Re: Transforming matrices

*To*: mathgroup at smc.vnet.net*Subject*: [mg29672] Re: Transforming matrices*From*: "Allan Hayes" <hay at haystack.demon.co.uk>*Date*: Tue, 3 Jul 2001 04:40:25 -0400 (EDT)*References*: <9hp4pa$2ef$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

Michael, Here are two ways - the second seems to be the quicker one: rates= {40, 38,37,36,33,32,31,30,27,23,22,21,20,16,14,13,12,10,9,6}; mat={{0, 0, 1, 2, 2, 2, 0, 0, 0, 0, 0, 0, 1, 2, 0, 1, 2, 2 ,2, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 1, 2, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}}; FIRST WAY f[0]:= (++i;rates[[k]]) f[_]:=(k=++i;0) (i=0;k=1;f/@#)&/@ mat {{40,40,0,0,0,0,32,32,32,32,32,32,0,0,16,0,0,0,0,9},{40,40,40,40,40,40,40,40 , 40,40,40,40,40,40,40,40,40,40,40,40},{40,40,0,0,0,0,32,32,32,32,32,32,32, 32,32,32,32,32,32,32}} SECOND WAY g[0,_]:=rates[[k]]; g[_,{n_}]:=(k=n;0) (k=1;MapIndexed[g,#])&/@mat {{40,40,0,0,0,0,32,32,32,32,32,32,0,0,16,0,0,0,0,9},{40,40,40,40,40,40,40,40 , 40,40,40,40,40,40,40,40,40,40,40,40},{40,40,0,0,0,0,32,32,32,32,32,32,32, 32,32,32,32,32,32,32}}-- Allan --------------------- Allan Hayes Mathematica Training and Consulting Leicester UK www.haystack.demon.co.uk hay at haystack.demon.co.uk Voice: +44 (0)116 271 4198 Fax: +44 (0)870 164 0565 "Michael Loop" <loopm at yahoo.com> wrote in message news:9hp4pa$2ef$1 at smc.vnet.net... > I am a relatively new user of Mathematica, and I am having some > trouble transforming a matrix. I would be appreciative of any advice. > The problem is as follows. > > Given a randomly formed matrix of form: > > 0 0 1 2 2 2 0 0 0 0 0 0 1 2 0 1 2 2 2 0 > 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 > 0 0 1 2 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 > > Each digit represents a different state, and therefore each digits > position must be preserved. I need to convert this matrix into a > matrix of rates instead. The zeros will be converted into constant > rates dependent on their position, and the rate will continue until a > 1 is reached. Both 1 and 2 represent a rate of 0. So given a vector > of rates: > > 40 38, 37, 36, 33, 32, 31, 30, 27, 23, 22, 21, 20, 16, 14, 13, 12, 10, > 9, 6 > > I need to convert the first randomly generated matrix to look like: > > 40 40 0 0 0 0 32 32 32 32 32 32 0 0 16 0 0 0 0 9 > 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 40 > 40 40 0 0 0 0 32 32 32 32 32 32 32 32 32 32 32 32 32 32 > > Besides the fact that the rate must stay constant until a 1 is > reached, the other subtlety of my problem is that when a rate starts > over after a 1 or 2, the new rate must begin in the position of the > next zero, but the rate must come from the position of the last 1 or > 2. I can convert a matrix of this form on an individual basis using > the Position and Table commands, but cannot find an efficient way of > converting the matrix on a large scale. The matrix I actually need to > convert is 240*1000, so if anyone can think of an efficient way of > doing this I would be grateful for your input. Thank you. > > Micahel Loop > Minneapolis, MN