Calculations

Calculations

• Number to text

  num2str(x): a short text form of a number.

  whole numbers in full; otherwise max(ceil(log₁₀|x|), 1) + 4 significant digits

  CraftScript core math functions cs-lib-core.js

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• Text to number

  str2double(s): reads a number from text.

  Number(text) for text matching a decimal pattern, else NaN

  CraftScript core math functions cs-lib-core.js

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• Conversion to single precision

  single(A): each value rounded to the nearest 32-bit floating-point number.

  x ← fround(x)

  CraftScript number type conversions cs-lib-core.js

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  32-bit in part

• Conversion to whole-number types

  int8, int16, int32, int64 and the unsigned forms: each value rounded to a whole number.

  x ← round(x); NaN → 0

  CraftScript number type conversions cs-lib-core.js

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• Read an STL file

  Reads the triangles of a binary or text STL file into a model's node coordinates.

  CraftScript file readers and writers cs-lib-io.js

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• Weld STL vertices

  Merges the repeated corners of an STL triangle list into shared nodes.

  CraftScript file readers and writers cs-lib-io.js

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  Exact

• Write a binary STL file

  Writes a triangle surface with a unit normal per triangle.

  n = (b − a) × (c − a) ÷ |(b − a) × (c − a)|

  CraftScript file readers and writers cs-lib-io.js

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• Write an OBJ file

  Writes node coordinates and triangle corner numbers as text.

  CraftScript file readers and writers cs-lib-io.js

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• Read an OBJ file

  Reads vertex lines and face lines into node coordinates and triangles.

  CraftScript file readers and writers cs-lib-io.js

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• Read a CSV file

  Reads a table of numbers into a matrix.

  CraftScript file readers and writers cs-lib-io.js

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• Write a CSV file

  Writes a matrix as rows of text.

  CraftScript file readers and writers cs-lib-io.js

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• Values to JSON

  Prepares a script value for a JSON file.

  CraftScript file readers and writers cs-lib-io.js

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• Read an NPY file

  Reads a NumPy array file into a tensor.

  CraftScript file readers and writers cs-lib-io.js

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• Write an NPY file

  Writes a tensor as a NumPy array file.

  CraftScript file readers and writers cs-lib-io.js

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• Write a tensor to HDF5

  Writes a tensor as an HDF5 dataset in row-major order.

  CraftScript file readers and writers cs-lib-io.js

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• Read an HDF5 dataset

  Reads a dataset into a number, a logical value or a tensor.

  CraftScript file readers and writers cs-lib-io.js

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• Plot data as CSV

  Writes the x and y values of a script plot as a CSV file.

  CraftScript file readers and writers cs-plot-export.js

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• One CSV cell

  Turns one value into the text of a CSV cell.

  CraftScript file readers and writers cs-plot-export.js

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• Matrix product

  The product of two dense matrices.

  C_ij = Σ_p A_ip × B_pj

  CraftScript dense linear algebra cs-lib-linalg.js

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• LU factorization

  Factors a square matrix with row exchanges.

  P A = L U

  CraftScript dense linear algebra cs-lib-linalg.js

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• Solve with an LU factorization

  Forward and back substitution for one or more right-hand sides.

  CraftScript dense linear algebra cs-lib-linalg.js

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• Cholesky factorization

  Factors a symmetric positive definite matrix as RᵀR.

  R_jj = √(A_jj − Σ_k R_kj²)

  CraftScript dense linear algebra cs-lib-linalg.js

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• Solve with a Cholesky factorization

  Solves RᵀR X = B by two triangular substitutions.

  CraftScript dense linear algebra cs-lib-linalg.js

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• QR factorization

  Factors a matrix as an orthogonal matrix times an upper triangular one.

  H = I − β v vᵀ, β = 2 ÷ (vᵀv)

  CraftScript dense linear algebra cs-lib-linalg.js

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• Symmetric eigenvalues and vectors

  All eigenvalues, and optionally eigenvectors, of a symmetric matrix, in ascending order.

  CraftScript dense linear algebra cs-lib-linalg.js

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• Generalized symmetric eigenproblem

  Eigenvalues and vectors of K v = λ M v for symmetric K and positive definite M.

  M = RᵀR; C = R⁻ᵀ K R⁻¹; C y = λ y; v = R⁻¹ y

  CraftScript dense linear algebra cs-lib-linalg.js

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• Choice of solver for A x = b

  Picks the method for the backslash operator and linsolve, for dense and sparse matrices.

  CraftScript dense linear algebra cs-lib-linalg.js

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• Matrix inverse

  The inverse of a square matrix.

  CraftScript dense linear algebra cs-lib-linalg.js

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• Determinant

  The determinant of a square matrix.

  det A = sign × Π U_ii

  CraftScript dense linear algebra cs-lib-linalg.js

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• Vector and matrix norms

  The 1, 2, infinity, p and Frobenius norms.

  ‖x‖₂ = √(Σ xᵢ²); ‖A‖₂ = √(λ_max(AᵀA))

  CraftScript dense linear algebra cs-lib-linalg.js

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• Condition number

  The 2-norm condition number of a matrix.

  cond A = √(λ_max(AᵀA) ÷ λ_min(AᵀA))

  CraftScript dense linear algebra cs-lib-linalg.js

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• Sparse matrix from triplets

  Builds a sparse matrix from row, column and value lists, adding values that share a place.

  CraftScript sparse matrices and direct factorization cs-lib-linalg.js

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• Weighted sum of two sparse matrices

  a·A + b·B for matrices of the same size.

  C_ij = a × A_ij + b × B_ij

  CraftScript sparse matrices and direct factorization cs-lib-linalg.js

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• Sparse matrix times vector

  The product of a sparse matrix and a vector.

  y_r = Σ_k val_k × x_col(k)

  CraftScript sparse matrices and direct factorization cs-lib-linalg.js

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• Sparse matrix times sparse matrix

  The product of two sparse matrices.

  CraftScript sparse matrices and direct factorization cs-lib-linalg.js

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• Symmetry test

  Decides whether a sparse matrix is symmetric, which selects the solver.

  max |S − Sᵀ| ≤ 1e-10 × max |S|

  CraftScript sparse matrices and direct factorization cs-lib-linalg.js

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• Envelope size after reordering

  Counts the stored entries and the work of the skyline factorization for an ordering.

  entries = Σ wᵢ; work = Σ wᵢ² ÷ 2, wᵢ = i − firstᵢ + 1

  CraftScript sparse matrices and direct factorization cs-lib-linalg.js

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• Envelope Cholesky factorization and solve

  Factors a symmetric positive definite sparse matrix and solves with the factor.

  L_ij = (A_ij − Σ_k L_ik L_jk) ÷ L_jj; L_ii = √(A_ii − Σ_k L_ik²)

  CraftScript sparse matrices and direct factorization cs-lib-linalg.js

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• Assembly of element matrices

  Adds weighted element matrices into one sparse matrix.

  K = Σ_e w_e × P_eᵀ Ke P_e

  CraftScript sparse matrices and direct factorization cs-lib-linalg.js

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• Preconditioned conjugate gradients

  Solves a symmetric positive definite sparse system with the pcg builtin.

  CraftScript iterative solvers and sparse eigenvalues cs-lib-linalg.js

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• Jacobi preconditioner

  Scales a residual by the inverse of the matrix diagonal.

  zᵢ = rᵢ ÷ A_ii

  CraftScript iterative solvers and sparse eigenvalues cs-lib-linalg.js

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• Incomplete LU factorization

  The ILU(0) preconditioner used by BiCGSTAB.

  CraftScript iterative solvers and sparse eigenvalues cs-lib-linalg.js

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• BiCGSTAB

  Solves a general sparse system by iteration.

  stop when ‖r‖ ÷ ‖b‖ < tol

  CraftScript iterative solvers and sparse eigenvalues cs-lib-linalg.js

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• Rigid-body vectors for AMG

  Builds the translation and rotation vectors the multigrid preconditioner uses.

  rotation about the centroid: (−(y − c_y), x − c_x)

  CraftScript iterative solvers and sparse eigenvalues cs-lib-linalg.js

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• Smallest eigenvalues of a sparse problem

  The k smallest eigenvalues and vectors of K v = λ M v.

  stop when |λⱼ − λⱼ(previous)| ≤ tol × |λⱼ| for every j ≤ k

  CraftScript iterative solvers and sparse eigenvalues cs-lib-linalg.js

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• One operator on two numbers

  Adds, subtracts, multiplies, divides, compares or takes the remainder of two numbers.

  mod(x, y) = x − ⌊x ÷ y⌋ × y; rem(x, y) = x − trunc(x ÷ y) × y

  CraftScript array arithmetic cs-tensor.js

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• Hypotenuse

  √(x² + y²) for two numbers.

  m × √((x ÷ m)² + (y ÷ m)²), m = max(|x|, |y|)

  CraftScript array arithmetic cs-tensor.js

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• Power

  x raised to the power y.

  CraftScript array arithmetic cs-tensor.js

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• Elementwise loops

  Applies an operator to every element of one or two arrays.

  CraftScript array arithmetic cs-tensor.js

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• Matrix product

  The product of two dense matrices in a script expression.

  C_ij = Σ_p A_ip × B_pj

  CraftScript array arithmetic cs-tensor.js

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