Vectors and matrices
These are plain numerical containers, with no lattice and no color: they carry the output of reductions, the contents of AFF and QIO records, and the small dense linear algebra a script does on the side.
vector
A vector is a fixed-length, mutable, one-dimensional array. Indexing is from zero, #v is the length, and writing past the end raises.
vector.int
vector.int(n) --> vector.int
vector.real
vector.real(n) --> vector.real
vector.complex
vector.complex(n) --> vector.complex
local v = vector.real(4)
v[0] = 1.5
print(#v, v[0]) --> 4 1.5
matrix
A matrix is a dense two-dimensional array of reals or complexes, with the linear algebra GSL provides. Indexing is m[{i,j}], from zero.
matrix.real
matrix.real{rows, cols} --> matrix.real
matrix.real(m) --> matrix.real
matrix.complex
matrix.complex{rows, cols} --> matrix.complex
matrix.complex(m) --> matrix.complex
Both kinds have:
| Method | Meaning |
|---|
m:dims() | two numbers: rows, columns | m:transpose() | the transpose | m:trace() | the trace | m:det() | the determinant | m:inverse() | the inverse | m:solve(b) | solves m x = b | m:qr() | the QR decomposition, as two matrices |
A matrix.real additionally has m:symmetric_eigen(), and a matrix.complex has m:conj(), m:adjoin() and m:hermitian_eigen(). Both eigen solvers return the eigenvalues and the matrix of eigenvectors.
Matrices add, subtract and multiply with each other and scale by a number; matrix.complex scales by a complex as well.
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