Mercurial > matrix-functions
annotate toolbox/gearm.m @ 2:c124219d7bfa draft
Re-add the 1995 toolbox after noticing the statement in the ~higham/mctoolbox/ webpage.
author | Antonio Pino Robles <data.script93@gmail.com> |
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date | Thu, 07 May 2015 18:36:24 +0200 |
parents | 8f23314345f4 |
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Create local repository for matrix toolboxes. Step #0 done.
Antonio Pino Robles <data.script93@gmail.com>
parents:
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1 function A = gearm(n, i, j) |
8f23314345f4
Create local repository for matrix toolboxes. Step #0 done.
Antonio Pino Robles <data.script93@gmail.com>
parents:
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2 %GEARM Gear matrix. |
8f23314345f4
Create local repository for matrix toolboxes. Step #0 done.
Antonio Pino Robles <data.script93@gmail.com>
parents:
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3 % A = GEARM(N,I,J) is the N-by-N matrix with ones on the sub- and |
8f23314345f4
Create local repository for matrix toolboxes. Step #0 done.
Antonio Pino Robles <data.script93@gmail.com>
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4 % super-diagonals, SIGN(I) in the (1,ABS(I)) position, SIGN(J) |
8f23314345f4
Create local repository for matrix toolboxes. Step #0 done.
Antonio Pino Robles <data.script93@gmail.com>
parents:
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5 % in the (N,N+1-ABS(J)) position, and zeros everywhere else. |
8f23314345f4
Create local repository for matrix toolboxes. Step #0 done.
Antonio Pino Robles <data.script93@gmail.com>
parents:
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6 % Defaults: I = N, j = -N. |
8f23314345f4
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Antonio Pino Robles <data.script93@gmail.com>
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7 % All eigenvalues are of the form 2*COS(a) and the eigenvectors |
8f23314345f4
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8 % are of the form [SIN(w+a), SIN(w+2a), ..., SIN(w+Na)]. |
8f23314345f4
Create local repository for matrix toolboxes. Step #0 done.
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9 % The values of a and w are given in the reference below. |
8f23314345f4
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10 % A can have double and triple eigenvalues and can be defective. |
8f23314345f4
Create local repository for matrix toolboxes. Step #0 done.
Antonio Pino Robles <data.script93@gmail.com>
parents:
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11 % GEARM(N) is singular. |
8f23314345f4
Create local repository for matrix toolboxes. Step #0 done.
Antonio Pino Robles <data.script93@gmail.com>
parents:
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12 |
8f23314345f4
Create local repository for matrix toolboxes. Step #0 done.
Antonio Pino Robles <data.script93@gmail.com>
parents:
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13 % (GEAR is a Simulink function, hence GEARM for Gear matrix.) |
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14 % Reference: |
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15 % C.W. Gear, A simple set of test matrices for eigenvalue programs, |
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16 % Math. Comp., 23 (1969), pp. 119-125. |
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Antonio Pino Robles <data.script93@gmail.com>
parents:
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17 |
8f23314345f4
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Antonio Pino Robles <data.script93@gmail.com>
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18 if nargin == 1, i = n; j = -n; end |
8f23314345f4
Create local repository for matrix toolboxes. Step #0 done.
Antonio Pino Robles <data.script93@gmail.com>
parents:
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19 |
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parents:
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20 if ~(i~=0 & abs(i)<=n & j~=0 & abs(j)<=n) |
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21 error('Invalid I and J parameters') |
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22 end |
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Antonio Pino Robles <data.script93@gmail.com>
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23 |
8f23314345f4
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24 A = diag(ones(n-1,1),-1) + diag(ones(n-1,1),1); |
8f23314345f4
Create local repository for matrix toolboxes. Step #0 done.
Antonio Pino Robles <data.script93@gmail.com>
parents:
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25 A(1, abs(i)) = sign(i); |
8f23314345f4
Create local repository for matrix toolboxes. Step #0 done.
Antonio Pino Robles <data.script93@gmail.com>
parents:
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26 A(n, n+1-abs(j)) = sign(j); |