doc: 完善文档和例程

README.md

+# SOLVER-EMBEDDED Model Examples
+
+This repository provides small model/example suites for an external solver, organized by model type:
+
+- [leq/](leq/): linear equation systems (Ax = b) examples
+- [neq/](neq/): nonlinear equation systems f(x)=0 examples
+- [nlp/](nlp/): nonlinear programming (NLP) examples (includes AC-OPF benchmarks)
+- [milp/](milp/): mixed-integer linear programming (MILP) examples
+
+Each folder contains paired `*.model` / `*.solution` files:
+
+- `*.model` is the input model text consumed by the solver
+- `*.solution` is the reference (ground-truth) result for validation
+
+All other top-level folders are currently **work in progress (WIP)**.
+
+## Other directories (WIP)
+
+The following top-level directories are under active development and are not part of the stable example suites yet:
+
+- [data/](data/)
+- [index/](index/)
+- [rsdss/](rsdss/)
+- [rspower/](rspower/)
+- [rustscript/](rustscript/)
+- [target/](target/)
+
+## CLI usage (model selection)
+
+The solver CLI supports selecting **at most one** model input at a time:
+
+- `./solver_embedded --nlp <FILE or String>`
+- `./solver_embedded --milp <FILE or String>`
+- `./solver_embedded --leq <FILE or String>`
+- `./solver_embedded --neq <FILE or String>`
+
+Inputs can be provided either as:
+
+- a file path, or
+- an inline string
+
+### Splitting rules (common)
+
+- If the input contains `;` -> split by `;`
+- Otherwise -> split by lines
+
+## Model formats (summary)
+
+### NLP (`--nlp`)
+
+- Overall:
+  - `<Objective>;`
+  - `<Constraint1>;`
+  - `...`
+  - `<VariableBounds>;` (**must be last**)
+- Constraints use range form: `<expr>:[lower/upper]`
+- Variables use bounds/initial value: `xi:[lower/upper/init]`
+
+### MILP (`--milp`)
+
+- Overall:
+  - `<Objective>;`
+  - `<Constraint1>;`
+  - `...`
+  - `<VariableTypes>;` (**must be last**)
+- Constraints use boolean comparisons: `<=`, `>=`, `==`
+- Variable types (last line): `x1:1, x2:2, ...`
+  - `1` binary, `2` integer, `3` real/continuous
+
+### LEQ (`--leq`)
+
+- Overall:
+  - `<Eq1>;`
+  - `<Eq2>;`
+  - `...`
+  - `<Variables>;` (**must be last**)
+- Each equation is interpreted as `<expr> = 0`
+- Variables (last line): `x1, x2, x3, ...`
+
+### NEQ (`--neq`)
+
+- Same overall format as `--leq`, but nonlinear:
+  - equations are interpreted as `<expr> = 0`
+  - variables are listed on the last line
+
+## Where to start
+
+- LEQ toy examples: [leq/examples/basic/](leq/examples/basic/)
+- NEQ toy examples: [neq/examples/basic/](neq/examples/basic/)
+- NLP toy examples: [nlp/examples/basic/](nlp/examples/basic/)
+- MILP toy examples: [milp/examples/basic/](milp/examples/basic/)

leq/README.md

+# LEQ Examples (Linear Equations)
+
+This folder contains **linear-equation (LEQ)** toy benchmarks.
+
+The purpose is to provide very small, solver-friendly instances so an external program can quickly validate:
+
+- parsing of `*.model`
+- solving a linear system
+- matching the reference `*.solution`
+
+## What the examples mean
+
+Each example is a reproducible linear-equations benchmark:
+
+- **Input**: a `*.model` file describing a system of equations (typically linear)
+- **Reference output**: a matching `*.solution` file containing a known-correct solution vector
+
+## `.model` format
+
+A `*.model` file is plain text:
+
+- one equation per line, terminated by `;`
+- the last line is the **variable list** (comma-separated)
+  - optional initial guesses can be provided using `name:value` (e.g., `x:0`)
+
+The variable list order defines the order of values in the `.solution` file.
+
+## `.solution` format
+
+A `*.solution` file contains one numeric value per line, ordered exactly as the variable list in the corresponding `.model`.
+
+## Directory layout
+
+- [leq/examples/basic/](leq/examples/basic/): simple LEQ toy problems
+
+## How to use this
+
+Run your solver in “nonlinear equations” mode and pass the model file, for example:
+
+- `solver_embedded --neq path/to/case5_pf_polar.model`
+
+Then compare your solver’s solution vector against `case5_pf_polar.solution`.
+
+> Note: the exact CLI flag name depends on your solver/application (this repo only defines the `*.model/*.solution` formats and the examples).
+
+

leq/examples/basic/linear_2x2.model

+x+y-3;
+2*x-y;
+x:0,y:0

leq/examples/basic/linear_2x2.solution

+Variable values:
+x: 1
+y: 2

leq/examples/basic/linear_3x3.model

+x+y+z-6;
+2*x-y+z-3;
+-x+2*y+3*z-14;
+x:0,y:0,z:0

leq/examples/basic/linear_3x3.solution

+Variable values:
+x: 0.5555555555555555
+y: 1.7777777777777777
+z: 3.6666666666666665

leq/examples/basic/linear_single.model

+2*x-6;
+x:0

leq/examples/basic/linear_single.solution

+Variable values:
+x: 3

milp/README.md

+# MILP Examples (Mixed-Integer Linear Programming)
+
+This folder contains **MILP** benchmark instances.
+
+The main purpose is to provide small, solver-friendly examples so an external program can validate its MILP pipeline:
+
+- `*.model`: the MILP instance (objective + constraints + variable type declarations)
+- `*.solution`: the **reference (ground-truth) solution** for that model
+
+These examples are intended for automated regression checks and solver benchmarking. Detailed format/CLI usage is documented elsewhere.
+
+## Directory layout
+
+- [milp/examples/basic/](milp/examples/basic/): small MILP toy problems
+
+## `.solution` format (reference solution)
+
+A `*.solution` file contains one numeric value per line.
+
+- The values are ordered **exactly as the variable list on the last line of the corresponding `.model` file**.
+
+## How to use this
+
+Run your solver in “nonlinear equations” mode and pass the model file, for example:
+
+- `solver_embedded --neq path/to/case5_pf_polar.model`
+
+Then compare your solver’s solution vector against `case5_pf_polar.solution`.
+
+> Note: the exact CLI flag name depends on your solver/application (this repo only defines the `*.model/*.solution` formats and the examples).
+

milp/examples/basic/assignment_2x2.model

+1*x11 + 3*x12 + 2*x21 + 1*x22;
+x11 + x12 == 1;
+x21 + x22 == 1;
+x11 + x21 == 1;
+x12 + x22 == 1;
+x11:1, x12:1, x21:1, x22:1;

milp/examples/basic/assignment_2x2.solution

+Reading model from file: milp/examples/basic/assignment_2x2.model
+Constructing model...
+Model constructed. Solving...
+Solution found.
+Objective value: 2
+Iteration count: 0
+Variable values:
+x11: 1
+x12: 0
+x21: 0
+x22: 1

milp/examples/basic/knapsack_3.model

+max(3*x1 + 2*x2 + 4*x3);
+2*x1 + 1*x2 + 3*x3 <= 4;
+x1:1, x2:1, x3:1;

milp/examples/basic/knapsack_3.solution

+Reading model from file: milp/examples/basic/knapsack_3.model
+Constructing model...
+Model constructed. Solving...
+Solution found.
+Objective value: 6
+Iteration count: 0
+Variable values:
+x1: 0
+x2: 1
+x3: 1

milp/examples/basic/mixed_types_small.model

+min(x + 2*y + 0.5*z);
+x + y >= 3;
+x - z == 1;
+y <= 4;
+x >= 0;
+y >= 0;
+z >= 0;
+x:2, y:2, z:3;

milp/examples/basic/mixed_types_small.solution

+Reading model from file: milp/examples/basic/mixed_types_small.model
+Constructing model...
+Model constructed. Solving...
+Solution found.
+Objective value: 4
+Iteration count: 0
+Variable values:
+x: 3
+y: -0
+z: 2

neq/README.md

+
+# NEQ Examples (AC Power Flow as Nonlinear Equations)
+
+This folder contains **nonlinear-equation (NEQ)** benchmark instances for **AC power flow (PF)**.
+
+The underlying test cases are based on **IEEE/MATPOWER** networks. The repository ships ready-to-use examples; you typically only need to point your external solver at a `*.model` file and validate against the matching `*.solution`.
+
+## What the examples mean (main point)
+
+Each example is a reproducible PF-NEQ benchmark:
+
+- **Input**: a `*.model` file describing a system of nonlinear equations $F(x)=0$
+- **Reference output**: a matching `*.solution` file containing a known-correct solution vector for that model
+
+Your external solver reads the `.model`, solves the nonlinear system, then compares its solution against the `.solution`.
+
+## Directory layout
+
+- [neq/examples/](neq/examples/)
+	- `pf_polar/`: power-flow equations in **polar** voltage coordinates
+	- `basic/`: small, solver-friendly NEQ toy problems (no power-system context)
+
+## Naming convention
+
+- Polar PF
+	- `pf_polar/<case>_pf_polar.model`
+	- `pf_polar/<case>_pf_polar.solution`
+
+- Basic NEQ
+	- `basic/<name>.model`
+	- `basic/<name>.solution`
+
+## `.model` format (NEQ model)
+
+A `*.model` file is plain text and typically contains:
+
+- A list of equations, one per line, each terminated by `;`
+- A final **variable list line**, where variables are comma-separated
+
+### Variable list and initial guesses
+
+The final line lists the variables (and optional initial guesses) in the exact order used by the solution vector.
+
+- Variables may optionally carry an initial guess using `name:value` (e.g., `V1:1`)
+- Variables without `:value` have no explicit initial guess in the file
+
+Example pattern:
+
+- `V1:1,V2:1,...,THETA1,THETA2,...,QG1,QG2,...,PG_balancenode`
+
+## `.solution` format (reference solution)
+
+A `*.solution` file contains one numeric value per line.
+
+- The values are ordered **exactly as the variable list on the last line of the corresponding `.model` file**.
+
+## How to use this
+
+Run your solver in “nonlinear equations” mode and pass the model file, for example:
+
+- `solver_embedded --neq path/to/case5_pf_polar.model`
+
+Then compare your solver’s solution vector against `case5_pf_polar.solution`.
+
+> Note: the exact CLI flag name depends on your solver/application (this repo only defines the `*.model/*.solution` formats and the examples).

neq/examples/basic/circle_line.model

+x^2+y^2-1;
+y-x;
+x:0.7,y:0.7

neq/examples/basic/circle_line.solution

+Variable values:
+x: 0.7071067811865476
+y: 0.7071067811865476

neq/examples/basic/linear_2x2.model

+x+y-3;
+2*x-y;
+x,y

neq/examples/basic/linear_2x2.solution

+Variable values:
+x: 1
+y: 2

neq/examples/basic/sqrt2.model

+x^2-2;
+x:1.414
\ No newline at end of file

neq/examples/basic/sqrt2.solution

+Variable values:
+x: 1.4142135623730951

neq/examples/basic/trig_single.model

+sin(x)-0.5;
+x:0.5

neq/examples/basic/trig_single.solution

+Variable values:
+x: 0.5235987755982988

neq/examples/pf_polar/case5_pf_polar.model

+2.10000000-0.00000000-V1*(V1*(22.25068569)+V2*(-3.52348402*cos(THETA1-THETA2)+35.23484021*sin(THETA1-THETA2))+V4*(-3.25690464*cos(THETA1-THETA4)+32.56904638*sin(THETA1-THETA4))+V5*(-15.47029703*cos(THETA1-THETA5)+154.70297030*sin(THETA1-THETA5)));
+0.00000000-3.00000000-V2*(V1*(-3.52348402*cos(THETA2-THETA1)+35.23484021*sin(THETA2-THETA1))+V2*(12.69106745)+V3*(-9.16758343*cos(THETA2-THETA3)+91.67583425*sin(THETA2-THETA3)));
+3.23490000-3.00000000-V3*(V2*(-9.16758343*cos(THETA3-THETA2)+91.67583425*sin(THETA3-THETA2))+V3*(12.50125013)+V4*(-3.33366670*cos(THETA3-THETA4)+33.33666700*sin(THETA3-THETA4)));
+PG_balancenode-4.00000000-V4*(V1*(-3.25690464*cos(THETA4-THETA1)+32.56904638*sin(THETA4-THETA1))+V3*(-3.33366670*cos(THETA4-THETA3)+33.33666700*sin(THETA4-THETA3))+V4*(9.92423804)+V5*(-3.33366670*cos(THETA4-THETA5)+33.33666700*sin(THETA4-THETA5)));
+4.66510000-0.00000000-V5*(V1*(-15.47029703*cos(THETA5-THETA1)+154.70297030*sin(THETA5-THETA1))+V4*(-3.33366670*cos(THETA5-THETA4)+33.33666700*sin(THETA5-THETA4))+V5*(18.80396373));
+QG1+QG2-0.00000000-V1*(V1*(--222.48437689)+V2*(-3.52348402*sin(THETA1-THETA2)-35.23484021*cos(THETA1-THETA2))+V4*(-3.25690464*sin(THETA1-THETA4)-32.56904638*cos(THETA1-THETA4))+V5*(-15.47029703*sin(THETA1-THETA5)-154.70297030*cos(THETA1-THETA5)));
+-0.98610000-V2*(V1*(-3.52348402*sin(THETA2-THETA1)-35.23484021*cos(THETA2-THETA1))+V2*(--126.89785446)+V3*(-9.16758343*sin(THETA2-THETA3)-91.67583425*cos(THETA2-THETA3)));
+QG3-0.98610000-V3*(V2*(-9.16758343*sin(THETA3-THETA2)-91.67583425*cos(THETA3-THETA2))+V3*(--124.99987125)+V4*(-3.33366670*sin(THETA3-THETA4)-33.33666700*cos(THETA3-THETA4)));
+QG4-1.31470000-V4*(V1*(-3.25690464*sin(THETA4-THETA1)-32.56904638*cos(THETA4-THETA1))+V3*(-3.33366670*sin(THETA4-THETA3)-33.33666700*cos(THETA4-THETA3))+V4*(--99.23235038)+V5*(-3.33366670*sin(THETA4-THETA5)-33.33666700*cos(THETA4-THETA5)));
+QG5-0.00000000-V5*(V1*(-15.47029703*sin(THETA5-THETA1)-154.70297030*cos(THETA5-THETA1))+V4*(-3.33366670*sin(THETA5-THETA4)-33.33666700*cos(THETA5-THETA4))+V5*(--188.02063730));
+V1-1.00000000;
+V3-1.00000000;
+V4-1.00000000;
+V5-1.00000000;
+THETA4;
+QG2-4.25*QG1;
+V1:1,V2:1,V3:1,V4:1,V5:1,THETA1,THETA2,THETA3,THETA4,THETA5,QG1,QG2,QG3,QG4,QG5,PG_balancenode
\ No newline at end of file

neq/examples/pf_polar/case5_pf_polar.solution

+Variable values:
+V1: 1
+V2: 0.9892612371183941
+V3: 1
+V4: 1
+V5: 1
+THETA1: 0.05713092450763908
+THETA2: -0.013251748935894637
+THETA3: -0.008591534693000804
+THETA4: 0
+THETA5: 0.07176847990433495
+QG1: 0.058524114048747106
+QG2: 0.2487274847071752
+QG3: 1.9465472018681285
+QG4: 1.841229301609696
+QG5: -0.38209623444663354
+PG_balancenode: 0.05027180043443861

nlp/README.md

+# NLP Examples (AC Optimal Power Flow)
+
+This folder provides **AC Optimal Power Flow (AC-OPF)** benchmark instances written as **Nonlinear Programming (NLP)** models in two coordinate systems:
+
+- **Polar**: voltage state variables are $V$ and $\theta$.
+- **Rectangular**: voltage state variables are $e$ and $f$ (i.e., $V\cos\theta$ and $V\sin\theta$).
+
+The underlying cases come from **IEEE test systems / MATPOWER**. This repo already ships ready-to-use `*.model/*.solution` examples. **MATLAB** (with MATPOWER; IPOPT used by MATPOWER OPF) is only needed if you want to regenerate or add new examples.
+
+The purpose of these examples is:
+
+- `*.model`: input for an **external solver** (e.g., via a `--nlp` flag)
+- `*.solution`: the **reference (ground-truth) solution** for that model, used to validate your solver
+
+## What the examples mean (main point)
+
+Each example is a reproducible OPF-NLP benchmark:
+
+- **Input**: a `*.model` file
+- **Reference output**: a matching `*.solution` file
+
+Your solver reads the `.model`, solves it, then you compare your solver’s objective/variables against the `.solution`.
+
+## `.model` (model file) and variable definitions
+
+`*.model` is a plain-text NLP description:
+
+1. **Line 1**: objective function (typically a polynomial cost in generator active powers `PGk`)
+2. **Last line**: variable definitions with bounds and an initial value, written like: `PG1:[lb/ub/x0]`
+
+Variables:
+
+- Polar: `PGk, QGk, Vi, THETAi`
+  - `Vi`: bus voltage magnitude
+  - `THETAi`: bus voltage angle (radians)
+- Rectangular: `PGk, QGk, ei, fi`
+  - `ei = Vi*cos(THETAi)`
+  - `fi = Vi*sin(THETAi)`
+
+## `.solution` (reference solution)
+
+`*.solution` is the reference answer for the corresponding `.model`:
+
+1. Line 1: optimal objective value
+2. Remaining lines: optimal variable values, written one value per line, in a fixed order (consistent with the generator that produced the files)
+
+## Directory layout
+
+- [nlp/examples/](nlp/examples/)
+  - `opf_polar/`: paired polar OPF `*.model/*.solution`
+  - `opf_rectangular/`: paired rectangular OPF `*.model/*.solution`
+  - `basic/`: small, solver-friendly NLP toy problems (no power-system context)
+
+## Naming convention
+
+- Polar
+  - `opf_polar/<case>_opf_polar.model`
+  - `opf_polar/<case>_opf_polar.solution`
+- Rectangular
+  - `opf_rectangular/<case>_opf_rectangular.model`
+  - `opf_rectangular/<case>_opf_rectangular.solution`
+
+- Basic NLP
+  - `basic/<name>.model`
+  - `basic/<name>.solution`
+
+## How to use this
+
+Run your solver in “nonlinear equations” mode and pass the model file, for example:
+
+- `solver_embedded --neq path/to/case5_pf_polar.model`
+
+Then compare your solver’s solution vector against `case5_pf_polar.solution`.
+
+> Note: the exact CLI flag name depends on your solver/application (this repo only defines the `*.model/*.solution` formats and the examples).
+

nlp/examples/basic/bound_only.model

+x^2
+x:[1/3/2]

nlp/examples/basic/bound_only.solution

+Objective value: 0.9999999800113316
+Variable values:
+x: 0.9999999900056658

nlp/examples/basic/linear_obj_box.model

+x+y
+x:[0/1/0.2],y:[0/1/0.8]

nlp/examples/basic/linear_obj_box.solution

+Objective value: -0.00000001998010154167314
+Variable values:
+x: -0.000000009990041325677582
+y: -0.000000009990060215995557

nlp/examples/basic/quad_eq_constraint.model

+x^2+y^2
+x+y-1:[0/0]
+x:[-10/10/0],y:[-10/10/0]

nlp/examples/basic/quad_eq_constraint.solution

+Objective value: 0.5
+Variable values:
+x: 0.5
+y: 0.5

nlp/examples/basic/quad_unconstrained.model

+(x-1)^2+(y+2)^2
+x:[-10/10/0],y:[-10/10/0]

nlp/examples/basic/quad_unconstrained.solution

+Objective value: 0.00000000000000000000000031936310214511156
+Variable values:
+x: 0.9999999999997539
+y: -1.9999999999994913

nlp/examples/opf_polar/case118_opf_polar.model

+100.00000000*PG1^2+4000.00000000*PG1+100.00000000*PG2^2+4000.00000000*PG2+100.00000000*PG3^2+4000.00000000*PG3+100.00000000*PG4^2+4000.00000000*PG4+222.22222200*PG5^2+2000.00000000*PG5+1176.47059000*PG6^2+2000.00000000*PG6+100.00000000*PG7^2+4000.00000000*PG7+100.00000000*PG8^2+4000.00000000*PG8+100.00000000*PG9^2+4000.00000000*PG9+100.00000000*PG10^2+4000.00000000*PG10+454.54545500*PG11^2+2000.00000000*PG11+318.47133800*PG12^2+2000.00000000*PG12+100.00000000*PG13^2+4000.00000000*PG13+14285.71430000*PG14^2+2000.00000000*PG14+100.00000000*PG15^2+4000.00000000*PG15+100.00000000*PG16^2+4000.00000000*PG16+100.00000000*PG17^2+4000.00000000*PG17+100.00000000*PG18^2+4000.00000000*PG18+100.00000000*PG19^2+4000.00000000*PG19+5263.15789000*PG20^2+2000.00000000*PG20+490.19607800*PG21^2+2000.00000000*PG21+2083.33333000*PG22^2+2000.00000000*PG22+100.00000000*PG23^2+4000.00000000*PG23+100.00000000*PG24^2+4000.00000000*PG24+645.16129000*PG25^2+2000.00000000*PG25+625.00000000*PG26^2+2000.00000000*PG26+100.00000000*PG27^2+4000.00000000*PG27+255.75447600*PG28^2+2000.00000000*PG28+255.10204100*PG29^2+2000.00000000*PG29+193.64833500*PG30^2+2000.00000000*PG30+100.00000000*PG31^2+4000.00000000*PG31+100.00000000*PG32^2+4000.00000000*PG32+100.00000000*PG33^2+4000.00000000*PG33+100.00000000*PG34^2+4000.00000000*PG34+100.00000000*PG35^2+4000.00000000*PG35+100.00000000*PG36^2+4000.00000000*PG36+209.64360600*PG37^2+2000.00000000*PG37+100.00000000*PG38^2+4000.00000000*PG38+25000.00000000*PG39^2+2000.00000000*PG39+164.74464600*PG40^2+2000.00000000*PG40+100.00000000*PG41^2+4000.00000000*PG41+100.00000000*PG42^2+4000.00000000*PG42+100.00000000*PG43^2+4000.00000000*PG43+100.00000000*PG44^2+4000.00000000*PG44+396.82539700*PG45^2+2000.00000000*PG45+2500.00000000*PG46^2+2000.00000000*PG46+100.00000000*PG47^2+4000.00000000*PG47+100.00000000*PG48^2+4000.00000000*PG48+100.00000000*PG49^2+4000.00000000*PG49+100.00000000*PG50^2+4000.00000000*PG50+2777.77778000*PG51^2+2000.00000000*PG51+100.00000000*PG52^2+4000.00000000*PG52+100.00000000*PG53^2+4000.00000000*PG53+100.00000000*PG54^2+4000.00000000*PG54
+PG1-0.51000000-V1*(V1*(9.34796078)+V2*(-2.78030115*cos(THETA1-THETA2)+9.16673549*sin(THETA1-THETA2))+V3*(-6.56765962*cos(THETA1-THETA3)+21.58672620*sin(THETA1-THETA3))):[0/0]
+-0.20000000-V2*(V1*(-2.78030115*cos(THETA2-THETA1)+9.16673549*sin(THETA2-THETA1))+V2*(7.29257720)+V12*(-4.51227605*cos(THETA2-THETA12)+14.86396815*sin(THETA2-THETA12))):[0/0]
+-0.39000000-V3*(V1*(-6.56765962*cos(THETA3-THETA1)+21.58672620*sin(THETA3-THETA1))+V3*(10.26796519)+V5*(-1.96818080*cos(THETA3-THETA5)+8.82006336*sin(THETA3-THETA5))+V12*(-1.73212476*cos(THETA3-THETA12)+5.72603226*sin(THETA3-THETA12))):[0/0]
+PG2-0.39000000-V4*(V4*(30.39834322)+V5*(-26.35598550*cos(THETA4-THETA5)+119.50043427*sin(THETA4-THETA5))+V11*(-4.04235772*cos(THETA4-THETA11)+13.30690005*sin(THETA4-THETA11))):[0/0]
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A24:[-3.14159000/3.14159000/0.41338777],THETA25:[-3.14159000/3.14159000/0.53307697],THETA26:[-3.14159000/3.14159000/0.56136820],THETA27:[-3.14159000/3.14159000/0.34634317],THETA28:[-3.14159000/3.14159000/0.32207388],THETA29:[-3.14159000/3.14159000/0.30912031],THETA30:[-3.14159000/3.14159000/0.40106279],THETA31:[-3.14159000/3.14159000/0.31165268],THETA32:[-3.14159000/3.14159000/0.33903989],THETA33:[-3.14159000/3.14159000/0.29175415],THETA34:[-3.14159000/3.14159000/0.30210930],THETA35:[-3.14159000/3.14159000/0.29625931],THETA36:[-3.14159000/3.14159000/0.29646799],THETA37:[-3.14159000/3.14159000/0.30913087],THETA38:[-3.14159000/3.14159000/0.37142993],THETA39:[-3.14159000/3.14159000/0.27975416],THETA40:[-3.14159000/3.14159000/0.27627294],THETA41:[-3.14159000/3.14159000/0.26874801],THETA42:[-3.14159000/3.14159000/0.29142344],THETA43:[-3.14159000/3.14159000/0.28957807],THETA44:[-3.14159000/3.14159000/0.31126585],THETA45:[-3.14159000/3.14159000/0.33448022],THETA46:[-3.14159000/3.14159000/0.37501490],THETA47:[-3.14159000/3.14159000/0.40707663],THETA48:[-3.14159000/3.14159000/0.39965145],THETA49:[-3.14159000/3.14159000/0.41675548],THETA50:[-3.14159000/3.14159000/0.38525599],THETA51:[-3.14159000/3.14159000/0.34578277],THETA52:[-3.14159000/3.14159000/0.33123488],THETA53:[-3.14159000/3.14159000/0.31809992],THETA54:[-3.14159000/3.14159000/0.33344598],THETA55:[-3.14159000/3.14159000/0.33237682],THETA56:[-3.14159000/3.14159000/0.33336168],THETA57:[-3.14159000/3.14159000/0.34888028],THETA58:[-3.14159000/3.14159000/0.33585950],THETA59:[-3.14159000/3.14159000/0.37881527],THETA60:[-3.14159000/3.14159000/0.42944913],THETA61:[-3.14159000/3.14159000/0.44271671],THETA62:[-3.14159000/3.14159000/0.43385103],THETA63:[-3.14159000/3.14159000/0.42516672],THETA64:[-3.14159000/3.14159000/0.45039080],THETA65:[-3.14159000/3.14159000/0.49932707],THETA66:[-3.14159000/3.14159000/0.50387539],THETA67:[-3.14159000/3.14159000/0.45820832],THETA68:[-3.14159000/3.14159000/0.48874522],THETA69:[0.52359878/0.52359878/0.52359878],THETA70:[-3.14159000/3.14159000/0.41354160],THETA71:[-3.14159000/3.14159000/0.40971820],THETA72:[-3.14159000/3.14159000/0.40113151],THETA73:[-3.14159000/3.14159000/0.40732132],THETA74:[-3.14159000/3.14159000/0.39981350],THETA75:[-3.14159000/3.14159000/0.41497683],THETA76:[-3.14159000/3.14159000/0.39974583],THETA77:[-3.14159000/3.14159000/0.45589929],THETA78:[-3.14159000/3.14159000/0.45111310],THETA79:[-3.14159000/3.14159000/0.45590421],THETA80:[-3.14159000/3.14159000/0.49307828],THETA81:[-3.14159000/3.14159000/0.49060039],THETA82:[-3.14159000/3.14159000/0.44459729],THETA83:[-3.14159000/3.14159000/0.45236386],THETA84:[-3.14159000/3.14159000/0.47424538],THETA85:[-3.14159000/3.14159000/0.48983668],THETA86:[-3.14159000/3.14159000/0.47038504],THETA87:[-3.14159000/3.14159000/0.47565394],THETA88:[-3.14159000/3.14159000/0.52651801],THETA89:[-3.14159000/3.14159000/0.58174294],THETA90:[-3.14159000/3.14159000/0.48726388],THETA91:[-3.14159000/3.14159000/0.49246602],THETA92:[-3.14159000/3.14159000/0.51349554],THETA93:[-3.14159000/3.14159000/0.48424617],THETA94:[-3.14159000/3.14159000/0.46585063],THETA95:[-3.14159000/3.14159000/0.45284414],THETA96:[-3.14159000/3.14159000/0.45332062],THETA97:[-3.14159000/3.14159000/0.46717221],THETA98:[-3.14159000/3.14159000/0.46577770],THETA99:[-3.14159000/3.14159000/0.45718833],THETA100:[-3.14159000/3.14159000/0.47378308],THETA101:[-3.14159000/3.14159000/0.47693659],THETA102:[-3.14159000/3.14159000/0.49972371],THETA103:[-3.14159000/3.14159000/0.43818979],THETA104:[-3.14159000/3.14159000/0.40071395],THETA105:[-3.14159000/3.14159000/0.39147953],THETA106:[-3.14159000/3.14159000/0.38706626],THETA107:[-3.14159000/3.14159000/0.37071725],THETA108:[-3.14159000/3.14159000/0.38627652],THETA109:[-3.14159000/3.14159000/0.38471749],THETA110:[-3.14159000/3.14159000/0.38584932],THETA111:[-3.14159000/3.14159000/0.41003292],THETA112:[-3.14159000/3.14159000/0.36698091],THETA113:[-3.14159000/3.14159000/0.33320714],THETA114:[-3.14159000/3.14159000/0.33364393],THETA115:[-3.14159000/3.14159000/0.33345519],THETA116:[-3.14159000/3.14159000/0.48145729],THETA117:[-3.14159000/3.14159000/0.28729529],THETA118:[-3.14159000/3.14159000/0.40072563]
\ No newline at end of file

nlp/examples/opf_polar/case118_opf_polar.solution

+Objective value: 129660.69426983486
+Variable values:
+PG1: 0.26489092101208167
+PG2: -0.000000009993851758870091
+PG3: -0.000000009664912395900949
+PG4: -0.00000000999467101247084
+PG5: 4.018745328555425
+PG6: 0.8579383495057311
+PG7: 0.20883885112454445
+PG8: 0.13226152573086974
+PG9: 0.2158327352125426
+PG10: -0.000000009994178676997486
+PG11: 1.9381383584149545
+PG12: 2.797622095372388
+PG13: 0.09922486524043164
+PG14: 0.0724827053269045
+PG15: 0.14862584892892652
+PG16: 0.048878115834592756
+PG17: 0.10662711228202874
+PG18: 0.4932182860801038
+PG19: 0.4099496408174295
+PG20: 0.19038967367981582
+PG21: 1.9333231299535356
+PG22: 0.49542311416148666
+PG23: 0.32134223196088957
+PG24: 0.32560171918065517
+PG25: 1.497048081053866
+PG26: 1.4841482180806427
+PG27: -0.000000009996732782577231
+PG28: 3.522362479932359
+PG29: 3.48858350175698
+PG30: 4.536660589674946
+PG31: -0.000000009984991977585135
+PG32: -0.000000009984028730641742
+PG33: -0.00000000997944924410842
+PG34: 0.16931259991382816
+PG35: 0.22853031987666378
+PG36: -0.000000009996121509350542
+PG37: 4.308410861586784
+PG38: -0.00000000999815833741593
+PG39: 0.03626209754123644
+PG40: 5.018441430759849
+PG41: -0.000000009997607223820696
+PG42: -0.000000009997813751427511
+PG43: -0.000000009998285413996858
+PG44: -0.000000009996964564425598
+PG45: 2.312945041057966
+PG46: 0.3824623084720315
+PG47: -0.000000009964471842154236
+PG48: 0.05163093439541828
+PG49: 0.2902752462615965
+PG50: 0.07034102631155857
+PG51: 0.3524183966197221
+PG52: 0.36482232403348375
+PG53: -0.00000000998093237045325
+PG54: -0.000000009997959610099635
+QG1: 0.1500000099854358
+QG2: 0.7151774496805137
+QG3: 0.3328592064878397
+QG4: -0.7863246462127866
+QG5: -0.9967651318891715
+QG6: 0.5443951671849059
+QG7: 0.23840554739787054
+QG8: 0.30453570313478506
+QG9: 0.23999999027885724
+QG10: -0.07305198077112256
+QG11: -0.47000000996901836
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nlp/examples/opf_polar/case13659pegase_opf_polar.solution

+
+thread 'main' (1267568) panicked at /home/dirreck/Desktop/eig-rc/rust-autograd/src/graph.rs:41:13:
+Maximum graph size exceeded: 10000000. Use Graph::clear, or stop using loops in the VariableEnvironment::run block
+note: run with `RUST_BACKTRACE=1` environment variable to display a backtrace

nlp/examples/opf_polar/case14_opf_polar.model

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\ No newline at end of file

nlp/examples/opf_polar/case14_opf_polar.solution

+Objective value: 8081.524863211893
+Variable values:
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nlp/examples/opf_polar/case300_opf_polar.solution

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nlp/examples/opf_polar/case30_opf_polar.model

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+V15*V14*(-2.48868778*cos(THETA15-THETA14)+2.26244344*sin(THETA15-THETA14))--2.48868778*V15^2:[/0.16000000]
+V17*V16*(-1.88235294*cos(THETA17-THETA16)+4.47058824*sin(THETA17-THETA16))--1.88235294*V17^2:[/0.16000000]
+V18*V15*(-1.81818182*cos(THETA18-THETA15)+3.63636364*sin(THETA18-THETA15))--1.81818182*V18^2:[/0.16000000]
+V19*V18*(-2.92682927*cos(THETA19-THETA18)+6.34146341*sin(THETA19-THETA18))--2.92682927*V19^2:[/0.16000000]
+V20*V19*(-5.17241379*cos(THETA20-THETA19)+12.06896552*sin(THETA20-THETA19))--5.17241379*V20^2:[/0.32000000]
+V20*V10*(-1.72413793*cos(THETA20-THETA10)+4.02298851*sin(THETA20-THETA10))--1.72413793*V20^2:[/0.32000000]
+V17*V10*(-4.10958904*cos(THETA17-THETA10)+10.95890411*sin(THETA17-THETA10))--4.10958904*V17^2:[/0.32000000]
+V21*V10*(-5.17241379*cos(THETA21-THETA10)+12.06896552*sin(THETA21-THETA10))--5.17241379*V21^2:[/0.32000000]
+V22*V10*(-2.55474453*cos(THETA22-THETA10)+5.47445255*sin(THETA22-THETA10))--2.55474453*V22^2:[/0.32000000]
+V22*V21*(-20.00000000*cos(THETA22-THETA21)+40.00000000*sin(THETA22-THETA21))--20.00000000*V22^2:[/0.32000000]
+V23*V15*(-2.00000000*cos(THETA23-THETA15)+4.00000000*sin(THETA23-THETA15))--2.00000000*V23^2:[/0.16000000]
+V24*V22*(-2.56410256*cos(THETA24-THETA22)+3.84615385*sin(THETA24-THETA22))--2.56410256*V24^2:[/0.16000000]
+V24*V23*(-1.44766147*cos(THETA24-THETA23)+3.00668151*sin(THETA24-THETA23))--1.44766147*V24^2:[/0.16000000]
+V25*V24*(-1.31034483*cos(THETA25-THETA24)+2.27586207*sin(THETA25-THETA24))--1.31034483*V25^2:[/0.16000000]
+V26*V25*(-1.20831319*cos(THETA26-THETA25)+1.83663606*sin(THETA26-THETA25))--1.20831319*V26^2:[/0.16000000]
+V27*V25*(-1.95729537*cos(THETA27-THETA25)+3.73665480*sin(THETA27-THETA25))--1.95729537*V27^2:[/0.16000000]
+V27*V28*(0.00000000*cos(THETA27-THETA28)+2.50000000*sin(THETA27-THETA28))-0.00000000*V27^2:[/0.65000000]
+V29*V27*(-0.97864769*cos(THETA29-THETA27)+1.86832740*sin(THETA29-THETA27))--0.97864769*V29^2:[/0.16000000]
+V30*V27*(-0.69204152*cos(THETA30-THETA27)+1.29757785*sin(THETA30-THETA27))--0.69204152*V30^2:[/0.16000000]
+V30*V29*(-0.92272203*cos(THETA30-THETA29)+1.73010381*sin(THETA30-THETA29))--0.92272203*V30^2:[/0.16000000]
+V28*V8*(-1.37614679*cos(THETA28-THETA8)+4.58715596*sin(THETA28-THETA8))--1.37614679*V28^2:[/0.32000000]
+V28*V6*(-5.00000000*cos(THETA28-THETA6)+15.00000000*sin(THETA28-THETA6))--5.00000000*V28^2:[/0.32000000]
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\ No newline at end of file

nlp/examples/opf_polar/case30_opf_polar.solution

+Objective value: 574.5168351061757
+Variable values:
+PG1: 0.4379181987032237
+PG2: 0.5796429749239124
+PG3: 0.23073891878937275
+PG4: 0.3263296811956212
+PG5: 0.16810627669802292
+PG6: 0.1734576202159641
+QG1: -0.010963516525375087
+QG2: 0.22888715630526785
+QG3: 0.2894227055194664
+QG4: 0.14374659429669598
+QG5: 0.07050588273243048
+QG6: 0.2673165121231683
+V1: 1.0500000104762623
+V2: 1.0469573776724015
+V3: 1.0338489263750754
+V4: 1.0310033980549977
+V5: 1.0321282860793302
+V6: 1.0245157064359474
+V7: 1.0185389936978686
+V8: 1.012941653254554
+V9: 1.0312848871836147
+V10: 1.0349395393767336
+V11: 1.0312848871836147
+V12: 1.0500000104953224
+V13: 1.084276589310438
+V14: 1.0391204134230072
+V15: 1.0410294159139941
+V16: 1.036701469646519
+V17: 1.0303889146759517
+V18: 1.0266410274202389
+V19: 1.0215485043798271
+V20: 1.0240257803619437
+V21: 1.0406838662461624
+V22: 1.046206307243475
+V23: 1.0540908830588862
+V24: 1.040702722788632
+V25: 1.0500000104928036
+V26: 1.0330440283655673
+V27: 1.0639819175758485
+V28: 1.0278108000351953
+V29: 1.0449327596869658
+V30: 1.0339907323418718
+THETA1: 0
+THETA2: -0.01261992737478855
+THETA3: -0.035669415888555475
+THETA4: -0.04244136328700221
+THETA5: -0.03883307626326938
+THETA6: -0.04877058917789466
+THETA7: -0.053439061740885696
+THETA8: -0.055901282510445155
+THETA9: -0.0651184495593664
+THETA10: -0.07359509090497185
+THETA11: -0.0651184495593664
+THETA12: -0.06934688779824631
+THETA13: -0.048015212098880815
+THETA14: -0.07862567197828611
+THETA15: -0.07515079654741144
+THETA16: -0.07603597691057812
+THETA17: -0.07785865802217148
+THETA18: -0.08681670457480062
+THETA19: -0.09053657445265119
+THETA20: -0.08721023598897869
+THETA21: -0.07346247989982667
+THETA22: -0.07133274132919219
+THETA23: -0.05839943589097019
+THETA24: -0.06273297308627393
+THETA25: -0.03790312558487085
+THETA26: -0.04486365585063378
+THETA27: -0.01824087029172949
+THETA28: -0.04828173405026866
+THETA29: -0.03823384306772252
+THETA30: -0.052218946830118226

nlp/examples/opf_polar/case39_opf_polar.model

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+-0.00000000-V2*(V1*(-2.05705688*cos(THETA2-THETA1)+24.15572508*sin(THETA2-THETA1))+V2*(64.64569545)+V3*(-5.65955594*cos(THETA2-THETA3)+65.73791902*sin(THETA2-THETA3))+V25*(-56.92908263*cos(THETA2-THETA25)+69.94144437*sin(THETA2-THETA25))+V30*(0.00000000*cos(THETA2-THETA30)+53.90109150*sin(THETA2-THETA30))):[0/0]
+-3.22000000-V3*(V2*(-5.65955594*cos(THETA3-THETA2)+65.73791902*sin(THETA3-THETA2))+V3*(14.69062005)+V4*(-2.85475866*cos(THETA3-THETA4)+46.77412271*sin(THETA3-THETA4))+V18*(-6.17630545*cos(THETA3-THETA18)+74.67714767*sin(THETA3-THETA18))):[0/0]
+-5.00000000-V4*(V3*(-2.85475866*cos(THETA4-THETA3)+46.77412271*sin(THETA4-THETA3))+V4*(12.50755723)+V5*(-4.86381323*cos(THETA4-THETA5)+77.82101167*sin(THETA4-THETA5))+V14*(-4.78898533*cos(THETA4-THETA14)+77.22238851*sin(THETA4-THETA14))):[0/0]
+-0.00000000-V5*(V4*(-4.86381323*cos(THETA5-THETA4)+77.82101167*sin(THETA5-THETA4))+V5*(40.62075560)+V6*(-29.41176471*cos(THETA5-THETA6)+382.35294118*sin(THETA5-THETA6))+V8*(-6.34517766*cos(THETA5-THETA8)+88.83248731*sin(THETA5-THETA8))):[0/0]
+-0.00000000-V6*(V5*(-29.41176471*cos(THETA6-THETA5)+382.35294118*sin(THETA6-THETA5))+V6*(46.80574252)+V7*(-7.05882353*cos(THETA6-THETA7)+108.23529412*sin(THETA6-THETA7))+V11*(-10.33515429*cos(THETA6-THETA11)+121.06895024*sin(THETA6-THETA11))+V31*(0.00000000*cos(THETA6-THETA31)+37.38317757*sin(THETA6-THETA31))):[0/0]
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+-5.22000000-V8*(V5*(-6.34517766*cos(THETA8-THETA5)+88.83248731*sin(THETA8-THETA5))+V7*(-18.76172608*cos(THETA8-THETA7)+215.75984991*sin(THETA8-THETA7))+V8*(26.84540319)+V9*(-1.73849945*cos(THETA8-THETA9)+27.43805651*sin(THETA8-THETA9))):[0/0]
+-0.06500000-V9*(V8*(-1.73849945*cos(THETA9-THETA8)+27.43805651*sin(THETA9-THETA8))+V9*(3.33594354)+V39*(-1.59744409*cos(THETA9-THETA39)+39.93610224*sin(THETA9-THETA39))):[0/0]
+-0.00000000-V10*(V10*(42.89544236)+V11*(-21.44772118*cos(THETA10-THETA11)+230.56300268*sin(THETA10-THETA11))+V13*(-21.44772118*cos(THETA10-THETA13)+230.56300268*sin(THETA10-THETA13))+V32*(0.00000000*cos(THETA10-THETA32)+46.72897196*sin(THETA10-THETA32))):[0/0]
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+-2.24000000-V25*(V2*(-56.92908263*cos(THETA25-THETA2)+69.94144437*sin(THETA25-THETA2))+V25*(61.02681073)+V26*(-3.03740757*cos(THETA25-THETA26)+30.65883269*sin(THETA25-THETA26))+V37*(-1.08682854*cos(THETA25-THETA37)+42.02403702*sin(THETA25-THETA37))):[0/0]
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+-2.81000000-V27*(V17*(-4.31922387*cos(THETA27-THETA17)+57.47890225*sin(THETA27-THETA17))+V26*(-6.42054575*cos(THETA27-THETA26)+67.41573034*sin(THETA27-THETA26))+V27*(10.73976962)):[0/0]
+-2.06000000-V28*(V26*(-1.89824523*cos(THETA28-THETA26)+20.92484273*sin(THETA28-THETA26))+V28*(7.98599580)+V29*(-6.08775058*cos(THETA28-THETA29)+65.66073836*sin(THETA28-THETA29))):[0/0]
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+V25*V2*(-56.92908263*cos(THETA25-THETA2)+69.94144437*sin(THETA25-THETA2))--56.92908263*V25^2:[/5.00000000]
+V30*V2*(0.00000000*cos(THETA30-THETA2)+53.90109150*sin(THETA30-THETA2))-0.00000000*V30^2:[/9.00000000]
+V4*V3*(-2.85475866*cos(THETA4-THETA3)+46.77412271*sin(THETA4-THETA3))--2.85475866*V4^2:[/5.00000000]
+V18*V3*(-6.17630545*cos(THETA18-THETA3)+74.67714767*sin(THETA18-THETA3))--6.17630545*V18^2:[/5.00000000]
+V5*V4*(-4.86381323*cos(THETA5-THETA4)+77.82101167*sin(THETA5-THETA4))--4.86381323*V5^2:[/6.00000000]
+V14*V4*(-4.78898533*cos(THETA14-THETA4)+77.22238851*sin(THETA14-THETA4))--4.78898533*V14^2:[/5.00000000]
+V6*V5*(-29.41176471*cos(THETA6-THETA5)+382.35294118*sin(THETA6-THETA5))--29.41176471*V6^2:[/12.00000000]
+V8*V5*(-6.34517766*cos(THETA8-THETA5)+88.83248731*sin(THETA8-THETA5))--6.34517766*V8^2:[/9.00000000]
+V7*V6*(-7.05882353*cos(THETA7-THETA6)+108.23529412*sin(THETA7-THETA6))--7.05882353*V7^2:[/9.00000000]
+V11*V6*(-10.33515429*cos(THETA11-THETA6)+121.06895024*sin(THETA11-THETA6))--10.33515429*V11^2:[/4.80000000]
+V31*V6*(0.00000000*cos(THETA31-THETA6)+37.38317757*sin(THETA31-THETA6))-0.00000000*V31^2:[/18.00000000]
+V8*V7*(-18.76172608*cos(THETA8-THETA7)+215.75984991*sin(THETA8-THETA7))--18.76172608*V8^2:[/9.00000000]
+V9*V8*(-1.73849945*cos(THETA9-THETA8)+27.43805651*sin(THETA9-THETA8))--1.73849945*V9^2:[/9.00000000]
+V39*V9*(-1.59744409*cos(THETA39-THETA9)+39.93610224*sin(THETA39-THETA9))--1.59744409*V39^2:[/9.00000000]
+V11*V10*(-21.44772118*cos(THETA11-THETA10)+230.56300268*sin(THETA11-THETA10))--21.44772118*V11^2:[/6.00000000]
+V13*V10*(-21.44772118*cos(THETA13-THETA10)+230.56300268*sin(THETA13-THETA10))--21.44772118*V13^2:[/6.00000000]
+V32*V10*(0.00000000*cos(THETA32-THETA10)+46.72897196*sin(THETA32-THETA10))-0.00000000*V32^2:[/9.00000000]
+V11*V12*(-0.83937559*cos(THETA11-THETA12)+22.82052378*sin(THETA11-THETA12))--0.83937559*V11^2:[/5.00000000]
+V13*V12*(-0.83937559*cos(THETA13-THETA12)+22.82052378*sin(THETA13-THETA12))--0.83937559*V13^2:[/5.00000000]
+V14*V13*(-8.75316086*cos(THETA14-THETA13)+98.22991636*sin(THETA14-THETA13))--8.75316086*V14^2:[/6.00000000]
+V15*V14*(-3.79642714*cos(THETA15-THETA14)+45.76803830*sin(THETA15-THETA14))--3.79642714*V15^2:[/6.00000000]
+V16*V15*(-10.09308063*cos(THETA16-THETA15)+105.41661994*sin(THETA16-THETA15))--10.09308063*V16^2:[/6.00000000]
+V17*V16*(-8.78293601*cos(THETA17-THETA16)+111.66875784*sin(THETA17-THETA16))--8.78293601*V17^2:[/6.00000000]
+V19*V16*(-4.17961913*cos(THETA19-THETA16)+50.93910817*sin(THETA19-THETA16))--4.17961913*V19^2:[/6.00000000]
+V21*V16*(-4.37421401*cos(THETA21-THETA16)+73.81486139*sin(THETA21-THETA16))--4.37421401*V21^2:[/6.00000000]
+V24*V16*(-8.59598854*cos(THETA24-THETA16)+169.05444126*sin(THETA24-THETA16))--8.59598854*V24^2:[/6.00000000]
+V18*V17*(-10.33515429*cos(THETA18-THETA17)+121.06895024*sin(THETA18-THETA17))--10.33515429*V18^2:[/6.00000000]
+V27*V17*(-4.31922387*cos(THETA27-THETA17)+57.47890225*sin(THETA27-THETA17))--4.31922387*V27^2:[/6.00000000]
+V20*V19*(-3.45874068*cos(THETA20-THETA19)+68.18660202*sin(THETA20-THETA19))--3.45874068*V20^2:[/9.00000000]
+V33*V19*(-3.23655869*cos(THETA33-THETA19)+65.65590480*sin(THETA33-THETA19))--3.23655869*V33^2:[/9.00000000]
+V34*V20*(-2.74613543*cos(THETA34-THETA20)+54.92270865*sin(THETA34-THETA20))--2.74613543*V34^2:[/9.00000000]
+V22*V21*(-4.06834825*cos(THETA22-THETA21)+71.19609439*sin(THETA22-THETA21))--4.06834825*V22^2:[/9.00000000]
+V23*V22*(-6.48508431*cos(THETA23-THETA22)+103.76134890*sin(THETA23-THETA22))--6.48508431*V23^2:[/6.00000000]
+V35*V22*(0.00000000*cos(THETA35-THETA22)+68.22445847*sin(THETA35-THETA22))-0.00000000*V35^2:[/9.00000000]
+V24*V23*(-1.78885058*cos(THETA24-THETA23)+28.45898653*sin(THETA24-THETA23))--1.78885058*V24^2:[/6.00000000]
+V36*V23*(-0.67559351*cos(THETA36-THETA23)+36.75228688*sin(THETA36-THETA23))--0.67559351*V36^2:[/9.00000000]
+V26*V25*(-3.03740757*cos(THETA26-THETA25)+30.65883269*sin(THETA26-THETA25))--3.03740757*V26^2:[/6.00000000]
+V37*V25*(-1.08682854*cos(THETA37-THETA25)+42.02403702*sin(THETA37-THETA25))--1.08682854*V37^2:[/9.00000000]
+V27*V26*(-6.42054575*cos(THETA27-THETA26)+67.41573034*sin(THETA27-THETA26))--6.42054575*V27^2:[/6.00000000]
+V28*V26*(-1.89824523*cos(THETA28-THETA26)+20.92484273*sin(THETA28-THETA26))--1.89824523*V28^2:[/6.00000000]
+V29*V26*(-1.44716331*cos(THETA29-THETA26)+15.86801871*sin(THETA29-THETA26))--1.44716331*V29^2:[/6.00000000]
+V29*V28*(-6.08775058*cos(THETA29-THETA28)+65.66073836*sin(THETA29-THETA28))--6.08775058*V29^2:[/6.00000000]
+V38*V29*(-3.19872051*cos(THETA38-THETA29)+62.37504998*sin(THETA38-THETA29))--3.19872051*V38^2:[/12.00000000]
+PG1:[0.00000000/10.40000000/6.71587922],PG2:[0.00000000/6.46000000/6.45999945],PG3:[0.00000000/7.25000000/6.71160735],PG4:[0.00000000/6.52000000/6.51999478],PG5:[0.00000000/5.08000000/5.07999989],PG6:[0.00000000/6.87000000/6.61454595],PG7:[0.00000000/5.80000000/5.79999979],PG8:[0.00000000/5.64000000/5.63999981],PG9:[0.00000000/8.65000000/6.54034996],PG10:[0.00000000/11.00000000/6.89588830],QG1:[1.40000000/4.00000000/1.40000555],QG2:[-1.00000000/3.00000000/2.99999320],QG3:[1.50000000/3.00000000/2.99989679],QG4:[0.00000000/2.50000000/1.15126560],QG5:[0.00000000/1.67000000/1.39609810],QG6:[-1.00000000/3.00000000/2.22938118],QG7:[0.00000000/2.40000000/0.60647736],QG8:[0.00000000/2.50000000/0.08850695],QG9:[-1.50000000/3.00000000/-0.32730061],QG10:[-1.00000000/3.00000000/0.81855745],V1:[0.94000000/1.06000000/1.04115668],V2:[0.94000000/1.06000000/1.05440715],V3:[0.94000000/1.06000000/1.04552112],V4:[0.94000000/1.06000000/1.03534069],V5:[0.94000000/1.06000000/1.04389819],V6:[0.94000000/1.06000000/1.04793927],V7:[0.94000000/1.06000000/1.03567718],V8:[0.94000000/1.06000000/1.03377315],V9:[0.94000000/1.06000000/1.05649386],V10:[0.94000000/1.06000000/1.05979223],V11:[0.94000000/1.06000000/1.05452563],V12:[0.94000000/1.06000000/1.04205589],V13:[0.94000000/1.06000000/1.05424819],V14:[0.94000000/1.06000000/1.04481319],V15:[0.94000000/1.06000000/1.03586609],V16:[0.94000000/1.06000000/1.04638166],V17:[0.94000000/1.06000000/1.04740781],V18:[0.94000000/1.06000000/1.04545121],V19:[0.94000000/1.06000000/1.05999980],V20:[0.94000000/1.06000000/0.99681644],V21:[0.94000000/1.06000000/1.04406583],V22:[0.94000000/1.06000000/1.05962708],V23:[0.94000000/1.06000000/1.05223911],V24:[0.94000000/1.06000000/1.05080091],V25:[0.94000000/1.06000000/1.05999991],V26:[0.94000000/1.06000000/1.05999993],V27:[0.94000000/1.06000000/1.04869477],V28:[0.94000000/1.06000000/1.05537909],V29:[0.94000000/1.06000000/1.05318343],V30:[0.94000000/1.06000000/1.04632685],V31:[0.94000000/1.06000000/1.03842595],V32:[0.94000000/1.06000000/1.03971579],V33:[0.94000000/1.06000000/1.00721662],V34:[0.94000000/1.06000000/1.01322162],V35:[0.94000000/1.06000000/1.05999969],V36:[0.94000000/1.06000000/1.05999968],V37:[0.94000000/1.06000000/1.03161555],V38:[0.94000000/1.06000000/1.02274018],V39:[0.94000000/1.06000000/1.03793953],THETA1:[-3.14159000/3.14159000/-0.23347051],THETA2:[-3.14159000/3.14159000/-0.09484430],THETA3:[-3.14159000/3.14159000/-0.15668822],THETA4:[-3.14159000/3.14159000/-0.18139773],THETA5:[-3.14159000/3.14159000/-0.16917860],THETA6:[-3.14159000/3.14159000/-0.15718276],THETA7:[-3.14159000/3.14159000/-0.19935112],THETA8:[-3.14159000/3.14159000/-0.21086018],THETA9:[-3.14159000/3.14159000/-0.26319090],THETA10:[-3.14159000/3.14159000/-0.11466562],THETA11:[-3.14159000/3.14159000/-0.12908266],THETA12:[-3.14159000/3.14159000/-0.12826098],THETA13:[-3.14159000/3.14159000/-0.12533058],THETA14:[-3.14159000/3.14159000/-0.15020734],THETA15:[-3.14159000/3.14159000/-0.15190761],THETA16:[-3.14159000/3.14159000/-0.12587363],THETA17:[-3.14159000/3.14159000/-0.14526109],THETA18:[-3.14159000/3.14159000/-0.15689498],THETA19:[-3.14159000/3.14159000/-0.04317590],THETA20:[-3.14159000/3.14159000/-0.06724224],THETA21:[-3.14159000/3.14159000/-0.08255087],THETA22:[-3.14159000/3.14159000/-0.00408340],THETA23:[-3.14159000/3.14159000/-0.00675096],THETA24:[-3.14159000/3.14159000/-0.12309677],THETA25:[-3.14159000/3.14159000/-0.07930390],THETA26:[-3.14159000/3.14159000/-0.13208472],THETA27:[-3.14159000/3.14159000/-0.15797352],THETA28:[-3.14159000/3.14159000/-0.10819760],THETA29:[-3.14159000/3.14159000/-0.07216799],THETA30:[-3.14159000/3.14159000/0.01833243],THETA31:[0.00000000/0.00000000/0.00000000],THETA32:[-3.14159000/3.14159000/0.01605451],THETA33:[-3.14159000/3.14159000/0.04893439],THETA34:[-3.14159000/3.14159000/0.02297467],THETA35:[-3.14159000/3.14159000/0.08234211],THETA36:[-3.14159000/3.14159000/0.13489177],THETA37:[-3.14159000/3.14159000/0.04360546],THETA38:[-3.14159000/3.14159000/0.02532681],THETA39:[-3.14159000/3.14159000/-0.29575697]
\ No newline at end of file

nlp/examples/opf_polar/case39_opf_polar.solution

+Objective value: 41864.177712614524
+Variable values:
+PG1: 6.715933533266847
+PG2: 6.460000064597665
+PG3: 6.711538595994945
+PG4: 6.520000065182512
+PG5: 5.080000050799529
+PG6: 6.614543604510545
+PG7: 5.800000057999096
+PG8: 5.640000056399209
+PG9: 6.5403383772384895
+PG10: 6.8959094914094035
+QG1: 1.3999999860248253
+QG2: 3.0000000299409155
+QG3: 3.0000000297297063
+QG4: 1.1507995782290479
+QG5: 1.3959169245107916
+QG6: 2.2290613345562336
+QG7: 0.6062982961948918
+QG8: 0.0863716908827201
+QG9: -0.32766086658561844
+QG10: 0.8208966086358357
+V1: 1.0412463945080808
+V2: 1.054425994834015
+V3: 1.0455451900720714
+V4: 1.0353823772549582
+V5: 1.0439517235505835
+V6: 1.0479931913117952
+V7: 1.035736646666691
+V8: 1.033835034506785
+V9: 1.0565958909268311
+V10: 1.059840138213194
+V11: 1.054575576867182
+V12: 1.0421048022645767
+V13: 1.0542937378390922
+V14: 1.0448523241087424
+V15: 1.0358865358513694
+V16: 1.0463936403011977
+V17: 1.047420866728084
+V18: 1.0454685075642403
+V19: 1.0600000105990612
+V20: 0.9968141720367603
+V21: 1.0440743795309788
+V22: 1.0596318164365857
+V23: 1.0522439989313461
+V24: 1.0508118678680898
+V25: 1.060000010599583
+V26: 1.0600000105997076
+V27: 1.0487008408405571
+V28: 1.055369687489924
+V29: 1.0531711702977964
+V30: 1.046344961412761
+V31: 1.0384749294987832
+V32: 1.0397613299518937
+V33: 1.0072102902534052
+V34: 1.0132162415049488
+V35: 1.0600000105978482
+V36: 1.060000010598431
+V37: 1.031566965909859
+V38: 1.0227224806914523
+V39: 1.0380682459946562
+THETA1: -0.23344727503107193
+THETA2: -0.0948296850378047
+THETA3: -0.1566704201772613
+THETA4: -0.1813791943618577
+THETA5: -0.16916171470003485
+THETA6: -0.15716715717857577
+THETA7: -0.19933113821161233
+THETA8: -0.21083899401868572
+THETA9: -0.2631631152020523
+THETA10: -0.11465387907301276
+THETA11: -0.12906965350750693
+THETA12: -0.12824783201595058
+THETA13: -0.1253174792027444
+THETA14: -0.15019118936893014
+THETA15: -0.15188897554938102
+THETA16: -0.1258546654855347
+THETA17: -0.1452414365057212
+THETA18: -0.15687583731116211
+THETA19: -0.04315687435483414
+THETA20: -0.06722313557598192
+THETA21: -0.08253256126651869
+THETA22: -0.004065893535564185
+THETA23: -0.006733425600468531
+THETA24: -0.12307781588817877
+THETA25: -0.07927676866102554
+THETA26: -0.13206096944222406
+THETA27: -0.1579515150846744
+THETA28: -0.1081732108914661
+THETA29: -0.07214273189613302
+THETA30: 0.018343966393653707
+THETA31: 0
+THETA32: 0.016053212758781552
+THETA33: 0.048954387614925716
+THETA34: 0.022994626468252764
+THETA35: 0.08235916992510342
+THETA36: 0.13490868256482458
+THETA37: 0.04363961097277546
+THETA38: 0.025355003076542856
+THETA39: -0.29572228361337954

nlp/examples/opf_polar/case57_opf_polar.model

+775.79519000*PG1^2+2000.00000000*PG1+100.00000000*PG2^2+4000.00000000*PG2+2500.00000000*PG3^2+2000.00000000*PG3+100.00000000*PG4^2+4000.00000000*PG4+222.22222200*PG5^2+2000.00000000*PG5+100.00000000*PG6^2+4000.00000000*PG6+322.58064500*PG7^2+2000.00000000*PG7
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+PG2-0.03000000-V2*(V1*(-9.73161838*cos(THETA2-THETA1)+32.82955598*sin(THETA2-THETA1))+V2*(13.40471749)+V3*(-3.67309911*cos(THETA2-THETA3)+10.47696055*sin(THETA2-THETA3))):[0/0]
+PG3-0.41000000-V3*(V2*(-3.67309911*cos(THETA3-THETA2)+10.47696055*sin(THETA3-THETA2))+V3*(16.59254928)+V4*(-7.64505119*cos(THETA3-THETA4)+24.98293515*sin(THETA3-THETA4))+V15*(-5.27439898*cos(THETA3-THETA15)+17.25574975*sin(THETA3-THETA15))):[0/0]
+-0.00000000-V4*(V3*(-7.64505119*cos(THETA4-THETA3)+24.98293515*sin(THETA4-THETA3))+V4*(12.38545983)+V5*(-2.93011099*cos(THETA4-THETA5)+6.18839442*sin(THETA4-THETA5))+V6*(-1.81029765*cos(THETA4-THETA6)+6.23079190*sin(THETA4-THETA6))+V18*(0.00000000*cos(THETA4-THETA18)+4.23542272*sin(THETA4-THETA18))):[0/0]
+-0.13000000-V5*(V4*(-2.93011099*cos(THETA5-THETA4)+6.18839442*sin(THETA5-THETA4))+V5*(8.94502879)+V6*(-6.01491779*cos(THETA5-THETA6)+12.76676260*sin(THETA5-THETA6))):[0/0]
+PG4-0.75000000-V6*(V4*(-1.81029765*cos(THETA6-THETA4)+6.23079190*sin(THETA6-THETA4))+V5*(-6.01491779*cos(THETA6-THETA5)+12.76676260*sin(THETA6-THETA5))+V6*(10.76717809)+V7*(-1.85116623*cos(THETA6-THETA7)+9.44094780*sin(THETA6-THETA7))+V8*(-1.09079641*cos(THETA6-THETA8)+5.56660117*sin(THETA6-THETA8))):[0/0]
+-0.00000000-V7*(V6*(-1.85116623*cos(THETA7-THETA6)+9.44094780*sin(THETA7-THETA6))+V7*(4.49242112)+V8*(-2.64125488*cos(THETA7-THETA8)+13.52930558*sin(THETA7-THETA8))+V29*(0.00000000*cos(THETA7-THETA29)+15.95873709*sin(THETA7-THETA29))):[0/0]
+PG5-1.50000000-V8*(V6*(-1.09079641*cos(THETA8-THETA6)+5.56660117*sin(THETA8-THETA6))+V7*(-2.64125488*cos(THETA8-THETA7)+13.52930558*sin(THETA8-THETA7))+V8*(7.47035494)+V9*(-3.73830364*cos(THETA8-THETA9)+19.06912463*sin(THETA8-THETA9))):[0/0]
+PG6-1.21000000-V9*(V8*(-3.73830364*cos(THETA9-THETA8)+19.06912463*sin(THETA9-THETA8))+V9*(10.74446910)+V10*(-1.24864561*cos(THETA9-THETA10)+5.68150671*sin(THETA9-THETA10))+V11*(-3.28382981*cos(THETA9-THETA11)+10.79336310*sin(THETA9-THETA11))+V12*(-0.71033907*cos(THETA9-THETA12)+3.23379671*sin(THETA9-THETA12))+V13*(-1.76335097*cos(THETA9-THETA13)+5.79229632*sin(THETA9-THETA13))+V55*(0.00000000*cos(THETA9-THETA55)+8.82846296*sin(THETA9-THETA55))):[0/0]
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\ No newline at end of file

nlp/examples/opf_polar/case57_opf_polar.solution

+Objective value: 41737.78705471332
+Variable values:
+PG1: 1.426262949933819
+PG2: 0.8779099063787555
+PG3: 0.4507094789914592
+PG4: 0.7286263549135764
+PG5: 4.598048197421617
+PG6: 0.9763449224423756
+PG7: 3.6152203003581502
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+THETA57: -0.16440088410974713

nlp/examples/opf_polar/case5_opf_polar.model

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\ No newline at end of file

nlp/examples/opf_polar/case5_opf_polar.solution

+Objective value: 17545.72542482958
+Variable values:
+V1: 1.084028076575362
+V2: 1.08586954933736
+V3: 1.1000000109973362
+V4: 1.059188481432394
+V5: 1.0789529707090493
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+THETA3: -0.010162641838136083
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+THETA5: 0.06098195216205381
+PG1: 0.4000000099986138
+PG2: 1.7000000169978795
+PG3: 3.241400961606251
+PG4: -0.000000009965249944440519
+PG5: 4.711522540376949
+QG1: 0.30000000998855963
+QG2: 1.275000012738577
+QG3: 3.900000038963795
+QG4: -1.205728139742629
+QG5: -0.543322993476943

nlp/examples/opf_polar/case9_opf_polar.model

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\ No newline at end of file

nlp/examples/opf_polar/case9_opf_polar.solution

+Objective value: 5296.68620431761
+Variable values:
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+PG2: 1.343206011886868
+PG3: 0.9418738089581109
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+THETA9: -0.08055116863692784

nlp/examples/opf_rectangular/case118_opf_rectangular.model

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\ No newline at end of file