| Type: | Package |
| Title: | Pseudo-Vectors Containing All Permutations, Combinations and Subsets of Objects Taken from a Vector. |
| Version: | 0.6 |
| Date: | 2014-09-05 |
| Author: | Richard Ambler |
| Maintainer: | Richard Ambler <rambler@ibwya.net> |
| Description: | Class definitions and constructors for pseudo-vectors containing all permutations, combinations and subsets of objects taken from a vector. Simplifies working with structures commonly encountered in combinatorics. |
| Depends: | methods |
| License: | GPL-3 |
| Packaged: | 2014-09-21 06:13:45 UTC; rambler |
| NeedsCompilation: | no |
| Repository: | CRAN |
| Date/Publication: | 2014-09-21 11:06:59 |
Retrieve an Amalgam by Index
Description
Access an amalgam (permutation with replacement) stored in an APV instance by index.
Usage
## S4 method for signature 'APV'
x[i, j, drop]
Arguments
x |
an instance of |
i |
an index specifying the position of the sought amalgam |
j |
not used. |
drop |
not used. |
Details
The amalgam at index i of pseudo-vector x is not actually
stored in memory but calculated as needed. The extract method is used solely
for interpretation.
Value
the amalgam located at position i in pseudo-vector x
See Also
Permutations Pseudo-Vector ppv
Combinations Pseudo-Vector cpv
Selections Pseudo-Vector spv
Subsets Pseudo-Vector sspv
Retrieve a Combination by Index
Description
Access a combination stored in a CPV instance by index.
Usage
## S4 method for signature 'CPV'
x[i, j, drop]
Arguments
x |
an instance of |
i |
an index specifying the position of the sought combination. |
j |
not used. |
drop |
not used. |
Details
The combination at index i of pseudo-vector x is not actually
stored in memory but calculated as needed. The extract method is used solely
for interpretation.
Value
the combination located at position i in pseudo-vector x
See Also
Permutations Pseudo-Vector ppv
Amalgams Pseudo-Vector apv
Selections Pseudo-Vector spv
Subsets Pseudo-Vector sspv
Retrieve a Permutation by Index
Description
Access a permutation stored in a PPV instance by index.
Usage
## S4 method for signature 'PPV'
x[i, j, drop]
Arguments
x |
an instance of |
i |
an index specifying the position of the sought permutation. |
j |
not used. |
drop |
not used. |
Details
The permutation at index i of pseudo-vector x is not actually
stored in memory but calculated as needed. The extract method is used solely
for interpretation.
Value
the permutation located at position i in pseudo-vector x
See Also
Combinations Pseudo-Vector cpv
Amalgams Pseudo-Vector apv
Selections Pseudo-Vector spv
Subsets Pseudo-Vector sspv
Retrieve a Selection by Index
Description
Access a selection (combination with replacement) stored in an SPV instance by index.
Usage
## S4 method for signature 'SPV'
x[i, j, drop]
Arguments
x |
an instance of |
i |
an index specifying the position of the sought selection. |
j |
not used. |
drop |
not used. |
Details
The selection at index i of pseudo-vector x is not actually
stored in memory but calculated as needed. The extract method is used solely
for interpretation.
Value
the selection located at position i in pseudo-vector x
See Also
Permutations Pseudo-Vector ppv
Combinations Pseudo-Vector cpv
Amalgams Pseudo-Vector apv
Subsets Pseudo-Vector sspv
Retrieve a Subset by Index
Description
Access asubset stored in an SSPV instance by index.
Usage
## S4 method for signature 'SSPV'
x[i, j, drop]
Arguments
x |
an instance of |
i |
an index specifying the position of the sought amalgam |
j |
not used. |
drop |
not used. |
Details
The subset at index i of pseudo-vector x is not actually
stored in memory but calculated as needed. The extract method is used solely
for interpretation.
Value
the subset located at position i in pseudo-vector x
See Also
Permutations Pseudo-Vector ppv
Combinations Pseudo-Vector cpv
Amalgams Pseudo-Vector apv
Selections Pseudo-Vector spv
Amalgams Pseudo-Vector Constructor
Description
The APV class defines a pseudo-vector containing all
the arranged k-amalgams (permutations with replacement) of the objects stored
in items. The function apv is a constructor for this class.
Usage
apv(k, items)
Arguments
k |
the number of objects taken at a time. |
items |
a vector of objects to be amalgamated. |
Details
The amalgams are arranged according to the order in which the objects
appear in items. The arrangement is very similar to that used by the PPV class
(see ppv) except that objects are replaced during permutation creation.
Value
an instance of APV.
Author(s)
Richard Ambler
References
Steinhaus-Johnson-Trotter algorithm. (2014, April 29). In Wikipedia, The Free Encyclopedia. Retrieved 13:24, September 5, 2014
See Also
Permutations Pseudo-Vector ppv
Combinations Pseudo-Vector cpv
Selections Pseudo-Vector spv
Subsets Pseudo-Vector sspv
Examples
# create a pseudo-vector of 10-amalgams from the first 15 letters
a <- apv(10, letters[1:15])
# generate a description
print(a)
# compatable with length
length(a)
# inspect a few of the combinations "stored" in a
a[1]
a[1000000]
a[576650390625]
Combinations Pseudo-Vector Constructor
Description
The CPV class defines a pseudo-vector containing all
the arranged k-combinations of the objects stored
in items. The function cpv is a constructor for this class.
Usage
cpv(k, items)
Arguments
k |
the number of objects taken at a time. |
items |
a vector of objects to be combined. |
Details
The combinations are arranged according to the order in which the objects
appear in items. Combinations containing the first object in
items are followed by combinations that contain the second object
but not the first, which are followed by combinations that contain the third
but neither the first or the second, etc.
Value
an instance of CPV.
Author(s)
Richard Ambler
References
Steinhaus-Johnson-Trotter algorithm. (2014, April 29). In Wikipedia, The Free Encyclopedia. Retrieved 13:24, September 5, 2014
See Also
Permutations Pseudo-Vector ppv
Amalgams Pseudo-Vector apv
Selections Pseudo-Vector spv
Subsets Pseudo-Vector sspv
Examples
# create a pseudo-vector of 10-combinations from the first 15 letters
c <- cpv(10, letters[1:15])
# generate a description
print(c)
# compatable with length
length(c)
# inspect a few of the combinations "stored" in c
c[1]
c[1000]
c[3003]
Amalgams Pseudo-Vector Length
Description
Get the length of an APV instance.
Usage
## S4 method for signature 'APV'
length(x)
Arguments
x |
an instance of |
Details
Since x contains all the k-amalgams of objects in vector
items, length(x) will return length(items) ^ k).
Value
the number of amalgams (permutations with replacement) in pseudo-vector x
See Also
Permutations Pseudo-Vector ppv
Combinations Pseudo-Vector cpv
Selections Pseudo-Vector spv
Subsets Pseudo-Vector sspv
Combinations Pseudo-Vector Length
Description
Get the length of a CPV instance.
Usage
## S4 method for signature 'CPV'
length(x)
Arguments
x |
an instance of |
Details
Since x contains all the k-combinations of objects in vector
items, length(x) will return choose(length(items), k).
Value
the number of combinations in pseudo-vector x
See Also
Permutations Pseudo-Vector ppv
Amalgams Pseudo-Vector apv
Selections Pseudo-Vector spv
Subsets Pseudo-Vector sspv
Permutations Pseudo-Vector Length
Description
Get the length of a PPV instance.
Usage
## S4 method for signature 'PPV'
length(x)
Arguments
x |
an instance of |
Details
Since x contains all the k-permutations of objects in vector
items, length(x) will return
choose(length(items), k) * factorial(k).
Value
the number of permutations in pseudo-vector x
See Also
Combinations Pseudo-Vector cpv
Amalgams Pseudo-Vector apv
Selections Pseudo-Vector spv
Subsets Pseudo-Vector sspv
Selections Pseudo-Vector Length
Description
Get the length of an SPV instance.
Usage
## S4 method for signature 'SPV'
length(x)
Arguments
x |
an instance of |
Details
Since x contains all the k-selections of objects in vector
items, length(x) will return choose(length(items) + k - 1, k).
Value
the number of selections (combinations with replacement) in pseudo-vector x
See Also
Permutations Pseudo-Vector ppv
Combinations Pseudo-Vector cpv
Amalgams Pseudo-Vector apv
Subsets Pseudo-Vector sspv
Subsets Pseudo-Vector Length
Description
Get the length of an SSPV instance.
Usage
## S4 method for signature 'SSPV'
length(x)
Arguments
x |
an instance of |
Details
Since x contains all the subsets of objects in vector
items, length(x) will return 2 ^ length(items).
Value
the number of subsets in pseudo-vector x
See Also
Permutations Pseudo-Vector ppv
Combinations Pseudo-Vector cpv
Amalgams Pseudo-Vector apv
Selections Pseudo-Vector spv
Permutations Pseudo-Vector Constructor
Description
The PPV class defines a pseudo-vector containing all
the k-permutations of the objects stored
in items. The function ppv is a constructor for this class.
Usage
ppv(k, items)
Arguments
k |
the number of objects taken at a time. |
items |
a vector of objects to be permuted. |
Details
The arrangement of permutations is similar, but in many cases not identical, to that obtained from the Steinhaus-Johnson-Trotter algorithm (see references).
Value
an instance of PPV.
Author(s)
Richard Ambler
References
Steinhaus-Johnson-Trotter algorithm. (2014, April 29). In Wikipedia, The Free Encyclopedia. Retrieved 13:24, September 5, 2014
See Also
Combinations Pseudo-Vector cpv
Amalgams Pseudo-Vector apv
Selections Pseudo-Vector spv
Subsets Pseudo-Vector sspv
Examples
# create a pseudo-vector of 5-permutations from the first 10 letters
p <- ppv(5, letters[1:10])
# generate a description
print(p)
# compatable with length
length(p)
# inspect a few of the permutations "stored" in p
p[1]
p[1000]
p[30240]
Selections Pseudo-Vector Constructor
Description
The SPV class defines a pseudo-vector containing all
the arranged k-selections (combinations with replacement) of the objects stored
in items. The function spv is a constructor for this class.
Usage
spv(k, items)
Arguments
k |
the number of objects taken at a time. |
items |
a vector of objects to be selected. |
Details
The selections are arranged according to the order in which the objects
appear in items. The arrangement is very similar to the arrangement
of combinations (see cpv) except that objects may be repeatedly selected.
Value
an instance of SPV.
Author(s)
Richard Ambler
References
Steinhaus-Johnson-Trotter algorithm. (2014, April 29). In Wikipedia, The Free Encyclopedia. Retrieved 13:24, September 5, 2014
See Also
Permutations Pseudo-Vector ppv
Combinations Pseudo-Vector cpv
Amalgams Pseudo-Vector apv
Subsets Pseudo-Vector sspv
Examples
# create a pseudo-vector of 10-selections from the first 15 letters
s <- spv(10, letters[1:15])
# generate a description
print(s)
# compatable with length
length(s)
# inspect a few of the combinations "stored" in s
s[1]
s[1000]
s[1961256]
Subsets Pseudo-Vector Constructor
Description
The SSPV class defines a pseudo-vector containing all
the arranged subsets of the objects stored
in items. The function sspv is a constructor for this class.
Usage
sspv(items)
Arguments
items |
a vector of objects to be subsetted. |
Details
The subsets are arranged according to the order in which the objects
appear in items. The first subset, containing none of the objects,
is NULL.
Value
an instance of SSPV.
Author(s)
Richard Ambler
See Also
Permutations Pseudo-Vector ppv
Combinations Pseudo-Vector cpv
Amalgams Pseudo-Vector apv
Selections Pseudo-Vector spv
Examples
# create a pseudo-vector of subsets from the first 15 letters
ss <- sspv(letters[1:15])
# generate a description
print(ss)
# compatable with length
length(ss)
# inspect a few of the combinations "stored" in ss
ss[1]
ss[1000]
ss[32768]