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comparison scripts/linear-algebra/rank.m @ 20160:03b9d17a2d95 stable

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doc: Update more docstrings to have one sentence summary as first line. Reviewed io, java, linear-algebra, prefs, and set script directories. * scripts/io/beep.m, scripts/io/dlmwrite.m, scripts/io/importdata.m, scripts/io/strread.m, scripts/io/textread.m, scripts/java/javaArray.m, scripts/java/java_get.m, scripts/java/java_set.m, scripts/java/javaaddpath.m, scripts/java/javachk.m, scripts/java/javaclasspath.m, scripts/java/javamem.m, scripts/java/javarmpath.m, scripts/linear-algebra/bandwidth.m, scripts/linear-algebra/commutation_matrix.m, scripts/linear-algebra/cond.m, scripts/linear-algebra/condest.m, scripts/linear-algebra/cross.m, scripts/linear-algebra/duplication_matrix.m, scripts/linear-algebra/expm.m, scripts/linear-algebra/housh.m, scripts/linear-algebra/isdefinite.m, scripts/linear-algebra/ishermitian.m, scripts/linear-algebra/issymmetric.m, scripts/linear-algebra/istril.m, scripts/linear-algebra/istriu.m, scripts/linear-algebra/krylov.m, scripts/linear-algebra/logm.m, scripts/linear-algebra/normest.m, scripts/linear-algebra/null.m, scripts/linear-algebra/onenormest.m, scripts/linear-algebra/orth.m, scripts/linear-algebra/qzhess.m, scripts/linear-algebra/rank.m, scripts/linear-algebra/rref.m, scripts/linear-algebra/vech.m, scripts/path/matlabroot.m, scripts/prefs/addpref.m, scripts/prefs/getpref.m, scripts/prefs/ispref.m, scripts/prefs/rmpref.m, scripts/prefs/setpref.m, scripts/set/powerset.m, scripts/set/setdiff.m: Update more docstrings to have one sentence summary as first line.
author Rik <rik@octave.org>
date Sun, 03 May 2015 15:36:23 -0700
parents 4197fc428c7d
children
comparison
equal deleted inserted replaced
20159:597991b19e40 20160:03b9d17a2d95
19 ## -*- texinfo -*- 19 ## -*- texinfo -*-
20 ## @deftypefn {Function File} {} rank (@var{A}) 20 ## @deftypefn {Function File} {} rank (@var{A})
21 ## @deftypefnx {Function File} {} rank (@var{A}, @var{tol}) 21 ## @deftypefnx {Function File} {} rank (@var{A}, @var{tol})
22 ## Compute the rank of matrix @var{A}, using the singular value decomposition. 22 ## Compute the rank of matrix @var{A}, using the singular value decomposition.
23 ## 23 ##
24 ## The rank is taken to be the number of singular values of @var{A} that 24 ## The rank is taken to be the number of singular values of @var{A} that are
25 ## are greater than the specified tolerance @var{tol}. If the second 25 ## greater than the specified tolerance @var{tol}. If the second argument is
26 ## argument is omitted, it is taken to be 26 ## omitted, it is taken to be
27 ## 27 ##
28 ## @example 28 ## @example
29 ## tol = max (size (@var{A})) * sigma(1) * eps; 29 ## tol = max (size (@var{A})) * sigma(1) * eps;
30 ## @end example 30 ## @end example
31 ## 31 ##
32 ## @noindent 32 ## @noindent
33 ## where @code{eps} is machine precision and @code{sigma(1)} is the largest 33 ## where @code{eps} is machine precision and @code{sigma(1)} is the largest
34 ## singular value of @var{A}. 34 ## singular value of @var{A}.
35 ## 35 ##
36 ## The rank of a matrix is the number of linearly independent rows or 36 ## The rank of a matrix is the number of linearly independent rows or columns
37 ## columns and determines how many particular solutions exist to a system 37 ## and determines how many particular solutions exist to a system of equations.
38 ## of equations. Use @code{null} for finding the remaining homogenous 38 ## Use @code{null} for finding the remaining homogenous solutions.
39 ## solutions.
40 ## 39 ##
41 ## Example: 40 ## Example:
42 ## 41 ##
43 ## @example 42 ## @example
44 ## @group 43 ## @group
49 ## @result{} 2 48 ## @result{} 2
50 ## @end group 49 ## @end group
51 ## @end example 50 ## @end example
52 ## 51 ##
53 ## @noindent 52 ## @noindent
54 ## The number of linearly independent rows is only 2 because the final row 53 ## The number of linearly independent rows is only 2 because the final row is a
55 ## is a linear combination of -1*row1 + 2*row2. 54 ## linear combination of -1*row1 + 2*row2.
56 ## 55 ##
57 ## @seealso{null, sprank, svd} 56 ## @seealso{null, sprank, svd}
58 ## @end deftypefn 57 ## @end deftypefn
59 58
60 ## Author: jwe 59 ## Author: jwe