Symmetry

Detailed Description

methods for symmetry handling

Functions
SCIP_RETCODE	SCIPcomputeOrbitsSym (SCIP *scip, SCIP_Bool issigned, SCIP_VAR **permvars, int npermvars, int **perms, int nperms, int *orbits, int *orbitbegins, int *norbits)
SCIP_RETCODE	SCIPcomputeOrbitsFilterSym (SCIP *scip, int npermvars, int **permstrans, int nperms, SCIP_Shortbool *inactiveperms, int *orbits, int *orbitbegins, int *norbits, int *components, int *componentbegins, int *vartocomponent, unsigned *componentblocked, int ncomponents, int nmovedpermvars)
SCIP_RETCODE	SCIPcomputeOrbitsComponentsSym (SCIP *scip, int npermvars, int **permstrans, int nperms, int *components, int *componentbegins, int *vartocomponent, int ncomponents, int *orbits, int *orbitbegins, int *norbits, int *varorbitmap)
SCIP_RETCODE	SCIPcomputeOrbitVar (SCIP *scip, int npermvars, int **perms, int **permstrans, int *components, int *componentbegins, SCIP_Shortbool *ignoredvars, SCIP_Shortbool *varfound, int varidx, int component, int *orbit, int *orbitsize)
SCIP_RETCODE	SCIPisInvolutionPerm (int *perm, SCIP_VAR **vars, int nvars, int *ntwocyclesperm, int *nbincyclesperm, SCIP_Bool earlytermination)
SCIP_RETCODE	SCIPdetermineNVarsAffectedSym (SCIP *scip, int **perms, int nperms, SCIP_VAR **permvars, int npermvars, int *nvarsaffected)
SCIP_RETCODE	SCIPcomputeComponentsSym (SCIP *scip, SYM_SYMTYPE symtype, int **perms, int nperms, SCIP_VAR **permvars, int npermvars, SCIP_Bool transposed, int **components, int **componentbegins, int **vartocomponent, unsigned **componentblocked, int *ncomponents)
SCIP_RETCODE	SCIPextendSubOrbitope (int **suborbitope, int nrows, int nfilledcols, int coltoextend, int *perm, SCIP_Bool leftextension, int **nusedelems, SCIP_VAR **permvars, SCIP_Shortbool *rowisbinary, SCIP_Bool *success, SCIP_Bool *infeasible)
SCIP_RETCODE	SCIPgenerateOrbitopeVarsMatrix (SCIP *scip, SCIP_VAR ****vars, int nrows, int ncols, SCIP_VAR **permvars, int npermvars, int **orbitopevaridx, int *columnorder, int *nusedelems, SCIP_Shortbool *rowisbinary, SCIP_Bool *infeasible, SCIP_Bool storelexorder, int **lexorder, int *nvarsorder, int *maxnvarsorder)
SCIP_RETCODE	SCIPisPackingPartitioningOrbitope (SCIP *scip, SCIP_VAR ***vars, int nrows, int ncols, SCIP_Bool **pprows, int *npprows, SCIP_ORBITOPETYPE *type)
SCIP_RETCODE	SCIPdetectSingleOrDoubleLexMatrices (SCIP *scip, SCIP_Bool detectsinglelex, int **perms, int nperms, int permlen, SCIP_Bool *success, SCIP_Bool *isorbitope, int ***lexmatrix, int *nrows, int *ncols, int **lexrowsbegin, int **lexcolsbegin, int *nrowmatrices, int *ncolmatrices)
SCIP_Bool	SCIPsymEQ (SCIP *scip, SCIP_Real val1, SCIP_Real val2)
SCIP_Bool	SCIPsymLE (SCIP *scip, SCIP_Real val1, SCIP_Real val2)
SCIP_Bool	SCIPsymGE (SCIP *scip, SCIP_Real val1, SCIP_Real val2)
SCIP_Bool	SCIPsymLT (SCIP *scip, SCIP_Real val1, SCIP_Real val2)
SCIP_Bool	SCIPsymGT (SCIP *scip, SCIP_Real val1, SCIP_Real val2)

Function Documentation

SCIPcomputeOrbitsSym()

SCIP_RETCODE SCIPcomputeOrbitsSym	(	SCIP *	scip,
		SCIP_Bool	issigned,
		SCIP_VAR **	permvars,
		int	npermvars,
		int **	perms,
		int	nperms,
		int *	orbits,
		int *	orbitbegins,
		int *	norbits
	)

compute non-trivial orbits of symmetry group

The non-trivial orbits of the group action are stored in the array orbits of length npermvars. This array contains the indices of variables from the permvars array such that variables that are contained in the same orbit appear consecutively in the orbits array. The variables of the i-th orbit have indices orbits[orbitbegins[i]], ... , orbits[orbitbegins[i + 1] - 1]. Note that the description of the orbits ends at orbitbegins[norbits] - 1.

Parameters

scip	SCIP instance
issigned	whether orbits for signed permutations shall be computed
permvars	variables considered in a permutation
npermvars	length of a permutation array
perms	matrix containing in each row a permutation of the symmetry group
nperms	number of permutations encoded in perms
orbits	array of non-trivial orbits
orbitbegins	array containing begin positions of new orbits in orbits array
norbits	pointer to number of orbits currently stored in orbits

Definition at line 52 of file symmetry.c.

References FALSE, NULL, SCIP_CALL, SCIP_OKAY, SCIP_Shortbool, SCIPallocBufferArray, SCIPfreeBufferArray, and TRUE.

SCIPcomputeOrbitsFilterSym()

SCIP_RETCODE SCIPcomputeOrbitsFilterSym	(	SCIP *	scip,
		int	npermvars,
		int **	permstrans,
		int	nperms,
		SCIP_Shortbool *	inactiveperms,
		int *	orbits,
		int *	orbitbegins,
		int *	norbits,
		int *	components,
		int *	componentbegins,
		int *	vartocomponent,
		unsigned *	componentblocked,
		int	ncomponents,
		int	nmovedpermvars
	)

compute non-trivial orbits of symmetry group using filtered generators

The non-trivial orbits of the group action are stored in the array orbits of length npermvars. This array contains the indices of variables from the permvars array such that variables that are contained in the same orbit appear consecutively in the orbits array. The variables of the i-th orbit have indices orbits[orbitbegins[i]], ... , orbits[orbitbegins[i + 1] - 1]. Note that the description of the orbits ends at orbitbegins[norbits] - 1.

Only permutations that are not inactive (as marked by inactiveperms) are used. Thus, one can use this array to filter out permutations.

Parameters

scip	SCIP instance
npermvars	length of a permutation array
permstrans	transposed matrix containing in each column a permutation of the symmetry group
nperms	number of permutations encoded in perms
inactiveperms	array to store whether permutations are inactive
orbits	array of non-trivial orbits
orbitbegins	array containing begin positions of new orbits in orbits array
norbits	pointer to number of orbits currently stored in orbits
components	array containing the indices of permutations sorted by components
componentbegins	array containing in i-th position the first position of component i in components array
vartocomponent	array containing for each permvar the index of the component it is contained in (-1 if not affected)
componentblocked	array to store which symmetry methods have been used on a component using the same bitset information as for misc/usesymmetry
ncomponents	number of components of symmetry group
nmovedpermvars	number of variables moved by any permutation in a symmetry component that is handled by orbital fixing

Definition at line 172 of file symmetry.c.

References FALSE, NULL, SCIP_CALL, SCIP_OKAY, SCIP_Shortbool, SCIPallocBufferArray, SCIPfreeBufferArray, and TRUE.

Referenced by addSSTConss().

SCIPcomputeOrbitsComponentsSym()

SCIP_RETCODE SCIPcomputeOrbitsComponentsSym	(	SCIP *	scip,
		int	npermvars,
		int **	permstrans,
		int	nperms,
		int *	components,
		int *	componentbegins,
		int *	vartocomponent,
		int	ncomponents,
		int *	orbits,
		int *	orbitbegins,
		int *	norbits,
		int *	varorbitmap
	)

compute non-trivial orbits of symmetry group

The non-trivial orbits of the group action are stored in the array orbits of length npermvars. This array contains the indices of variables from the permvars array such that variables that are contained in the same orbit appear consecutively in the orbits array. The variables of the i-th orbit have indices orbits[orbitbegins[i]], ... , orbits[orbitbegins[i + 1] - 1]. Note that the description of the orbits ends at orbitbegins[norbits] - 1.

This function is adapted from SCIPcomputeOrbitsFilterSym().

compute non-trivial orbits of symmetry group

The non-trivial orbits of the group action are stored in the array orbits of length npermvars. This array contains the indices of variables from the permvars array such that variables that are contained in the same orbit appear consecutively in the orbits array. The variables of the i-th orbit have indices orbits[orbitbegins[i]], ... , orbits[orbitbegins[i + 1] - 1]. Note that the description of the orbits ends at orbitbegins[norbits] - 1.

This function is adapted from computeGroupOrbitsFilter().

Parameters

scip	SCIP instance
npermvars	length of a permutation array
permstrans	transposed matrix containing in each column a permutation of the symmetry group
nperms	number of permutations encoded in perms
components	array containing the indices of permutations sorted by components
componentbegins	array containing in i-th position the first position of component i in components array
vartocomponent	array containing for each permvar the index of the component it is contained in (-1 if not affected)
ncomponents	number of components of symmetry group
orbits	array of non-trivial orbits
orbitbegins	array containing begin positions of new orbits in orbits array
norbits	pointer to number of orbits currently stored in orbits
varorbitmap	array for storing the orbits for each variable

Definition at line 420 of file symmetry.c.

References FALSE, NULL, SCIP_CALL, SCIP_OKAY, SCIP_Shortbool, SCIPallocBufferArray, SCIPfreeBufferArray, and TRUE.

Referenced by initOrbits().

SCIPcomputeOrbitVar()

SCIP_RETCODE SCIPcomputeOrbitVar	(	SCIP *	scip,
		int	npermvars,
		int **	perms,
		int **	permstrans,
		int *	components,
		int *	componentbegins,
		SCIP_Shortbool *	ignoredvars,
		SCIP_Shortbool *	varfound,
		int	varidx,
		int	component,
		int *	orbit,
		int *	orbitsize
	)

Compute orbit of a given variable and store it in orbit. The first entry of the orbit will be the given variable index and the rest is filled with the remaining variables excluding the ones specified in ignoredvars.

Precondition

orbit is an initialized array of size propdata->npermvars

at least one of perms and permstrans should not be NULL

Parameters

scip	SCIP instance
npermvars	number of variables in permvars
perms	the generators of the permutation group (or NULL)
permstrans	the transposed matrix of generators (or NULL)
components	the components of the permutation group
componentbegins	array containing the starting index of each component
ignoredvars	array indicating which variables should be ignored
varfound	bitmap to mark which variables have been added (or NULL)
varidx	index of variable for which the orbit is requested
component	component that var is in
orbit	array in which the orbit should be stored
orbitsize	buffer to store the size of the orbit

Definition at line 320 of file symmetry.c.

References NULL, SCIP_CALL, SCIP_OKAY, SCIP_Shortbool, SCIPallocClearBufferArray, SCIPfreeBufferArray, and TRUE.

Referenced by addWeakSBCsSubgroup().

SCIPisInvolutionPerm()

SCIP_RETCODE SCIPisInvolutionPerm	(	int *	perm,
		SCIP_VAR **	vars,
		int	nvars,
		int *	ntwocyclesperm,
		int *	nbincyclesperm,
		SCIP_Bool	earlytermination
	)

Checks whether a permutation is a composition of 2-cycles and in this case determine the number of overall 2-cycles and binary 2-cycles. It is a composition of 2-cycles iff ntwocyclesperm > 0 upon termination.

Checks whether a permutation is a composition of 2-cycles and in this case determines the number of overall 2-cycles and binary 2-cycles. It is a composition of 2-cycles iff ntwocyclesperm > 0 upon termination.

Parameters

perm	permutation
vars	array of variables perm is acting on
nvars	number of variables
ntwocyclesperm	pointer to store number of 2-cycles or 0 if perm is not an involution
nbincyclesperm	pointer to store number of binary cycles
earlytermination	whether we terminate early if not all affected variables are binary

Definition at line 542 of file symmetry.c.

References NULL, SCIP_OKAY, and SCIPvarIsBinary().

Referenced by chooseOrderOfGenerators().

SCIPdetermineNVarsAffectedSym()

SCIP_RETCODE SCIPdetermineNVarsAffectedSym	(	SCIP *	scip,
		int **	perms,
		int	nperms,
		SCIP_VAR **	permvars,
		int	npermvars,
		int *	nvarsaffected
	)

determine number of variables affected by symmetry group

Parameters

scip	SCIP instance
perms	permutations
nperms	number of permutations in perms
permvars	variables corresponding to permutations
npermvars	number of permvars in perms
nvarsaffected	pointer to store number of all affected variables

Definition at line 593 of file symmetry.c.

References NULL, SCIP_CALL, SCIP_OKAY, SCIP_Shortbool, SCIPallocClearBufferArray, SCIPfreeBufferArray, and TRUE.

Referenced by determineSymmetry().

SCIPcomputeComponentsSym()

SCIP_RETCODE SCIPcomputeComponentsSym	(	SCIP *	scip,
		SYM_SYMTYPE	symtype,
		int **	perms,
		int	nperms,
		SCIP_VAR **	permvars,
		int	npermvars,
		SCIP_Bool	transposed,
		int **	components,
		int **	componentbegins,
		int **	vartocomponent,
		unsigned **	componentblocked,
		int *	ncomponents
	)

compute components of symmetry group

Parameters

scip	SCIP instance
symtype	type of symmetries in perms
perms	permutation generators as (either nperms x npermvars or npermvars x nperms) matrix
nperms	number of permutations
permvars	variables on which permutations act
npermvars	number of variables for permutations
transposed	transposed permutation generators as (npermvars x nperms) matrix
components	array containing the indices of permutations sorted by components
componentbegins	array containing in i-th position the first position of component i in components array
vartocomponent	array containing for each permvar the index of the component it is contained in (-1 if not affected)
componentblocked	array to store which symmetry methods have been used on a component using the same bitset information as for misc/usesymmetry
ncomponents	pointer to store number of components of symmetry group

Definition at line 775 of file symmetry.c.

References NULL, SCIP_CALL, SCIP_OKAY, SCIPallocBlockMemoryArray, SCIPallocBufferArray, SCIPblkmem(), SCIPdisjointsetCreate(), SCIPdisjointsetFind(), SCIPdisjointsetFree(), SCIPdisjointsetUnion(), SCIPfreeBufferArray, SCIPsortIntInt(), SYM_SYMTYPE_SIGNPERM, and TRUE.

Referenced by ensureSymmetryComponentsComputed().

SCIPextendSubOrbitope()

SCIP_RETCODE SCIPextendSubOrbitope	(	int **	suborbitope,
		int	nrows,
		int	nfilledcols,
		int	coltoextend,
		int *	perm,
		SCIP_Bool	leftextension,
		int **	nusedelems,
		SCIP_VAR **	permvars,
		SCIP_Shortbool *	rowisbinary,
		SCIP_Bool *	success,
		SCIP_Bool *	infeasible
	)

Given a matrix with nrows and #perms + 1 columns whose first nfilledcols columns contain entries of variables, this routine checks whether the 2-cycles of perm intersect each row of column coltoextend in exactly one position. In this case, we add one column to the suborbitope of the first nfilledcols columns.

Precondition

Every non-trivial cycle of perm is a 2-cycle.

perm has nrows many 2-cycles

Parameters

suborbitope	matrix containing suborbitope entries
nrows	number of rows of suborbitope
nfilledcols	number of columns of suborbitope which are filled with entries
coltoextend	index of column that should be extended by perm
perm	permutation
leftextension	whether we extend the suborbitope to the left
nusedelems	pointer to array storing how often an element was used in the orbitope
permvars	permutation vars array
rowisbinary	array encoding whether variables in an orbitope row are binary (or NULL)
success	pointer to store whether extension was successful
infeasible	pointer to store if the number of intersecting cycles is too small

Definition at line 645 of file symmetry.c.

References FALSE, NULL, SCIP_OKAY, SCIPvarIsBinary(), and TRUE.

Referenced by checkTwoCyclePermsAreOrbitope().

SCIPgenerateOrbitopeVarsMatrix()

SCIP_RETCODE SCIPgenerateOrbitopeVarsMatrix	(	SCIP *	scip,
		SCIP_VAR ****	vars,
		int	nrows,
		int	ncols,
		SCIP_VAR **	permvars,
		int	npermvars,
		int **	orbitopevaridx,
		int *	columnorder,
		int *	nusedelems,
		SCIP_Shortbool *	rowisbinary,
		SCIP_Bool *	infeasible,
		SCIP_Bool	storelexorder,
		int **	lexorder,
		int *	nvarsorder,
		int *	maxnvarsorder
	)

generate variable matrix for orbitope constraint handler

generate variable matrix for orbitope constraint handler

Precondition

if storelexorder is TRUE, then the permutations define an orbitope

Parameters

scip	SCIP instance
vars	pointer to matrix of orbitope variables
nrows	number of rows of orbitope
ncols	number of columns of orbitope
permvars	superset of variables that are contained in orbitope
npermvars	number of variables in permvars array
orbitopevaridx	permuted index table of variables in permvars that are contained in orbitope
columnorder	permutation to reorder column of orbitopevaridx
nusedelems	array storing how often an element was used in the orbitope
rowisbinary	array encoding whether a row contains only binary variables (or NULL)
infeasible	pointer to store whether the potential orbitope is not an orbitope
storelexorder	whether the lexicographic order induced by the orbitope shall be stored
lexorder	pointer to array storing the lexorder (or NULL)
nvarsorder	pointer to store number of variables in lexorder (or NULL)
maxnvarsorder	pointer to store maximum number of variables in lexorder (or NULL)

Definition at line 987 of file symmetry.c.

References NULL, SCIP_CALL, SCIP_OKAY, SCIPallocBlockMemoryArray, SCIPreallocBlockMemoryArray, SCIPvarIsBinary(), and TRUE.

Referenced by addOrbitopeSubgroup().

SCIPisPackingPartitioningOrbitope()

SCIP_RETCODE SCIPisPackingPartitioningOrbitope	(	SCIP *	scip,
		SCIP_VAR ***	vars,
		int	nrows,
		int	ncols,
		SCIP_Bool **	pprows,
		int *	npprows,
		SCIP_ORBITOPETYPE *	type
	)

checks whether an orbitope is a packing or partitioning orbitope

checks whether an orbitope is a packing or partitioning orbitope; if npprows != NULL, count how many rows are contained in packing/partitioning constraints

Parameters

scip	SCIP data structure
vars	variable matrix of orbitope constraint
nrows	pointer to number of rows of variable matrix
ncols	number of columns of variable matrix
pprows	pointer to store which rows are are contained in packing/partitioning constraints or NULL if not needed
npprows	pointer to store how many rows are contained in packing/partitioning constraints or NULL if not needed
type	pointer to store type of orbitope constraint after strengthening

Definition at line 1178 of file symmetry.c.

References NULL, SCIP_CALL, SCIP_OKAY, SCIP_ORBITOPETYPE_FULL, SCIP_ORBITOPETYPE_PACKING, SCIP_ORBITOPETYPE_PARTITIONING, SCIP_SETPPCTYPE_COVERING, SCIP_SETPPCTYPE_PARTITIONING, SCIPallocBlockMemoryArray, SCIPallocBufferArray, SCIPallocCleanBufferArray, SCIPallocClearBufferArray, SCIPconshdlrGetConss(), SCIPconshdlrGetNConss(), SCIPfindConshdlr(), SCIPfreeBufferArray, SCIPfreeCleanBufferArray, SCIPgetNTotalVars(), SCIPgetNVarsSetppc(), SCIPgetTypeSetppc(), SCIPgetVarsSetppc(), and SCIPvarGetIndex().

Referenced by addOrbitopesDynamic(), packingUpgrade(), and strengthenOrbitopeConstraint().

SCIPdetectSingleOrDoubleLexMatrices()

SCIP_RETCODE SCIPdetectSingleOrDoubleLexMatrices	(	SCIP *	scip,
		SCIP_Bool	detectsinglelex,
		int **	perms,
		int	nperms,
		int	permlen,
		SCIP_Bool *	success,
		SCIP_Bool *	isorbitope,
		int ***	lexmatrix,
		int *	nrows,
		int *	ncols,
		int **	lexrowsbegin,
		int **	lexcolsbegin,
		int *	nrowmatrices,
		int *	ncolmatrices
	)

detects whether permutations define single or double lex matrices

A single lex matrix is a matrix whose columns can be partitioned into blocks such that the columns within each block can be permuted arbitrarily. A double lex matrix is a single lex matrix such that also blocks of rows have the aforementioned property.

Parameters

scip	SCIP pointer
detectsinglelex	whether single lex matrices shall be detected
perms	array of permutations
nperms	number of permutations in perms
permlen	number of variables in a permutation
success	pointer to store whether structure could be detected
isorbitope	pointer to store whether detected matrix is orbitopal
lexmatrix	pointer to store single or double lex matrix
nrows	pointer to store number of rows of lexmatrix
ncols	pointer to store number of columns of lexmatrix
lexrowsbegin	pointer to store array indicating begin of new row-lexmatrix
lexcolsbegin	pointer to store array indicating begin of new col-lexmatrix
nrowmatrices	pointer to store number of single lex row matrices in rows
ncolmatrices	pointer to store number of single lex column matrices in rows

Definition at line 2052 of file symmetry.c.

References detectOrbitopalSymmetries(), FALSE, isDoublelLexSym(), isPermInvolution(), NULL, SCIP_Bool, SCIP_CALL, SCIP_OKAY, SCIPallocBlockMemoryArray, SCIPallocBufferArray, SCIPfreeBlockMemoryArray, SCIPfreeBlockMemoryArrayNull, SCIPfreeBufferArray, and TRUE.

Referenced by tryHandleSingleOrDoubleLexMatricesComponent().

SCIPsymEQ()

SCIP_Bool SCIPsymEQ	(	SCIP *	scip,
		SCIP_Real	val1,
		SCIP_Real	val2
	)

helper function to test if val1 = val2 while permitting infinity-values

Parameters

scip	SCIP data structure
val1	left-hand side value
val2	right-hand side value

Definition at line 2212 of file symmetry.c.

References FALSE, SCIP_Bool, SCIPisEQ(), SCIPisInfinity(), and TRUE.

Referenced by assertIsOrbitopeMatrix(), identifyOrbitalSymmetriesBroken(), propagateStaticLexred(), propagateStaticOrbitope(), testColumnsAreSymmetricallyEquivalent(), and updateColumnOrderWhenBranchingOnColumn().

SCIPsymLE()

SCIP_Bool SCIPsymLE	(	SCIP *	scip,
		SCIP_Real	val1,
		SCIP_Real	val2
	)

helper function to test if val1 <= val2 while permitting infinity-values

Parameters

scip	SCIP data structure
val1	left-hand side value
val2	right-hand side value

Definition at line 2246 of file symmetry.c.

References FALSE, SCIP_Bool, SCIPisInfinity(), SCIPisLE(), and TRUE.

Referenced by assertIsOrbitopeMatrix(), identifyOrbitalSymmetriesBroken(), propagateStaticLexred(), and propagateStaticOrbitope().

SCIPsymGE()

SCIP_Bool SCIPsymGE	(	SCIP *	scip,
		SCIP_Real	val1,
		SCIP_Real	val2
	)

helper function to test if val1 >= val2 while permitting infinity-values

Parameters

scip	SCIP data structure
val1	left-hand side value
val2	right-hand side value

Definition at line 2284 of file symmetry.c.

References FALSE, SCIP_Bool, SCIPisGE(), SCIPisInfinity(), and TRUE.

Referenced by assertIsOrbitopeMatrix(), identifyOrbitalSymmetriesBroken(), propagateStaticLexred(), and propagateStaticOrbitope().

SCIPsymLT()

SCIP_Bool SCIPsymLT	(	SCIP *	scip,
		SCIP_Real	val1,
		SCIP_Real	val2
	)

helper function to test if val1 < val2 while permitting infinity-values

Parameters

scip	SCIP data structure
val1	left-hand side value
val2	right-hand side value

Definition at line 2322 of file symmetry.c.

References FALSE, SCIP_Bool, SCIPisInfinity(), SCIPisLT(), and TRUE.

Referenced by identifyOrbitalSymmetriesBroken(), and propagateStaticOrbitope().

SCIPsymGT()

SCIP_Bool SCIPsymGT	(	SCIP *	scip,
		SCIP_Real	val1,
		SCIP_Real	val2
	)

helper function to test if val1 > val2 while permitting infinity-values

Parameters

scip	SCIP data structure
val1	left-hand side value
val2	right-hand side value

Definition at line 2360 of file symmetry.c.

References FALSE, SCIP_Bool, SCIPisGT(), SCIPisInfinity(), and TRUE.

Referenced by assertIsOrbitopeMatrix(), identifyOrbitalSymmetriesBroken(), propagateStaticLexred(), and propagateStaticOrbitope().