Re: Confluent hypergeometric function of matrix argument

*To*: mathgroup at smc.vnet.net*Subject*: [mg24592] Re: Confluent hypergeometric function of matrix argument*From*: Roland Franzius <Roland.Franzius at uos.de>*Date*: Tue, 25 Jul 2000 00:56:24 -0400 (EDT)*References*: <8lgu6j$2j8@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

If your matrix power means matrix product, for a diagonal matrix simply map the function into the matrix: 1F1[ { (0,0,0),(0,a,0),(0,0,b)} ] ={ (0,0,0),(0,1F1(a),0),(0,0,1F1(b) } Of course you can save time using only the diagonal vector and use multiplication like scalar product without sum (a,b,c) * (A,B,C) =(a*A,b*B,c*C) Matt Antone wrote: > > Hello, > > I'm looking for some code (preferably C, but FORTRAN or pseudocode for an > algorithm would also be fine) to compute the confluent hypergeometric > function of matrix argument, 1F1(a; b; M). > > I only need to evaluate for a couple of specific cases: > > 1F1(0.5; 1.5; D) where D is a real 3x3 diagonal matrix with one diagonal > entry = 0, and > > 1F1(0.5; 2; D) where D is a real 4x4 diagonal matrix with one diagonal entry > = 0. > > I've seen various implementations of the function of scalar arguments on > netlib and in other areas but I don't think they can be used in this case. > Ideally I'd like code to compute the above values of 1F1, or the logarithm > of these values, and also take first and second derivatives with respect to > the matrix parameters in D. -- Roland Franzius +++ exactly <<n>> lines of this message have value <<FALSE>> +++