Package 'CVXR'

Description

This class represents the negation of an affine expression.

Usage

## S4 method for signature 'Expression,missing'
e1 - e2

## S4 method for signature 'Expression,Expression'
e1 - e2

## S4 method for signature 'Expression,ConstVal'
e1 - e2

## S4 method for signature 'ConstVal,Expression'
e1 - e2

## S4 method for signature 'NegExpression'
dim_from_args(object)

## S4 method for signature 'NegExpression'
sign_from_args(object)

## S4 method for signature 'NegExpression'
is_incr(object, idx)

## S4 method for signature 'NegExpression'
is_decr(object, idx)

## S4 method for signature 'NegExpression'
is_symmetric(object)

## S4 method for signature 'NegExpression'
is_hermitian(object)

## S4 method for signature 'NegExpression'
graph_implementation(object, arg_objs, dim, data = NA_real_)

Arguments

Methods (by generic)

• dim_from_args(NegExpression): The (row, col) dimensions of the expression.

• sign_from_args(NegExpression): The (is positive, is negative) sign of the expression.

• is_incr(NegExpression): The expression is not weakly increasing in any argument.

• is_decr(NegExpression): The expression is weakly decreasing in every argument.

• is_symmetric(NegExpression): Is the expression symmetric?

• is_hermitian(NegExpression): Is the expression Hermitian?

• graph_implementation(NegExpression): The graph implementation of the expression.

Description

Get the sparse flag field for the LinOp object

Usage

.build_matrix_0(xp, v)

Arguments

Value

a XPtr to ProblemData Object

Description

Get the sparse flag field for the LinOp object

Usage

.build_matrix_1(xp, v1, v2)

Arguments

Value

a XPtr to ProblemData Object

Description

Compute sgn, scale, M such that $P = sgn * scale * dot(M, t(M))$.

Usage

.decomp_quad(P, cond = NA, rcond = NA)

Arguments

Value

A list consisting of induced matrix 2-norm of P and a rectangular matrix such that P = scale * (dot(M1, t(M1)) - dot(M2, t(M2)))

Description

Perform a push back operation on the args field of LinOp

Usage

.LinOp__args_push_back(xp, yp)

Arguments

Description

Get the field dense_data for the LinOp object

Usage

.LinOp__get_dense_data(xp)

Arguments

Value

a MatrixXd object

Description

Get the id field of the LinOp Object

Usage

.LinOp__get_id(xp)

Arguments

Value

the value of the id field of the LinOp Object

Description

Get the field size for the LinOp object

Usage

.LinOp__get_size(xp)

Arguments

Value

an integer vector

Description

Get the slice field of the LinOp Object

Usage

.LinOp__get_slice(xp)

Arguments

Value

the value of the slice field of the LinOp Object

Description

Get the sparse flag field for the LinOp object

Usage

.LinOp__get_sparse(xp)

Arguments

Value

TRUE or FALSE

Description

Get the field named sparse_data from the LinOp object

Usage

.LinOp__get_sparse_data(xp)

Arguments

Value

a dgCMatrix-class object

Description

Get the field named type for the LinOp object

Usage

.LinOp__get_type(xp)

Arguments

Value

an integer value for type

Description

Create a new LinOp object.

Usage

.LinOp__new()

Value

an external ptr (Rcpp::XPtr) to a LinOp object instance.

Description

Set the field dense_data of the LinOp object

Usage

.LinOp__set_dense_data(xp, denseMat)

Arguments

Description

Set the field size of the LinOp object

Usage

.LinOp__set_size(xp, value)

Arguments

Description

Set the slice field of the LinOp Object

Usage

.LinOp__set_slice(xp, value)

Arguments

Value

the value of the slice field of the LinOp Object

Description

Set the flag sparse of the LinOp object

Usage

.LinOp__set_sparse(xp, sparseSEXP)

Arguments

Description

Set the field named sparse_data of the LinOp object

Usage

.LinOp__set_sparse_data(xp, sparseMat)

Arguments

Description

Set the field named type for the LinOp object

Usage

.LinOp__set_type(xp, typeValue)

Arguments

Description

Perform a push back operation on the size field of LinOp

Usage

.LinOp__size_push_back(xp, intVal)

Arguments

Description

Perform a push back operation on the slice field of LinOp

Usage

.LinOp__slice_push_back(xp, intVec)

Arguments

Description

Return the LinOp element at index i (0-based)

Usage

.LinOp_at_index(lvec, i)

Arguments

Description

Create a new LinOpVector object.

Usage

.LinOpVector__new()

Value

an external ptr (Rcpp::XPtr) to a LinOp object instance.

Description

Perform a push back operation on the args field of LinOp

Usage

.LinOpVector__push_back(xp, yp)

Arguments

Description

Internal method for calculating the p-norm

Usage

.p_norm(x, p)

Arguments

Value

Returns the specified norm of matrix x

Description

Get the const_to_row field of the ProblemData Object

Usage

.ProblemData__get_const_to_row(xp)

Arguments

Value

the const_to_row field as a named integer vector where the names are integers converted to characters

Description

Get the const_vec field from the ProblemData Object

Usage

.ProblemData__get_const_vec(xp)

Arguments

Value

a numeric vector of the field const_vec from the ProblemData Object

Description

Get the I field of the ProblemData Object

Usage

.ProblemData__get_I(xp)

Arguments

Value

an integer vector of the field I from the ProblemData Object

Description

Get the id_to_col field of the ProblemData Object

Usage

.ProblemData__get_id_to_col(xp)

Arguments

Value

the id_to_col field as a named integer vector where the names are integers converted to characters

Description

Get the J field of the ProblemData Object

Usage

.ProblemData__get_J(xp)

Arguments

Value

an integer vector of the field J from the ProblemData Object

Description

Get the V field of the ProblemData Object

Usage

.ProblemData__get_V(xp)

Arguments

Value

a numeric vector of doubles (the field V) from the ProblemData Object

Description

Create a new ProblemData object.

Usage

.ProblemData__new()

Value

an external ptr (Rcpp::XPtr) to a ProblemData object instance.

Description

Set the const_to_row map of the ProblemData Object

Usage

.ProblemData__set_const_to_row(xp, iv)

Arguments

Description

Set the const_vec field in the ProblemData Object

Usage

.ProblemData__set_const_vec(xp, cvp)

Arguments

Description

Set the I field in the ProblemData Object

Usage

.ProblemData__set_I(xp, ip)

Arguments

Description

Set the id_to_col field of the ProblemData Object

Usage

.ProblemData__set_id_to_col(xp, iv)

Arguments

Description

Set the J field in the ProblemData Object

Usage

.ProblemData__set_J(xp, jp)

Arguments

Description

Set the V field in the ProblemData Object

Usage

.ProblemData__set_V(xp, vp)

Arguments

Description

This class represents indexing using logical indexing or a list of indices into a matrix.

Usage

## S4 method for signature 'Expression,index,missing,ANY'
x[i, j, ..., drop = TRUE]

## S4 method for signature 'Expression,missing,index,ANY'
x[i, j, ..., drop = TRUE]

## S4 method for signature 'Expression,index,index,ANY'
x[i, j, ..., drop = TRUE]

## S4 method for signature 'Expression,matrix,index,ANY'
x[i, j, ..., drop = TRUE]

## S4 method for signature 'Expression,index,matrix,ANY'
x[i, j, ..., drop = TRUE]

## S4 method for signature 'Expression,matrix,matrix,ANY'
x[i, j, ..., drop = TRUE]

## S4 method for signature 'Expression,matrix,missing,ANY'
x[i, j, ..., drop = TRUE]

SpecialIndex(expr, key)

## S4 method for signature 'SpecialIndex'
name(x)

## S4 method for signature 'SpecialIndex'
is_atom_log_log_convex(object)

## S4 method for signature 'SpecialIndex'
is_atom_log_log_concave(object)

## S4 method for signature 'SpecialIndex'
get_data(object)

## S4 method for signature 'SpecialIndex'
.grad(object)

Arguments

Methods (by generic)

• name(SpecialIndex): Returns the index in string form.

• is_atom_log_log_convex(SpecialIndex): Is the atom log-log convex?

• is_atom_log_log_concave(SpecialIndex): Is the atom log-log concave?

• get_data(SpecialIndex): A list containing key.

• .grad(SpecialIndex): Gives the (sub/super)gradient of the atom w.r.t. each variable

Slots

expr

An Expression representing a vector or matrix.

key

A list containing the start index, end index, and step size of the slice.

Description

This class represents indexing or slicing into a matrix.

Usage

## S4 method for signature 'Expression,missing,missing,ANY'
x[i, j, ..., drop = TRUE]

## S4 method for signature 'Expression,numeric,missing,ANY'
x[i, j, ..., drop = TRUE]

## S4 method for signature 'Expression,missing,numeric,ANY'
x[i, j, ..., drop = TRUE]

## S4 method for signature 'Expression,numeric,numeric,ANY'
x[i, j, ..., drop = TRUE]

Index(expr, key)

## S4 method for signature 'Index'
to_numeric(object, values)

## S4 method for signature 'Index'
dim_from_args(object)

## S4 method for signature 'Index'
is_atom_log_log_convex(object)

## S4 method for signature 'Index'
is_atom_log_log_concave(object)

## S4 method for signature 'Index'
get_data(object)

## S4 method for signature 'Index'
graph_implementation(object, arg_objs, dim, data = NA_real_)

## S4 method for signature 'SpecialIndex'
to_numeric(object, values)

## S4 method for signature 'SpecialIndex'
dim_from_args(object)

Arguments

Methods (by generic)

• to_numeric(Index): The index/slice into the given value.

• dim_from_args(Index): The dimensions of the atom.

• is_atom_log_log_convex(Index): Is the atom log-log convex?

• is_atom_log_log_concave(Index): Is the atom log-log concave?

• get_data(Index): A list containing key.

• graph_implementation(Index): The graph implementation of the atom.

• to_numeric(SpecialIndex): The index/slice into the given value.

• dim_from_args(SpecialIndex): The dimensions of the atom.

Slots

expr

An Expression representing a vector or matrix.

key

A list containing the start index, end index, and step size of the slice.

Description

Elementwise multiplication operator

Usage

## S4 method for signature 'Expression,Expression'
e1 * e2

## S4 method for signature 'Expression,ConstVal'
e1 * e2

## S4 method for signature 'ConstVal,Expression'
e1 * e2

Arguments

Description

This class represents one expression divided by another expression.

Usage

## S4 method for signature 'Expression,Expression'
e1 / e2

## S4 method for signature 'Expression,ConstVal'
e1 / e2

## S4 method for signature 'ConstVal,Expression'
e1 / e2

## S4 method for signature 'DivExpression'
to_numeric(object, values)

## S4 method for signature 'DivExpression'
is_quadratic(object)

## S4 method for signature 'DivExpression'
is_qpwa(object)

## S4 method for signature 'DivExpression'
dim_from_args(object)

## S4 method for signature 'DivExpression'
is_atom_convex(object)

## S4 method for signature 'DivExpression'
is_atom_concave(object)

## S4 method for signature 'DivExpression'
is_atom_log_log_convex(object)

## S4 method for signature 'DivExpression'
is_atom_log_log_concave(object)

## S4 method for signature 'DivExpression'
is_incr(object, idx)

## S4 method for signature 'DivExpression'
is_decr(object, idx)

## S4 method for signature 'DivExpression'
graph_implementation(object, arg_objs, dim, data = NA_real_)

Arguments

Methods (by generic)

• to_numeric(DivExpression): Matrix division by a scalar.

• is_quadratic(DivExpression): Is the left-hand expression quadratic and the right-hand expression constant?

• is_qpwa(DivExpression): Is the expression quadratic of piecewise affine?

• dim_from_args(DivExpression): The (row, col) dimensions of the left-hand expression.

• is_atom_convex(DivExpression): Division is convex (affine) in its arguments only if the denominator is constant.

• is_atom_concave(DivExpression): Division is concave (affine) in its arguments only if the denominator is constant.

• is_atom_log_log_convex(DivExpression): Is the atom log-log convex?

• is_atom_log_log_concave(DivExpression): Is the atom log-log concave?

• is_incr(DivExpression): Is the right-hand expression positive?

• is_decr(DivExpression): Is the right-hand expression negative?

• graph_implementation(DivExpression): The graph implementation of the expression.

Description

This class represents the matrix product of two linear expressions. See Multiply for the elementwise product.

Usage

## S4 method for signature 'Expression,Expression'
x %*% y

## S4 method for signature 'Expression,ConstVal'
x %*% y

## S4 method for signature 'ConstVal,Expression'
x %*% y

## S4 method for signature 'MulExpression'
to_numeric(object, values)

## S4 method for signature 'MulExpression'
dim_from_args(object)

## S4 method for signature 'MulExpression'
is_atom_convex(object)

## S4 method for signature 'MulExpression'
is_atom_concave(object)

## S4 method for signature 'MulExpression'
is_atom_log_log_convex(object)

## S4 method for signature 'MulExpression'
is_atom_log_log_concave(object)

## S4 method for signature 'MulExpression'
is_incr(object, idx)

## S4 method for signature 'MulExpression'
is_decr(object, idx)

## S4 method for signature 'MulExpression'
.grad(object, values)

## S4 method for signature 'MulExpression'
graph_implementation(object, arg_objs, dim, data = NA_real_)

Arguments

Methods (by generic)

• to_numeric(MulExpression): Matrix multiplication.

• dim_from_args(MulExpression): The (row, col) dimensions of the expression.

• is_atom_convex(MulExpression): Multiplication is convex (affine) in its arguments only if one of the arguments is constant.

• is_atom_concave(MulExpression): If the multiplication atom is convex, then it is affine.

• is_atom_log_log_convex(MulExpression): Is the atom log-log convex?

• is_atom_log_log_concave(MulExpression): Is the atom log-log concave?

• is_incr(MulExpression): Is the left-hand expression positive?

• is_decr(MulExpression): Is the left-hand expression negative?

• .grad(MulExpression): Gives the (sub/super)gradient of the atom w.r.t. each variable

• graph_implementation(MulExpression): The graph implementation of the expression.

See Also

Multiply

Description

This class represents the positive semidefinite constraint, $\frac{1}{2}(X + X^T) \succeq 0$, i.e. $z^T(X + X^T)z \geq 0$ for all $z$.

Usage

e1 %>>% e2

e1 %<<% e2

## S4 method for signature 'Expression,Expression'
e1 %>>% e2

## S4 method for signature 'Expression,ConstVal'
e1 %>>% e2

## S4 method for signature 'ConstVal,Expression'
e1 %>>% e2

## S4 method for signature 'Expression,Expression'
e1 %<<% e2

## S4 method for signature 'Expression,ConstVal'
e1 %<<% e2

## S4 method for signature 'ConstVal,Expression'
e1 %<<% e2

PSDConstraint(expr, id = NA_integer_)

## S4 method for signature 'PSDConstraint'
name(x)

## S4 method for signature 'PSDConstraint'
is_dcp(object)

## S4 method for signature 'PSDConstraint'
is_dgp(object)

## S4 method for signature 'PSDConstraint'
residual(object)

## S4 method for signature 'PSDConstraint'
canonicalize(object)

Arguments

Methods (by generic)

• name(PSDConstraint): The string representation of the constraint.

• is_dcp(PSDConstraint): The constraint is DCP if the left-hand and right-hand expressions are affine.

• is_dgp(PSDConstraint): Is the constraint DGP?

• residual(PSDConstraint): A Expression representing the residual of the constraint.

• canonicalize(PSDConstraint): The graph implementation of the object. Marks the top level constraint as the dual_holder so the dual value will be saved to the PSDConstraint.

Slots

expr

An Expression, numeric element, vector, or matrix representing $X$.

Description

Raises each element of the input to the power $p$. If expr is a CVXR expression, then expr^p is equivalent to power(expr,p).

Usage

## S4 method for signature 'Expression,numeric'
e1 ^ e2

power(x, p, max_denom = 1024)

Arguments

Details

For $p = 0$ and $f(x) = 1$, this function is constant and positive. For $p = 1$ and $f(x) = x$, this function is affine, increasing, and the same sign as $x$. For $p = 2,4,8,\ldots$ and $f(x) = |x|^p$, this function is convex, positive, with signed monotonicity. For $p < 0$ and $f(x) =$

$x^p$

for $x > 0$

$+\infty$

$x \leq 0$

, this function is convex, decreasing, and positive. For $0 < p < 1$ and $f(x) =$

$x^p$

for $x \geq 0$

$-\infty$

$x < 0$

, this function is concave, increasing, and positivea. For $p > 1, p \neq 2,4,8,\ldots$ and $f(x) =$

$x^p$

for $x \geq 0$

$+\infty$

$x < 0$

, this function is convex, increasing, and positive.

Examples

## Not run: 
x <- Variable()
prob <- Problem(Minimize(power(x,1.7) + power(x,-2.3) - power(x,0.45)))
result <- solve(prob)
result$value
result$getValue(x)

## End(Not run)

Description

This class represents the sum of any number of expressions.

Usage

## S4 method for signature 'Expression,missing'
e1 + e2

## S4 method for signature 'Expression,Expression'
e1 + e2

## S4 method for signature 'Expression,ConstVal'
e1 + e2

## S4 method for signature 'ConstVal,Expression'
e1 + e2

## S4 method for signature 'AddExpression'
dim_from_args(object)

## S4 method for signature 'AddExpression'
name(x)

## S4 method for signature 'AddExpression'
to_numeric(object, values)

## S4 method for signature 'AddExpression'
is_atom_log_log_convex(object)

## S4 method for signature 'AddExpression'
is_atom_log_log_concave(object)

## S4 method for signature 'AddExpression'
is_symmetric(object)

## S4 method for signature 'AddExpression'
is_hermitian(object)

## S4 method for signature 'AddExpression'
copy(object, args = NULL, id_objects = list())

## S4 method for signature 'AddExpression'
graph_implementation(object, arg_objs, dim, data = NA_real_)

Arguments

Methods (by generic)

• dim_from_args(AddExpression): The dimensions of the expression.

• name(AddExpression): The string form of the expression.

• to_numeric(AddExpression): Sum all the values.

• is_atom_log_log_convex(AddExpression): Is the atom log-log convex?

• is_atom_log_log_concave(AddExpression): Is the atom log-log convex?

• is_symmetric(AddExpression): Is the atom symmetric?

• is_hermitian(AddExpression): Is the atom hermitian?

• copy(AddExpression): Returns a shallow copy of the AddExpression atom

• graph_implementation(AddExpression): The graph implementation of the expression.

Slots

arg_groups

A list of Expressions and numeric data.frame, matrix, or vector objects.

Description

The IneqConstraint class

Usage

## S4 method for signature 'Expression,Expression'
e1 <= e2

## S4 method for signature 'Expression,ConstVal'
e1 <= e2

## S4 method for signature 'ConstVal,Expression'
e1 <= e2

## S4 method for signature 'Expression,Expression'
e1 < e2

## S4 method for signature 'Expression,ConstVal'
e1 < e2

## S4 method for signature 'ConstVal,Expression'
e1 < e2

## S4 method for signature 'Expression,Expression'
e1 >= e2

## S4 method for signature 'Expression,ConstVal'
e1 >= e2

## S4 method for signature 'ConstVal,Expression'
e1 >= e2

## S4 method for signature 'Expression,Expression'
e1 > e2

## S4 method for signature 'Expression,ConstVal'
e1 > e2

## S4 method for signature 'ConstVal,Expression'
e1 > e2

## S4 method for signature 'IneqConstraint'
name(x)

## S4 method for signature 'IneqConstraint'
dim(x)

## S4 method for signature 'IneqConstraint'
size(object)

## S4 method for signature 'IneqConstraint'
expr(object)

## S4 method for signature 'IneqConstraint'
is_dcp(object)

## S4 method for signature 'IneqConstraint'
is_dgp(object)

## S4 method for signature 'IneqConstraint'
residual(object)

Arguments

Methods (by generic)

• name(IneqConstraint): The string representation of the constraint.

• dim(IneqConstraint): The dimensions of the constrained expression.

• size(IneqConstraint): The size of the constrained expression.

• expr(IneqConstraint): The expression to constrain.

• is_dcp(IneqConstraint): A non-positive constraint is DCP if its argument is convex.

• is_dgp(IneqConstraint): Is the constraint DGP?

• residual(IneqConstraint): The residual of the constraint.

Description

The EqConstraint class

Usage

## S4 method for signature 'Expression,Expression'
e1 == e2

## S4 method for signature 'Expression,ConstVal'
e1 == e2

## S4 method for signature 'ConstVal,Expression'
e1 == e2

## S4 method for signature 'EqConstraint'
name(x)

## S4 method for signature 'EqConstraint'
dim(x)

## S4 method for signature 'EqConstraint'
size(object)

## S4 method for signature 'EqConstraint'
expr(object)

## S4 method for signature 'EqConstraint'
is_dcp(object)

## S4 method for signature 'EqConstraint'
is_dgp(object)

## S4 method for signature 'EqConstraint'
residual(object)

Arguments

Methods (by generic)

• name(EqConstraint): The string representation of the constraint.

• dim(EqConstraint): The dimensions of the constrained expression.

• size(EqConstraint): The size of the constrained expression.

• expr(EqConstraint): The expression to constrain.

• is_dcp(EqConstraint): Is the constraint DCP?

• is_dgp(EqConstraint): Is the constraint DGP?

• residual(EqConstraint): The residual of the constraint..

Description

This class represents the elementwise absolute value.

Usage

Abs(x)

## S4 method for signature 'Abs'
to_numeric(object, values)

## S4 method for signature 'Abs'
allow_complex(object)

## S4 method for signature 'Abs'
sign_from_args(object)

## S4 method for signature 'Abs'
is_atom_convex(object)

## S4 method for signature 'Abs'
is_atom_concave(object)

## S4 method for signature 'Abs'
is_incr(object, idx)

## S4 method for signature 'Abs'
is_decr(object, idx)

## S4 method for signature 'Abs'
is_pwl(object)

Arguments

Methods (by generic)

• to_numeric(Abs): The elementwise absolute value of the input.

• allow_complex(Abs): Does the atom handle complex numbers?

• sign_from_args(Abs): The atom is positive.

• is_atom_convex(Abs): The atom is convex.

• is_atom_concave(Abs): The atom is not concave.

• is_incr(Abs): A logical value indicating whether the atom is weakly increasing.

• is_decr(Abs): A logical value indicating whether the atom is weakly decreasing.

• is_pwl(Abs): Is x piecewise linear?

Slots

x

An Expression object.

Description

The elementwise absolute value.

Usage

## S4 method for signature 'Expression'
abs(x)

Arguments

Value

An Expression representing the absolute value of the input.

Examples

A <- Variable(2,2)
prob <- Problem(Minimize(sum(abs(A))), list(A <= -2))
result <- solve(prob)
result$value
result$getValue(A)

Description

Determine whether the reduction accepts a problem.

Usage

accepts(object, problem)

Arguments

Value

A logical value indicating whether the reduction can be applied.

Description

This virtual class represents an affine atomic expression.

Usage

## S4 method for signature 'AffAtom'
allow_complex(object)

## S4 method for signature 'AffAtom'
sign_from_args(object)

## S4 method for signature 'AffAtom'
is_imag(object)

## S4 method for signature 'AffAtom'
is_complex(object)

## S4 method for signature 'AffAtom'
is_atom_convex(object)

## S4 method for signature 'AffAtom'
is_atom_concave(object)

## S4 method for signature 'AffAtom'
is_incr(object, idx)

## S4 method for signature 'AffAtom'
is_decr(object, idx)

## S4 method for signature 'AffAtom'
is_quadratic(object)

## S4 method for signature 'AffAtom'
is_qpwa(object)

## S4 method for signature 'AffAtom'
is_pwl(object)

## S4 method for signature 'AffAtom'
is_psd(object)

## S4 method for signature 'AffAtom'
is_nsd(object)

## S4 method for signature 'AffAtom'
.grad(object, values)

Arguments

Methods (by generic)

• allow_complex(AffAtom): Does the atom handle complex numbers?

• sign_from_args(AffAtom): The sign of the atom.

• is_imag(AffAtom): Is the atom imaginary?

• is_complex(AffAtom): Is the atom complex valued?

• is_atom_convex(AffAtom): The atom is convex.

• is_atom_concave(AffAtom): The atom is concave.

• is_incr(AffAtom): The atom is weakly increasing in every argument.

• is_decr(AffAtom): The atom is not weakly decreasing in any argument.

• is_quadratic(AffAtom): Is every argument quadratic?

• is_qpwa(AffAtom): Is every argument quadratic of piecewise affine?

• is_pwl(AffAtom): Is every argument piecewise linear?

• is_psd(AffAtom): Is the atom a positive semidefinite matrix?

• is_nsd(AffAtom): Is the atom a negative semidefinite matrix?

• .grad(AffAtom): Gives the (sub/super)gradient of the atom w.r.t. each variable

Description

Are the arguments affine?

Usage

are_args_affine(constraints)

Arguments

Value

All the affine arguments in given constraints.

Description

This virtual class represents atomic expressions in CVXR.

Usage

## S4 method for signature 'Atom'
name(x)

## S4 method for signature 'Atom'
validate_args(object)

## S4 method for signature 'Atom'
dim(x)

## S4 method for signature 'Atom'
nrow(x)

## S4 method for signature 'Atom'
ncol(x)

## S4 method for signature 'Atom'
allow_complex(object)

## S4 method for signature 'Atom'
is_nonneg(object)

## S4 method for signature 'Atom'
is_nonpos(object)

## S4 method for signature 'Atom'
is_imag(object)

## S4 method for signature 'Atom'
is_complex(object)

## S4 method for signature 'Atom'
is_convex(object)

## S4 method for signature 'Atom'
is_concave(object)

## S4 method for signature 'Atom'
is_log_log_convex(object)

## S4 method for signature 'Atom'
is_log_log_concave(object)

## S4 method for signature 'Atom'
canonicalize(object)

## S4 method for signature 'Atom'
graph_implementation(object, arg_objs, dim, data = NA_real_)

## S4 method for signature 'Atom'
value_impl(object)

## S4 method for signature 'Atom'
value(object)

## S4 method for signature 'Atom'
grad(object)

## S4 method for signature 'Atom'
domain(object)

## S4 method for signature 'Atom'
atoms(object)

Arguments

Methods (by generic)

• name(Atom): Returns the string representtation of the function call

• validate_args(Atom): Raises an error if the arguments are invalid.

• dim(Atom): The c(row, col) dimensions of the atom.

• nrow(Atom): The number of rows in the atom.

• ncol(Atom): The number of columns in the atom.

• allow_complex(Atom): Does the atom handle complex numbers?

• is_nonneg(Atom): A logical value indicating whether the atom is nonnegative.

• is_nonpos(Atom): A logical value indicating whether the atom is nonpositive.

• is_imag(Atom): A logical value indicating whether the atom is imaginary.

• is_complex(Atom): A logical value indicating whether the atom is complex valued.

• is_convex(Atom): A logical value indicating whether the atom is convex.

• is_concave(Atom): A logical value indicating whether the atom is concave.

• is_log_log_convex(Atom): A logical value indicating whether the atom is log-log convex.

• is_log_log_concave(Atom): A logical value indicating whether the atom is log-log concave.

• canonicalize(Atom): Represent the atom as an affine objective and conic constraints.

• graph_implementation(Atom): The graph implementation of the atom.

• value_impl(Atom): Returns the value of each of the componets in an Atom. Returns an empty matrix if it's an empty atom

• value(Atom): Returns the value of the atom.

• grad(Atom): The (sub/super)-gradient of the atom with respect to each variable.

• domain(Atom): A list of constraints describing the closure of the region where the expression is finite.

• atoms(Atom): Returns a list of the atom types present amongst this atom's arguments

Description

This virtual class represents atomic expressions that can be applied along an axis in CVXR.

Usage

## S4 method for signature 'AxisAtom'
dim_from_args(object)

## S4 method for signature 'AxisAtom'
get_data(object)

## S4 method for signature 'AxisAtom'
validate_args(object)

## S4 method for signature 'AxisAtom'
.axis_grad(object, values)

## S4 method for signature 'AxisAtom'
.column_grad(object, value)

Arguments

Methods (by generic)

• dim_from_args(AxisAtom): The dimensions of the atom determined from its arguments.

• get_data(AxisAtom): A list containing axis and keepdims.

• validate_args(AxisAtom): Check that the new dimensions have the same number of entries as the old.

• .axis_grad(AxisAtom): Gives the (sub/super)gradient of the atom w.r.t. each variable

• .column_grad(AxisAtom): Gives the (sub/super)gradient of the atom w.r.t. each column variable

Slots

expr

A numeric element, data.frame, matrix, vector, or Expression.

axis

(Optional) The dimension across which to apply the function: 1 indicates rows, 2 indicates columns, and NA indicates rows and columns. The default is NA.

keepdims

(Optional) Should dimensions be maintained when applying the atom along an axis? If FALSE, result will be collapsed into an $n x 1$ column vector. The default is FALSE.

Description

This base class represents expressions involving binary operators.

Usage

## S4 method for signature 'BinaryOperator'
name(x)

## S4 method for signature 'BinaryOperator'
to_numeric(object, values)

## S4 method for signature 'BinaryOperator'
sign_from_args(object)

## S4 method for signature 'BinaryOperator'
is_imag(object)

## S4 method for signature 'BinaryOperator'
is_complex(object)

Arguments

Methods (by generic)

• name(BinaryOperator): Returns the name of the BinaryOperator object.

• to_numeric(BinaryOperator): Apply the binary operator to the values.

• sign_from_args(BinaryOperator): Default to rule for multiplication.

• is_imag(BinaryOperator): Is the expression imaginary?

• is_complex(BinaryOperator): Is the expression complex valued?

Slots

lh_exp

The Expression on the left-hand side of the operator.

rh_exp

The Expression on the right-hand side of the operator.

op_name

A character string indicating the binary operation.

Description

Constructs a block matrix from a list of lists. Each internal list is stacked horizontally, and the internal lists are stacked vertically.

Usage

bmat(block_lists)

Arguments

Value

An Expression representing the block matrix.

Examples

x <- Variable()
expr <- bmat(list(list(matrix(1, nrow = 3, ncol = 1), matrix(2, nrow = 3, ncol = 2)),
                list(matrix(3, nrow = 1, ncol = 2), x)
             ))
prob <- Problem(Minimize(sum_entries(expr)), list(x >= 0))
result <- solve(prob)
result$value

Description

This class represents a parameter whose value is obtained by evaluating a function.

Usage

CallbackParam(callback, dim = NULL, ...)

## S4 method for signature 'CallbackParam'
value(object)

Arguments

Slots

callback

A callback function that generates the parameter value.

dim

The dimensions of the parameter.

Examples

x <- Variable(2)
fun <- function() { value(x) }
y <- CallbackParam(fun, dim(x), nonneg = TRUE)
get_data(y)

Description

This virtual class represents a canonical expression.

Usage

## S4 method for signature 'Canonical'
expr(object)

## S4 method for signature 'Canonical'
id(object)

## S4 method for signature 'Canonical'
canonical_form(object)

## S4 method for signature 'Canonical'
variables(object)

## S4 method for signature 'Canonical'
parameters(object)

## S4 method for signature 'Canonical'
constants(object)

## S4 method for signature 'Canonical'
atoms(object)

## S4 method for signature 'Canonical'
get_data(object)

Arguments

Methods (by generic)

• expr(Canonical): The expression associated with the input.

• id(Canonical): The unique ID of the canonical expression.

• canonical_form(Canonical): The graph implementation of the input.

• variables(Canonical): List of Variable objects in the expression.

• parameters(Canonical): List of Parameter objects in the expression.

• constants(Canonical): List of Constant objects in the expression.

• atoms(Canonical): List of Atom objects in the expression.

• get_data(Canonical): Information needed to reconstruct the expression aside from its arguments.

Description

This class represents a canonicalization reduction.

Usage

## S4 method for signature 'Canonicalization,Problem'
perform(object, problem)

## S4 method for signature 'Canonicalization,Solution,InverseData'
invert(object, solution, inverse_data)

## S4 method for signature 'Canonicalization'
canonicalize_tree(object, expr)

## S4 method for signature 'Canonicalization'
canonicalize_expr(object, expr, args)

Arguments

Methods (by generic)

• perform(object = Canonicalization, problem = Problem): Recursively canonicalize the objective and every constraint.

• invert( object = Canonicalization, solution = Solution, inverse_data = InverseData ): Performs the reduction on a problem and returns an equivalent problem.

• canonicalize_tree(Canonicalization): Recursively canonicalize an Expression.

• canonicalize_expr(Canonicalization): Canonicalize an expression, w.r.t. canonicalized arguments.

Description

Computes the graph implementation of a canonical expression.

Usage

canonicalize(object)

canonical_form(object)

Arguments

Value

A list of list(affine expression, list(constraints)).

Description

An interface to the CBC solver

Usage

CBC_CONIC()

## S4 method for signature 'CBC_CONIC'
mip_capable(solver)

## S4 method for signature 'CBC_CONIC'
status_map(solver, status)

## S4 method for signature 'CBC_CONIC'
status_map_mip(solver, status)

## S4 method for signature 'CBC_CONIC'
status_map_lp(solver, status)

## S4 method for signature 'CBC_CONIC'
name(x)

## S4 method for signature 'CBC_CONIC'
import_solver(solver)

## S4 method for signature 'CBC_CONIC,Problem'
accepts(object, problem)

## S4 method for signature 'CBC_CONIC,Problem'
perform(object, problem)

## S4 method for signature 'CBC_CONIC,list,list'
invert(object, solution, inverse_data)

## S4 method for signature 'CBC_CONIC'
solve_via_data(
  object,
  data,
  warm_start,
  verbose,
  feastol,
  reltol,
  abstol,
  num_iter,
  solver_opts,
  solver_cache
)

Arguments

Methods (by generic)

• mip_capable(CBC_CONIC): Can the solver handle mixed-integer programs?

• status_map(CBC_CONIC): Converts status returned by the CBC solver to its respective CVXPY status.

• status_map_mip(CBC_CONIC): Converts status returned by the CBC solver to its respective CVXPY status for mixed integer problems.

• status_map_lp(CBC_CONIC): Converts status returned by the CBC solver to its respective CVXPY status for linear problems.

• name(CBC_CONIC): Returns the name of the solver

• import_solver(CBC_CONIC): Imports the solver

• accepts(object = CBC_CONIC, problem = Problem): Can CBC_CONIC solve the problem?

• perform(object = CBC_CONIC, problem = Problem): Returns a new problem and data for inverting the new solution.

• invert(object = CBC_CONIC, solution = list, inverse_data = list): Returns the solution to the original problem given the inverse_data.

• solve_via_data(CBC_CONIC): Solve a problem represented by data returned from apply.

Description

Global Monthly and Annual Temperature Anomalies (degrees C), 1850-2015 (Relative to the 1961-1990 Mean) (May 2016)

Usage

cdiac

Format

A data frame with 166 rows and 14 variables:

year

Year

jan

Anomaly for month of January

feb

Anomaly for month of February

mar

Anomaly for month of March

apr

Anomaly for month of April

may

Anomaly for month of May

jun

Anomaly for month of June

jul

Anomaly for month of July

aug

Anomaly for month of August

sep

Anomaly for month of September

oct

Anomaly for month of October

nov

Anomaly for month of November

dec

Anomaly for month of December

annual

Annual anomaly for the year

Source

https://ess-dive.lbl.gov/

References

https://ess-dive.lbl.gov/

Description

This class represents a reduction that replaces symbolic parameters with their constraint values.

Usage

## S4 method for signature 'Chain'
as.character(x)

## S4 method for signature 'Chain,Problem'
accepts(object, problem)

## S4 method for signature 'Chain,Problem'
perform(object, problem)

## S4 method for signature 'Chain,SolutionORList,list'
invert(object, solution, inverse_data)

Arguments

Methods (by generic)

• accepts(object = Chain, problem = Problem): A problem is accepted if the sequence of reductions is valid. In particular, the i-th reduction must accept the output of the i-1th reduction, with the first reduction (self.reductions[0]) in the sequence taking as input the supplied problem.

• perform(object = Chain, problem = Problem): Applies the chain to a problem and returns an equivalent problem.

• invert(object = Chain, solution = SolutionORList, inverse_data = list): Performs the reduction on a problem and returns an equivalent problem.

Description

An interface for the CLARABEL solver

Usage

CLARABEL()

## S4 method for signature 'CLARABEL'
mip_capable(solver)

## S4 method for signature 'CLARABEL'
status_map(solver, status)

## S4 method for signature 'CLARABEL'
name(x)

## S4 method for signature 'CLARABEL'
import_solver(solver)

## S4 method for signature 'CLARABEL'
reduction_format_constr(object, problem, constr, exp_cone_order)

## S4 method for signature 'CLARABEL,Problem'
perform(object, problem)

## S4 method for signature 'CLARABEL,list,list'
invert(object, solution, inverse_data)

## S4 method for signature 'CLARABEL'
solve_via_data(
  object,
  data,
  warm_start,
  verbose,
  feastol,
  reltol,
  abstol,
  num_iter,
  solver_opts,
  solver_cache
)

Arguments

Methods (by generic)

• mip_capable(CLARABEL): Can the solver handle mixed-integer programs?

• status_map(CLARABEL): Converts status returned by CLARABEL solver to its respective CVXPY status.

• name(CLARABEL): Returns the name of the solver

• import_solver(CLARABEL): Imports the solver

• reduction_format_constr(CLARABEL): Return a linear operator to multiply by PSD constraint coefficients.

• perform(object = CLARABEL, problem = Problem): Returns a new problem and data for inverting the new solution

• invert(object = CLARABEL, solution = list, inverse_data = list): Returns the solution to the original problem given the inverse_data.

• solve_via_data(CLARABEL): Solve a problem represented by data returned from apply.

Description

Utility method for formatting a ConeDims instance into a dictionary that can be supplied to Clarabel

Usage

CLARABEL.dims_to_solver_dict(cone_dims)

Arguments

Value

The dimensions of the cones.

Description

Special cases PSD constraints, as per the CLARABEL specification.

Usage

CLARABEL.extract_dual_value(result_vec, offset, constraint)

Arguments

Value

The dual values for the corresponding PSD constraints

Description

Basic atoms that support complex arithmetic.

Usage

## S4 method for signature 'Expression'
Re(z)

## S4 method for signature 'Expression'
Im(z)

## S4 method for signature 'Expression'
Conj(z)

Arguments

Value

An Expression object that represents the real, imaginary, or complex conjugate.

Description

Determine if an expression is real, imaginary, or complex.

Usage

is_real(object)

is_imag(object)

is_complex(object)

Arguments

Value

A logical value.

Description

This reduction takes in a complex problem and returns an equivalent real problem.

Usage

## S4 method for signature 'Complex2Real,Problem'
accepts(object, problem)

## S4 method for signature 'Complex2Real,Problem'
perform(object, problem)

## S4 method for signature 'Complex2Real,Solution,InverseData'
invert(object, solution, inverse_data)

Arguments

Methods (by generic)

• accepts(object = Complex2Real, problem = Problem): Checks whether or not the problem involves any complex numbers.

• perform(object = Complex2Real, problem = Problem): Converts a Complex problem into a Real one.

• invert(object = Complex2Real, solution = Solution, inverse_data = InverseData): Returns a solution to the original problem given the inverse data.

Description

Complex canonicalizer for the absolute value atom

Usage

Complex2Real.abs_canon(expr, real_args, imag_args, real2imag)

Arguments

Value

A canonicalization of the absolute value atom of a complex expression, where the returned variables are its real and imaginary components parsed out.

Description

Helper function to sum arguments.

Usage

Complex2Real.add(lh_arg, rh_arg, neg = FALSE)

Arguments

Description

Upcast 0D and 1D to 2D.

Usage

Complex2Real.at_least_2D(expr)

Arguments

Value

An expression of dimension at least 2.

Description

Complex canonicalizer for the binary atom

Usage

Complex2Real.binary_canon(expr, real_args, imag_args, real2imag)

Arguments

Value

A canonicalization of a binary atom, where the returned variables are the real component and the imaginary component.

Description

Canonicalizes a Complex Expression

Usage

Complex2Real.canonicalize_expr(expr, real_args, imag_args, real2imag, leaf_map)

Arguments

Value

A list of the parsed out real and imaginary components of the expression at hand.

Description

Recursively Canonicalizes a Complex Expression.

Usage

Complex2Real.canonicalize_tree(expr, real2imag, leaf_map)

Arguments

Value

A list of the parsed out real and imaginary components of the expression that was constructed by performing the canonicalization of each leaf in the tree.

Description

Complex canonicalizer for the conjugate atom

Usage

Complex2Real.conj_canon(expr, real_args, imag_args, real2imag)

Arguments

Value

A canonicalization of a conjugate atom, where the returned variables are the real components and negative of the imaginary component.

Description

Complex canonicalizer for the constant atom

Usage

Complex2Real.constant_canon(expr, real_args, imag_args, real2imag)

Arguments

Value

A canonicalization of a constant atom, where the returned variables are the real component and the imaginary component in the Constant atom.

Description

Complex canonicalizer for the hermitian atom

Usage

Complex2Real.hermitian_canon(expr, real_args, imag_args, real2imag)

Arguments

Value

A canonicalization of a hermitian matrix atom, where the returned variables are the real component and the imaginary component.

Description

Complex canonicalizer for the imaginary atom

Usage

Complex2Real.imag_canon(expr, real_args, imag_args, real2imag)

Arguments

Value

A canonicalization of an imaginary atom, where the returned variables are the imaginary component and NULL for the real component.

Description

Helper function to combine arguments.

Usage

Complex2Real.join(expr, lh_arg, rh_arg)

Arguments

Value

A joined expression of both left and right expressions

Description

Complex canonicalizer for the largest sum atom

Usage

Complex2Real.lambda_sum_largest_canon(expr, real_args, imag_args, real2imag)

Arguments

Value

A canonicalization of the largest sum atom, where the returned variables are the real component and the imaginary component.

Description

Complex canonicalizer for the matrix fraction atom

Usage

Complex2Real.matrix_frac_canon(expr, real_args, imag_args, real2imag)

Arguments

Value

A canonicalization of a matrix atom, where the returned variables are converted to real variables.

Description

Complex canonicalizer for the non-positive atom

Usage

Complex2Real.nonpos_canon(expr, real_args, imag_args, real2imag)

Arguments

Value

A canonicalization of a non positive atom, where the returned variables are the real component and the imaginary component.

Description

Complex canonicalizer for the nuclear norm atom

Usage

Complex2Real.norm_nuc_canon(expr, real_args, imag_args, real2imag)

Arguments

Value

A canonicalization of a nuclear norm matrix atom, where the returned variables are the real component and the imaginary component.

Description

Complex canonicalizer for the parameter matrix atom

Usage

Complex2Real.param_canon(expr, real_args, imag_args, real2imag)

Arguments

Value

A canonicalization of a parameter matrix atom, where the returned variables are the real component and the imaginary component.

Description

Complex canonicalizer for the p norm atom

Usage

Complex2Real.pnorm_canon(expr, real_args, imag_args, real2imag)

Arguments

Value

A canonicalization of a pnorm atom, where the returned variables are the real component and the NULL imaginary component.

Description

Complex canonicalizer for the positive semidefinite atom

Usage

Complex2Real.psd_canon(expr, real_args, imag_args, real2imag)

Arguments

Value

A canonicalization of a positive semidefinite atom, where the returned variables are the real component and the NULL imaginary component.

Description

Complex canonicalizer for the quadratic atom

Usage

Complex2Real.quad_canon(expr, real_args, imag_args, real2imag)

Arguments

Value

A canonicalization of a quadratic atom, where the returned variables are the real component and the imaginary component as NULL.

Description

Complex canonicalizer for the quadratic over linear term atom

Usage

Complex2Real.quad_over_lin_canon(expr, real_args, imag_args, real2imag)

Arguments

Value

A canonicalization of a quadratic over a linear term atom, where the returned variables are the real component and the imaginary component.

Description

Complex canonicalizer for the real atom

Usage

Complex2Real.real_canon(expr, real_args, imag_args, real2imag)

Arguments

Value

A canonicalization of a real atom, where the returned variables are the real component and NULL for the imaginary component.

Description

Complex canonicalizer for the separable atom

Usage

Complex2Real.separable_canon(expr, real_args, imag_args, real2imag)

Arguments

Value

A canonicalization of a separable atom, where the returned variables are its real and imaginary components parsed out.

Description

Complex canonicalizer for the SOC atom

Usage

Complex2Real.soc_canon(expr, real_args, imag_args, real2imag)

Arguments

Value

A canonicalization of a SOC atom, where the returned variables are the real component and the NULL imaginary component.

Description

Complex canonicalizer for the variable atom

Usage

Complex2Real.variable_canon(expr, real_args, imag_args, real2imag)

Arguments

Value

A canonicalization of a variable atom, where the returned variables are the real component and the NULL imaginary component.

Description

Complex canonicalizer for the zero atom

Usage

Complex2Real.zero_canon(expr, real_args, imag_args, real2imag)

Arguments

Value

A canonicalization of a zero atom, where the returned variables are the real component and the imaginary component.

Description

The number of elementwise cones or a list of the sizes of the elementwise cones.

Usage

num_cones(object)

cone_sizes(object)

Arguments

Value

The number of cones, or the size of a cone.

Description

Constraints must be formatted as dictionary that maps from constraint type to a list of constraints of that type.

Details

Attributes ———- zero : int The dimension of the zero cone. nonpos : int The dimension of the non-positive cone. exp : int The dimension of the exponential cone. soc : list of int A list of the second-order cone dimensions. psd : list of int A list of the positive semidefinite cone dimensions, where the dimension of the PSD cone of k by k matrices is k.

Description

Linear cone problems are assumed to have a linear objective and cone constraints, which may have zero or more arguments, all of which must be affine.

Usage

## S4 method for signature 'ConeMatrixStuffing,Problem'
accepts(object, problem)

## S4 method for signature 'ConeMatrixStuffing,Problem,CoeffExtractor'
stuffed_objective(object, problem, extractor)

Arguments

Details

minimize c^Tx subject to cone_constr1(A_1*x + b_1, ...) ... cone_constrK(A_K*x + b_K, ...)

Methods (by generic)

• accepts(object = ConeMatrixStuffing, problem = Problem): Is the solver accepted?

• stuffed_objective( object = ConeMatrixStuffing, problem = Problem, extractor = CoeffExtractor ): Returns a list of the stuffed matrices

Description

Conic solver class with reduction semantics.

Usage

## S4 method for signature 'ConicSolver,Problem'
accepts(object, problem)

## S4 method for signature 'ConicSolver'
reduction_format_constr(object, problem, constr, exp_cone_order)

## S4 method for signature 'ConicSolver'
group_coeff_offset(object, problem, constraints, exp_cone_order)

## S4 method for signature 'ConicSolver,Solution,InverseData'
invert(object, solution, inverse_data)

Arguments

Methods (by generic)

• accepts(object = ConicSolver, problem = Problem): Can the problem be solved with a conic solver?

• reduction_format_constr(ConicSolver): Return a list representing a cone program whose problem data tensors will yield the coefficient "A" and offset "b" for the respective constraints: Linear Equations: $A x = b$, Linear inequalities: $A x \leq b$, Second order cone: $A x \leq_{SOC} b$, Exponential cone: $A x \leq_{EXP} b$, Semidefinite cone: $A x \leq_{SOP} b$.

• group_coeff_offset(ConicSolver): Combine the constraints into a single matrix, offset.

• invert(object = ConicSolver, solution = Solution, inverse_data = InverseData): Returns the solution to the original problem given the inverse_data.

Description

Return the coefficient and offset in $Ax + b$.

Usage

ConicSolver.get_coeff_offset(expr)

Arguments

Value

The coefficient and offset in $Ax + b$.

Description

Returns a sparse matrix that spaces out an expression.

Usage

ConicSolver.get_spacing_matrix(dim, spacing, offset)

Arguments

Value

A sparse matrix that spaces out an expression

Description

This class represents the complex conjugate of an expression.

Usage

Conjugate(expr)

## S4 method for signature 'Conjugate'
to_numeric(object, values)

## S4 method for signature 'Conjugate'
dim_from_args(object)

## S4 method for signature 'Conjugate'
is_incr(object, idx)

## S4 method for signature 'Conjugate'
is_decr(object, idx)

## S4 method for signature 'Conjugate'
is_symmetric(object)

## S4 method for signature 'Conjugate'
is_hermitian(object)

Arguments

Methods (by generic)

• to_numeric(Conjugate): Elementwise complex conjugate of the constant.

• dim_from_args(Conjugate): The (row, col) dimensions of the expression.

• is_incr(Conjugate): Is the composition weakly increasing in argument idx?

• is_decr(Conjugate): Is the composition weakly decreasing in argument idx?

• is_symmetric(Conjugate): Is the expression symmetric?

• is_hermitian(Conjugate): Is the expression hermitian?

Slots

expr

An Expression or R numeric data.

Description

This class represents a constant.

Coerce an R object or expression into the Constant class.

Usage

Constant(value)

## S4 method for signature 'Constant'
show(object)

## S4 method for signature 'Constant'
name(x)

## S4 method for signature 'Constant'
constants(object)

## S4 method for signature 'Constant'
value(object)

## S4 method for signature 'Constant'
is_pos(object)

## S4 method for signature 'Constant'
grad(object)

## S4 method for signature 'Constant'
dim(x)

## S4 method for signature 'Constant'
canonicalize(object)

## S4 method for signature 'Constant'
is_nonneg(object)

## S4 method for signature 'Constant'
is_nonpos(object)

## S4 method for signature 'Constant'
is_imag(object)

## S4 method for signature 'Constant'
is_complex(object)

## S4 method for signature 'Constant'
is_symmetric(object)

## S4 method for signature 'Constant'
is_hermitian(object)

## S4 method for signature 'Constant'
is_psd(object)

## S4 method for signature 'Constant'
is_nsd(object)

as.Constant(expr)

Arguments

Value

A Constant representing the input as a constant.

Methods (by generic)

• name(Constant): The name of the constant.

• constants(Constant): Returns itself as a constant.

• value(Constant): The value of the constant.

• is_pos(Constant): A logical value indicating whether all elements of the constant are positive.

• grad(Constant): An empty list since the gradient of a constant is zero.

• dim(Constant): The c(row, col) dimensions of the constant.

• canonicalize(Constant): The canonical form of the constant.

• is_nonneg(Constant): A logical value indicating whether all elements of the constant are non-negative.

• is_nonpos(Constant): A logical value indicating whether all elements of the constant are non-positive.

• is_imag(Constant): A logical value indicating whether the constant is imaginary.

• is_complex(Constant): A logical value indicating whether the constant is complex-valued.

• is_symmetric(Constant): A logical value indicating whether the constant is symmetric.

• is_hermitian(Constant): A logical value indicating whether the constant is a Hermitian matrix.

• is_psd(Constant): A logical value indicating whether the constant is a positive semidefinite matrix.

• is_nsd(Constant): A logical value indicating whether the constant is a negative semidefinite matrix.

Slots

value

A numeric element, vector, matrix, or data.frame. Vectors are automatically cast into a matrix column.

sparse

(Internal) A logical value indicating whether the value is a sparse matrix.

is_pos

(Internal) A logical value indicating whether all elements are non-negative.

is_neg

(Internal) A logical value indicating whether all elements are non-positive.

Examples

x <- Constant(5)
y <- Constant(diag(3))
get_data(y)
value(y)
is_nonneg(y)
size(y)
as.Constant(y)

Description

The ConstantSolver class.

Usage

## S4 method for signature 'ConstantSolver'
mip_capable(solver)

## S4 method for signature 'ConstantSolver,Problem'
accepts(object, problem)

## S4 method for signature 'ConstantSolver,Problem'
perform(object, problem)

## S4 method for signature 'ConstantSolver,Solution,list'
invert(object, solution, inverse_data)

## S4 method for signature 'ConstantSolver'
name(x)

## S4 method for signature 'ConstantSolver'
import_solver(solver)

## S4 method for signature 'ConstantSolver'
is_installed(solver)

## S4 method for signature 'ConstantSolver'
solve_via_data(
  object,
  data,
  warm_start,
  verbose,
  feastol,
  reltol,
  abstol,
  num_iter,
  solver_opts,
  solver_cache
)

## S4 method for signature 'ConstantSolver,ANY'
reduction_solve(object, problem, warm_start, verbose, solver_opts)

Arguments

Methods (by generic)

• mip_capable(ConstantSolver): Can the solver handle mixed-integer programs?

• accepts(object = ConstantSolver, problem = Problem): Is the solver capable of solving the problem?

• perform(object = ConstantSolver, problem = Problem): Returns a list of the ConstantSolver, Problem, and an empty list.

• invert(object = ConstantSolver, solution = Solution, inverse_data = list): Returns the solution.

• name(ConstantSolver): Returns the name of the solver.

• import_solver(ConstantSolver): Imports the solver.

• is_installed(ConstantSolver): Is the solver installed?

• solve_via_data(ConstantSolver): Solve a problem represented by data returned from apply.

• reduction_solve(object = ConstantSolver, problem = ANY): Solve the problem and return a Solution object.

Description

Checks whether the constraint violation is less than a tolerance.

Usage

constr_value(object, tolerance = 1e-08)

Arguments

Value

A logical value indicating whether the violation is less than the tolerance. Raises an error if the residual is NA.

Description

This virtual class represents a mathematical constraint.

Usage

## S4 method for signature 'Constraint'
as.character(x)

## S4 method for signature 'Constraint'
dim(x)

## S4 method for signature 'Constraint'
size(object)

## S4 method for signature 'Constraint'
is_real(object)

## S4 method for signature 'Constraint'
is_imag(object)

## S4 method for signature 'Constraint'
is_complex(object)

## S4 method for signature 'Constraint'
is_dcp(object)

## S4 method for signature 'Constraint'
is_dgp(object)

## S4 method for signature 'Constraint'
residual(object)

## S4 method for signature 'Constraint'
violation(object)

## S4 method for signature 'Constraint'
constr_value(object, tolerance = 1e-08)

## S4 method for signature 'Constraint'
get_data(object)

## S4 method for signature 'Constraint'
dual_value(object)

## S4 replacement method for signature 'Constraint'
dual_value(object) <- value

## S4 method for signature 'ZeroConstraint'
size(object)

Arguments

Methods (by generic)

• dim(Constraint): The dimensions of the constrained expression.

• size(Constraint): The size of the constrained expression.

• is_real(Constraint): Is the constraint real?

• is_imag(Constraint): Is the constraint imaginary?

• is_complex(Constraint): Is the constraint complex?

• is_dcp(Constraint): Is the constraint DCP?

• is_dgp(Constraint): Is the constraint DGP?

• residual(Constraint): The residual of a constraint

• violation(Constraint): The violation of a constraint.

• constr_value(Constraint): The value of a constraint.

• get_data(Constraint): Information needed to reconstruct the object aside from the args.

• dual_value(Constraint): The dual values of a constraint.

• dual_value(Constraint) <- value: Replaces the dual values of a constraint..

• size(ZeroConstraint): The size of the constrained expression.

Description

Builds a chain that rewrites a problem into an intermediate representation suitable for numeric reductions.

Usage

## S4 method for signature 'Problem,list'
construct_intermediate_chain(problem, candidates, gp = FALSE)

Arguments

Value

A Chain object that can be used to convert the problem to an intermediate form.

Description

Build a reduction chain from a problem to an installed solver.

Usage

construct_solving_chain(problem, candidates)

Arguments

Value

A SolvingChain that can be used to solve the problem.

Description

The 1-D discrete convolution of two vectors.

Usage

conv(lh_exp, rh_exp)

Arguments

Value

An Expression representing the convolution of the input.

Examples

set.seed(129)
x <- Variable(5)
h <- matrix(stats::rnorm(2), nrow = 2, ncol = 1)
prob <- Problem(Minimize(sum(conv(h, x))))
result <- solve(prob)
result$value
result$getValue(x)

Description

This class represents the 1-D discrete convolution of two vectors.

Usage

Conv(lh_exp, rh_exp)

## S4 method for signature 'Conv'
to_numeric(object, values)

## S4 method for signature 'Conv'
validate_args(object)

## S4 method for signature 'Conv'
dim_from_args(object)

## S4 method for signature 'Conv'
sign_from_args(object)

## S4 method for signature 'Conv'
is_incr(object, idx)

## S4 method for signature 'Conv'
is_decr(object, idx)

## S4 method for signature 'Conv'
graph_implementation(object, arg_objs, dim, data = NA_real_)

Arguments

Methods (by generic)

• to_numeric(Conv): The convolution of the two values.

• validate_args(Conv): Check both arguments are vectors and the first is a constant.

• dim_from_args(Conv): The dimensions of the atom.

• sign_from_args(Conv): The sign of the atom.

• is_incr(Conv): Is the left-hand expression positive?

• is_decr(Conv): Is the left-hand expression negative?

• graph_implementation(Conv): The graph implementation of the atom.

Slots

lh_exp

An Expression or R numeric data representing the left-hand vector.

rh_exp

An Expression or R numeric data representing the right-hand vector.

Description

An interface for the CPLEX solver

Usage

CPLEX_CONIC()

CPLEX_CONIC()

## S4 method for signature 'CPLEX_CONIC'
mip_capable(solver)

## S4 method for signature 'CPLEX_CONIC'
name(x)

## S4 method for signature 'CPLEX_CONIC'
import_solver(solver)

## S4 method for signature 'CPLEX_CONIC,Problem'
accepts(object, problem)

## S4 method for signature 'CPLEX_CONIC'
status_map(solver, status)

## S4 method for signature 'CPLEX_CONIC,Problem'
perform(object, problem)

## S4 method for signature 'CPLEX_CONIC,list,list'
invert(object, solution, inverse_data)

## S4 method for signature 'CPLEX_CONIC'
solve_via_data(
  object,
  data,
  warm_start,
  verbose,
  feastol,
  reltol,
  abstol,
  num_iter,
  solver_opts,
  solver_cache
)

Arguments

Methods (by generic)

• mip_capable(CPLEX_CONIC): Can the solver handle mixed-integer programs?

• name(CPLEX_CONIC): Returns the name of the solver.

• import_solver(CPLEX_CONIC): Imports the solver.

• accepts(object = CPLEX_CONIC, problem = Problem): Can CPLEX solve the problem?

• status_map(CPLEX_CONIC): Converts status returned by the CPLEX solver to its respective CVXPY status.

• perform(object = CPLEX_CONIC, problem = Problem): Returns a new problem and data for inverting the new solution.

• invert(object = CPLEX_CONIC, solution = list, inverse_data = list): Returns the solution to the original problem given the inverse_data.

• solve_via_data(CPLEX_CONIC): Solve a problem represented by data returned from apply.

Description

An interface for the CPLEX solver.

Usage

CPLEX_QP()

## S4 method for signature 'CPLEX_QP'
mip_capable(solver)

## S4 method for signature 'CPLEX_QP'
status_map(solver, status)

## S4 method for signature 'CPLEX_QP'
name(x)

## S4 method for signature 'CPLEX_QP'
import_solver(solver)

## S4 method for signature 'CPLEX_QP,list,InverseData'
invert(object, solution, inverse_data)

## S4 method for signature 'CPLEX_QP'
solve_via_data(
  object,
  data,
  warm_start,
  verbose,
  feastol,
  reltol,
  abstol,
  num_iter,
  solver_opts,
  solver_cache
)

Arguments

Methods (by generic)

• mip_capable(CPLEX_QP): Can the solver handle mixed-integer programs?

• status_map(CPLEX_QP): Converts status returned by the CPLEX solver to its respective CVXPY status.

• name(CPLEX_QP): Returns the name of the solver.

• import_solver(CPLEX_QP): Imports the solver.

• invert(object = CPLEX_QP, solution = list, inverse_data = InverseData): Returns the solution to the original problem given the inverse_data.

• solve_via_data(CPLEX_QP): Solve a problem represented by data returned from apply.

Description

The cumulative maximum, $\max_{i=1,\ldots,k} x_i$ for $k=1,\ldots,n$. When calling cummax, matrices are automatically flattened into column-major order before the max is taken.

Usage

cummax_axis(expr, axis = 2)

## S4 method for signature 'Expression'
cummax(x)

Arguments

Examples

val <- cbind(c(1,2), c(3,4))
value(cummax(Constant(val)))
value(cummax_axis(Constant(val)))

x <- Variable(2,2)
prob <- Problem(Minimize(cummax(x)[4]), list(x == val))
result <- solve(prob)
result$value
result$getValue(cummax(x))

Description

This class represents the cumulative maximum of an expression.

Usage

CumMax(expr, axis = 2)

## S4 method for signature 'CumMax'
to_numeric(object, values)

## S4 method for signature 'CumMax'
.grad(object, values)

## S4 method for signature 'CumMax'
.column_grad(object, value)

## S4 method for signature 'CumMax'
dim_from_args(object)

## S4 method for signature 'CumMax'
sign_from_args(object)

## S4 method for signature 'CumMax'
get_data(object)

## S4 method for signature 'CumMax'
is_atom_convex(object)

## S4 method for signature 'CumMax'
is_atom_concave(object)

## S4 method for signature 'CumMax'
is_incr(object, idx)

## S4 method for signature 'CumMax'
is_decr(object, idx)

Arguments

Methods (by generic)

• to_numeric(CumMax): The cumulative maximum along the axis.

• .grad(CumMax): Gives the (sub/super)gradient of the atom w.r.t. each variable

• .column_grad(CumMax): Gives the (sub/super)gradient of the atom w.r.t. each column variable

• dim_from_args(CumMax): The dimensions of the atom determined from its arguments.

• sign_from_args(CumMax): The (is positive, is negative) sign of the atom.

• get_data(CumMax): Returns the axis along which the cumulative max is taken.

• is_atom_convex(CumMax): Is the atom convex?

• is_atom_concave(CumMax): Is the atom concave?

• is_incr(CumMax): Is the atom weakly increasing in the index?

• is_decr(CumMax): Is the atom weakly decreasing in the index?

Slots

expr

An Expression.

axis

A numeric vector indicating the axes along which to apply the function. For a 2D matrix, 1 indicates rows, 2 indicates columns, and c(1,2) indicates rows and columns.

Description

The cumulative sum, $\sum_{i=1}^k x_i$ for $k=1,\ldots,n$. When calling cumsum, matrices are automatically flattened into column-major order before the sum is taken.

Usage

cumsum_axis(expr, axis = 2)

## S4 method for signature 'Expression'
cumsum(x)