Commit 65d0154b authored by Jay Belanger's avatar Jay Belanger
Browse files

(Vector/Matrix Functions): Add index entries for both "v" and "V" key

bindings.  Mention that `calc-matrix-brackets' only affects matrices
with more than one row.
parent 1586503c
2009-07-30 Jay Belanger <jay.p.belanger@gmail.com>
* calc.texi (Vector/Matrix Functions): Add index entries for both
"v" and "V" key bindings. Mention that `calc-matrix-brackets' only
affects matrices with more than one row.
2009-07-29 Jay Belanger <jay.p.belanger@gmail.com>
* calc.texi (Stack Manipulation Commands): Add documentation for
......
......@@ -16553,6 +16553,7 @@ or matrix argument, these functions operate element-wise.
@mindex v p
@end ignore
@kindex v p (complex)
@kindex V p (complex)
@pindex calc-pack
The @kbd{v p} (@code{calc-pack}) command can pack the top two numbers on
the stack into a composite object such as a complex number. With
......@@ -16564,6 +16565,7 @@ with an argument of @mathit{-2}, it produces a polar complex number.
@mindex v u
@end ignore
@kindex v u (complex)
@kindex V u (complex)
@pindex calc-unpack
The @kbd{v u} (@code{calc-unpack}) command takes the complex number
(or other composite object) on the top of the stack and unpacks it
......@@ -19365,6 +19367,7 @@ described in this chapter because they are most often used to build
vectors.
@kindex v p
@kindex V p
@pindex calc-pack
The @kbd{v p} (@code{calc-pack}) [@code{pack}] command collects several
elements from the stack into a matrix, complex number, HMS form, error
......@@ -19497,6 +19500,7 @@ number of data items does not match the number of items required
by the mode.
@kindex v u
@kindex V u
@pindex calc-unpack
The @kbd{v u} (@code{calc-unpack}) command takes the vector, complex
number, HMS form, or other composite object on the top of the stack and
......@@ -19614,6 +19618,7 @@ two stack arguments in the opposite order. Thus @kbd{I |} is equivalent
to @kbd{@key{TAB} |}, but possibly more convenient and also a bit faster.
@kindex v d
@kindex V d
@pindex calc-diag
@tindex diag
The @kbd{v d} (@code{calc-diag}) [@code{diag}] function builds a diagonal
......@@ -19632,6 +19637,7 @@ matrix first and then add a constant value to that matrix. (Another
alternative would be to use @kbd{v b} and @kbd{v a}; see below.)
@kindex v i
@kindex V i
@pindex calc-ident
@tindex idn
The @kbd{v i} (@code{calc-ident}) [@code{idn}] function builds an identity
......@@ -19652,6 +19658,7 @@ identity matrices are immediately expanded to the current default
dimensions.
@kindex v x
@kindex V x
@pindex calc-index
@tindex index
The @kbd{v x} (@code{calc-index}) [@code{index}] function builds a vector
......@@ -19676,6 +19683,7 @@ sequence to be generated. For example, @samp{index(-3, a, b)} produces
is one for positive @var{n} or two for negative @var{n}.
@kindex v b
@kindex V b
@pindex calc-build-vector
@tindex cvec
The @kbd{v b} (@code{calc-build-vector}) [@code{cvec}] function builds a
......@@ -19686,7 +19694,9 @@ can also be used to build an @var{n}-by-@var{m} matrix of copies of @var{x}.
to build a matrix of copies of that row.)
@kindex v h
@kindex V h
@kindex I v h
@kindex I V h
@pindex calc-head
@pindex calc-tail
@tindex head
......@@ -19697,6 +19707,7 @@ function returns the vector with its first element removed. In both
cases, the argument must be a non-empty vector.
@kindex v k
@kindex V k
@pindex calc-cons
@tindex cons
The @kbd{v k} (@code{calc-cons}) [@code{cons}] function takes a value @var{h}
......@@ -19706,15 +19717,18 @@ if @var{h} is itself a vector, @kbd{|} will concatenate the two vectors
whereas @code{cons} will insert @var{h} at the front of the vector @var{t}.
@kindex H v h
@kindex H V h
@tindex rhead
@ignore
@mindex @idots
@end ignore
@kindex H I v h
@kindex H I V h
@ignore
@mindex @null
@end ignore
@kindex H v k
@kindex H V k
@ignore
@mindex @null
@end ignore
......@@ -19736,6 +19750,7 @@ Also, @samp{head([a, b, c, d]) = a}, @samp{tail([a, b, c, d]) = [b, c, d]},
@noindent
@kindex v r
@kindex V r
@pindex calc-mrow
@tindex mrow
The @kbd{v r} (@code{calc-mrow}) [@code{mrow}] command extracts one row of
......@@ -19786,6 +19801,7 @@ of a square matrix in the form of a vector. In algebraic form this
function is called @code{getdiag}.
@kindex v c
@kindex V c
@pindex calc-mcol
@tindex mcol
@tindex mrcol
......@@ -19803,6 +19819,7 @@ use subscript notation: @samp{m_i_j} gives row @expr{i}, column @expr{j}
of matrix @expr{m}.
@kindex v s
@kindex V s
@pindex calc-subvector
@tindex subvec
The @kbd{v s} (@code{calc-subvector}) [@code{subvec}] command extracts
......@@ -19823,6 +19840,7 @@ end of the vector are used. The infinity symbol, @code{inf}, also
has this effect when used as the ending index.
@kindex I v s
@kindex I V s
@tindex rsubvec
With the Inverse flag, @kbd{I v s} [@code{rsubvec}] removes a subvector
from a vector. The arguments are interpreted the same as for the
......@@ -19838,6 +19856,7 @@ vectors one element at a time.
@noindent
@kindex v l
@kindex V l
@pindex calc-vlength
@tindex vlen
The @kbd{v l} (@code{calc-vlength}) [@code{vlen}] command computes the
......@@ -19846,6 +19865,7 @@ Note that matrices are just vectors of vectors for the purposes of this
command.
@kindex H v l
@kindex H V l
@tindex mdims
With the Hyperbolic flag, @kbd{H v l} [@code{mdims}] computes a vector
of the dimensions of a vector, matrix, or higher-order object. For
......@@ -19856,6 +19876,7 @@ its argument is a
matrix.
@kindex v f
@kindex V f
@pindex calc-vector-find
@tindex find
The @kbd{v f} (@code{calc-vector-find}) [@code{find}] command searches
......@@ -19866,6 +19887,7 @@ Otherwise, the result is zero. The numeric prefix argument, if given,
allows you to select any starting index for the search.
@kindex v a
@kindex V a
@pindex calc-arrange-vector
@tindex arrange
@cindex Arranging a matrix
......@@ -19896,7 +19918,9 @@ matrix), and @kbd{v a 0} produces the flattened list
@samp{[1, 2, @w{3, 4}]}.
@cindex Sorting data
@kindex v S
@kindex V S
@kindex I v S
@kindex I V S
@pindex calc-sort
@tindex sort
......@@ -19919,7 +19943,9 @@ The @kbd{I V S} [@code{rsort}] command sorts a vector into decreasing order.
@cindex Inverse of permutation
@cindex Index tables
@cindex Rank tables
@kindex v G
@kindex V G
@kindex I v G
@kindex I V G
@pindex calc-grade
@tindex grade
......@@ -19951,6 +19977,7 @@ 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.
@cindex Histograms
@kindex v H
@kindex V H
@pindex calc-histogram
@ignore
......@@ -19968,6 +19995,7 @@ 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.)
@kindex H v H
@kindex H V H
With the Hyperbolic flag, @kbd{H V H} pulls two vectors from the stack.
The second-to-top vector is the list of numbers as before. The top
......@@ -19977,6 +20005,7 @@ 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.
@kindex v t
@kindex V t
@pindex calc-transpose
@tindex trn
The @kbd{v t} (@code{calc-transpose}) [@code{trn}] command computes
......@@ -19985,6 +20014,7 @@ is a plain vector, it is treated as a row vector and transposed into
a one-column matrix.
@kindex v v
@kindex V v
@pindex calc-reverse-vector
@tindex rev
The @kbd{v v} (@code{calc-reverse-vector}) [@code{rev}] command reverses
......@@ -19994,6 +20024,7 @@ principle can be used to apply other vector commands to the columns of
a matrix.)
@kindex v m
@kindex V m
@pindex calc-mask-vector
@tindex vmask
The @kbd{v m} (@code{calc-mask-vector}) [@code{vmask}] command uses
......@@ -20006,6 +20037,7 @@ to zeros in the mask vector deleted. Thus, for example,
@xref{Logical Operations}.
@kindex v e
@kindex V e
@pindex calc-expand-vector
@tindex vexp
The @kbd{v e} (@code{calc-expand-vector}) [@code{vexp}] command
......@@ -20019,6 +20051,7 @@ unreplaced in the result. Thus @samp{vexp([2, 0, 3, 0, 7], [a, b])}
produces @samp{[a, 0, b, 0, 7]}.
@kindex H v e
@kindex H V e
With the Hyperbolic flag, @kbd{H v e} takes a filler value from the
top of the stack; the mask and target vectors come from the third and
second elements of the stack. This filler is used where the mask is
......@@ -20051,6 +20084,7 @@ vectors or matrices: @code{change-sign}, @code{conj}, @code{arg},
@code{re}, @code{im}, @code{polar}, @code{rect}, @code{clean},
@code{float}, @code{frac}. @xref{Function Index}.
@kindex v J
@kindex V J
@pindex calc-conj-transpose
@tindex ctrn
......@@ -20074,6 +20108,7 @@ a point in two- or three-dimensional space, this is the distance
from that point to the origin.
@kindex v n
@kindex V n
@pindex calc-rnorm
@tindex rnorm
The @kbd{v n} (@code{calc-rnorm}) [@code{rnorm}] command computes the
......@@ -20082,6 +20117,7 @@ vector, this is the maximum of the absolute values of the elements. For
a matrix, this is the maximum of the row-absolute-value-sums, i.e., of
the sums of the absolute values of the elements along the various rows.
@kindex v N
@kindex V N
@pindex calc-cnorm
@tindex cnorm
......@@ -20093,6 +20129,7 @@ General @expr{k}-norms for @expr{k} other than one or infinity are
not provided. However, the 2-norm (or Frobenius norm) is provided for
vectors by the @kbd{A} (@code{calc-abs}) command.
@kindex v C
@kindex V C
@pindex calc-cross
@tindex cross
......@@ -20121,12 +20158,14 @@ command simply computes @expr{1/x}. This is okay, because the
@samp{/} operator also does a matrix inversion when dividing one
by a matrix.
@kindex v D
@kindex V D
@pindex calc-mdet
@tindex det
The @kbd{V D} (@code{calc-mdet}) [@code{det}] command computes the
determinant of a square matrix.
@kindex v L
@kindex V L
@pindex calc-mlud
@tindex lud
......@@ -20137,6 +20176,7 @@ The first is a permutation matrix that arises from pivoting in the
algorithm, the second is lower-triangular with ones on the diagonal,
and the third is upper-triangular.
@kindex v T
@kindex V T
@pindex calc-mtrace
@tindex tr
......@@ -20144,6 +20184,7 @@ The @kbd{V T} (@code{calc-mtrace}) [@code{tr}] command computes the
trace of a square matrix. This is defined as the sum of the diagonal
elements of the matrix.
@kindex v K
@kindex V K
@pindex calc-kron
@tindex kron
......@@ -20184,6 +20225,7 @@ single interval, the interval itself is returned instead.
a certain value is a member of a given set. To test if the set @expr{A}
is a subset of the set @expr{B}, use @samp{vdiff(A, B) = []}.
@kindex v +
@kindex V +
@pindex calc-remove-duplicates
@tindex rdup
......@@ -20196,6 +20238,7 @@ necessary. You rarely need to use @kbd{V +} explicitly, since all the
other set-based commands apply @kbd{V +} to their inputs before using
them.
@kindex v V
@kindex V V
@pindex calc-set-union
@tindex vunion
......@@ -20205,6 +20248,7 @@ only if it is in either (or both) of the input sets. (You could
accomplish the same thing by concatenating the sets with @kbd{|},
then using @kbd{V +}.)
@kindex v ^
@kindex V ^
@pindex calc-set-intersect
@tindex vint
......@@ -20221,6 +20265,7 @@ and
@texline intersection@tie{}(@math{A \cap B}).
@infoline intersection.
@kindex v -
@kindex V -
@pindex calc-set-difference
@tindex vdiff
......@@ -20235,6 +20280,7 @@ Obviously this is only practical if the set of all possible values in
your problem is small enough to list in a Calc vector (or simple
enough to express in a few intervals).
@kindex v X
@kindex V X
@pindex calc-set-xor
@tindex vxor
......@@ -20244,6 +20290,7 @@ An object is in the symmetric difference of two sets if and only
if it is in one, but @emph{not} both, of the sets. Objects that
occur in both sets ``cancel out.''
@kindex v ~
@kindex V ~
@pindex calc-set-complement
@tindex vcompl
......@@ -20253,6 +20300,7 @@ Thus @samp{vcompl(x)} is equivalent to @samp{vdiff([-inf .. inf], x)}.
For example, @samp{vcompl([2, (3 .. 4]])} evaluates to
@samp{[[-inf .. 2), (2 .. 3], (4 .. inf]]}.
@kindex v F
@kindex V F
@pindex calc-set-floor
@tindex vfloor
......@@ -20265,6 +20313,7 @@ complement of the set @samp{[2, 6, 7, 8]} is messy, but if you wanted
the complement with respect to the set of integers you could type
@kbd{V ~ V F} to get @samp{[[-inf .. 1], [3 .. 5], [9 .. inf]]}.
@kindex v E
@kindex V E
@pindex calc-set-enumerate
@tindex venum
......@@ -20274,6 +20323,7 @@ the set are expanded out to lists of all integers encompassed by
the intervals. This only works for finite sets (i.e., sets which
do not involve @samp{-inf} or @samp{inf}).
@kindex v :
@kindex V :
@pindex calc-set-span
@tindex vspan
......@@ -20283,6 +20333,7 @@ The lower limit will be the smallest element in the set; the upper
limit will be the largest element. For an empty set, @samp{vspan([])}
returns the empty interval @w{@samp{[0 .. 0)}}.
@kindex v #
@kindex V #
@pindex calc-set-cardinality
@tindex vcard
......@@ -20702,6 +20753,7 @@ $$ r_{x\!y} = { \sigma_{x\!y}^2 \over \sigma_x^2 \sigma_y^2 } $$
The commands in this section allow for more general operations on the
elements of vectors.
@kindex v A
@kindex V A
@pindex calc-apply
@tindex apply
......@@ -20879,6 +20931,7 @@ about it.)
@subsection Mapping
@noindent
@kindex v M
@kindex V M
@pindex calc-map
@tindex map
......@@ -20975,6 +21028,7 @@ variable's stored value using a @kbd{V M}-like operator.
@subsection Reducing
@noindent
@kindex v R
@kindex V R
@pindex calc-reduce
@tindex reduce
......@@ -20987,6 +21041,7 @@ the remaining elements. Reducing @code{max} computes the maximum element
and so on. In general, reducing @code{f} over the vector @samp{[a, b, c, d]}
produces @samp{f(f(f(a, b), c), d)}.
@kindex I v R
@kindex I V R
@tindex rreduce
The @kbd{I V R} [@code{rreduce}] command is similar to @kbd{V R} except
......@@ -20996,6 +21051,7 @@ but @kbd{I V R -} on the same vector produces @samp{a - (b - (c - d))},
or @samp{a - b + c - d}. This ``alternating sum'' occurs frequently
in power series expansions.
@kindex v U
@kindex V U
@tindex accum
The @kbd{V U} (@code{calc-accumulate}) [@code{accum}] command does an
......@@ -21005,6 +21061,7 @@ a vector of all the intermediate results. Accumulating @code{+} over
the vector @samp{[a, b, c, d]} produces the vector
@samp{[a, a + b, a + b + c, a + b + c + d]}.
@kindex I v U
@kindex I V U
@tindex raccum
The @kbd{I V U} [@code{raccum}] command does a right-to-left accumulation.
......@@ -21052,6 +21109,7 @@ rows of the matrix. @xref{Grabbing From Buffers}.
@subsection Nesting and Fixed Points
@noindent
@kindex H v R
@kindex H V R
@tindex nest
The @kbd{H V R} [@code{nest}] command applies a function to a given
......@@ -21062,6 +21120,7 @@ is 3, the result is @samp{f(f(f(a)))}. The number @samp{n} may be
negative if Calc knows an inverse for the function @samp{f}; for
example, @samp{nest(sin, a, -2)} returns @samp{arcsin(arcsin(a))}.
@kindex H v U
@kindex H V U
@tindex anest
The @kbd{H V U} [@code{anest}] command is an accumulating version of
......@@ -21070,6 +21129,7 @@ The @kbd{H V U} [@code{anest}] command is an accumulating version of
@samp{F} is the inverse of @samp{f}, then the result is of the
form @samp{[a, F(a), F(F(a)), F(F(F(a)))]}.
@kindex H I v R
@kindex H I V R
@tindex fixp
@cindex Fixed points
......@@ -21078,6 +21138,7 @@ that it takes only an @samp{a} value from the stack; the function is
applied until it reaches a ``fixed point,'' i.e., until the result
no longer changes.
@kindex H I v U
@kindex H I V U
@tindex afixp
The @kbd{H I V U} [@code{afixp}] command is an accumulating @code{fixp}.
......@@ -21127,6 +21188,7 @@ when 20 steps have been taken, whichever is sooner.
@node Generalized Products, , Nesting and Fixed Points, Reducing and Mapping
@subsection Generalized Products
@kindex v O
@kindex V O
@pindex calc-outer-product
@tindex outer
......@@ -21138,6 +21200,7 @@ and @samp{[x, y, z]} on the stack produces a multiplication table:
the result matrix is obtained by applying the operator to element @var{r}
of the lefthand vector and element @var{c} of the righthand vector.
@kindex v I
@kindex V I
@pindex calc-inner-product
@tindex inner
......@@ -21170,10 +21233,13 @@ in the same way (@pxref{Display Modes}). Matrix display is also
influenced by the @kbd{d O} (@code{calc-flat-language}) mode;
@pxref{Normal Language Modes}.
@kindex v <
@kindex V <
@pindex calc-matrix-left-justify
@kindex v =
@kindex V =
@pindex calc-matrix-center-justify
@kindex v >
@kindex V >
@pindex calc-matrix-right-justify
The commands @kbd{v <} (@code{calc-matrix-left-justify}), @kbd{v >}
......@@ -21181,10 +21247,13 @@ The commands @kbd{v <} (@code{calc-matrix-left-justify}), @kbd{v >}
(@code{calc-matrix-center-justify}) control whether matrix elements
are justified to the left, right, or center of their columns.
@kindex v [
@kindex V [
@pindex calc-vector-brackets
@kindex v @{
@kindex V @{
@pindex calc-vector-braces
@kindex v (
@kindex V (
@pindex calc-vector-parens
The @kbd{v [} (@code{calc-vector-brackets}) command turns the square
......@@ -21199,15 +21268,21 @@ display mode, either brackets or braces may be used to enter vectors,
and parentheses may never be used for this purpose.
@kindex V ]
@kindex v ]
@kindex V )
@kindex v )
@kindex V @}
@kindex v @}
@pindex calc-matrix-brackets
The @kbd{v ]} (@code{calc-matrix-brackets}) command controls the
``big'' style display of matrices. It prompts for a string of code
letters; currently implemented letters are @code{R}, which enables
brackets on each row of the matrix; @code{O}, which enables outer
brackets in opposite corners of the matrix; and @code{C}, which
enables commas or semicolons at the ends of all rows but the last.
The default format is @samp{RO}. (Before Calc 2.00, the format
was fixed at @samp{ROC}.) Here are some example matrices:
``big'' style display of matrices, for matrices which have more than
one row. It prompts for a string of code letters; currently
implemented letters are @code{R}, which enables brackets on each row
of the matrix; @code{O}, which enables outer brackets in opposite
corners of the matrix; and @code{C}, which enables commas or
semicolons at the ends of all rows but the last. The default format
is @samp{RO}. (Before Calc 2.00, the format was fixed at @samp{ROC}.)
Here are some example matrices:
@example
@group
......@@ -21246,6 +21321,7 @@ Note that of the formats shown here, @samp{RO}, @samp{ROC}, and
@samp{OC} are all recognized as matrices during reading, while
the others are useful for display only.
@kindex v ,
@kindex V ,
@pindex calc-vector-commas
The @kbd{v ,} (@code{calc-vector-commas}) command turns commas on and
......@@ -21261,6 +21337,7 @@ case as @samp{[(a b)]}. You can disable these extra parentheses
ambiguity) by adding the letter @code{P} to the control string you
give to @kbd{v ]} (as described above).
@kindex v .
@kindex V .
@pindex calc-full-vectors
The @kbd{v .} (@code{calc-full-vectors}) command turns abbreviated
......@@ -21282,6 +21359,7 @@ unable to recover those vectors. If you are working with very
large vectors, this mode will improve the speed of all operations
that involve the trail.
@kindex v /
@kindex V /
@pindex calc-break-vectors
The @kbd{v /} (@code{calc-break-vectors}) command turns multi-line
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