zcl(1) - f32

1zcl(1)                           User Commands                          zcl(1)
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NAME

6       zcl - clean matrix
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SYNOPSIS

9       zcl [OPTIONS] <Subsp> <Mat> <CleanedMat> <Ops>
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DESCRIPTION

12       This  program  "cleans"  Mat  with Subsp, i.e., it adds suitable linear
13       combinations of rows of Subsp to each row of Mat such  that  all  pivot
14       columns  in  the result are zero.  It writes two matrices to CleanedMat
15       and Ops such that Mat = Ops·Subsp + CleanedMat.  If  Subsp  is  not  in
16       echelon  form,  it  is  first reduced to echelon form, and the previous
17       equation holds for the reduced Matrix.  Subsp and Mat must be over  the
18       same field and have the same number of columns.
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20       One use of this program is to calculate the action of a generator on an
21       invariant subspace: Take the subspace in echelon form (as it is on out‐
22       put  from zsp(1)), and multiply it by a generator.  Cleaning the result
23       with the original basis yields a zero matrix, and RowOps is the  action
24       of  the  generator on the invariant subspace.  For example, if subsp is
25       the subspace and gen is the generator,
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27         # zmu subsp gen image
28         # zcl subsp image null gen_s
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30       calculates the action on the subspace in gen_s.
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32       The action on the quotient of a given subspace can be  calculated  with
33       the zqt program.
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OPTIONS

36       -Q     Quiet, no messages.
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38       -V     Verbose, more messages.
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40       -T <MaxTime>
41              Set CPU time limit
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IMPLEMENTATION DETAILS

44       The  subspace is loaded into memory and, if necessary, reduced to eche‐
45       lon form.  The second matrix, is then processed a row at a  time.   Row
46       operations are performed to clear out the pivot points of the input row
47       using the rows of the first input matrix.  A row  describing  what  was
48       done  is  written  out to Ops, and the remnant (clean) row is output to
49       CleanedMat.
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INPUT FILES

52       Subsp  The subspace to clean with.
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54       Mat    The matrix to be cleaned.
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OUTPUT FILES

57       CleanedMat
58              The cleaned matrix.
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60       Ops    Row operations that were performed.
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