Scilab/ScicosLab/NSP does not implement (min,+) algebra natively.
In the Julia REPL, type ? and the name of the function to show its documentation and examples. Functions are given in the alphabetical order of ScicosLab functions.
| ScicosLab | Julia | Comment |
|---|
| astarb | astarb | Return the x of the equation x = A x + b |
| / (division) | Base.:(/) | (max,+) division operator on scalar, dense or sparse matrix. |
| full | full, dense, Array | Transform a (max,+) sparse matrix to a (max,+) dense matrix. |
| howard | howardmpeigen | Return eigenvalues and eigenvectors from a sparse matrix using Howard algorithm. |
| inv | Base.inv, Base.:(^,-1) | Compute the inverse of the (max,+) matrix |
| karp | howardmpeigen | Karp algorithm is not implemented since Howard algorithm is faster. |
| LaTeX, show MIME"text/latex" | Output a (max,+) matrix to LaTeX code. |
| # (maxplus) | MP | Create a (max,+) number or dense array or sparse array. |
| & (min) | Base.min | Return the min of two (max,+) scalars or matrix. |
| - (minus) | Base.:(-) | (max,+) minus unary and binary operators on scalar, dense or sparse matrix. |
| mnorm | norm | Compute the norm of a (max,+) dense or sparse matrix. |
| mptrace | tr | Compute the trace of a (max,+) dense or sparse matrix. |
| percent0, %0 | Base.zero, zero, mp0, MaxPlus.ε | Return the (max,+) element zero. |
| percent1, %1 | Base.one, one, mp1,mpe | Return the (max,+) element one. |
| percenteye, %eye | eye | Return the (max,+) identity matrix. |
| mpI | The diagonal elements used for creating (max,+) identity matrix. |
| percentones, %ones | ones | Return the once (max,+) matrix or column vector. |
| percenttop, %top | mptop | Return the min+ element zero. |
| percentzeros, %zeros | spzeros | Return the zero (max,+) sparse matrix or column vector (Julia builtin). |
| zeros | Return the zero (max,+) dense matrix or column vector. |
| + (plus) | Base.:(+) | (max,+) plus operator on scalar, dense or sparse matrix. |
| plus | plus | Compute the (max,+) matrix A^+ |
| plustimes | plustimes | Convert a (max,+) number or matrix to a standard number or matrix (where plus and times operators are the classic operators). |
| ^ (power) | Base.:(^) | Compute the power of a (max,+) number or matrix. |
| Base.show | Display a (max,+) number or sparse or dense matrix. |
| SparseArrays.sparse | Create a (max,+) sparse matrix or convert a (max,+) dense matrix. |
| \ (residu) | Base.:(\) | Return the x of the equation A x = b |
| semihoward | semihoward | Critical cycles |
| star | star | Compute the (max,+) matrix A^* |
| * (times) | Base.:(*) | (max,+) times operator on scalar, dense or sparse matrix. |
| typeof | Base.typeof | Return the type of the (max,+) number. |
| ScicosLab | Julia | Comment |
|---|
| mpsyslin | MPSysLin | Structure holding state matrices of the syslin. In Scilab its a function. |
| LaTeX | Output a (max,+) syslin to a LaTeX formula. |
| simul | mpsimul | Simulation of the (max,+) linear system. |
| explicit | mpexplicit | Conversion of an implicit dynamic linear (max,+) system to an explicit form (where D state matrix is zero'ed). |
| Base.show | Display the (max,+) syslin. |
| plus, + | Base.:(+) | (max,+) plus operator, or product with a (max,+) scalar or (max,+) matrix. |
| times, * | Base.:(*) | Series composition. |
| | Base.:( |
| /. | Base.:(/) | Feedback composition. |
| [;] | Base.:vcat, [;] | Inputs in common and concatenation of outputs. |
| [,] | Base.:hcat, [,] | Concatenation of inputs and addition of outputs. |
| typeof | typeof | Return the type of the (max,+) syslin. |
| ScicosLab | Julia | Comment |
|---|
| flowshop | | Flowshop maxplus linear system builder. |
| LaTeX | Generate the flowshop graph as a LaTeX formula. |
| flowshop_graph | | Flowshop graph builder. |
| flowshop_simu | | Maxplus linear system simulation. |
| saturation_graph | | Saturation graph. |
| showcrgraph | | Flowshop critical graph. |
| strongconnexgraph | | Strong connected component extracting. |
| Function | ScicosLab | NSP | Julia | Comment |
|---|
| length(mpzeros(2,2)) | 2 | 4 | 4 | 4 is the correct answer |
| norm, trace, min | not implemented | not implemented | implemented | |
| MP^(-x) | not implemented | not implemented | implemented | Negative power (x > 0) |