Fresh Fish 8/FreshFishVol8-CD1.bin/gnu/info/calc.info-16

GNU Info File | 1994-12-22 | 50KB | 788 lines

This is Info file calc.info, produced by Makeinfo-1.55 from the input
file calc.texinfo.
   This file documents Calc, the GNU Emacs calculator.
   Copyright (C) 1990, 1991 Free Software Foundation, Inc.
   Permission is granted to make and distribute verbatim copies of this
manual provided the copyright notice and this permission notice are
preserved on all copies.
   Permission is granted to copy and distribute modified versions of
this manual under the conditions for verbatim copying, provided also
that the section entitled "GNU General Public License" is included
exactly as in the original, and provided that the entire resulting
derived work is distributed under the terms of a permission notice
identical to this one.
   Permission is granted to copy and distribute translations of this
manual into another language, under the above conditions for modified
versions, except that the section entitled "GNU General Public License"
may be included in a translation approved by the author instead of in
the original English.
File: calc.info,  Node: Manipulating Vectors,  Next: Vector and Matrix Arithmetic,  Prev: Extracting Elements,  Up: Matrix Functions
Manipulating Vectors
====================
The `v l' (`calc-vlength') [`vlen'] command computes the length of a
vector.  The length of a non-vector is considered to be zero.  Note
that matrices are just vectors of vectors for the purposes of this
command.
   With the Hyperbolic flag, `H v l' [`mdims'] computes a vector of the
dimensions of a vector, matrix, or higher-order object.  For example,
`mdims([[a,b,c],[d,e,f]])' returns `[2, 3]' since its argument is a 2x3
matrix.
   The `v f' (`calc-vector-find') [`find'] command searches along a
vector for the first element equal to a given target.  The target is on
the top of the stack; the vector is in the second-to-top position.  If
a match is found, the result is the index of the matching element.
Otherwise, the result is zero.  The numeric prefix argument, if given,
allows you to select any starting index for the search.
   The `v a' (`calc-arrange-vector') [`arrange'] command rearranges a
vector to have a certain number of columns and rows.  The numeric
prefix argument specifies the number of columns; if you do not provide
an argument, you will be prompted for the number of columns.  The
vector or matrix on the top of the stack is "flattened" into a plain
vector.  If the number of columns is nonzero, this vector is then
formed into a matrix by taking successive groups of N elements.  If the
number of columns does not evenly divide the number of elements in the
vector, the last row will be short and the result will not be suitable
for use as a matrix.  For example, with the matrix `[[1, 2], [3, 4]]'
on the stack, `v a 4' produces `[[1, 2, 3, 4]]' (a 1x4 matrix), `v a 1'
produces `[[1], [2], [3], [4]]' (a 4x1 matrix), `v a 2' produces `[[1,
2], [3, 4]]' (the original 2x2 matrix), `v a 3' produces `[[1, 2, 3],
[4]]' (not a matrix), and `v a 0' produces the flattened list `[1, 2,
3, 4]'.
   The `V S' (`calc-sort') [`sort'] command sorts the elements of a
vector into increasing order.  Real numbers, real infinities, and
constant interval forms come first in this ordering; next come other
kinds of numbers, then variables (in alphabetical order), then finally
come formulas and other kinds of objects; these are sorted according to
a kind of lexicographic ordering with the useful property that one
vector is less or greater than another if the first corresponding
unequal elements are less or greater, respectively.  Since quoted
strings are stored by Calc internally as vectors of ASCII character
codes (*note Strings::.), this means vectors of strings are also sorted
into alphabetical order by this command.
   The `I V S' [`rsort'] command sorts a vector into decreasing order.
   The `V G' (`calc-grade') [`grade', `rgrade'] command produces an
index table or permutation vector which, if applied to the input vector
(as the index of `C-u v r', say), would sort the vector.  A permutation
vector is just a vector of integers from 1 to N, where each integer
occurs exactly once.  One application of this is to sort a matrix of
data rows using one column as the sort key; extract that column, grade
it with `V G', then use the result to reorder the original matrix with
`C-u v r'.  Another interesting property of the `V G' command is that,
if the input is itself a permutation vector, the result will be the
inverse of the permutation.  The inverse of an index table is a rank
table, whose Kth element says where the Kth original vector element
will rest when the vector is sorted.  To get a rank table, just use `V
G V G'.
   With the Inverse flag, `I V G' produces an index table that would
sort the input into decreasing order.  Note that `V S' and `V G' use a
"stable" sorting algorithm, i.e., any two elements which are equal will
not be moved out of their original order.  Generally there is no way to
tell with `V S', since two elements which are equal look the same, but
with `V G' this can be an important issue.  In the matrix-of-rows
example, suppose you have names and telephone numbers as two columns and
you wish to sort by phone number primarily, and by name when the numbers
are equal.  You can sort the data matrix by names first, and then again
by phone numbers.  Because the sort is stable, any two rows with equal
phone numbers will remain sorted by name even after the second sort.
   The `V H' (`calc-histogram') [`histogram'] command builds a
histogram of a vector of numbers.  Vector elements are assumed to be
integers or real numbers in the range [0..N) for some "number of bins"
N, which is the numeric prefix argument given to the command.  The
result is a vector of N counts of how many times each value appeared in
the original vector.  Non-integers in the input are rounded down to
integers.  Any vector elements outside the specified range are ignored.
(You can tell if elements have been ignored by noting that the counts
in the result vector don't add up to the length of the input vector.)
   With the Hyperbolic flag, `H V H' pulls two vectors from the stack.
The second-to-top vector is the list of numbers as before.  The top
vector is an equal-sized list of "weights" to attach to the elements of
the data vector.  For example, if the first data element is 4.2 and the
first weight is 10, then 10 will be added to bin 4 of the result
vector.  Without the hyperbolic flag, every element has a weight of one.
   The `v t' (`calc-transpose') [`trn'] command computes the transpose
of the matrix at the top of the stack.  If the argument is a plain
vector, it is treated as a row vector and transposed into a one-column
matrix.
   The `v v' (`calc-reverse-vector') [`vec'] command reverses a vector
end-for-end.  Given a matrix, it reverses the order of the rows.  (To
reverse the columns instead, just use `v t v v v t'.  The same
principle can be used to apply other vector commands to the columns of
a matrix.)
   The `v m' (`calc-mask-vector') [`vmask'] command uses one vector as
a mask to extract elements of another vector.  The mask is in the
second-to-top position; the target vector is on the top of the stack.
These vectors must have the same length.  The result is the same as the
target vector, but with all elements which correspond to zeros in the
mask vector deleted.  Thus, for example, `vmask([1, 0, 1, 0, 1], [a, b,
c, d, e])' produces `[a, c, e]'.  *Note Logical Operations::.
   The `v e' (`calc-expand-vector') [`vexp'] command expands a vector
according to another mask vector.  The result is a vector the same
length as the mask, but with nonzero elements replaced by successive
elements from the target vector.  The length of the target vector is
normally the number of nonzero elements in the mask.  If the target
vector is longer, its last few elements are lost.  If the target vector
is shorter, the last few nonzero mask elements are left unreplaced in
the result.  Thus `vexp([2, 0, 3, 0, 7], [a, b])' produces `[a, 0, b,
0, 7]'.
   With the Hyperbolic flag, `H v e' takes a filler value from the top
of the stack; the mask and target vectors come from the third and
second ele