjIyMjIyMmVtRicvJSdyc3BhY2VHRlUvJSllcXVhbGl0eUdGOy1GLDYmUSJBRidGNkY5RjxGOUZDRitGOUZDRitGOUZD of the non-central Wishart distribution.
<Text-field style="Heading 3" layout="Heading 3">The Code</Text-field> 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
<Text-field style="Heading 3" layout="Heading 3">Example</Text-field>In (5.5.2.1) the joint moment in (1) with 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 LCYqJkkibkc2IiIiIi1JI1RyR0YlNiMtSSIuRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YlNiRJJlNpZ21hR0YlJkkiSEdGJTYjRiZGJkYmLUYoNiMtRis2JUkmT21lZ2FHRiVGMEYxRiY= In (5.5.2.2) the joint moment in (1) with LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2J0YrLUYjNictSSVtc3ViR0YkNiUtRiw2JlEiaUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUYjNiUtSSNtbkdGJDYlUSIxRidGPC9GQFEnbm9ybWFsRidGPEZILyUvc3Vic2NyaXB0c2hpZnRHUSIwRictSSNtb0dGJDYvUSI9RidGPEZILyUmZmVuY2VHRj4vJSpzZXBhcmF0b3JHRj4vJSlzdHJldGNoeUdGPi8lKnN5bW1ldHJpY0dGPi8lKGxhcmdlb3BHRj4vJS5tb3ZhYmxlbGltaXRzR0Y+LyUnYWNjZW50R0Y+LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGW28vJSllcXVhbGl0eUdGPkZERjxGSEYrRjxGSEYrRjxGSA== and 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 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JFEqbkNXaXNoYXJ0RicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYlLUYjNiYtSSNtbkdGJDYlUSIxRicvJSdpdGFsaWNHUSZmYWxzZUYnL0YwUSdub3JtYWxGJy1JI21vR0YkNi9RIixGJ0Y7Rj4vJSZmZW5jZUdGPS8lKnNlcGFyYXRvckdRJXRydWVGJy8lKXN0cmV0Y2h5R0Y9LyUqc3ltbWV0cmljR0Y9LyUobGFyZ2VvcEdGPS8lLm1vdmFibGVsaW1pdHNHRj0vJSdhY2NlbnRHRj0vJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR1EsMC4zMzMzMzMzZW1GJy8lKWVxdWFsaXR5R0Y9RjdGL0Y7Rj5GOy8lK2V4ZWN1dGFibGVHRj1GPg== LDAqKEkibkc2IiIiIy1JI1RyR0YlNiMtSSIuRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YlNiRJJlNpZ21hR0YlJkkiSEdGJTYjRiYiIiItRig2Iy1GKzYkRjAmRjI2I0Y0RjRGNCooRiRGNC1GKDYjLUYrNiVJJk9tZWdhR0YlRjBGMUY0RjVGNEY0KihGJEY0LUYoNiMtRis2JUZARjBGOUY0RidGNEY0KiZGPEY0RkJGNEY0KiZGJEY0LUYoNiMtRis2JkYwRjlGMEYxRjRGNC1GKDYjLUYrNidGQEYwRjlGMEYxRjQtRig2Iy1GKzYnRkBGMEYxRjBGOUY0 In (5.5.2.3) the joint moment in (1) with 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 and 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Remark: ncWishart(1,1,1) allows the computation of the expectation of 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
<Text-field style="Heading 2" layout="Heading 2">The nCWishart function (using diff command)</Text-field> The function evTr verifies the cyclic property of the trace, namely its invariance under circular shifts. For example: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The vector produced as output is subsequently utilized in the simplification step of the results (cf. Example 5.6.7). 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 NyI= 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 NyQvLUkjVHJHNiI2JCokJkkiQUdGJjYjIiIjRiwmRio2IyIiIi1GJTYkRi1GKC8tRiU2JUYpRi1GKUYw 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 NyQvLUkjVHJHNiI2JCokJkkiQUdGJjYjIiIjRiwmRio2IyIiIi1GJTYkRi1GKC8tRiU2JUYpRi1GKUYw 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 NyMvLUkjVHJHNiI2JCZJIkFHNiI2IyIiIyZJIkFHNiI2IyIiIi1JI1RyRzYiNiQmSSJBRzYiNiMiIiImSSJBRzYiNiMiIiM= 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 NyI= 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 NyQvLUkjVHJHNiI2JCokJkkiQUdGJjYjIiIjRiwmRio2IyIiIi1GJTYkRi1GKC8tRiU2JUYpRi1GKUYw LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzZALUkjbWlHRiQ2JFEjZVZGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSSNtb0dGJDYvUSomY29sb25lcTtGJy8lJ2l0YWxpY0dRJmZhbHNlRicvRjBRJ25vcm1hbEYnLyUmZmVuY2VHRjgvJSpzZXBhcmF0b3JHRjgvJSlzdHJldGNoeUdGOC8lKnN5bW1ldHJpY0dGOC8lKGxhcmdlb3BHRjgvJS5tb3ZhYmxlbGltaXRzR0Y4LyUnYWNjZW50R0Y4LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGSy8lKWVxdWFsaXR5R0Y4LUYsNiRRJWV2VHJGJ0YvLUkobWZlbmNlZEdGJDYkLUYjNictSSVtc3ViR0YkNiUtRiw2JFEiQUYnRi8tRiM2JC1JI21uR0YkNiVRIjFGJ0Y2RjlGLy8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYnLUYzNi9RIixGJ0Y2RjlGOy9GPlEldHJ1ZUYnRj9GQUZDRkVGRy9GSlEmMC4wZW1GJy9GTVEsMC4zMzMzMzMzZW1GJ0ZOLUkobXN1YnN1cEdGJDYnRmVuLUYjNiQtRltvNiVRIjJGJ0Y2RjlGL0ZfcC8lMXN1cGVyc2NyaXB0c2hpZnRHRmBvRl5vLUYsNiNRIUYnRi9GLy1GMzYvUSI7RidGNkY5RjtGZG9GP0ZBRkNGRUZHRmZvRkxGTi1JJ21zcGFjZUdGJDYmLyUnaGVpZ2h0R1EmMC4wZXhGJy8lJndpZHRoR0Znby8lJmRlcHRoR0ZfcS8lKmxpbmVicmVha0dRKG5ld2xpbmVGJy1GLDYkUSRmdW5GJ0YvLUYzNi5GNUYvRjtGPUY/RkFGQ0ZFRkdGSUZMRk4tSSZtZnJhY0dGJDYoRmpuLUYjNiQtRltvNiVRIjNGJ0Y2RjlGLy8lLmxpbmV0aGlja25lc3NHRl1vLyUrZGVub21hbGlnbkdRJ2NlbnRlckYnLyUpbnVtYWxpZ25HRmhyLyUpYmV2ZWxsZWRHRjgtRiw2JFEjVHJGJ0YvLUZUNiQtRiM2JkZqb0Zhb0ZYRi9GLy1GMzYvUSIrRidGNkY5RjtGPUY/RkFGQ0ZFRkcvRkpRLDAuMjIyMjIyMmVtRicvRk1GaHNGTkZcckZdcy1GVDYkLUYjNigtRlk2JUZlbkZdcEZeb0Zhb0ZYRmFvRl50Ri9GL0Zkc0ZcckZdcy1GVDYkLUYjNiZGWEZhb0Zqb0YvRi9GZ3BGanAtRiw2JVElZXZhbEYnRjZGOS1GVDYlLUYjNilGZ3FGYW8tRjM2L1EifkYnRjZGOUY7Rj1GP0ZBRkNGRUZHRmZvL0ZNRmdvRk5GK0Y2LyUrZXhlY3V0YWJsZUdGOEY5RjZGOUZncEZqcC1GW3E2JkZdcUZgcUZicS9GZXFRJWF1dG9GJ0ZkcEY2Rl91Rjk= LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSNlVkdGKDckLy1JI1RyR0YoNiQqJCZJIkFHRig2IyIiI0Y3JkY1NiMiIiItRjE2JEY4RjMvLUYxNiVGNEY4RjRGOzcjRi4= LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSRmdW5HRigsKC1JI1RyR0YoNiQqJCZJIkFHRig2IyIiI0Y2JkY0NiMiIiIjRjkiIiQtRjA2JUYzRjdGM0Y6LUYwNiRGN0YyRjo3I0Yu LUkjVHJHNiI2JCZJIkFHRiQ2IyIiIiokJkYnNiMiIiNGLQ== The function expV computes the power of a monomial without applying the commutative property of multiplication. The first parameter specifies the vector v of monomials, while the second specifies the power. Each block of the vector v has dimension two: the first entry contains the variable, and the second the index of the matrix "A". For 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 corresponds to 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 Example 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 = 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 NyY3JCokJkkiekc2IjYjIiIiIiIjNyM3JEYpRik3JComJkYmNiNGKkYpRiVGKTckNyNGKjcjRik3JEYuNyRGM0YyNyQqJEYvRio3IzckRipGKg== The function vMaps transforms a polynomial into a vector by separating the variable blocks from the coefficient blocks. LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzZoXmwtSSNtaUdGJDYkUSZ2TWFwc0YnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi9RKiZjb2xvbmVxO0YnLyUnaXRhbGljR1EmZmFsc2VGJy9GMFEnbm9ybWFsRicvJSZmZW5jZUdGOC8lKnNlcGFyYXRvckdGOC8lKXN0cmV0Y2h5R0Y4LyUqc3ltbWV0cmljR0Y4LyUobGFyZ2VvcEdGOC8lLm1vdmFibGVsaW1pdHNHRjgvJSdhY2NlbnRHRjgvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZLLyUpZXF1YWxpdHlHRjgtRjM2MVElcHJvY0YnLyUlYm9sZEdRJXRydWVGJ0Y2L0YwUSVib2xkRicvJStmb250d2VpZ2h0R0ZXRjtGPUY/RkFGQ0ZFRkcvRkpRJjAuMGVtRicvRk1GZW5GTi1JKG1mZW5jZWRHRiQ2JS1GIzYkLUYsNiRRI3BWRidGL0YvRjZGOS1GMzYvUSJ+RidGNkY5RjtGPUY/RkFGQ0ZFRkdGWkZmbkZOLUknbXNwYWNlR0YkNiYvJSdoZWlnaHRHUSYwLjBleEYnLyUmd2lkdGhHRmVuLyUmZGVwdGhHRmdvLyUqbGluZWJyZWFrR1EobmV3bGluZUYnRl9vRl9vRl9vRl9vLUYzNjFRJmxvY2FsRidGU0Y2RlZGWEY7Rj1GP0ZBRkNGRUZHRlpGZm5GTkZfby1GLDYkUSd2QmxvY2tGJ0YvRjItRmhuNictRiM2JC1GLDYjUSFGJ0YvRjZGOS8lJW9wZW5HUSJbRicvJSZjbG9zZUdRIl1GJy1GMzYvUSIsRidGNkY5RjsvRj5GVUY/RkFGQ0ZFRkdGWi9GTVEsMC4zMzMzMzMzZW1GJ0ZOLUYsNiRRIkxGJ0YvRmJxLUYsNiRRImxGJ0YvRmJxLUYsNiRRI3ZjRidGL0ZicS1GLDYkUSN2bkYnRi9GYnEtRiw2JFEjdkxGJ0YvRmJxLUYsNiRRI3ZJRidGL0ZicS1GLDYkUSJWRidGLy1GMzYvUSI6RidGNkY5RjtGPUY/RkFGQ0ZFRkdGSUZMRk5GYm9GX29GX29GX29GX28tRjM2MVEjaWZGJ0ZTRjZGVkZYRjtGPUY/RkFGQ0ZFRkdGWkZmbkZORl9vLUYsNiRRKXdoYXR0eXBlRidGL0Znbi1GMzYvUSI9RidGNkY5RjtGPUY/RkFGQ0ZFRkdGSUZMRk4tRiw2JFEkYCtgRidGL0Zfb0Zfb0Zib0Zfb0Zfb0Zfb0Zfb0Zfb0Zfb0Zfby1GMzYxUSV0aGVuRidGU0Y2RlZGWEY7Rj1GP0ZBRkNGRUZHRlpGZm5GTkZfb0ZqckYyRlxvLUYzNi9RIjtGJ0Y2RjlGO0ZlcUY/RkFGQ0ZFRkdGWkZMRk5GX29GYm9GX29GX29GX29GX29GX29GX29GX28tRjM2MVElZWxpZkYnRlNGNkZWRlhGO0Y9Rj9GQUZDRkVGR0ZaRmZuRk5GX29GY3NGZ25GZnMtRiw2JFEpYCZzZG90O2BGJ0YvRl9vRmJvRl9vRl9vRl9vRl9vRl9vRl9vRl9vRl9vRl9vRl9vRl9vRl9vRl9vRlx0Rl9vRmpyRjItRmhuNidGam5GNkY5RlxxRl9xRl90Rl9vRmJvRl9vRl9vRl9vRl9vRl9vRl9vRl9vRl9vRl9vRl9vRl9vRl9vRl9vRmJ0Rl9vRmNzRmduRmZzLUYsNiRRJGBeYEYnRi9GX29GYm9GX29GX29GX29GX29GX29GX29GX29GX29GX29GX29GX29GX29GX29GX29GX29GX29GX29GX29GX29GXHRGX29GanJGMi1GaG42Jy1GIzYmLUYsNiRRI29wRidGL0Znbi1GaG42Jy1GIzYkLUkjbW5HRiQ2JVEiMUYnRjZGOUYvRjZGOUZccUZfcUYvRjZGOUZccUZfcUZfdEZib0Zfb0Zfb0Zfb0Zfb0Zfb0Zfb0Zfb0Zfb0Zfb0Zfb0Zfb0Zfb0Zfb0Zfb0Zfb0Zfb0Zfb0Zfb0Zfby1GMzYxUSVlbHNlRidGU0Y2RlZGWEY7Rj1GP0ZBRkNGRUZHRlpGZm5GTkZfb0Zfb0ZqckYyRmh0Rl90Rl9vRmJvRl9vRl9vRl9vRl9vLUYzNjFRI2ZpRidGU0Y2RlZGWEY7Rj1GP0ZBRkNGRUZHRlpGZm5GTkZfdEZib0Zfb0Zfb0Zfb0Zfby1GMzYxUSRmb3JGJ0ZTRjZGVkZYRjtGPUY/RkFGQ0ZFRkdGWkZmbkZORl9vRmhxRl9vLUYzNjFRI2luRidGU0Y2RlZGWEY7Rj1GP0ZBRkNGRUZHRlpGZm5GTkZfby1GaG42Jy1GIzYlRmF1LUZobjYlLUYjNiRGanJGL0Y2RjlGL0Y2RjlGXHFGX3FGX28tRjM2MVEjZG9GJ0ZTRjZGVkZYRjtGPUY/RkFGQ0ZFRkdGWkZmbkZORmJvRl9vRl9vRl9vRl9vRl9vRl9vRl9vRl9vRl9vRl5yRjItRiw2JFEnY29lZmZzRidGLy1GaG42JS1GIzYkRmhxRi9GNkY5Rl1zRmJvRl9vRl9vRl9vRl9vRl9vRl9vRl9vRl9vRl9vRmFyRjItSSZtZnJhY0dGJDYoLUYsNiVGanFGNkY5LUYjNiZGaXAtRiM2JkZpcEZjdy1GaG42JS1GIzYnRmhxRmJxRl9vLUZobjYnLUYjNiQtRiw2JFEibkYnRi9GL0Y2RjkvRl1xUSJ8ZnJGJy9GYHFRInxockYnRi9GNkY5Ri9GaXBGLy8lLmxpbmV0aGlja25lc3NHRlt2LyUrZGVub21hbGlnbkdRJ2NlbnRlckYnLyUpbnVtYWxpZ25HRmZ5LyUpYmV2ZWxsZWRHRjhGX3RGYm9GX29GX29GX29GX29GX29GX29GX29GX29GX29GZHJGMkZfby1GW3g2KEZocS1GIzYmRl5yLUYzNi9RJyZzZG90O0YnRjZGOUY7Rj1GP0ZBRkNGRUZHRlpGZm5GTkZhckYvRmJ5RmR5Rmd5Rml5Rl1zRmJvRl9vRl9vRl9vRl9vRl9vRl9vRl9vRl9vRl9vRmdyRjItRiw2JFEnaW5kZXRzRidGLy1GaG42JS1GIzYkRmRyRi9GNkY5Rl90Rl9vRmJvRl9vRl9vRl9vRl9vRl9vRl9vRl9vRl9vRl9vRmBzRl9vRmNzRmV6RmZzLUYsNiRRJGAqYEYnRi9GX29GXHRGX29GZHJGMi1GaG42Jy1GIzYlRmF1RmV6Ri9GNkY5RlxxRl9xRl9vRlx2Rl9vRmRyRjItRmhuNidGZ3pGNkY5RlxxRl9xRl1zRl9vRl92LUYzNjFGX3NGU0Y2RlZGWEY7Rj1GP0ZBRkNGRUZHRklGTEZORmJvRl9vRl9vRl9vRl9vRl9vRl9vRl9vRl9vRl9vRmJwRjItRmhuNictRiM2KEZhdS1GaG42JS1GIzYkRmJwRi9GNkY5RmJxRl9vLUZobjYnLUYjNihGZHJGYnFGXnJGYnFGYXJGL0Y2RjlGXHFGX3FGL0Y2RjlGXHFGX3FGXXNGYm9GX29GX29GX29GX29GX28tRjM2MVEjb2RGJ0ZTRjZGVkZYRjtGPUY/RkFGQ0ZFRkdGWkZmbkZORmJbbEZiby1GMzYxRmFvRlNGNkZWRlhGO0Y9Rj9GQUZDRkVGR0ZaRmZuRk5GY1xsLUYsNiZGZHBGUy9GMFEsYm9sZC1pdGFsaWNGJ0ZYRmJbbEZib0ZjXGwtRjM2MVEkZW5kRidGU0Y2RlZGWEY7Rj1GP0ZBRkNGRUZHRlpGZm5GTkZdc0Y2LyUrZXhlY3V0YWJsZUdGOEY5 Examples: 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 NyM3JTcjLUkjVHJHNiI2JkkmT21lZ2FHNiIqJkkmU2lnbWFHNiIiIiImSSJIRzYiNiMiIiIiIiIqJkkmU2lnbWFHNiIiIiImSSJIRzYiNiMiIiMiIiIqJkkmU2lnbWFHNiIiIiImSSJIRzYiNiMiIiQiIiIiIiIiIiI= 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 NyM3JTcjLUkjVHJHNiI2JkkmT21lZ2FHNiIqJkkmU2lnbWFHNiIiIiImSSJIRzYiNiMiIiIiIiIqJkkmU2lnbWFHNiIiIiImSSJIRzYiNiMiIiMiIiIqJkkmU2lnbWFHNiIiIiImSSJIRzYiNiMiIiQiIiIiIiMiIiI= 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 NyM3JTcjLUkjVHJHNiI2JkkmT21lZ2FHNiIqJkkmU2lnbWFHNiIiIiImSSJIRzYiNiMiIiIiIiIqJkkmU2lnbWFHNiIiIiImSSJIRzYiNiMiIiMiIiIqJkkmU2lnbWFHNiIiIiImSSJIRzYiNiMiIiQiIiIiIiNJIm5HNiI= 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 NyQ3JTcjKiQtSSNUckc2IjYmSSZPbWVnYUdGKComSSZTaWdtYUdGKCIiIiZJIkhHRig2I0YtRi0qJkYsRi0mRi82IyIiI0YtKiZGLEYtJkYvNiMiIiRGLUY0RjRJIm5HRig3JTcjKiQtRic2JUYrRjFGNUY0RjgqJEY5RjQ= 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 NyU3JC1JI1RyRzYiNiMtSSIuRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YmNiRJJlNpZ21hR0YmJkkiSEdGJjYjIiIjLUYlNiMtRik2JEYuJkYwNiMiIiJGOSokSSJuR0YmRjI= NyU3JC1JI1RyRzYiNiMtSSIuRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YmNiVJJk9tZWdhR0YmSSZTaWdtYUdGJiZJIkhHRiY2IyIiIy1GJTYjLUYpNiRGLyZGMTYjIiIiRjpJIm5HRiY= NyU3JC1JI1RyRzYiNiMtSSIuRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YmNiVJJk9tZWdhR0YmSSZTaWdtYUdGJiZJIkhHRiY2IyIiIi1GJTYjLUYpNiRGLyZGMTYjIiIjRjNJIm5HRiY= NyU3JC1JI1RyRzYiNiMtSSIuRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YmNiVJJk9tZWdhR0YmSSZTaWdtYUdGJiZJIkhHRiY2IyIiIy1GJTYjLUYpNiVGLkYvJkYxNiMiIiJGOkY6 NyU3Iy1JI1RyRzYiNiMtSSIuRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YmNiZJJlNpZ21hR0YmJkkiSEdGJjYjIiIiRi4mRjA2IyIiI0YySSJuR0Ym NyU3Iy1JI1RyRzYiNiMtSSIuRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YmNidJJk9tZWdhR0YmSSZTaWdtYUdGJiZJIkhHRiY2IyIiIkYvJkYxNiMiIiNGM0Yz NyU3Iy1JI1RyRzYiNiMtSSIuRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YmNidJJk9tZWdhR0YmSSZTaWdtYUdGJiZJIkhHRiY2IyIiI0YvJkYxNiMiIiJGNkY2 After applying suitable transformations, the moment generating function in (1) can be rewritten as a product of exponentials. For example, for n=3, we have 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 The procedure nCWishartDiff computes moments of a complex non-central Wishart distribution by taking the partial derivatives of the expressions h and h1 with respect to 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 and then setting 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 Example: nCWishart(1,1) can be computed using 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 LDAqKEkibkc2IiIiIy1JI1RyR0YlNiMtSSIuRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YlNiRJJlNpZ21hR0YlJkkiSEdGJTYjRiYiIiItRig2Iy1GKzYkRjAmRjI2I0Y0RjRGNCooRiRGNC1GKDYjLUYrNiVJJk9tZWdhR0YlRjBGMUY0RjVGNEY0KihGJEY0LUYoNiMtRis2JUZARjBGOUY0RidGNEY0KiZGPEY0RkJGNEY0KiZGJEY0LUYoNiMtRis2JkYwRjlGMEYxRjRGNC1GKDYjLUYrNidGQEYwRjlGMEYxRjQtRig2Iy1GKzYnRkBGMEYxRjBGOUY0 nCWishartDiff(4,1) output when \316\251=0: 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<Text-field style="Heading 2" layout="Heading 2">Time Comparation</Text-field> The function Check_and_Times performs a consistency check between the results of nCWishart and nCWishartDiff, and also reports the number of result blocks as well as the execution time of both functions. 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 NyYvSSpUaW1lX0RpZmZHNiIkIiV5RCEiJC9JLFRpbWVfbmV3QWxnR0YlJCIkRCJGKC9JKm51bV9CbG9ja0dGJSIldzgvSSVURVNUR0YlSSV0cnVlRyUqcHJvdGVjdGVkRw== 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 NyYvSSpUaW1lX0RpZmZHNiIkIiQ0IiEiJC9JLFRpbWVfbmV3QWxnR0YlJCIjSkYoL0kqbnVtX0Jsb2NrR0YlIiQ0Iy9JJVRFU1RHRiVJJXRydWVHJSpwcm90ZWN0ZWRH 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 NyYvSSpUaW1lX0RpZmZHNiIkIiU+IyohIiQvSSxUaW1lX25ld0FsZ0dGJSQiJHMiRigvSSpudW1fQmxvY2tHRiUiJVk6L0klVEVTVEdGJUkldHJ1ZUclKnByb3RlY3RlZEc=
<Text-field style="Heading 1" layout="Heading 1">Conclusions</Text-field> The proposed algorithm computes joint moments (1) of a complex non-central Wishart distribution, by using a symbolic representation as convolution of the central Wishart distribution and of a matrix of formal variables. The moments either of the central Wishart distribution either of the matrix of formal variables are computed by using necklaces of multisets having multiplicities given by the vector 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 The results are verified by taking the partial derivatives of the moment generating function (2) and evaluating them at LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEiekYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW5HRiQ2JVEiMUYnRjUvRjlRJ25vcm1hbEYnLyUvc3Vic2NyaXB0c2hpZnRHUSIwRidGNUY/=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEiekYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW5HRiQ2JVEiMkYnRjUvRjlRJ25vcm1hbEYnLyUvc3Vic2NyaXB0c2hpZnRHUSIwRidGNUY/= ... =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
<Text-field style="Heading 1" layout="Heading 1">References</Text-field> [1] Di Nardo E. (2013) On a symbolic representation of non-central Wishart random matrices with applications. Jour. Mult. Anal. Vol.125, 121--135.[2] Di Nardo E., G. Guarino, D. Senato (2009) Multiset Subdivision, source Maple algorithm located in www.maplesoft.com (http://www.maplesoft.com/applications/view.aspx?SID=33039)[3] Di Nardo E., G. Guarino, D. Senato (2011) A new algorithm for computing the multivariate Fa\303\240 di Bruno's formula, source Maple algorithm located in www.maplesoft.com (https://www.maplesoft.com/Applications/Detail.aspx?id=101396) [4] Letac G., Massam H. (2008) The noncentral Wishart as an exponential family and its moments, Jour. Mult. Anal. Vol. 99 (1), 1393--1417[5] Kan, R., J. Pan. (2025) An Explicit Expression for the Expectation of a Product of Quadratic Forms in Multivariate Normal Random Variables. Available at SSRN 5400512.Legal Notice: The copyright for this application is owned by the author(s). Neither Maplesoft nor the author are responsible for any errors contained within and are not liable for any damages resulting from the use of this material. This application is intended for non-commercial, non-profit use only. Contact the author for permission if you wish to use this application in for-profit activities JSFH