Package {tropicalSparse}

Check Infinity in Matrix

Description

check.infinityM checks infinite value in a matrix based on algebraType input.

Usage

check.infinityM(M, algebraType)

Arguments

Details

The input of this function is a matrix and type of tropical algebra. A matrix may contain infinite values that can be positive or negative. Both the positive and negative infinite values works differently on each algebra type. Due to the difference between minplus and maxplus tropical algebra, it is important to manage them so they can work in their own bounderies. In minplus -Inf cannot be used while in maxplus Inf cannot be used. So the main purpose of this funnction is to check such possibilities that can cause errors. If this function finds a -Inf in the matrix and the type of algebra is minplus then the function generates an error. Similarly, if the function finds a Inf in the matrix and the type of algebra is maxplus then the function also generates an error.

Value

Returns nothing but generates an error if specific conditions met.

See Also

check.infinityV

Examples

a <- matrix(data = c(2, Inf, Inf, 0, Inf, Inf, Inf, 10, Inf),
nrow = 3, ncol = 3, byrow = TRUE)
check.infinityM(a, 'minplus')

Check Infinity in Vector

Description

check.infinityV checks infinite value in a vector based on algebraType input.

Usage

check.infinityV(V, algebraType)

Arguments

Details

The input of this function is a vector and type of tropical algebra. A vector may contain infinite values that can be positive or negative. Both the positive and negative infinite values works differently on each algebra type. Due to the difference between minplus and maxplus tropical algebra, it is important to manage them so they can work in their own bounderies. In minplus -Inf cannot be used while in maxplus Inf cannot be used. So the main purpose of this funnction is to check such possibilities that can cause errors. If this function finds a -Inf in the vector and the type of algebra is minplus then the function generates an error. Similarly, if the function finds a Inf in the vector and the type of algebra is maxplus then the function also generates an error.

Value

Returns nothing but generates an error if specific conditions met.

See Also

check.infinityM

Examples

a <- c(2, Inf, Inf, 0, Inf, Inf, Inf, 10, Inf)
check.infinityV(a, 'minplus')

Count non-infinit values

Description

counter is used to get total number of non-infinit values in a matrix.

Usage

counter(M)

Arguments

Details

The input of this function is a matrix. This function returns the total number of non-infinite values in the given matrix. In order to work properly, M must be a matrix otherwise this method generates an error.

Value

Returns total number of non-infinit values.

Examples

a <- matrix(data = c(2, Inf, Inf, 0, Inf, Inf, Inf, 10, Inf), nrow = 3, ncol = 3, byrow = TRUE)

counter(a)

# [1] 3

Row/Column Number of a Value

Description

row.col.Number method is used to get the row or column number of a specific value in the matrix.

Usage

row.col.Number(i, x, arr)

Arguments

Details

The function row.col.Number recieves three parameters i, x and arr. As mentioned above i is an index of array containing non-infinite values of the matrix. This array can only be obtained in the CSR and CSC storage techniques and has zero sparsity. x is total number of rows in case of CSR or total number of columns in case of CSC of the matrix. arr is an array containing row pointer in case of CSR or column pointer in case of CSC of the matrix. From these inputs row.col.Number finds row or column number of a specific value in the matrix. This function is used especially for CSR and CSC storage techniques.

Value

Returns the row or column number of a specific value if succeded, otherwise NA.

See Also

tropicalsparse.add, tropicalsparse.mul.

Examples

a <- matrix(data = c(2, Inf, Inf, 0, Inf, Inf, Inf, 10, Inf),
nrow = 3, ncol = 3, byrow = TRUE)

List = tropicalsparse.storage(a,'csr','minplus')
i = 2
row.col.Number(i, nrow(a), List[[1]])
# [1] 2

Addition With or Without Storage Techniques

Description

tropicalsparse.add function adds the provided inputs in Tropical Algebra based on type of Tropical Algebra.

Usage

tropicalsparse.add(A, B, store = NULL, algebraType)

Arguments

Details

The compulsory inputs of the function tropicalsparse.add are A, B and algebraType while the remaining input is optional that is store. The inputs A and B can be matrix/matrix, matrix/vector, vector/matrix and vector/vector otherwise the function generates an error. For A and B, the order of the input does not matter. It can be in any of the following way: the first input of the function is matrix and second input is a vector. Similarly, vise versa. store can be coo, csc and csr for applying following storage techniques respectively: Coordinate-Wise, Compressed Sparse Row, Compressed Sparse Column. This input is case sensitive. If the store input is other than the specified storage techniques then the function generates an error. The input algebraType is used to specify type of Tropical Algebra. This can be minplus or maxplus. For more details about algebraType, see detail section of check.infinityM or check.infinityV. tropicalsparse.storage function is used to apply storage technique depends upon the input given. If store input is not specified then the functionality will be performed without using any storage technique.

Value

Addition of A and B in Tropical Algebra.

See Also

tropicalsparse.mul, tropicalsparse.storage

Examples

a <- matrix(data = c(2, Inf, Inf, 0, Inf, Inf, Inf, 10, Inf),
nrow = 3, ncol = 3, byrow = TRUE)

b <- matrix(data = c(Inf, Inf, 4, Inf, -0.3, Inf, Inf, 2, Inf),
nrow = 3, ncol = 3, byrow = TRUE)

tropicalsparse.add(a, b, 'csr', 'minplus')

#     [,1] [,2]  [,3]
# [1,]    2  Inf    4
# [2,]    0 -0.3  Inf
# [3,]  Inf  2.0  Inf

# also

a <- matrix(data = c(5, -Inf, -Inf, -Inf, -Inf, -Inf, -Inf, 10, 2),
nrow = 3, ncol = 3, byrow = TRUE)

b <- matrix(data = c(-Inf, -Inf, 3, -Inf, -0.5, -Inf, 1.1, -Inf, -Inf),
nrow = 3, ncol = 3, byrow = TRUE)

tropicalsparse.add(a, b, 'coo', 'maxplus')

#      [,1] [,2] [,3]
# [1,]  5.0 -Inf    3
# [2,] -Inf -0.5 -Inf
# [3,]  1.1 10.0    2

# also

a <- matrix(data = c(2, Inf, Inf, 0, Inf, Inf, Inf, 2, Inf),
nrow = 3, ncol = 3, byrow = TRUE)

b <- c(Inf, 0, 10)

tropicalsparse.add(a, b, algebraType = 'minplus')

#      [,1] [,2] [,3]
# [1,]    2  Inf  Inf
# [2,]    0    0    0
# [3,]   10    2   10

tropicalsparse.axpyi()

Description

tropicalsparse.axpyi function multiplies the vector x by the constant alpha and adds the result to the vector y.

Usage

tropicalsparse.axpyi(y, alpha, x, algebraType)

Arguments

Details

The input of the function tropicalsparse.axpyi is two vectors, a constant and type of Tropical Algebra. algebraType is used to specify type of Tropical Algebra. This can be minplus or maxplus. For more details about algebraType, see detail section of check.infinityM or check.infinityV. All inputs of this method are compulsory. The operation is expressed as: y = y + alpha * x where x and y must be a vector while alpha must be a constant.

Value

Returns a vector.

See Also

tropicalsparse.doti

Examples

a <- c(2, Inf, 5, 0, Inf, Inf, Inf, 10, Inf)
b <- c(0, 5, Inf, Inf, 12, 2, Inf, Inf, 3)
alpha <- 5

tropicalsparse.axpyi(a, alpha, b, 'minplus')

# [1]   2  10   5   0  17   7 Inf  10   8

tropicalsparse.doti()

Description

tropicalsparse.doti function multiplies the vector y with the vector x.

Usage

tropicalsparse.doti(x, y, algebraType)

Arguments

Details

The input of this function is x, y and algebraType. If any of the input is missing then the function generates an error. The operation is expressed as: result = yx where x and y must be a vector. algebraType is used to specify type of Tropical Algebra. This can be minplus or maxplus. For more details about algebraType, see detail section of check.infinityM or check.infinityV.

Value

Returns a vector.

See Also

tropicalsparse.axpyi

Examples

a <- c(2, Inf, 5, 0, Inf, Inf, Inf, 10, Inf)
b <- c(0, 5, Inf, Inf, 12, 2, Inf, Inf, 3)

tropicalsparse.doti(a, b, 'minplus')

# [1]   2 Inf Inf Inf Inf Inf Inf Inf Inf

tropicalsparse.mm()

Description

tropicalsparse.mm function performs the matrix-matrix operation on the equation: y = alpha * op(A) * op(B) + beta * op(C).

Usage

tropicalsparse.mm(
  alpha = NULL,
  A,
  opA = FALSE,
  B,
  opB = FALSE,
  beta = NULL,
  C,
  opC = FALSE,
  store = NULL,
  algebraType
)

Arguments

Details

The input of this function is three matrices, two constants, operation on these matrices, storage technique and type of Tropical Algebra. Matrices and algebraType inputs are compulsory while all other inputs are optional. A, B and C must be the matrix of same dimensions and these matrices must be sparse otherwise error occured. alpha and beta must be the single real value. opA, opB and opC can be set to TRUE to take transpose of A, B and C matrices repectively. store input can be coo, csc and csr for applying following storage techniques respectively: Coordinate-Wise, Compressed Sparse Row, Compressed Sparse Column. If store is not specified then functionality is performed without using any storage technique. algebraType is used to specify type of Tropical Algebra. This can be minplus or maxplus. For more details about algebraType, see detail section of check.infinityM or check.infinityV. First of all A is multiplied with B and if alpha is given then the product of A and B will be multipied with alpha otherwise it remais the same. After this, beta is multiplied with C only if beta is given. Finally, both result are added to each other and the resultant matrix is obtained. Same functionailty is applied if any of the store technique is specified.

Value

Returns the resultant matrix.

Examples

a <- matrix(data = c(2, Inf, Inf, 0, Inf, Inf, Inf, 10, Inf),
nrow = 3, ncol = 3, byrow = TRUE)

b <- matrix(data = c(Inf, Inf, 4, Inf, -0.3, Inf, Inf, 2, Inf),
nrow = 3, ncol = 3, byrow = TRUE)

c <- matrix(data = c(1, Inf, Inf, Inf, 0, 6, Inf, Inf, Inf),
nrow = 3, ncol = 3, byrow = TRUE)

tropicalsparse.mm(A = a, alpha = 5, opB = TRUE, B = b, C = c,
store = 'csr', algebraType = 'minplus')

#      [,1] [,2] [,3]
# [1,]    1  Inf  Inf
# [2,]  Inf  0.0    6
# [3,]  Inf 14.7   17

Multiplication With or Without Storage Techniques

Description

tropicalsparse.mul function multiplies the provided inputs in Tropical Algebra based on type of Tropical Algebra.

Usage

tropicalsparse.mul(A, B, store = NULL, algebraType)

Arguments

Details

The compulsory inputs of the function tropicalsparse.mul are A, B and algebraType while the remaining input is optional that is store. The inputs A and B can be matrix/matrix, matrix/vector, vector/matrix and vector/vector otherwise the function generates an error. For A and B, the order of the input does not matter. It can be in any of the following way: the first input of the function is matrix and second input is a vector. Similarly, vise versa. store can be coo, csc and csr for applying following storage techniques respectively: Coordinate-Wise, Compressed Sparse Row, Compressed Sparse Column. This input is case sensitive. If the store input is other than the specified storage techniques then the function generates an error. The input algebraType is used to specify type of Tropical Algebra. This can be minplus or maxplus. For more details about algebraType, see detail section of check.infinityM or check.infinityV. tropicalsparse.storage function is used to apply storage technique depends upon the input given. If store input is not specified then the functionality will be performed without using any storage technique.

Value

Multiplication of A and B in Tropical Algebra.

See Also

tropicalsparse.add, tropicalsparse.storage

Examples

a <- matrix(data = c(2, Inf, Inf, 0, Inf, Inf, Inf, 10, Inf),
nrow = 3, ncol = 3, byrow = TRUE)

b <- matrix(data = c(Inf, Inf, 4, Inf, -0.3, Inf, Inf, 2, Inf),
nrow = 3, ncol = 3, byrow = TRUE)

tropicalsparse.mul(a, b, 'csr', 'minplus')

#      [,1] [,2] [,3]
# [1,]  Inf  Inf    6
# [2,]  Inf  Inf    4
# [3,]  Inf  9.7  Inf

# also

a <- matrix(data = c(5, -Inf, -Inf, -Inf, -Inf, -Inf, -Inf, 10, 2),
nrow = 3, ncol = 3, byrow = TRUE)

b <- matrix(data = c(-Inf, -Inf, 3, -Inf, 0.5, -Inf, 1.1, -Inf, -Inf),
nrow = 3, ncol = 3, byrow = TRUE)

tropicalsparse.mul(a, b, 'coo', 'maxplus')

#      [,1] [,2] [,3]
# [1,] -Inf -Inf    8
# [2,] -Inf -Inf -Inf
# [3,]  3.1 10.5 -Inf

# also

a <- matrix(data = c(2, Inf, Inf, 0, Inf, Inf, Inf, 2, Inf),
nrow = 3, ncol = 3, byrow = TRUE)

b <- c(Inf, 0, 10)

tropicalsparse.mul(a, b, algebraType = 'minplus')

#      [,1] [,2] [,3]
# [1,]  Inf  Inf  Inf
# [2,]    0  Inf  Inf
# [3,]  Inf   12  Inf

tropicalsparse.mv()

Description

tropicalsparse.mv function performs the matrix-vector operation on the equation: y = alpha * op(A) * x + beta * y.

Usage

tropicalsparse.mv(
  alpha = NULL,
  A,
  opA = FALSE,
  x,
  beta = NULL,
  y,
  store = NULL,
  algebraType
)

Arguments

Details

The input of this function is one matrix, transpose of that matrix, two vectors, two constants, storage technique and type of Tropical Algebra. The inputs of the matrix, vectors and algebraType are compulsory while all other inputs are optional. The matrix must be sparse otherwise error occured. alpha and beta must be a single real value. opA can be set to TRUE to take transpose of A. store input can be coo, csc and csr for applying following storage techniques respectively: Coordinate-Wise, Compressed Sparse Row, Compressed Sparse Column. If store is not specified then functionality is performed without using any storage technique. algebraType is used to specify type of Tropical Algebra. This can be minplus or maxplus. For more details about algebraType, see detail section of check.infinityM or check.infinityV. First of all A is multiplied with x and if alpha is given then the product of A and x will be multipied with alpha otherwise it remais the same. After this, beta is multiplied with y only if beta is given. Finally, both result are added to each other and the resultant matrix is obtained. Same functionailty is applied if any of the store technique is specified.

Value

Returns the resultant matrix.

Examples

a <- matrix(data = c(2, Inf, Inf, 0, Inf, Inf, Inf, 10, Inf),
nrow = 3, ncol = 3, byrow = TRUE)

b <- c(2, Inf, 5)

c <- c(Inf, 9, Inf)

tropicalsparse.mv(A = a, alpha = 5, opA = TRUE, x = b, y = c,
store = 'csr', algebraType = 'minplus')

#      [,1] [,2] [,3]
# [1,]    9  Inf  Inf
# [2,]    9    9    9
# [3,]  Inf   20  Inf

Storage Techniques

Description

tropicalsparse.storage function is used to apply coo, csr and csc storage techniques on the sparse matrix in Tropical Algebra.

Usage

tropicalsparse.storage(M, store, algebraType)

Arguments

Details

The function tropicalsparse.storage recieves a matrix as first input, storage technique as second input and the type of Tropical Algebra as third input. All the inputs are compulsory. store can be coo, csr and csc. algebraType is used to specify type of Tropical Algebra. This can be minplus or maxplus. For more details about algebraType, see detail section of check.infinityM or check.infinityV. If store is equal to coo then the function returns a list containing three arrays that are row_Indices_COO, col_Indices_COO and values_COO. If store is equal to csc then the function returns a list containing three arrays that are col_Pointer_CSC, row_Indices_CSC and values_CSC. If store is equal to csr then the function returns a list containing three arrays that are row_Pointer_CSR, col_Indices_CSR and values_CSR. These storage techniques are especially designed for sparse matrices and are very helpful and time saving.

Value

Returns a list result that contains three arrays depends upon the store input.

See Also

tropicalsparse.add, tropicalsparse.mv.

Examples

a <- matrix(data = c(2, Inf, Inf, 0, Inf, Inf, Inf, 10, Inf),
nrow = 3, ncol = 3, byrow = TRUE)

tropicalsparse.storage(a, 'coo', 'minplus')

# $row_Indices_COO
# [1] 1 2 3

# $col_Indices_COO
# [1] 1 1 2

# $values_COO
# [1]  2  0 10