


  mcxsubs(1)                USER COMMANDS                mcxsubs(1)


  NAME
      mcxsubs - extract submatrices (subgraphs) of a matrix (graph).

      mcxsubs  can  be used to inspect local cluster structure in a graph, for
      example by looking at the subgraph induced by a single cluster or a cou-
      ple  of clusterings, or the edge set where all tail nodes are from a set
      of domains and all head nodes are from the complement of this  set,  and
      many other variants and refinements.

      Additionally, mcxsubs enables

      o selecting matrix entries based on value.
      o making the result characteristic (set all nonzero values to 1.0).
      o pruning empty columns and empty rows.
      o transposing the result.
      o remapping the indices of the result to consecutive indices.
      o and other miscellaneous operations.

  SYNOPSIS
      mcxsubs -imx <fname> [options] <specs>+

      mcxsubs  -imx <fname> (input matrix) [-dom <fname> (domain matrix)] [-tf
      spec (apply tf-spec to  input  matrix)]  [--block  (use  block  matrix)]
      [--blockc  (use  complement  of block matrix)] [--skin-read (read domain
      structure without entries)] [--extend (read extended submatrices)] [-tab
      (read  tab  file)]  [--from-disk  (space/speed optimizer)] [-out <fname>
      (special purpose output file name)] [-efac  <num>  (random  edge  selec-
      tion)] [-dfac <num> (random domain selection)] [-rfac <num> (random col-
      umn selection)] [-cfac <num>  (random  row  selection)]  [--rand-discard
      (remove  random  selections)]  [--rand-merge  (merge random selections)]
      [--rand-intersect (intersect random selections)] [--rand-exclusive (only
      random  selections)] [-tag-digits k (set precision)] [--tag (tag nodes)]
      <specs>+

      If you are a frequent mcxsubs user with very large graphs, consider con-
      verting  the  input  matrix into binary format using mcxconvert and then
      using the mcxsubs --from-disk option. This should give  you  a  400-fold
      speed gain.

  DESCRIPTION
      mcxsubs  lets you extract submatrices/subgraphs corresponding with index
      sets and (possibly) sets of domains from a given domain matrix (e.g.   a
      matrix representing a clustering). Columns and rows of the target subma-
      trix can be specified both independently and simultaneously, and can  be
      specified as unions of simple index and domain ranges and complements of
      these.

      Because a submatrix or subgraph specification is composed of type, loca-
      tion, column, row, index, and set specifications, the word specification
      is abbreviated as spec. Multiple submatrices can be specified simultane-
      ously.  A  submatrix  is  created  for  each  submatrix spec. Everything
      encountered after the mcxsubs options are exhausted should  be  a  spec.
      The  syntax  of  specs is described in the SUBMATRIX SPECIFICATIONS sec-
      tion.  By default, the domains of the  submatrix  will  be  set  to  the



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      domains as described in the specification. This can be changed using the
      uni directives from the fin part.

  OPTIONS
      -imx <fname> (input matrix)
        Submatrices will all be selected from  the  matrix  in  file  <fname>.
        This  option is obligatory, and throughout this manual its argument is
        called the source matrix.

      -dom <fname> (domain matrix)
        Submatrices are specified in terms of sets (or  domains)  of  indices.
        These sets are specified by (the label of) the vectors from the matrix
        given by this options.

      --block (use block matrix)
        This replaces the input matrix by the block diagonal matrix induced by
        the domain matrix specified by the -dom option.  It works by including
        a block for each domain in the domain matrix, and will work  if  there
        are  overlapping  domains.  That  is,  it will not include overlapping
        parts more than once.  The output file name can either be specified in
        the  submatrix  specification language using the out(fname) directive,
        or with the -out option.

      --blockc (use complement of block matrix)
        This replaces the input matrix by the complement of the block diagonal
        matrix  described  above,  and selection of the output name is exactly
        the same.

      --skin-read (read domain structure without entries)
        This reads a skeleton matrix by only considering its domain  structure
        and not reading any entries, pertaining to the matrix specified by the
        -imx option.  Transform the input matrix values according to the  syn-
        tax described in mcxio(5).

      -tab (read tab file)
        Read a tab file. Its domain can be used by the t and T indicators.

      --extend (read extended submatrices)
        This  causes  the selection of submatrices where either a row index is
        in the selected row domain or a columns index is in the selected  col-
        umn  domain  or both. Equivalently it only excludes matrix entries for
        which neither the column nor row index is  in  the  selected  domains.
        The resulting matrix has both domains equal to the source matrix.

      -out <fname> (special purpose output file name)
        This  specifies  an output name that can be used for special purposes.
        Normally, output file names are specified in the submatrix  specifica-
        tion using the out(fname) directive.

      -efac <num> (random edge selection)
        num  should be inbetween zero and one. It denotes the probability with
        which each edge is selected.

      -dfac <num> (random domain selection)



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        num should be inbetween zero and one. It denotes the probability  with
        which  entries  in the domains will make it into the randomized selec-
        tion used for subsequent processing. By default the randomized  selec-
        tion  is  intersected  with  whatever the other selection criteria (if
        any) yield, i.e. the behaviour under the --rand-intersect option.

        If the column and row domain are identical, they are submitted to  the
        same  selection  process  and will end up identical. If you don't want
        this, use -rfac and -cfac separately.

        If you just want a randomized selection, doing

        mcxsubs -imx foo -dfac 0.5 'out(foo.rnd)'

        will not yield the expected result. Randomized selections only work if
        a  domain  has  explicitly  been specified. The minimal way to achieve
        this is the following:

        mcxsubs -imx foo -dfac 0.5 'dom(cr), out(foo.rnd)'


      -rfac <num> (random column selection)
        As -dfac, limited to the column domain.

      -cfac <num> (random row selection)
        As -dfac, limited to the row domain.

      --rand-merge (merge random selections)
        The random selection(s) of domains identify parts of the  matrix  that
        will  be  merged  with  the  result  of  the  main  selection  process
        (default).

      --rand-discard (remove random selections)
        The random selection(s) of domains identify parts of the  matrix  that
        will be removed from the result of the main selection process.

      --rand-intersect (intersect random selections)
        The  random  selection(s) of domains identify parts of the matrix that
        will be intersected with the result of  the  main  selection  process.
        This is the default.

      --rand-exclusive (only random selections)
        The  random  selection(s) of domains identify parts of the matrix from
        which the result of the main selection process will be removed.

      -tag-digits k (set precision)
        Sets the precision for tagged output.  Setting  it  to  -tag-digits -1
        disables  the  output of values altogether - only the node indices and
        the cluster indices are written.

      --tag (tag nodes)
        Each node in the column (tail node) listing of the matrix (graph) spec
        is  tagged with the domain it is in. This requires the use of the -dom
        option.  This output mode, called  tagged  matrix,  is  currently  not



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        recognized  by  any  of  the  mcl/mcx input routines. It is present to
        facilitate easier visual inspection of clustering results.

      --from-disk (space/speed optimizer)
        Use this if the input graph is in binary format, or if the input graph
        is  very large and the subgraph(s) to extract are small in comparison,
        or if the available memory does not comfortably exceed the size of the
        graph.

        The  effect  of this option is that the subgraph will be read directly
        from disk, without reading in the entire graph in advance.  This  will
        be done repeatedly for all subgraphs that are specified.

        This  option reduces memory consumption to the size of the subgraph(s)
        to be extracted.

        For graphs in interchange format, the speed gain is not  dramatic.  If
        more  than one subgraph is specified, there will most likely be a loss
        in speed.

        With input graphs in  binary  format,  mcxsubs  will  be  *very*  much
        faster,  to  the  extent  of 400-fold speed gains.  It does not matter
        whether more than one subgraph is specified.

  SUBMATRIX SPECIFICATIONS
      A submatrix or subgraph spec may contain a number of  spec  parts.  Each
      part is specified in a function-style notation. Different parts are sep-
      arated by commas. Parts may occur multiple times,  but  for  most  parts
      only  the  last  one specified will be effective. The spec parts are the
      following: dom, ext, val, size, fin, and out. These are described  below
      in the sections DOMAINS, EXTENSION, VALUES, SIZE, FINALIZE and OUTPUT.

      DOMAINS
      The domain part is specified as

      dom(X <, Y(ispec) >+)

      Here  X is the row/column indicator. Rows are indicated with either r or
      R, columns are indicated with either c or C. X may contain  one  or  two
      indicators,  with  a  single  indicator per column domain and row domain
      allowed.  Uppercase indicators indicate that  the  complement  is  being
      specified relative to the corresponding domain in the target matrix.

      Y is the type indicator, it is exactly one of i, I, d, D, c, r, t, or T.
      The i/I indicators specify that ispec contains a simple  index  specifa-
      tion.   The  d/D specify that ispec contains domain indices.  ispec must
      contain a comma-separated list of integers or integer ranges (e.g. 2, 5,
      4-8).   c  and  r are restricted indicators that refer to the domains in
      the domain matrix.  t and T are restricted indicators that refer to  the
      domain  encoded  in  the tab file as specified by the -tab option. Their
      usage is described further below.

      For domain specifications (d/D) the columns indexed by these integers in
      the  matrix  specified in the -dom option will be fetched and merged. If



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      -dom was not used the target matrix itself (as  specified  by  the  -imx
      option) will be used. For simple specifications (i/I) the result is sim-
      ply the list of integers itself. Uppercase indicators indicate that  the
      complement is being specified.

      Examples:

      dom(cr, i(0-6,10,11-14))
        Principal submatrix on indices 0-6, 10, and 11-14 - all column and row
        indices are from this set. Equivalently, this encodes the subgraph  on
        nodes  0-6, 10, 11-14. The 'c' stands for column, the 'r' for row, and
        the 'i' for index. It is also possible to specify a 'd' part (standing
        for domain), this is shown further below.

      dom(c, i(0-6,10,11-14)), dom(r, i(1-6,10,11-14))
        Equivalent (but less clear) spec of the above.

      dom(cR, i(0-6,10,11-14))
        Matrix  with  column indices in 0-6, 10, 11-14, and row indices in the
        complement of this set. Corresponds with all edges going out from  the
        set 0-6, 10, 11-14. Complements are triggered by the use of a capital;
        see the next examples.

      dom(c, i(0-6,10,11-14)), dom(R, i(1-6,10,11-14))
      dom(c, i(0-6,10,11-14)), dom(r, I(1-6,10,11-14))
        Both these examples are equivalent to the previous one.  In  the  last
        example,  the  capital  'I'  indicates  that  the complement should be
        taken. In this example, 'r' combined with 'I' has the same  effect  as
        'R' combined with 'i'.

      dom(c, d(3,5-9)), dom(r, d(8-14), i(10-30))
        Column  indices  are  taken  from  the domains 3, 5-9 (from the domain
        matrix specified by -dom), row indices are  taken  from  domains  8-14
        plus the indices 10-30.

      dom(cR, d(0-2))
        Column  indices  are all indices from domains 0-2, row indices are all
        other indices. This gives all edges going out from domains 0-2.

        The use of 'D' is analogous to that  of  'C',  'R',  and  'I'.   Thus,
        D(0-3,8,21-30)  specifies  all  indices which are in the complement of
        the set formed by taking the union of domains 0-3,8,21-30.

      The c and r indicators must be followed by a pair of matching  parenthe-
      ses.  They  specify  to  take respectively the column domain and the row
      domain of the domain matrix (cf. -dom).

      The t and T indicators must be followed by a pair of matching  parenthe-
      ses.  They  specify to take the domain found in the tab file or its com-
      plement.

      As seen above, indices (either representing themselves or  domains)  are
      entered  as  comma-separated  lists of single indices, ranges of indices
      (which may overlap), or staircases of indices (lists of indices  with  a



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      fixed  increment inbetween successive indices).  The union of the corre-
      sponding elements is taken and passed along. Before anything  else,  the
      result set is replaced by its complement if 'I' is specified (for simple
      indices) or 'D' is specified (for domains). If there is  both  an  index
      and  a  set  spec  string, the union of the results of both is taken and
      passed along. If the latter result is passed to either 'C' or 'R', it is
      replaced by its complement.

      A range is specified e.g. as 10-14 and it is inclusive, denoting in this
      case the indices {10,11,12,13,14}.

      EXTENSION
      The extension part is specified as

      ext( < disc(k) | cdisc(k) | rdisc(k) >)

      This option requires the input matrix to be held in memory. This implies
      it will not work with the --from-disk option.

      This  assumes  that  the input matrix encodes a graph, so the column and
      row domains must be equal.  It will take the currently  selected  domain
      (column  domain  for  disc and cdisc, row domain for rdisc), and add all
      nodes to it that are reachable in k steps.  The  disc  variant  replaces
      both  column  and row domains by the extended domain, the other variants
      just change a single domain.

      Setting k to -1 results in adding all nodes that can be reached from the
      start domain.

      VALUES
      The value part is specified as

      val(<tf-spec>)

      It  transforms  or  removes  values  according  to  <tf-spec>.  Refer to
      mcxio(5) for a description of the  transformation  specification  syntax
      and the available transformation primitives.

      SIZE
      The size part is specified as

      size( < lt(x) | ceil(x) | gq(x) | rmgq(x) > + )

      Where  x is a nonnegative integer, and multiple specifications are sepa-
      rated by commas.  The  strings  'lt',  'lq',  'gq',  'gt',  respectively
      denote  less  than, less than or equal to, greater than or equal to, and
      greater than.

      This prunes or removes column vectors based on  their  size.  If  lt  is
      used,  column  vectors  are removed if the number of entries exceeds the
      specified bound. If gq is used, vectors are discarded if the  number  of
      entries  is  smaller than the specified bound. If a column vector has an
      excess of entries over the bound specified by ceil, the smallest entries
      are  removed.  Ties  are  not  arbitrarily  broken,  implying  that  the



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      resulting vector may still have more entries than the specified bound.

      FINALIZE
      The finalize part is specified as fin( < key > ) where key is  a  string
      and multiple keys are separated by commas. The corresponding actions are
      generally applied to the matrix that  was  extracted  according  to  the
      domain  and  value  specifications. Exceptions are indicated below. Cur-
      rently, there is a fixed order in which actions are  considered,  corre-
      sponding with the order in which they are listed below.

      skel
        This creates an empty submatrix on the specified domains, and does not
        fill it  with  the  corresponding  entries  from  the  source  matrix.
        Options  from the fin part that affect the column and row domains of a
        matrix will still be in effect.

      uni
      unir
      unic
        After the submatrix is selected from the source  matrix,  its  domains
        are changed to mirror one or both of the domains of the source matrix.

      tp
        The resulting submatrix is replaced by its transpose.

      cc
        The resulting submatrix is made characteristic.

      scrubc
      scrubr
      scrubg
      scrub
        Domains are shrunk if  there  are  no  corresponding  entries  in  the
        matrix.   This is done for both domains if scrub is specified, for the
        column domain if scrubc is specified, and for the row domain if scrubr
        is  specified.  Thus,  with scrubc columns are removed from the domain
        and the matrix if they are  empty.   With  scrubg  the  union  of  the
        resulting domains is taken.

      mapc
      mapr
      map
        The  appropriate  domains are mapped onto consecutive indices starting
        at zero.

      OUTPUT
      The output part is specified as out( fname <, key  >*  )  that  is,  the
      fname option is obligatory if the out part is specified.  Currently, key
      can be a single directive,  namely  wb  specifying  that  the  resulting
      matrix should be output in binary format.

  AUTHOR
      Stijn van Dongen.




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  mcxsubs(1)                USER COMMANDS                mcxsubs(1)


  SEE ALSO
      mcx(1),  and  mclfamily(7)  for an overview of all the documentation and
      the utilities in the mcl family.






















































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