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scip_expr.h
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1/* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * */
2/* */
3/* This file is part of the program and library */
4/* SCIP --- Solving Constraint Integer Programs */
5/* */
6/* Copyright (c) 2002-2023 Zuse Institute Berlin (ZIB) */
7/* */
8/* Licensed under the Apache License, Version 2.0 (the "License"); */
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23/* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * */
24
25/**@file scip_expr.h
26 * @ingroup PUBLICCOREAPI
27 * @brief public functions to work with algebraic expressions
28 * @author Ksenia Bestuzheva
29 * @author Benjamin Mueller
30 * @author Felipe Serrano
31 * @author Stefan Vigerske
32 */
33
34#ifndef SCIP_SCIP_EXPR_H_
35#define SCIP_SCIP_EXPR_H_
36
37#include "scip/type_scip.h"
38#include "scip/type_expr.h"
39#include "scip/type_misc.h"
40
41#ifdef NDEBUG
42#include "scip/struct_scip.h"
43#include "scip/struct_set.h"
44#include "scip/struct_mem.h"
45#include "scip/struct_stat.h"
46#include "scip/set.h"
47#include "scip/expr.h"
48#endif
49
50#ifdef __cplusplus
51extern "C" {
52#endif
53
54/**@addtogroup PublicExprHandlerMethods
55 * @{
56 */
57
58/** creates the handler for an expression handler and includes it into SCIP */
61 SCIP* scip, /**< SCIP data structure */
62 SCIP_EXPRHDLR** exprhdlr, /**< buffer where to store created expression handler */
63 const char* name, /**< name of expression handler (must not be NULL) */
64 const char* desc, /**< description of expression handler (can be NULL) */
65 unsigned int precedence, /**< precedence of expression operation (used for printing) */
66 SCIP_DECL_EXPREVAL((*eval)), /**< point evaluation callback (must not be NULL) */
67 SCIP_EXPRHDLRDATA* data /**< data of expression handler (can be NULL) */
68 );
69
70/** gives expression handlers */
73 SCIP* scip /**< SCIP data structure */
74);
75
76/** gives number of expression handlers */
79 SCIP* scip /**< SCIP data structure */
80);
81
82/** returns an expression handler of a given name (or NULL if not found) */
85 SCIP* scip, /**< SCIP data structure */
86 const char* name /**< name of expression handler */
87 );
88
89/** returns expression handler for variable expressions (or NULL if not included) */
92 SCIP* scip /**< SCIP data structure */
93 );
94
95/** returns expression handler for constant value expressions (or NULL if not included) */
98 SCIP* scip /**< SCIP data structure */
99 );
100
101/** returns expression handler for sum expressions (or NULL if not included) */
104 SCIP* scip /**< SCIP data structure */
105 );
106
107/** returns expression handler for product expressions (or NULL if not included) */
110 SCIP* scip /**< SCIP data structure */
111 );
112
113/** returns expression handler for power expressions (or NULL if not included) */
116 SCIP* scip /**< SCIP data structure */
117 );
118
119#ifdef NDEBUG
120/* If NDEBUG is defined, the function calls are overwritten by defines to reduce the number of function calls and
121 * speed up the algorithms.
122 */
123#define SCIPgetExprhdlrs(scip) (scip)->set->exprhdlrs
124#define SCIPgetNExprhdlrs(scip) (scip)->set->nexprhdlrs
125#define SCIPfindExprhdlr(scip, name) SCIPsetFindExprhdlr((scip)->set, name)
126#define SCIPgetExprhdlrVar(scip) (scip)->set->exprhdlrvar
127#define SCIPgetExprhdlrValue(scip) (scip)->set->exprhdlrval
128#define SCIPgetExprhdlrSum(scip) (scip)->set->exprhdlrsum
129#define SCIPgetExprhdlrProduct(scip) (scip)->set->exprhdlrproduct
130#define SCIPgetExprhdlrPower(scip) (scip)->set->exprhdlrpow
131#endif
132
133/** @} */
134
135/**@addtogroup PublicExprMethods
136 * @{
137 */
138
139/**@name Expressions */
140/**@{ */
141
142/** creates and captures an expression with given expression data and children */
145 SCIP* scip, /**< SCIP data structure */
146 SCIP_EXPR** expr, /**< pointer where to store expression */
147 SCIP_EXPRHDLR* exprhdlr, /**< expression handler */
148 SCIP_EXPRDATA* exprdata, /**< expression data (expression assumes ownership) */
149 int nchildren, /**< number of children */
150 SCIP_EXPR** children, /**< children (can be NULL if nchildren is 0) */
151 SCIP_DECL_EXPR_OWNERCREATE((*ownercreate)), /**< function to call to create ownerdata */
152 void* ownercreatedata /**< data to pass to ownercreate */
153 );
154
155/** creates and captures an expression with given expression data and up to two children */
158 SCIP* scip, /**< SCIP data structure */
159 SCIP_EXPR** expr, /**< pointer where to store expression */
160 SCIP_EXPRHDLR* exprhdlr, /**< expression handler */
161 SCIP_EXPRDATA* exprdata, /**< expression data */
162 SCIP_EXPR* child1, /**< first child (can be NULL) */
163 SCIP_EXPR* child2, /**< second child (can be NULL) */
164 SCIP_DECL_EXPR_OWNERCREATE((*ownercreate)), /**< function to call to create ownerdata */
165 void* ownercreatedata /**< data to pass to ownercreate */
166 );
167
168/** creates and captures an expression representing a quadratic function */
171 SCIP* scip, /**< SCIP data structure */
172 SCIP_EXPR** expr, /**< pointer where to store expression */
173 int nlinvars, /**< number of linear terms */
174 SCIP_VAR** linvars, /**< array with variables in linear part */
175 SCIP_Real* lincoefs, /**< array with coefficients of variables in linear part */
176 int nquadterms, /**< number of quadratic terms */
177 SCIP_VAR** quadvars1, /**< array with first variables in quadratic terms */
178 SCIP_VAR** quadvars2, /**< array with second variables in quadratic terms */
179 SCIP_Real* quadcoefs, /**< array with coefficients of quadratic terms */
180 SCIP_DECL_EXPR_OWNERCREATE((*ownercreate)), /**< function to call to create ownerdata */
181 void* ownercreatedata /**< data to pass to ownercreate */
182 );
183
184/** creates and captures an expression representing a monomial
185 *
186 * @note In deviation from the actual definition of monomials, we also allow for negative and rational exponents.
187 * So this function actually creates an expression for a signomial that has exactly one term.
188 */
191 SCIP* scip, /**< SCIP data structure */
192 SCIP_EXPR** expr, /**< pointer where to store expression */
193 int nfactors, /**< number of factors in monomial */
194 SCIP_VAR** vars, /**< variables in the monomial */
195 SCIP_Real* exponents, /**< exponent in each factor, or NULL if all 1.0 */
196 SCIP_DECL_EXPR_OWNERCREATE((*ownercreate)), /**< function to call to create ownerdata */
197 void* ownercreatedata /**< data to pass to ownercreate */
198 );
199
200/** appends child to the children list of expr
201 *
202 * @attention Only use if you really know what you are doing. The expression handler of the expression needs to be able to handle an increase in the number of children.
203 */
206 SCIP* scip, /**< SCIP data structure */
207 SCIP_EXPR* expr, /**< expression */
208 SCIP_EXPR* child /**< expression to be appended */
209 );
210
211/** overwrites/replaces a child of an expressions
212 *
213 * The old child is released and the newchild is captured, unless they are the same (=same pointer).
214 */
217 SCIP* scip, /**< SCIP data structure */
218 SCIP_EXPR* expr, /**< expression which is going to replace a child */
219 int childidx, /**< index of child being replaced */
220 SCIP_EXPR* newchild /**< the new child */
221 );
222
223/** remove all children of expr
224 *
225 * @attention Only use if you really know what you are doing. The expression handler of the expression needs to be able to handle the removal of all children.
226 */
229 SCIP* scip, /**< SCIP data structure */
230 SCIP_EXPR* expr /**< expression */
231 );
232
233/** duplicates the given expression and its children */
236 SCIP* scip, /**< SCIP data structure */
237 SCIP_EXPR* expr, /**< original expression */
238 SCIP_EXPR** copyexpr, /**< buffer to store duplicate of expr */
239 SCIP_DECL_EXPR_MAPEXPR((*mapexpr)), /**< expression mapping function, or NULL for creating new expressions */
240 void* mapexprdata, /**< data of expression mapping function */
241 SCIP_DECL_EXPR_OWNERCREATE((*ownercreate)), /**< function to call on expression copy to create ownerdata */
242 void* ownercreatedata /**< data to pass to ownercreate */
243 );
244
245/** duplicates the given expression, but reuses its children */
248 SCIP* scip, /**< SCIP data structure */
249 SCIP_EXPR* expr, /**< original expression */
250 SCIP_EXPR** copyexpr, /**< buffer to store (shallow) duplicate of expr */
251 SCIP_DECL_EXPR_OWNERCREATE((*ownercreate)), /**< function to call to create ownerdata */
252 void* ownercreatedata /**< data to pass to ownercreate */
253 );
254
255/** copies an expression including children to use in a (possibly different) SCIP instance */
258 SCIP* sourcescip, /**< source SCIP data structure */
259 SCIP* targetscip, /**< target SCIP data structure */
260 SCIP_EXPR* expr, /**< original expression */
261 SCIP_EXPR** copyexpr, /**< buffer to store duplicate of expr */
262 SCIP_DECL_EXPR_OWNERCREATE((*ownercreate)), /**< function to call on expression copy to create ownerdata */
263 void* ownercreatedata, /**< data to pass to ownercreate */
264 SCIP_HASHMAP* varmap, /**< a SCIP_HASHMAP mapping variables of the source SCIP to the corresponding
265 * variables of the target SCIP, or NULL */
266 SCIP_HASHMAP* consmap, /**< a hashmap to store the mapping of source constraints to the corresponding
267 * target constraints, or NULL */
268 SCIP_Bool global, /**< create a global or a local copy? */
269 SCIP_Bool* valid /**< pointer to store whether all checked or enforced constraints were validly copied */
270 );
271
272/** creates an expression from a string
273 *
274 * We specify the grammar that defines the syntax of an expression.
275 * Loosely speaking, a `Base` will be any "block", a `Factor` is a `Base` to a power,
276 * a `Term` is a product of `Factors` and an `Expression` is a sum of `Terms`.
277 *
278 * The actual definition:
279 * <pre>
280 * Expression -> ["+" | "-"] Term { ("+" | "-" | "number *") ] Term }
281 * Term -> Factor { ("*" | "/" ) Factor }
282 * Factor -> Base [ "^" "number" | "^(" "number" ")" ]
283 * Base -> "number" | "<varname>" | "(" Expression ")" | Op "(" OpExpression ")
284 * </pre>
285 * where `[a|b]` means `a` or `b` or none, `(a|b)` means `a` or `b`, `{a}` means 0 or more `a`.
286 *
287 * Note that `Op` and `OpExpression` are undefined.
288 * `Op` corresponds to the name of an expression handler and `OpExpression` to whatever string the expression handler accepts (through its parse method).
289 */
292 SCIP* scip, /**< SCIP data structure */
293 SCIP_EXPR** expr, /**< pointer to store the expr parsed */
294 const char* exprstr, /**< string with the expr to parse */
295 const char** finalpos, /**< buffer to store the position of exprstr where we finished reading, or NULL if not of interest */
296 SCIP_DECL_EXPR_OWNERCREATE((*ownercreate)), /**< function to call to create ownerdata */
297 void* ownercreatedata /**< data to pass to ownercreate */
298 );
299
300/** captures an expression (increments usage count) */
302void SCIPcaptureExpr(
303 SCIP_EXPR* expr /**< expression to be captured */
304 );
305
306/** releases an expression (decrements usage count and possibly frees expression) */
309 SCIP* scip, /**< SCIP data structure */
310 SCIP_EXPR** expr /**< pointer to expression to be released */
311 );
312
313/** returns whether an expression is a variable expression */
315SCIP_Bool SCIPisExprVar(
316 SCIP* scip, /**< SCIP data structure */
317 SCIP_EXPR* expr /**< expression */
318 );
319
320/** returns whether an expression is a value expression */
322SCIP_Bool SCIPisExprValue(
323 SCIP* scip, /**< SCIP data structure */
324 SCIP_EXPR* expr /**< expression */
325 );
326
327/** returns whether an expression is a sum expression */
329SCIP_Bool SCIPisExprSum(
330 SCIP* scip, /**< SCIP data structure */
331 SCIP_EXPR* expr /**< expression */
332 );
333
334/** returns whether an expression is a product expression */
336SCIP_Bool SCIPisExprProduct(
337 SCIP* scip, /**< SCIP data structure */
338 SCIP_EXPR* expr /**< expression */
339 );
340
341/** returns whether an expression is a power expression */
343SCIP_Bool SCIPisExprPower(
344 SCIP* scip, /**< SCIP data structure */
345 SCIP_EXPR* expr /**< expression */
346 );
347
348/** print an expression as info-message */
351 SCIP* scip, /**< SCIP data structure */
352 SCIP_EXPR* expr, /**< expression to be printed */
353 FILE* file /**< file to print to, or NULL for stdout */
354 );
355
356/** initializes printing of expressions in dot format to a give FILE* pointer */
359 SCIP* scip, /**< SCIP data structure */
360 SCIP_EXPRPRINTDATA** printdata, /**< buffer to store dot printing data */
361 FILE* file, /**< file to print to, or NULL for stdout */
362 SCIP_EXPRPRINT_WHAT whattoprint /**< info on what to print for each expression */
363 );
364
365/** initializes printing of expressions in dot format to a file with given filename */
368 SCIP* scip, /**< SCIP data structure */
369 SCIP_EXPRPRINTDATA** printdata, /**< buffer to store dot printing data */
370 const char* filename, /**< name of file to print to */
371 SCIP_EXPRPRINT_WHAT whattoprint /**< info on what to print for each expression */
372 );
373
374/** main part of printing an expression in dot format */
377 SCIP* scip, /**< SCIP data structure */
378 SCIP_EXPRPRINTDATA* printdata, /**< data as initialized by \ref SCIPprintExprDotInit() */
379 SCIP_EXPR* expr /**< expression to be printed */
380 );
381
382/** finishes printing of expressions in dot format */
385 SCIP* scip, /**< SCIP data structure */
386 SCIP_EXPRPRINTDATA** printdata /**< buffer where dot printing data has been stored */
387 );
388
389/** shows a single expression by use of dot and gv
390 *
391 * This function is meant for debugging purposes.
392 * It's signature is kept as simple as possible to make it
393 * easily callable from gdb, for example.
394 *
395 * It prints the expression into a temporary file in dot format, then calls dot to create a postscript file, then calls ghostview (gv) to show the file.
396 * SCIP will hold until ghostscript is closed.
397 */
400 SCIP* scip, /**< SCIP data structure */
401 SCIP_EXPR* expr /**< expression to be printed */
402 );
403
404/** prints structure of an expression a la Maple's dismantle */
407 SCIP* scip, /**< SCIP data structure */
408 FILE* file, /**< file to print to, or NULL for stdout */
409 SCIP_EXPR* expr /**< expression to dismantle */
410 );
411
412/** evaluate an expression in a point
413 *
414 * Iterates over expressions to also evaluate children, if necessary.
415 * Value can be received via SCIPexprGetEvalValue().
416 * If an evaluation error (division by zero, ...) occurs, this value will
417 * be set to SCIP_INVALID.
418 *
419 * If a nonzero \p soltag is passed, then only (sub)expressions are
420 * reevaluated that have a different solution tag. If a soltag of 0
421 * is passed, then subexpressions are always reevaluated.
422 * The tag is stored together with the value and can be received via
423 * SCIPexprGetEvalTag().
424 */
427 SCIP* scip, /**< SCIP data structure */
428 SCIP_EXPR* expr, /**< expression to be evaluated */
429 SCIP_SOL* sol, /**< solution to be evaluated */
430 SCIP_Longint soltag /**< tag that uniquely identifies the solution (with its values), or 0. */
431 );
432
433/** returns a previously unused solution tag for expression evaluation */
435SCIP_Longint SCIPgetExprNewSoltag(
436 SCIP* scip /**< SCIP data structure */
437 );
438
439/**@} */
440
441/** @name Differentiation
442 * @anchor SCIP_EXPR_DIFF
443 *
444 * @par Gradients (Automatic differentiation Backward mode)
445 *
446 * Given a function, say, \f$f(s(x,y),t(x,y))\f$ there is a common mnemonic technique to compute its partial derivatives, using a tree diagram.
447 * Suppose we want to compute the partial derivative of \f$f\f$ w.r.t. \f$x\f$.
448 * Write the function as a tree:
449 *
450 * f
451 * |-----|
452 * s t
453 * |--| |--|
454 * x y x y
455 *
456 * The weight of an edge between two nodes represents the partial derivative of the parent w.r.t. the children, e.g.,
457 *
458 * f
459 * |
460 * s
461 *
462 * is \f$ \partial_sf \f$.
463 * The weight of a path is the product of the weight of the edges in the path.
464 * The partial derivative of \f$f\f$ w.r.t. \f$x\f$ is then the sum of the weights of all paths connecting \f$f\f$ with \f$x\f$:
465 * \f[ \frac{\partial f}{\partial x} = \partial_s f \cdot \partial_x s + \partial_t f \cdot \partial_x t. \f]
466 *
467 * We follow this method in order to compute the gradient of an expression (root) at a given point (point).
468 * Note that an expression is a DAG representation of a function, but there is a 1-1 correspondence between paths
469 * in the DAG and path in a tree diagram of a function.
470 * Initially, we set `root->derivative` to 1.0.
471 * Then, traversing the tree in Depth First (see \ref SCIPexpriterInit), for every expr that *has* children,
472 * we store in its i-th child, `child[i]->derivative`, the derivative of expr w.r.t. child evaluated at point multiplied with `expr->derivative`.
473 *
474 * For example:
475 * 1. `f->derivative` = 1.0
476 * 2. `s->derivative` = \f$\partial_s f \,\cdot\f$ `f->derivative` = \f$\partial_s f\f$
477 * 3. `x->derivative` = \f$\partial_x s \,\cdot\f$ `s->derivative` = \f$\partial_x s \cdot \partial_s f\f$
478 *
479 * However, when the child is a variable expressions, we actually need to initialize `child->derivative` to 0.0
480 * and afterwards add, instead of overwrite the computed value.
481 * The complete example would then be:
482 *
483 * 1. `f->derivative` = 1.0, `x->derivative` = 0.0, `y->derivative` = 0.0
484 * 2. `s->derivative` = \f$\partial_s f \,\cdot\f$ `f->derivative` = \f$\partial_s f\f$
485 * 3. `x->derivative` += \f$\partial_x s \,\cdot\f$ `s->derivative` = \f$\partial_x s \cdot \partial_s f\f$
486 * 4. `y->derivative` += \f$\partial_y s \,\cdot\f$ `s->derivative` = \f$\partial_y s \cdot \partial_s f\f$
487 * 5. `t->derivative` = \f$\partial_t f \,\cdot\f$ `f->derivative` = \f$\partial_t f\f$
488 * 6. `x->derivative` += \f$\partial_x t \,\cdot\f$ `t->derivative` = \f$\partial_x t \cdot \partial_t f\f$
489 * 7. `y->derivative` += \f$\partial_y t \,\cdot\f$ `t->derivative` = \f$\partial_y t \cdot \partial_t f\f$
490 *
491 * Note that, to compute this, we only need to know, for each expression, its partial derivatives w.r.t a given child at a point.
492 * This is what the callback `SCIP_DECL_EXPRBWDIFF` should return.
493 * Indeed, from "derivative of expr w.r.t. child evaluated at point multiplied with expr->derivative",
494 * note that at the moment of processing a child, we already know `expr->derivative`, so the only
495 * missing piece of information is "the derivative of expr w.r.t. child evaluated at point".
496 *
497 * An equivalent way of interpreting the procedure is that `expr->derivative` stores the derivative of the root w.r.t. expr.
498 * This way, `x->derivative` and `y->derivative` will contain the partial derivatives of root w.r.t. the variable, that is, the gradient.
499 * Note, however, that this analogy is only correct for leave expressions, since the derivative value of an intermediate expression gets overwritten.
500 *
501 *
502 * \par Hessian (Automatic differentiation Backward on Forward mode)
503 *
504 * Computing the Hessian is more complicated since it is the derivative of the gradient, which is a function with more than one output.
505 * We compute the Hessian by computing "directions" of the Hessian, that is \f$H\cdot u\f$ for different \f$u\f$.
506 * This is easy in general, since it is the gradient of the *scalar* function \f$\nabla f u\f$, that is,
507 * the directional derivative of \f$f\f$ in the direction \f$u\f$: \f$D_u f\f$.
508 *
509 * This is easily computed via the so called forward mode.
510 * Just as `expr->derivative` stores the partial derivative of the root w.r.t. expr,
511 * `expr->dot` stores the directional derivative of expr in the direction \f$u\f$.
512 * Then, by the chain rule, `expr->dot` = \f$\sum_{c:\text{children}} \partial_c \text{expr} \,\cdot\f$ `c->dot`.
513 *
514 * Starting with `x[i]->dot` = \f$u_i\f$, we can compute `expr->dot` for every expression at the same time we evaluate expr.
515 * Computing `expr->dot` is the purpose of the callback `SCIP_DECL_EXPRFWDIFF`.
516 * Obviously, when this callback is called, the "dots" of all children are known
517 * (just like evaluation, where the value of all children are known).
518 *
519 * Once we have this information, we compute the gradient of this function, following the same idea as before.
520 * We define `expr->bardot` to be the directional derivative in direction \f$u\f$ of the partial derivative of the root w.r.t `expr`,
521 * that is \f$D_u (\partial_{\text{expr}} f) = D_u\f$ (`expr->derivative`).
522 *
523 * This way, `x[i]->bardot` = \f$D_u (\partial_{x_i} f) = e_i^T H_f u\f$.
524 * Hence `vars->bardot` contain \f$H_f u\f$.
525 * By the chain rule, product rule, and definition we have
526 * \f{eqnarray*}{
527 * \texttt{expr->bardot} & = & D_u (\partial_{\text{expr}} f) \\
528 * & = & D_u ( \partial_{\text{parent}} f \cdot \partial_{\text{expr}} \text{parent} ) \\
529 * & = & D_u ( \texttt{parent->derivative} \cdot \partial_{\text{expr}} \text{parent} ) \\
530 * & = & \partial_{\text{expr}} \text{parent} \cdot D_u (\texttt{parent->derivative}) + \texttt{parent->derivative} \cdot D_u (\partial_{\text{expr}} \text{parent}) \\
531 * & = & \texttt{parent->bardot} \cdot \partial_{\text{expr}} \text{parent} + \texttt{parent->derivative} \cdot D_u (\partial_{\text{expr}} \text{parent})
532 * \f}
533 *
534 * Note that we have computed `parent->bardot` and `parent->derivative` at this point,
535 * while \f$\partial_{\text{expr}} \text{parent}\f$ is the return of `SCIP_DECL_EXPRBWDIFF`.
536 * Hence the only information we need to compute is \f$D_u (\partial_{\text{expr}} \text{parent})\f$.
537 * This is the purpose of the callback `SCIP_DECL_EXPRBWFWDIFF`.
538 *
539 * @{
540 */
541
542/** evaluates gradient of an expression for a given point
543 *
544 * Initiates an expression walk to also evaluate children, if necessary.
545 * Value can be received via SCIPgetExprPartialDiffNonlinear().
546 * If an error (division by zero, ...) occurs, this value will
547 * be set to SCIP_INVALID.
548 */
551 SCIP* scip, /**< SCIP data structure */
552 SCIP_EXPR* expr, /**< expression to be differentiated */
553 SCIP_SOL* sol, /**< solution to be evaluated (NULL for the current LP solution) */
554 SCIP_Longint soltag /**< tag that uniquely identifies the solution (with its values), or 0. */
555 );
556
557/** evaluates Hessian-vector product of an expression for a given point and direction
558 *
559 * Evaluates children, if necessary.
560 * Value can be received via SCIPgetExprPartialDiffGradientDirNonlinear().
561 * If an error (division by zero, ...) occurs, this value will
562 * be set to SCIP_INVALID.
563 */
566 SCIP* scip, /**< SCIP data structure */
567 SCIP_EXPR* expr, /**< expression to be differentiated */
568 SCIP_SOL* sol, /**< solution to be evaluated (NULL for the current LP solution) */
569 SCIP_Longint soltag, /**< tag that uniquely identifies the solution (with its values), or 0. */
570 SCIP_SOL* direction /**< direction */
571 );
572
573/**@} */ /* end of differentiation methods */
574
575/**@name Expressions
576 * @{
577 */
578
579/** possibly reevaluates and then returns the activity of the expression
580 *
581 * Reevaluate activity if currently stored is no longer uptodate (some bound was changed since last evaluation).
582 *
583 * The owner of the expression may overwrite the methods used to evaluate the activity,
584 * including whether the local or global domain of variables is used.
585 * By default (no owner, or owner doesn't overwrite activity evaluation),
586 * the local domain of variables is used.
587 *
588 * @note If expression is set to be integral, then activities are tightened to integral values.
589 * Thus, ensure that the integrality information is valid (if set to TRUE; the default (FALSE) is always ok).
590 */
593 SCIP* scip, /**< SCIP data structure */
594 SCIP_EXPR* expr /**< expression */
595 );
596
597/** compare expressions
598 * @return -1, 0 or 1 if expr1 <, =, > expr2, respectively
599 * @note The given expressions are assumed to be simplified.
600 */
603 SCIP* scip, /**< SCIP data structure */
604 SCIP_EXPR* expr1, /**< first expression */
605 SCIP_EXPR* expr2 /**< second expression */
606 );
607
608/** compute the hash value of an expression */
611 SCIP* scip, /**< SCIP data structure */
612 SCIP_EXPR* expr, /**< expression */
613 unsigned int* hashval /**< pointer to store the hash value */
614 );
615
616/** simplifies an expression
617 *
618 * This is largely inspired by Joel Cohen's
619 * *Computer algebra and symbolic computation: Mathematical methods*,
620 * in particular Chapter 3.
621 * The other fountain of inspiration are the simplifying methods of expr.c in SCIP 7.
622 *
623 * Note: The things to keep in mind when adding simplification rules are the following.
624 * I will be using the product expressions (see expr_product.c) as an example.
625 * There are mainly 3 parts of the simplification process. You need to decide
626 * at which stage the simplification rule makes sense.
627 * 1. Simplify each factor (simplifyFactor()): At this stage we got the children of the product expression.
628 * At this point, each child is simplified when viewed as a stand-alone expression, but not necessarily when viewed as child of a product expression.
629 * Rules like SP2, SP7, etc are enforced at this point.
630 * 2. Multiply the factors (mergeProductExprlist()): At this point rules like SP4, SP5 and SP14 are enforced.
631 * 3. Build the actual simplified product expression (buildSimplifiedProduct()):
632 * At this point rules like SP10, SP11, etc are enforced.
633 *
634 * During steps 1 and 2 do not forget to set the flag `changed` to TRUE when something actually changes.
635 *
636 * \par Definition of simplified expressions
637 *
638 * An expression is simplified if it
639 * - is a value expression
640 * - is a var expression
641 * - is a product expression such that
642 * - SP1: every child is simplified
643 * - SP2: no child is a product
644 * - SP4: no two children are the same expression (those should be multiplied)
645 * - SP5: the children are sorted [commutative rule]
646 * - SP7: no child is a value
647 * - SP8: its coefficient is 1.0 (otherwise should be written as sum)
648 * - SP10: it has at least two children
649 * - TODO?: at most one child is an `abs`
650 * - SP11: no two children are `expr*log(expr)`
651 * (TODO: we could handle more complicated stuff like \f$xy\log(x) \to - y * \mathrm{entropy}(x)\f$, but I am not sure this should happen at the simplification level;
652 * similar for \f$(xy) \log(xy)\f$, which currently simplifies to \f$xy \log(xy)\f$)
653 * - SP12: if it has two children, then neither of them is a sum (expand sums)
654 * - SP13: no child is a sum with a single term
655 * - SP14: at most one child is an `exp`
656 * - is a power expression such that
657 * - POW1: exponent is not 0
658 * - POW2: exponent is not 1
659 * - POW3: its child is not a value
660 * - POW4: its child is simplified
661 * - POW5: if exponent is integer, its child is not a product
662 * - POW6: if exponent is integer, its child is not a sum with a single term (\f$(2x)^2 \to 4x^2\f$)
663 * - POW7: if exponent is 2, its child is not a sum (expand sums)
664 * - POW8: its child is not a power unless \f$(x^n)^m\f$ with \f$nm\f$ being integer and \f$n\f$ or \f$m\f$ fractional and \f$n\f$ not being even integer
665 * - POW9: its child is not a sum with a single term with a positive coefficient: \f$(25x)^{0.5} \to 5 x^{0.5}\f$
666 * - POW10: its child is not a binary variable: \f$b^e, e > 0 \to b\f$; \f$b^e, e < 0 \to b := 1\f$
667 * - POW11: its child is not an exponential: \f$\exp(\text{expr})^e \to \exp(e\cdot\text{expr})\f$
668 * - is a signedpower expression such that
669 * - SPOW1: exponent is not 0
670 * - SPOW2: exponent is not 1
671 * - SPOW3: its child is not a value
672 * - SPOW4: its child is simplified
673 * - SPOW5: (TODO) do we want to distribute signpowers over products like we do for powers?
674 * - SPOW6: exponent is not an odd integer: (signpow odd expr) -> (pow odd expr)
675 * - SPOW8: if exponent is integer, its child is not a power
676 * - SPOW9: its child is not a sum with a single term: \f$\mathrm{signpow}(25x,0.5) \to 5\mathrm{signpow}(x,0.5)\f$
677 * - SPOW10: its child is not a binary variable: \f$\mathrm{signpow}(b,e), e > 0 \to b\f$; \f$\mathrm{signpow}(b,e), e < 0 \to b := 1\f$
678 * - SPOW11: its child is not an exponential: \f$\mathrm{signpow}(\exp(\text{expr}),e) \to \exp(e\cdot\text{expr})\f$
679 * - TODO: what happens when child is another signed power?
680 * - TODO: if child &ge; 0 -> transform to normal power; if child < 0 -> transform to - normal power
681 *
682 * TODO: Some of these criteria are too restrictive for signed powers; for example, the exponent does not need to be
683 * an integer for signedpower to distribute over a product (SPOW5, SPOW6, SPOW8). Others can also be improved.
684 * - is a sum expression such that
685 * - SS1: every child is simplified
686 * - SS2: no child is a sum
687 * - SS3: no child is a value (values should go in the constant of the sum)
688 * - SS4: no two children are the same expression (those should be summed up)
689 * - SS5: the children are sorted [commutative rule]
690 * - SS6: it has at least one child
691 * - SS7: if it consists of a single child, then either constant is != 0.0 or coef != 1
692 * - SS8: no child has coefficient 0
693 * - SS9: if a child c is a product that has an exponential expression as one of its factors, then the coefficient of c is +/-1.0
694 * - SS10: if a child c is an exponential, then the coefficient of c is +/-1.0
695 * - it is a function with simplified arguments, but not all of them can be values
696 * - TODO? a logarithm doesn't have a product as a child
697 * - TODO? the exponent of an exponential is always 1
698 *
699 * \par Ordering Rules (see SCIPexprCompare())
700 * \anchor EXPR_ORDER
701 * These rules define a total order on *simplified* expressions.
702 * There are two groups of rules, when comparing equal type expressions and different type expressions.
703 *
704 * Equal type expressions:
705 * - OR1: u,v value expressions: u < v &hArr; val(u) < val(v)
706 * - OR2: u,v var expressions: u < v &hArr; `SCIPvarGetIndex(var(u))` < `SCIPvarGetIndex(var(v))`
707 * - OR3: u,v are both sum or product expression: < is a lexicographical order on the terms
708 * - OR4: u,v are both pow: u < v &hArr; base(u) < base(v) or, base(u) = base(v) and expo(u) < expo(v)
709 * - OR5: u,v are \f$u = f(u_1, ..., u_n), v = f(v_1, ..., v_m)\f$: u < v &hArr; For the first k such that \f$u_k \neq v_k\f$, \f$u_k < v_k\f$, or if such a \f$k\f$ doesn't exist, then \f$n < m\f$.
710 *
711 * Different type expressions:
712 * - OR6: u value, v other: u < v always
713 * - OR7: u sum, v var or func: u < v &hArr; u < 0+v;
714 * In other words, if \f$u = \sum_{i=1}^n \alpha_i u_i\f$, then u < v &hArr; \f$u_n\f$ < v or if \f$u_n\f$ = v and \f$\alpha_n\f$ < 1.
715 * - OR8: u product, v pow, sum, var or func: u < v &hArr; u < 1*v;
716 * In other words, if \f$u = \prod_{i=1}^n u_i\f$, then u < v &hArr; \f$u_n\f$ < v.
717 * Note: since this applies only to simplified expressions, the form of the product is correct.
718 * Simplified products do *not* have constant coefficients.
719 * - OR9: u pow, v sum, var or func: u < v &hArr; u < v^1
720 * - OR10: u var, v func: u < v always
721 * - OR11: u func, v other type of func: u < v &hArr; name(type(u)) < name(type(v))
722 * - OR12: none of the rules apply: u < v &hArr; ! v < u
723 *
724 * Examples:
725 * - x < x^2 ?: x is var and x^2 power, so none applies (OR12).
726 * Hence, we try to answer x^2 < x ?: x^2 < x &hArr; x < x or if x = x and 2 < 1 &hArr; 2 < 1 &hArr; False. So x < x^2 is True.
727 * - x < x^-1 --OR12&rarr; ~(x^-1 < x) --OR9&rarr; ~(x^-1 < x^1) --OR4&rarr; ~(x < x or -1 < 1) &rarr; ~True &rarr; False
728 * - x*y < x --OR8&rarr; x*y < 1*x --OR3&rarr; y < x --OR2&rarr; False
729 * - x*y < y --OR8&rarr; x*y < 1*y --OR3&rarr; y < x --OR2&rarr; False
730 *
731 * \par Algorithm
732 *
733 * The recursive version of the algorithm is
734 *
735 * EXPR simplify(expr)
736 * for c in 1..expr->nchildren
737 * expr->children[c] = simplify(expr->children[c])
738 * end
739 * return expr->exprhdlr->simplify(expr)
740 * end
741 *
742 * Important: Whatever is returned by a simplify callback **has** to be simplified.
743 * Also, all children of the given expression **are** already simplified.
744 */
747 SCIP* scip, /**< SCIP data structure */
748 SCIP_EXPR* rootexpr, /**< expression to be simplified */
749 SCIP_EXPR** simplified, /**< buffer to store simplified expression */
750 SCIP_Bool* changed, /**< buffer to store if rootexpr actually changed */
751 SCIP_Bool* infeasible, /**< buffer to store whether infeasibility has been detected */
752 SCIP_DECL_EXPR_OWNERCREATE((*ownercreate)), /**< function to call to create ownerdata */
753 void* ownercreatedata /**< data to pass to ownercreate */
754 );
755
756/** replaces common sub-expressions in a given expression graph by using a hash key for each expression
757 *
758 * The algorithm consists of two steps:
759 *
760 * 1. traverse through all given expressions and compute for each of them a (not necessarily unique) hash
761 *
762 * 2. initialize an empty hash table and traverse through all expression; check for each of them if we can find a
763 * structural equivalent expression in the hash table; if yes we replace the expression by the expression inside the
764 * hash table, otherwise we add it to the hash table
765 *
766 * @note the hash keys of the expressions are used for the hashing inside the hash table; to compute if two expressions
767 * (with the same hash) are structurally the same we use the function SCIPexprCompare().
768 */
771 SCIP* scip, /**< SCIP data structure */
772 SCIP_EXPR** exprs, /**< expressions (possibly replaced by equivalent on output) */
773 int nexprs, /**< total number of expressions */
774 SCIP_Bool* replacedroot /**< buffer to store whether any root expression (expression in exprs) was replaced */
775);
776
777/** computes the curvature of a given expression and all its subexpressions
778 *
779 * @note this function also evaluates all subexpressions w.r.t. current variable bounds
780 * @note this function relies on information from the curvature callback of expression handlers only,
781 * consider using function @ref SCIPhasExprCurvature() of the convex-nlhdlr instead, as that uses more information to deduce convexity
782 */
785 SCIP* scip, /**< SCIP data structure */
786 SCIP_EXPR* expr /**< expression */
787 );
788
789/** computes integrality information of a given expression and all its subexpressions
790 *
791 * The integrality information can be accessed via SCIPexprIsIntegral().
792 */
795 SCIP* scip, /**< SCIP data structure */
796 SCIP_EXPR* expr /**< expression */
797 );
798
799/** returns the total number of variable expressions in an expression
800 *
801 * The function counts variable expressions in common sub-expressions only once, but
802 * counts variables appearing in several variable expressions multiple times.
803 */
806 SCIP* scip, /**< SCIP data structure */
807 SCIP_EXPR* expr, /**< expression */
808 int* nvars /**< buffer to store the total number of variables */
809 );
810
811/** returns all variable expressions contained in a given expression
812 *
813 * The array to store all variable expressions needs to be at least of size
814 * the number of unique variable expressions in the expression which is given by SCIPgetExprNVars().
815 *
816 * If every variable is represented by only one variable expression (common subexpression have been removed)
817 * then SCIPgetExprNVars() can be bounded by SCIPgetNTotalVars().
818 * If, in addition, non-active variables have been removed from the expression, e.g., by simplifying,
819 * then SCIPgetExprNVars() can be bounded by SCIPgetNVars().
820 *
821 * @note function captures variable expressions
822 */
825 SCIP* scip, /**< SCIP data structure */
826 SCIP_EXPR* expr, /**< expression */
827 SCIP_EXPR** varexprs, /**< array to store all variable expressions */
828 int* nvarexprs /**< buffer to store the total number of variable expressions */
829 );
830
831/** @} */
832
833/**@name Expression Handler Callbacks
834 * @{
835 */
836
837/** calls the print callback for an expression
838 *
839 * @see SCIP_DECL_EXPRPRINT
840 */
843
844/** calls the curvature callback for an expression
845 *
846 * @see SCIP_DECL_EXPRCURVATURE
847 *
848 * Returns unknown curvature if callback not implemented.
849 */
852
853/** calls the monotonicity callback for an expression
854 *
855 * @see SCIP_DECL_EXPRMONOTONICITY
856 *
857 * Returns unknown monotonicity if callback not implemented.
858 */
861
862/** calls the eval callback for an expression with given values for children
863 *
864 * Does not iterates over expressions, but requires values for children to be given.
865 * Value is not stored in expression, but returned in `val`.
866 * If an evaluation error (division by zero, ...) occurs, this value will
867 * be set to `SCIP_INVALID`.
868 */
871 SCIP* scip, /**< SCIP data structure */
872 SCIP_EXPR* expr, /**< expression to be evaluated */
873 SCIP_Real* childrenvalues, /**< values for children */
874 SCIP_Real* val /**< buffer to store evaluated value */
875 );
876
877/** calls the eval and fwdiff callback of an expression with given values for children
878 *
879 * Does not iterates over expressions, but requires values for children and direction to be given.
880 *
881 * Value is not stored in expression, but returned in `val`.
882 * If an evaluation error (division by zero, ...) occurs, this value will be set to `SCIP_INVALID`.
883 *
884 * Direction is not stored in expression, but returned in `dot`.
885 * If an differentiation error (division by zero, ...) occurs, this value will be set to `SCIP_INVALID`.
886 */
889 SCIP* scip, /**< SCIP data structure */
890 SCIP_EXPR* expr, /**< expression to be evaluated */
891 SCIP_Real* childrenvalues, /**< values for children */
892 SCIP_Real* direction, /**< direction in which to differentiate */
893 SCIP_Real* val, /**< buffer to store evaluated value */
894 SCIP_Real* dot /**< buffer to store derivative value */
895 );
896
897/** calls the interval evaluation callback for an expression
898 *
899 * @see SCIP_DECL_EXPRINTEVAL
900 *
901 * Returns entire interval if callback not implemented.
902 */
905
906/** calls the estimate callback for an expression
907 *
908 * @see SCIP_DECL_EXPRESTIMATE
909 *
910 * Returns without success if callback not implemented.
911 */
914
915/** calls the initial estimators callback for an expression
916 *
917 * @see SCIP_DECL_EXPRINITESTIMATES
918 *
919 * Returns no estimators if callback not implemented.
920 */
923
924/** calls the simplify callback for an expression
925 *
926 * @see SCIP_DECL_EXPRSIMPLIFY
927 *
928 * Returns unmodified expression if simplify callback not implemented.
929 *
930 * Does not simplify descendants (children, etc). Use SCIPsimplifyExpr() for that.
931 */
934
935/** calls the reverse propagation callback for an expression
936 *
937 * @see SCIP_DECL_EXPRREVERSEPROP
938 *
939 * Returns unmodified `childrenbounds` if reverseprop callback not implemented.
940 */
943
944#ifdef NDEBUG
945#define SCIPappendExprChild(scip, expr, child) SCIPexprAppendChild((scip)->set, (scip)->mem->probmem, expr, child)
946#define SCIPreplaceExprChild(scip, expr, childidx, newchild) SCIPexprReplaceChild((scip)->set, (scip)->stat, (scip)->mem->probmem, expr, childidx, newchild)
947#define SCIPremoveExprChildren(scip, expr) SCIPexprRemoveChildren((scip)->set, (scip)->stat, (scip)->mem->probmem, expr)
948#define SCIPduplicateExpr(scip, expr, copyexpr, mapexpr, mapexprdata, ownercreate, ownercreatedata) SCIPexprCopy((scip)->set, (scip)->stat, (scip)->mem->probmem, (scip)->set, (scip)->stat, (scip)->mem->probmem, expr, copyexpr, mapexpr, mapexprdata, ownercreate, ownercreatedata)
949#define SCIPduplicateExprShallow(scip, expr, copyexpr, ownercreate, ownercreatedata) SCIPexprDuplicateShallow((scip)->set, (scip)->mem->probmem, expr, copyexpr, ownercreate, ownercreatedata)
950#define SCIPcaptureExpr(expr) SCIPexprCapture(expr)
951#define SCIPreleaseExpr(scip, expr) SCIPexprRelease((scip)->set, (scip)->stat, (scip)->mem->probmem, expr)
952#define SCIPisExprVar(scip, expr) SCIPexprIsVar((scip)->set, expr)
953#define SCIPisExprValue(scip, expr) SCIPexprIsValue((scip)->set, expr)
954#define SCIPisExprSum(scip, expr) SCIPexprIsSum((scip)->set, expr)
955#define SCIPisExprProduct(scip, expr) SCIPexprIsProduct((scip)->set, expr)
956#define SCIPisExprPower(scip, expr) SCIPexprIsPower((scip)->set, expr)
957#define SCIPprintExpr(scip, expr, file) SCIPexprPrint((scip)->set, (scip)->stat, (scip)->mem->probmem, (scip)->messagehdlr, file, expr)
958#define SCIPevalExpr(scip, expr, sol, soltag) SCIPexprEval((scip)->set, (scip)->stat, (scip)->mem->probmem, expr, sol, soltag)
959#define SCIPgetExprNewSoltag(scip) (++((scip)->stat->exprlastsoltag))
960#define SCIPevalExprGradient(scip, expr, sol, soltag) SCIPexprEvalGradient((scip)->set, (scip)->stat, (scip)->mem->probmem, expr, sol, soltag)
961#define SCIPevalExprHessianDir(scip, expr, sol, soltag, direction) SCIPexprEvalHessianDir((scip)->set, (scip)->stat, (scip)->mem->probmem, expr, sol, soltag, direction)
962#define SCIPevalExprActivity(scip, expr) SCIPexprEvalActivity((scip)->set, (scip)->stat, (scip)->mem->probmem, expr)
963#define SCIPcompareExpr(scip, expr1, expr2) SCIPexprCompare((scip)->set, expr1, expr2)
964#define SCIPsimplifyExpr(scip, rootexpr, simplified, changed, infeasible, ownercreate, ownercreatedata) SCIPexprSimplify((scip)->set, (scip)->stat, (scip)->mem->probmem, rootexpr, simplified, changed, infeasible, ownercreate, ownercreatedata)
965#define SCIPcallExprCurvature(scip, expr, exprcurvature, success, childcurv) SCIPexprhdlrCurvatureExpr(SCIPexprGetHdlr(expr), (scip)->set, expr, exprcurvature, success, childcurv)
966#define SCIPcallExprMonotonicity(scip, expr, childidx, result) SCIPexprhdlrMonotonicityExpr(SCIPexprGetHdlr(expr), (scip)->set, expr, childidx, result)
967#define SCIPcallExprEval(scip, expr, childrenvalues, val) SCIPexprhdlrEvalExpr(SCIPexprGetHdlr(expr), (scip)->set, (scip)->mem->buffer, expr, val, childrenvalues, NULL)
968#define SCIPcallExprEvalFwdiff(scip, expr, childrenvalues, direction, val, dot) SCIPexprhdlrEvalFwDiffExpr(SCIPexprGetHdlr(expr), (scip)->set, (scip)->mem->buffer, expr, val, dot, childrenvalues, NULL, direction, NULL)
969#define SCIPcallExprInteval(scip, expr, interval, intevalvar, intevalvardata) SCIPexprhdlrIntEvalExpr(SCIPexprGetHdlr(expr), (scip)->set, expr, interval, intevalvar, intevalvardata)
970#define SCIPcallExprEstimate(scip, expr, localbounds, globalbounds, refpoint, overestimate, targetvalue, coefs, constant, islocal, success, branchcand) SCIPexprhdlrEstimateExpr(SCIPexprGetHdlr(expr), (scip)->set, expr, localbounds, globalbounds, refpoint, overestimate, targetvalue, coefs, constant, islocal, success, branchcand)
971#define SCIPcallExprInitestimates(scip, expr, bounds, overestimate, coefs, constant, nreturned) SCIPexprhdlrInitEstimatesExpr(SCIPexprGetHdlr(expr), (scip)->set, expr, bounds, overestimate, coefs, constant, nreturned)
972#define SCIPcallExprSimplify(scip, expr, simplifiedexpr, ownercreate, ownercreatedata) SCIPexprhdlrSimplifyExpr(SCIPexprGetHdlr(expr), (scip)->set, expr, simplifiedexpr, ownercreate, ownercreatedata)
973#define SCIPcallExprReverseprop(scip, expr, bounds, childrenbounds, infeasible) SCIPexprhdlrReversePropExpr(SCIPexprGetHdlr(expr), (scip)->set, expr, bounds, childrenbounds, infeasible)
974#endif
975
976/** @} */
977
978
979/**@name Expression Iterator */
980/**@{ */
981
982/** creates an expression iterator */
985 SCIP* scip, /**< SCIP data structure */
986 SCIP_EXPRITER** iterator /**< buffer to store expression iterator */
987 );
988
989/** frees an expression iterator */
992 SCIP_EXPRITER** iterator /**< pointer to the expression iterator */
993 );
994
995#ifdef NDEBUG
996#define SCIPcreateExpriter(scip, iterator) SCIPexpriterCreate((scip)->stat, (scip)->mem->probmem, iterator)
997#define SCIPfreeExpriter(iterator) SCIPexpriterFree(iterator)
998#endif
999
1000/** @} */
1001
1002
1003/**@name Quadratic Expressions */
1004/**@{ */
1005
1006/** checks whether an expression is quadratic
1007 *
1008 * An expression is quadratic if it is either a square (of some expression), a product (of two expressions),
1009 * or a sum of terms where at least one is a square or a product.
1010 *
1011 * Use SCIPexprGetQuadraticData() to get data about the representation as quadratic.
1012 */
1015 SCIP* scip, /**< SCIP data structure */
1016 SCIP_EXPR* expr, /**< expression */
1017 SCIP_Bool* isquadratic /**< buffer to store result */
1018 );
1019
1020/** frees information on quadratic representation of an expression
1021 *
1022 * Before doing changes to an expression, it can be useful to call this function.
1023 */
1026 SCIP* scip, /**< SCIP data structure */
1027 SCIP_EXPR* expr /**< expression */
1028 );
1029
1030/** evaluates quadratic term in a solution
1031 *
1032 * \note This requires that every expressiion used in the quadratic data is a variable expression.
1033 */
1035SCIP_Real SCIPevalExprQuadratic(
1036 SCIP* scip, /**< SCIP data structure */
1037 SCIP_EXPR* expr, /**< quadratic expression */
1038 SCIP_SOL* sol /**< solution to evaluate, or NULL for LP solution */
1039 );
1040
1041/** prints quadratic expression */
1044 SCIP* scip, /**< SCIP data structure */
1045 SCIP_EXPR* expr /**< quadratic expression */
1046 );
1047
1048/** checks the curvature of the quadratic expression
1049 *
1050 * For this, it builds the matrix Q of quadratic coefficients and computes its eigenvalues using LAPACK.
1051 * If Q is
1052 * - semidefinite positive -> curv is set to convex,
1053 * - semidefinite negative -> curv is set to concave,
1054 * - otherwise -> curv is set to unknown.
1055 *
1056 * If `assumevarfixed` is given and some expressions in quadratic terms correspond to variables present in
1057 * this hashmap, then the corresponding rows and columns are ignored in the matrix Q.
1058 */
1061 SCIP* scip, /**< SCIP data structure */
1062 SCIP_EXPR* expr, /**< quadratic expression */
1063 SCIP_EXPRCURV* curv, /**< pointer to store the curvature of quadratics */
1064 SCIP_HASHMAP* assumevarfixed, /**< hashmap containing variables that should be assumed to be fixed, or NULL */
1065 SCIP_Bool storeeigeninfo /**< whether the eigenvalues and eigenvectors should be stored */
1066 );
1067
1068#ifdef NDEBUG
1069#define SCIPcheckExprQuadratic(scip, expr, isquadratic) SCIPexprCheckQuadratic((scip)->set, (scip)->mem->probmem, expr, isquadratic)
1070#define SCIPfreeExprQuadratic(scip, expr) SCIPexprFreeQuadratic((scip)->mem->probmem, expr)
1071#define SCIPcomputeExprQuadraticCurvature(scip, expr, curv, assumevarfixed, storeeigeninfo) SCIPexprComputeQuadraticCurvature((scip)->set, (scip)->mem->probmem, (scip)->mem->buffer, (scip)->messagehdlr, expr, curv, assumevarfixed, storeeigeninfo)
1072#endif
1073
1074/** @} */
1075
1076/** @} */
1077
1078#ifdef __cplusplus
1079}
1080#endif
1081
1082#endif /* SCIP_SCIP_EXPR_H_ */
private functions to work with algebraic expressions
static SCIP_RETCODE eval(SCIP *scip, SCIP_EXPR *expr, SCIP_EXPRINTDATA *exprintdata, const vector< Type > &x, Type &val)
int SCIPgetNExprhdlrs(SCIP *scip)
Definition scip_expr.c:848
SCIP_EXPRHDLR * SCIPgetExprhdlrProduct(SCIP *scip)
Definition scip_expr.c:904
SCIP_EXPRHDLR * SCIPgetExprhdlrVar(SCIP *scip)
Definition scip_expr.c:871
SCIP_EXPRHDLR ** SCIPgetExprhdlrs(SCIP *scip)
Definition scip_expr.c:837
SCIP_EXPRHDLR * SCIPgetExprhdlrValue(SCIP *scip)
Definition scip_expr.c:882
SCIP_EXPRHDLR * SCIPgetExprhdlrSum(SCIP *scip)
Definition scip_expr.c:893
SCIP_RETCODE SCIPincludeExprhdlr(SCIP *scip, SCIP_EXPRHDLR **exprhdlr, const char *name, const char *desc, unsigned int precedence, SCIP_DECL_EXPREVAL((*eval)), SCIP_EXPRHDLRDATA *data)
Definition scip_expr.c:814
SCIP_EXPRHDLR * SCIPgetExprhdlrPower(SCIP *scip)
Definition scip_expr.c:915
SCIP_EXPRHDLR * SCIPfindExprhdlr(SCIP *scip, const char *name)
Definition scip_expr.c:859
SCIP_RETCODE SCIPcreateExprQuadratic(SCIP *scip, SCIP_EXPR **expr, int nlinvars, SCIP_VAR **linvars, SCIP_Real *lincoefs, int nquadterms, SCIP_VAR **quadvars1, SCIP_VAR **quadvars2, SCIP_Real *quadcoefs, SCIP_DECL_EXPR_OWNERCREATE((*ownercreate)), void *ownercreatedata)
Definition scip_expr.c:1023
SCIP_RETCODE SCIPcreateExprMonomial(SCIP *scip, SCIP_EXPR **expr, int nfactors, SCIP_VAR **vars, SCIP_Real *exponents, SCIP_DECL_EXPR_OWNERCREATE((*ownercreate)), void *ownercreatedata)
Definition scip_expr.c:1131
SCIP_RETCODE SCIPcreateExpr(SCIP *scip, SCIP_EXPR **expr, SCIP_EXPRHDLR *exprhdlr, SCIP_EXPRDATA *exprdata, int nchildren, SCIP_EXPR **children, SCIP_DECL_EXPR_OWNERCREATE((*ownercreate)), void *ownercreatedata)
Definition scip_expr.c:964
SCIP_RETCODE SCIPappendExprChild(SCIP *scip, SCIP_EXPR *expr, SCIP_EXPR *child)
Definition scip_expr.c:1220
SCIP_RETCODE SCIPevalExprHessianDir(SCIP *scip, SCIP_EXPR *expr, SCIP_SOL *sol, SCIP_Longint soltag, SCIP_SOL *direction)
Definition scip_expr.c:1679
SCIP_RETCODE SCIPevalExpr(SCIP *scip, SCIP_EXPR *expr, SCIP_SOL *sol, SCIP_Longint soltag)
Definition scip_expr.c:1625
SCIP_RETCODE SCIPprintExprQuadratic(SCIP *scip, SCIP_EXPR *expr)
Definition scip_expr.c:2429
SCIP_RETCODE SCIPcomputeExprIntegrality(SCIP *scip, SCIP_EXPR *expr)
Definition scip_expr.c:1989
SCIP_Bool SCIPisExprProduct(SCIP *scip, SCIP_EXPR *expr)
Definition scip_expr.c:1454
SCIP_RETCODE SCIPevalExprGradient(SCIP *scip, SCIP_EXPR *expr, SCIP_SOL *sol, SCIP_Longint soltag)
Definition scip_expr.c:1657
SCIP_RETCODE SCIPprintExprDotInit2(SCIP *scip, SCIP_EXPRPRINTDATA **printdata, const char *filename, SCIP_EXPRPRINT_WHAT whattoprint)
Definition scip_expr.c:1507
SCIP_Longint SCIPgetExprNewSoltag(SCIP *scip)
Definition scip_expr.c:1641
SCIP_Bool SCIPisExprSum(SCIP *scip, SCIP_EXPR *expr)
Definition scip_expr.c:1443
SCIP_RETCODE SCIPgetExprNVars(SCIP *scip, SCIP_EXPR *expr, int *nvars)
Definition scip_expr.c:2032
SCIP_RETCODE SCIPduplicateExprShallow(SCIP *scip, SCIP_EXPR *expr, SCIP_EXPR **copyexpr, SCIP_DECL_EXPR_OWNERCREATE((*ownercreate)), void *ownercreatedata)
Definition scip_expr.c:1291
SCIP_RETCODE SCIPreplaceExprChild(SCIP *scip, SCIP_EXPR *expr, int childidx, SCIP_EXPR *newchild)
Definition scip_expr.c:1238
SCIP_Bool SCIPisExprValue(SCIP *scip, SCIP_EXPR *expr)
Definition scip_expr.c:1432
SCIP_RETCODE SCIPcreateExpr2(SCIP *scip, SCIP_EXPR **expr, SCIP_EXPRHDLR *exprhdlr, SCIP_EXPRDATA *exprdata, SCIP_EXPR *child1, SCIP_EXPR *child2, SCIP_DECL_EXPR_OWNERCREATE((*ownercreate)), void *ownercreatedata)
Definition scip_expr.c:985
void SCIPfreeExprQuadratic(SCIP *scip, SCIP_EXPR *expr)
Definition scip_expr.c:2354
SCIP_RETCODE SCIPprintExprDot(SCIP *scip, SCIP_EXPRPRINTDATA *printdata, SCIP_EXPR *expr)
Definition scip_expr.c:1523
int SCIPcompareExpr(SCIP *scip, SCIP_EXPR *expr1, SCIP_EXPR *expr2)
Definition scip_expr.c:1724
SCIP_RETCODE SCIPreleaseExpr(SCIP *scip, SCIP_EXPR **expr)
Definition scip_expr.c:1407
SCIP_Bool SCIPisExprVar(SCIP *scip, SCIP_EXPR *expr)
Definition scip_expr.c:1421
SCIP_RETCODE SCIPparseExpr(SCIP *scip, SCIP_EXPR **expr, const char *exprstr, const char **finalpos, SCIP_DECL_EXPR_OWNERCREATE((*ownercreate)), void *ownercreatedata)
Definition scip_expr.c:1370
SCIP_RETCODE SCIPhashExpr(SCIP *scip, SCIP_EXPR *expr, unsigned int *hashval)
Definition scip_expr.c:1736
SCIP_RETCODE SCIPcomputeExprQuadraticCurvature(SCIP *scip, SCIP_EXPR *expr, SCIP_EXPRCURV *curv, SCIP_HASHMAP *assumevarfixed, SCIP_Bool storeeigeninfo)
Definition scip_expr.c:2545
SCIP_RETCODE SCIPcallExprEval(SCIP *scip, SCIP_EXPR *expr, SCIP_Real *childrenvalues, SCIP_Real *val)
Definition scip_expr.c:2159
SCIP_RETCODE SCIPcreateExpriter(SCIP *scip, SCIP_EXPRITER **iterator)
Definition scip_expr.c:2296
SCIP_RETCODE SCIPcallExprEvalFwdiff(SCIP *scip, SCIP_EXPR *expr, SCIP_Real *childrenvalues, SCIP_Real *direction, SCIP_Real *val, SCIP_Real *dot)
Definition scip_expr.c:2186
SCIP_RETCODE SCIPprintExpr(SCIP *scip, SCIP_EXPR *expr, FILE *file)
Definition scip_expr.c:1476
SCIP_Bool SCIPisExprPower(SCIP *scip, SCIP_EXPR *expr)
Definition scip_expr.c:1465
SCIP_RETCODE SCIPreplaceCommonSubexpressions(SCIP *scip, SCIP_EXPR **exprs, int nexprs, SCIP_Bool *replacedroot)
Definition scip_expr.c:1794
SCIP_RETCODE SCIPcheckExprQuadratic(SCIP *scip, SCIP_EXPR *expr, SCIP_Bool *isquadratic)
Definition scip_expr.c:2336
SCIP_RETCODE SCIPprintExprDotFinal(SCIP *scip, SCIP_EXPRPRINTDATA **printdata)
Definition scip_expr.c:1537
SCIP_RETCODE SCIPprintExprDotInit(SCIP *scip, SCIP_EXPRPRINTDATA **printdata, FILE *file, SCIP_EXPRPRINT_WHAT whattoprint)
Definition scip_expr.c:1491
SCIP_RETCODE SCIPcopyExpr(SCIP *sourcescip, SCIP *targetscip, SCIP_EXPR *expr, SCIP_EXPR **copyexpr, SCIP_DECL_EXPR_OWNERCREATE((*ownercreate)), void *ownercreatedata, SCIP_HASHMAP *varmap, SCIP_HASHMAP *consmap, SCIP_Bool global, SCIP_Bool *valid)
Definition scip_expr.c:1308
SCIP_RETCODE SCIPshowExpr(SCIP *scip, SCIP_EXPR *expr)
Definition scip_expr.c:1559
SCIP_Real SCIPevalExprQuadratic(SCIP *scip, SCIP_EXPR *expr, SCIP_SOL *sol)
Definition scip_expr.c:2369
SCIP_RETCODE SCIPcomputeExprCurvature(SCIP *scip, SCIP_EXPR *expr)
Definition scip_expr.c:1909
void SCIPfreeExpriter(SCIP_EXPRITER **iterator)
Definition scip_expr.c:2310
SCIP_RETCODE SCIPduplicateExpr(SCIP *scip, SCIP_EXPR *expr, SCIP_EXPR **copyexpr, SCIP_DECL_EXPR_MAPEXPR((*mapexpr)), void *mapexprdata, SCIP_DECL_EXPR_OWNERCREATE((*ownercreate)), void *ownercreatedata)
Definition scip_expr.c:1271
void SCIPcaptureExpr(SCIP_EXPR *expr)
Definition scip_expr.c:1399
SCIP_RETCODE SCIPgetExprVarExprs(SCIP *scip, SCIP_EXPR *expr, SCIP_EXPR **varexprs, int *nvarexprs)
Definition scip_expr.c:2070
SCIP_RETCODE SCIPdismantleExpr(SCIP *scip, FILE *file, SCIP_EXPR *expr)
Definition scip_expr.c:1598
SCIP_RETCODE SCIPremoveExprChildren(SCIP *scip, SCIP_EXPR *expr)
Definition scip_expr.c:1257
SCIP_RETCODE SCIPsimplifyExpr(SCIP *scip, SCIP_EXPR *rootexpr, SCIP_EXPR **simplified, SCIP_Bool *changed, SCIP_Bool *infeasible, SCIP_DECL_EXPR_OWNERCREATE((*ownercreate)), void *ownercreatedata)
Definition scip_expr.c:1763
SCIP_RETCODE SCIPevalExprActivity(SCIP *scip, SCIP_EXPR *expr)
Definition scip_expr.c:1707
static SCIP_SOL * sol
int nvars
static SCIP_VAR ** vars
internal methods for global SCIP settings
datastructures for block memory pools and memory buffers
SCIP main data structure.
datastructures for global SCIP settings
datastructures for problem statistics
type and macro definitions related to algebraic expressions
#define SCIP_DECL_EXPR_OWNERCREATE(x)
Definition type_expr.h:140
#define SCIP_DECL_EXPRREVERSEPROP(x)
Definition type_expr.h:654
#define SCIP_DECL_EXPRINITESTIMATES(x)
Definition type_expr.h:605
#define SCIP_DECL_EXPRCURVATURE(x)
Definition type_expr.h:337
struct SCIP_ExprhdlrData SCIP_EXPRHDLRDATA
Definition type_expr.h:192
struct SCIP_ExprData SCIP_EXPRDATA
Definition type_expr.h:53
SCIP_EXPRCURV
Definition type_expr.h:58
#define SCIP_DECL_EXPRINTEVAL(x)
Definition type_expr.h:536
#define SCIP_DECL_EXPRMONOTONICITY(x)
Definition type_expr.h:355
unsigned int SCIP_EXPRPRINT_WHAT
Definition type_expr.h:724
#define SCIP_DECL_EXPRSIMPLIFY(x)
Definition type_expr.h:629
#define SCIP_DECL_EXPREVAL(x)
Definition type_expr.h:423
#define SCIP_DECL_EXPRPRINT(x)
Definition type_expr.h:286
#define SCIP_DECL_EXPR_MAPEXPR(x)
Definition type_expr.h:179
struct SCIP_ExprPrintData SCIP_EXPRPRINTDATA
Definition type_expr.h:725
#define SCIP_DECL_EXPRESTIMATE(x)
Definition type_expr.h:572
type definitions for miscellaneous datastructures
enum SCIP_Retcode SCIP_RETCODE
type definitions for SCIP's main datastructure