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Simulation and scientific computing
power-flow-sim
power system load flow and stability
PSS/E, pandapower
System
Techniques · 9
Primitives · 17
power-flow-sim
Wls state estimation
control · medium: Weighted-least-squares grid state estimation with bad-data detection
Ac power flow
embedded · medium: Newton-Raphson AC power flow on the sparse bus admittance matrix to get voltages and line flows
Automatic generation control
embedded · medium: Load-frequency control: area control error integrated and dispatched to generators
Contingency analysis
embedded · medium: N-1 screening: simulate outages with fast DC/AC approximations and flag violations
Optimal power flow
embedded · medium: Minimize generation cost subject to AC/DC power flow and network limits
Fill-reducing ordering
numerics · medium: Permute a sparse symmetric matrix before Cholesky/LU so the factor has few new nonzeros; minimum degree, nested dissection and RCM trade quality, speed and parallelism.
›
Sparse direct solver
numerics · medium: Solve sparse Ax = b exactly by reordering, symbolic analysis, numeric LLᵀ/LU and triangular solves; fill-in, not flops per entry, decides the cost.
›
LU and Cholesky factorization
numerics · low: Factor A = PLU (any square matrix, partial pivoting) or A = LLᵀ (SPD) once in O(n³), then solve each right-hand side in O(n²).
›
Newton root finding
numerics · low: Linearize at the guess and jump to the tangent root; quadratic convergence near a simple root, made robust by brackets (1D) or line search.
›
Sparse matrices (CSR)
numerics · low: Compressed sparse row stores only nonzeros as row pointers, column indices and values; SpMV streams them once, so it is memory-bandwidth bound.
›
Droop control
embedded · low: Frequency/voltage droop: proportional power response that lets inverters share load without communication
Simplex method
optimization · low: Solves linear programs by walking along the edges of the feasible polytope from vertex to vertex, one basis swap (pivot) at a time; the workhorse behind MIP solvers.
›
Synchrophasor estimation
embedded · low: GPS-timed DFT phasor, frequency and ROCOF estimation in PMUs
BFS and DFS
graphs · low: The two basic graph traversals; BFS gives hop distances and levels, DFS gives discovery/finish order for cycles, components and topological order.
›
Union-find
graphs · low: Disjoint-set forest with union by size and path compression; merges sets and answers same-set queries in effectively constant time.
›
Stiff solvers (implicit, BDF)
numerics · low: Implicit steps solve a small nonlinear system so fast decaying modes stay stable at any step size; BDF methods are the stiff-ODE workhorse.
›
Robust statistics
statistics · low: Location and scale estimates (median, MAD, trimmed mean, Huber M-estimator) that stay correct when a minority of the data is garbage.
›
Fixed-rate control loop
embedded · low: Run a controller at an exact period using absolute deadlines and a fixed dt, so jitter never accumulates and the math stays valid.
›
PID controller
robotics · low: Drive a measured value to a setpoint with three terms on the error: proportional, integral, derivative. The default feedback loop for motors, heaters, drones and gimbals.
›
d-ary heap
data-structures · low: Array heap with d children per node (d = 4 typical): half the binary heap's depth, siblings in one cache line, faster priority queues.
›
PRNGs (PCG, xoshiro)
numerics · low: Small, fast, statistically strong non-cryptographic generators: PCG32 and xoshiro256**, with seeding, parallel streams and unbiased ranges.
›
Dma transfers
embedded · low: DMA controllers: descriptors, circular buffers, cache coherence for zero-CPU data movement
PWM generation
embedded · low: A timer's counter, period and compare registers draw the pulse train; preload, dead time and DMA make duty changes glitch-free, shoot-through-free and cheap.
›
+ 2 more techniques
+ 1 more primitives
System
Techniques · 9
Primitives · 17
power-flow-sim
Wls state estimation
control · medium: Weighted-least-squares grid state estimation with bad-data detection
Ac power flow
embedded · medium: Newton-Raphson AC power flow on the sparse bus admittance matrix to get voltages and line flows
Automatic generation control
embedded · medium: Load-frequency control: area control error integrated and dispatched to generators
Contingency analysis
embedded · medium: N-1 screening: simulate outages with fast DC/AC approximations and flag violations
Optimal power flow
embedded · medium: Minimize generation cost subject to AC/DC power flow and network limits
Fill-reducing ordering
numerics · medium: Permute a sparse symmetric matrix before Cholesky/LU so the factor has few new nonzeros; minimum degree, nested dissection and RCM trade quality, speed and parallelism.
›
Sparse direct solver
numerics · medium: Solve sparse Ax = b exactly by reordering, symbolic analysis, numeric LLᵀ/LU and triangular solves; fill-in, not flops per entry, decides the cost.
›
Interior-point method (primal-dual,…
optimization · medium: Follows the central path with Newton steps on the perturbed KKT system, one sparse Cholesky per iteration; Mehrotra's predictor-corrector makes it fast.
›
Graph partitioning
graphs · medium: Split a graph into k balanced parts with few edges between them; multilevel coarsen-partition-refine (METIS, KaHIP) for quality, streaming heuristics (LDG, Fennel) for one-pass scale.
›
LU and Cholesky factorization
numerics · low: Factor A = PLU (any square matrix, partial pivoting) or A = LLᵀ (SPD) once in O(n³), then solve each right-hand side in O(n²).
›
Newton root finding
numerics · low: Linearize at the guess and jump to the tangent root; quadratic convergence near a simple root, made robust by brackets (1D) or line search.
›
Sparse matrices (CSR)
numerics · low: Compressed sparse row stores only nonzeros as row pointers, column indices and values; SpMV streams them once, so it is memory-bandwidth bound.
›
Droop control
embedded · low: Frequency/voltage droop: proportional power response that lets inverters share load without communication
Simplex method
optimization · low: Solves linear programs by walking along the edges of the feasible polytope from vertex to vertex, one basis swap (pivot) at a time; the workhorse behind MIP solvers.
›
Synchrophasor estimation
embedded · low: GPS-timed DFT phasor, frequency and ROCOF estimation in PMUs
BFS and DFS
graphs · low: The two basic graph traversals; BFS gives hop distances and levels, DFS gives discovery/finish order for cycles, components and topological order.
›
Union-find
graphs · low: Disjoint-set forest with union by size and path compression; merges sets and answers same-set queries in effectively constant time.
›
Stiff solvers (implicit, BDF)
numerics · low: Implicit steps solve a small nonlinear system so fast decaying modes stay stable at any step size; BDF methods are the stiff-ODE workhorse.
›
Robust statistics
statistics · low: Location and scale estimates (median, MAD, trimmed mean, Huber M-estimator) that stay correct when a minority of the data is garbage.
›
Fixed-rate control loop
embedded · low: Run a controller at an exact period using absolute deadlines and a fixed dt, so jitter never accumulates and the math stays valid.
›
PID controller
robotics · low: Drive a measured value to a setpoint with three terms on the error: proportional, integral, derivative. The default feedback loop for motors, heaters, drones and gimbals.
›
d-ary heap
data-structures · low: Array heap with d children per node (d = 4 typical): half the binary heap's depth, siblings in one cache line, faster priority queues.
›
PRNGs (PCG, xoshiro)
numerics · low: Small, fast, statistically strong non-cryptographic generators: PCG32 and xoshiro256**, with seeding, parallel streams and unbiased ranges.
›
Dma transfers
embedded · low: DMA controllers: descriptors, circular buffers, cache coherence for zero-CPU data movement
PWM generation
embedded · low: A timer's counter, period and compare registers draw the pulse train; preload, dead time and DMA make duty changes glitch-free, shoot-through-free and cheap.
›
Floating-point error
numerics · low: How IEEE 754 rounding error accumulates and how to contain it: compensated (Kahan/Neumaier) and pairwise summation, error-free transformations with FMA, ULP comparisons.
›
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