Matrix & Vector Functions

CalcTree supports a wide range of matrix and array functions using MathJS syntax. These functions are useful for vector operations, 2D geometry, and working with tabular data.

To create a matrix or vector, use square brackets:

[1, 2, 3]          // 1D vector  
[[1, 2], [3, 4]]   // 2x2 matrix

Construction & Access

Function	Description	CalcTree Example
identity(n)	Identity matrix (n × n)	identity(3) → [[1,0,0],[0,1,0],[0,0,1]]
zeros(m, n)	Matrix of zeros	zeros(2, 3) → [[0,0,0],[0,0,0]]
ones(m, n)	Matrix of ones	ones(2, 2) → [[1,1],[1,1]]
range(start, end [, step])	Create array with range	range(1, 5) → [1,2,3,4]
size(x)	Shape of array or matrix	size([[1,2],[3,4]]) → [2,2]
row(M, i)	Return row at index i	row([[1,2],[3,4]], 1) → [3, 4]
column(M, i)	Return column at index i	column([[1,2],[3,4]], 0) → [1, 3]
count(x)	Count number of elements	count([[1,2],[3,4]]) → 4
diag(x)	Create diagonal matrix or extract diagonal	diag([1,2,3]) → [[1,0,0],[0,2,0],[0,0,3]]

Transformation & Operations

Function	Description	CalcTree Example
transpose(x)	Transpose matrix or vector	transpose([[1,2],[3,4]]) → [[1,3],[2,4]]
ctranspose(x)	Complex transpose + conjugate	ctranspose([[1+2i],[3-4i]]) → [[1-2i, 3+4i]]
flatten(x)	Flatten to 1D array	flatten([[1,2],[3,4]]) → [1,2,3,4]
reshape(x, sizes)	Reshape array	reshape([1,2,3,4], [2,2]) → [[1,2],[3,4]]
squeeze(x)	Remove singleton dimensions	squeeze([[1]]) → 1
resize(x, size [, default])	Resize and pad	resize([1,2], [4], 0) → [1,2,0,0]
rotate(vec, theta)	Rotate 2D vector counter-clockwise	rotate([1, 0], pi/2) → [0, 1]
getMatrixDataType(x)	Type of values in a matrix	getMatrixDataType([[1,2],[3,4]]) → "number"

Vector & Matrix Math

Function	Description	CalcTree Example
dot(a, b)	Dot product (vectors)	dot([2,3], [4,5]) → 23
cross(a, b)	Cross product (3D vectors)	cross([1,0,0], [0,1,0]) → [0,0,1]
norm(x [, p])	Vector or matrix norm	norm([3, 4]) → 5
det(A)	Determinant	det([[1,2],[3,4]]) → -2
inv(A)	Inverse of matrix	inv([[4,7],[2,6]])
trace(A)	Trace (sum of diagonal)	trace([[1,2],[3,4]]) → 5
sqrtm(A)	Matrix square root	sqrtm([[4,0],[0,9]]) → [[2,0],[0,3]]
expm(A)	Matrix exponential	expm([[0,1],[-1,0]])

Signal Transformations

Function	Description	CalcTree Example
fft(x)	Fast Fourier Transform	fft([0,1,0,0]) → complex array
ifft(x)	Inverse FFT	ifft([...]) → original signal

Sorting & Selection

Function	Description	CalcTree Example
sort(x)	Sort 1D array	sort([3,1,2]) → [1,2,3]
partitionSelect(x, k)	k-th order statistic in a 1D array (quickselect)	partitionSelect([3,5,1,2], 1) → 2

Matrix Decomposition (Advanced)

These are available in MathJS, but may have limited or no support in CalcTree yet.

Function	Description
eigs(A)	Eigenvalues & eigenvectors
pinv(A)	Pseudo-inverse
kron(A, B)	Kronecker product
matrixFromRows(...)	Build matrix from row vectors
matrixFromColumns(...)	Build matrix from column vectors

Notes for CalcTree

• Use standard [a, b] and [[a, b], [c, d]] notation for vectors and matrices.

• Most elementwise operations like dotMultiply, dotDivide, map, and reshape are supported.

• Matrix algebra (inv, det, transpose, etc.) can be used for linear system calculations.

• You can pass arrays from tables and use them directly in these functions.

📘 Looking for more functions? CalcTree’s expression engine is powered by MathJS. For a full list of available functions, visit the MathJS Function Reference. Most functions listed there are supported in CalcTree unless otherwise noted.