14.2.13 Class Expr¶
- mosek::fusion::Expr¶
It represents an expression of the form \(Ax+b\), where \(A\) is a matrix on sparse form, \(x\) is a variable vector and \(b\) is a vector of scalars.
Additionally, the class defines a set of static methods for constructing and manipulating various expressions.
- Implements
- Members
BaseExpression.getDim – Return the d’th dimension in the expression.
BaseExpression.getND – Return the number of dimensions in the expression.
BaseExpression.getShape – Get the shape of the expression.
BaseExpression.getSize – Return the total number of elements in the expression (the product of the dimensions).
BaseExpression.index – Get a single element in the expression.
BaseExpression.pick – Pick a number of elements from the expression.
BaseExpression.slice – Get a slice of the expression.
BaseExpression.toString – Return a string representation of the expression object.
Expr.eval – Evaluate the expression and push the result onto the work stack.
- Static members
Expr.add – Compute the sum of expressions.
Expr.condense – Flatten expression and remove all structural zeros.
Expr.constTerm – Create an expression consisting of a constant vector of values.
Expr.dot – Return a scalar expression object representing the dot-product of two items.
Expr.flatten – Reshape the expression into a vector.
Expr.hstack – Stack a list of expressions horizontally (i.e. along the second dimension).
Expr.mul – Multiply two items.
Expr.mulDiag – Compute the diagonal of the product of two matrices.
Expr.mulElm – Element-wise product of two items.
Expr.neg – Change the sign of an expression
Expr.ones – Create an expression consisting of ones.
Expr.outer – Return the outer-product of two vectors.
Expr.repeat – Repeat an expression a number of times in the given dimension.
Expr.reshape – Reshape the expression into a different shape with the same number of elements.
Expr.stack – Stack a list of expressions in an arbitrary dimension.
Expr.sub – Compute the difference of two expressions.
Expr.sum – Sum the elements of an expression.
Expr.transpose – Transpose a two-dimensional expression.
Expr.vstack – Stack a list of expressions vertically (i.e. along the first dimension).
Expr.zeros – Create an expression consisting of zeros.
- Expr.add¶
Expression::t Expr::add(Expression::t e1, Expression::t e2) Expression::t Expr::add(Expression::t e1, shared_ptr<ndarray<double,1>> a1) Expression::t Expr::add(Expression::t e1, shared_ptr<ndarray<double,2>> a2) Expression::t Expr::add(shared_ptr<ndarray<double,1>> a1, Expression::t e2) Expression::t Expr::add(shared_ptr<ndarray<double,2>> a2, Expression::t e2) Expression::t Expr::add(Expression::t e1, double c) Expression::t Expr::add(double c, Expression::t e2) Expression::t Expr::add(Expression::t e1, Matrix::t m) Expression::t Expr::add(Matrix::t m, Expression::t e2) Expression::t Expr::add(Expression::t e1, NDSparseArray::t n) Expression::t Expr::add(NDSparseArray::t n, Expression::t e2) Expression::t Expr::add(shared_ptr<ndarray<Variable::t,1>> vs) Expression::t Expr::add(shared_ptr<ndarray<Expression::t,1>> exps)
Computes the sum of two or more expressions or variables. The following types of arguments are allowed:
A
B
VariableVariableExpressionExpressiondoubledouble[]double[,]MatrixNDSparseArrayBy symmetry both
add(A,B)andadd(B,A)are available.The arguments must have the same shapes and the returned expression also has that shape. If one of the arguments is a single scalar, it is promoted to the shape that matches the shape of the other argument, i.e. the scalar is added to all entries of the other argument.
- Parameters
e1(Expression) – An expression.e2(Expression) – An expression.a1(double[]) – A one-dimensional array of constants.a2(double[][]) – A two-dimensional array of constants.c(double) – A constant.m(Matrix) – A Matrix object.n(NDSparseArray) – An NDSparseArray object.vs(Variable[]) – A list of variables. All variables in the array must have the same shape. The list must contain at least one element.exps(Expression[]) – A list of expressions. All expressions in the array must have the same shape. The list must contain at least one element.
- Return
- Expr.condense¶
Expression::t Expr::condense(Expression::t e)
Flatten expression and remove all structural zeros.
- Parameters
e(Expression) – Expression to be condensed.- Return
- Expr.constTerm¶
Expression::t Expr::constTerm(shared_ptr<ndarray<double,1>> vals1) Expression::t Expr::constTerm(shared_ptr<ndarray<double,2>> vals2) Expression::t Expr::constTerm(int size, double val) Expression::t Expr::constTerm(shared_ptr<ndarray<int,1>> shp, double val) Expression::t Expr::constTerm(shared_ptr<ndarray<int,1>> shp, shared_ptr<ndarray<int,2>> sparsity, shared_ptr<ndarray<double,1>> vals1) Expression::t Expr::constTerm(shared_ptr<ndarray<int,1>> shp, shared_ptr<ndarray<int,2>> sparsity, double val) Expression::t Expr::constTerm(double val) Expression::t Expr::constTerm(Matrix::t m) Expression::t Expr::constTerm(NDSparseArray::t nda)
Create an expression consisting of a constant vector of values.
- Parameters
vals1(double[]) – A vector initializing the expression.vals2(double[][]) – An array initializing the expression.size(int) – Length of the vector to be constructed.val(double) – A scalar value to be repeated in all entries of the expression.shp(int[]) – Defines the shape of the expression.sparsity(int[][]) – Sparsity pattern.m(Matrix) – A matrix of values initializing the expression.nda(NDSparseArray) – An multi-dimensional sparse array initializing the expression.
- Return
- Expr.dot¶
Expression::t Expr::dot(Parameter::t p, Expression::t e) Expression::t Expr::dot(Expression::t e, Parameter::t p) Expression::t Expr::dot(shared_ptr<ndarray<double,1>> c1, Expression::t e) Expression::t Expr::dot(shared_ptr<ndarray<double,2>> c2, Expression::t e) Expression::t Expr::dot(NDSparseArray::t nda, Expression::t e) Expression::t Expr::dot(Matrix::t m, Expression::t e) Expression::t Expr::dot(Expression::t e, shared_ptr<ndarray<double,1>> c1) Expression::t Expr::dot(Expression::t e, NDSparseArray::t nda) Expression::t Expr::dot(Expression::t e, shared_ptr<ndarray<double,2>> c2) Expression::t Expr::dot(Expression::t e, Matrix::t m)
Return an object representing the inner product (dot product) \(x^Ty = \sum_{i=1}^nx_iy_i\) of two objects \(x,y\) of size \(n\).
Both arguments must have the same length when flattened. In particular, they can be two vectors of the same length or two matrices of the same shape.
- Parameters
p(Parameter) – A parameter.e(Expression) – An expression object.c1(double[]) – A one-dimensional coefficient vector.c2(double[][]) – A two-dimensional coefficient array.nda(NDSparseArray) – A multi-dimensional sparse array.m(Matrix) – A matrix object.
- Return
- Expr.eval¶
void eval(WorkStack::t rs, WorkStack::t ws, WorkStack::t xs)
Evaluate the expression and push the result onto the
rswork stack.
- Expr.flatten¶
Expression::t Expr::flatten(Expression::t e)
Reshape the expression into a vector.
- Parameters
e(Expression) – The expression to be flattened.- Return
- Expr.hstack¶
Expression::t Expr::hstack(shared_ptr<ndarray<Expression::t,1>> exprs) Expression::t Expr::hstack(Expression::t e1, Expression::t e2) Expression::t Expr::hstack(Expression::t e1, double a2) Expression::t Expr::hstack(double a1, Expression::t e2) Expression::t Expr::hstack(double a1, double a2, Expression::t e3) Expression::t Expr::hstack(double a1, Expression::t e2, double a3) Expression::t Expr::hstack(double a1, Expression::t e2, Expression::t e3) Expression::t Expr::hstack(Expression::t e1, double a2, double a3) Expression::t Expr::hstack(Expression::t e1, double a2, Expression::t e3) Expression::t Expr::hstack(Expression::t e1, Expression::t e2, double a3) Expression::t Expr::hstack(Expression::t e1, Expression::t e2, Expression::t e3)
Stack a list of expressions horizontally (i.e. along the second dimension). The expressions must have the same shape, except for the second dimension. The arguments may be any combination of expressions, scalar constants and variables.
For example, if \(x^1,x^2,x^3\) are three vectors of length \(n\) then their horizontal stack is the matrix
\[\begin{split}\left[ \begin{array}{ccc} | & | & | \\ x^1 & x^2 & x^3 \\ | & | & | \end{array}\right]\end{split}\]of shape
(n,3).- Parameters
exprs(Expression[]) – A list of expressions.e1(Expression) – An expression.e2(Expression) – An expression.a2(double) – A scalar constant.a1(double) – A scalar constant.e3(Expression) – An expression.a3(double) – A scalar constant.
- Return
- Expr.mul¶
Expression::t Expr::mul(Parameter::t p, Expression::t expr) Expression::t Expr::mul(Expression::t expr, Parameter::t p) Expression::t Expr::mul(Matrix::t mx, Variable::t v) Expression::t Expr::mul(Variable::t v, Matrix::t mx) Expression::t Expr::mul(shared_ptr<ndarray<double,2>> mx, Variable::t v) Expression::t Expr::mul(Variable::t v, shared_ptr<ndarray<double,2>> mx) Expression::t Expr::mul(Matrix::t mx, Expression::t expr) Expression::t Expr::mul(Expression::t expr, Matrix::t mx) Expression::t Expr::mul(shared_ptr<ndarray<double,2>> a, Expression::t expr) Expression::t Expr::mul(Expression::t expr, shared_ptr<ndarray<double,2>> a) Expression::t Expr::mul(shared_ptr<ndarray<double,1>> a, Expression::t expr) Expression::t Expr::mul(Expression::t expr, shared_ptr<ndarray<double,1>> a) Expression::t Expr::mul(double c, Expression::t expr) Expression::t Expr::mul(Expression::t expr, double c)
Compute the product (in the sense of matrix multiplication or scalar-by-matrix multiplication) of two arguments.
The operands must be at most two-dimensional. One of the arguments must be a constant, a vector of constants or a matrix of constants. The other argument can be a variable or expression. This allows to produce matrix expressions where the entries are linear combinations of variables.
The size and shape of the arguments must adhere to the rules of linear algebra.
- Parameters
p(Parameter) – A parameter object.expr(Expression) – An expression.mx(Matrix) – A matrix.mx(double[][]) – A matrix.v(Variable) – A variable.a(double[][]) – Scalar data.a(double[]) – Scalar data.c(double) – A scalar value.
- Return
- Expr.mulDiag¶
Expression::t Expr::mulDiag(shared_ptr<ndarray<double,2>> a, Expression::t expr) Expression::t Expr::mulDiag(shared_ptr<ndarray<double,2>> a, Variable::t v) Expression::t Expr::mulDiag(Expression::t expr, shared_ptr<ndarray<double,2>> a) Expression::t Expr::mulDiag(Variable::t v, shared_ptr<ndarray<double,2>> a) Expression::t Expr::mulDiag(Matrix::t mx, Expression::t expr) Expression::t Expr::mulDiag(Expression::t expr, Matrix::t mx) Expression::t Expr::mulDiag(Matrix::t mx, Variable::t v) Expression::t Expr::mulDiag(Variable::t v, Matrix::t mx) Expression::t Expr::mulDiag(Parameter::t p, Expression::t expr) Expression::t Expr::mulDiag(Expression::t expr, Parameter::t p) Expression::t Expr::mulDiag(Parameter::t p, Variable::t v) Expression::t Expr::mulDiag(Variable::t v, Parameter::t p)
Compute the diagonal of the product of two matrices. If \(A\in\mathbb{M}(m,n)\) and \(B\in\mathbb{M}(n,m)\), the result is a vector expression of length \(m\) equal to \(\diag(AB)\).
- Parameters
a(double[][]) – A constant matrix.expr(Expression) – An expression object.v(Variable) – A variable object.mx(Matrix) – A matrix object.p(Parameter) – A parameter object.
- Return
- Expr.mulElm¶
Expression::t Expr::mulElm(Expression::t expr, Parameter::t p) Expression::t Expr::mulElm(Parameter::t p, Expression::t expr) Expression::t Expr::mulElm(Expression::t expr, NDSparseArray::t spm) Expression::t Expr::mulElm(Expression::t expr, shared_ptr<ndarray<double,1>> a1) Expression::t Expr::mulElm(Expression::t expr, shared_ptr<ndarray<double,2>> a2) Expression::t Expr::mulElm(Expression::t expr, Matrix::t m) Expression::t Expr::mulElm(shared_ptr<ndarray<double,1>> a1, Expression::t expr) Expression::t Expr::mulElm(shared_ptr<ndarray<double,2>> a2, Expression::t expr) Expression::t Expr::mulElm(NDSparseArray::t spm, Expression::t expr) Expression::t Expr::mulElm(Matrix::t m, Expression::t expr)
Returns the element-wise product of two items. The two operands must have the same shape and the returned expression also has this shape.
- Parameters
expr(Expression) – An expression object.p(Parameter) – A parameter object.spm(NDSparseArray) – A multidimensional sparse array object.a1(double[]) – A one-dimensional coefficient array.a2(double[][]) – A two-dimensional coefficient array.m(Matrix) – A matrix object.
- Return
- Expr.neg¶
Expression::t Expr::neg(Expression::t e)
Return a new expression object representing the given one with opposite sign.
- Parameters
e(Expression) – An expression object.- Return
- Expr.ones¶
Expression::t Expr::ones(int size) Expression::t Expr::ones(shared_ptr<ndarray<int,1>> shp) Expression::t Expr::ones(shared_ptr<ndarray<int,1>> shp, shared_ptr<ndarray<int,2>> sparsity) Expression::t Expr::ones()
Create an expression consisting of ones.
- Parameters
size(int) – Length of the vector to be constructed.shp(int[]) – Defines the shape of the expression.sparsity(int[][]) – Defines the sparsity pattern of the expression - everything outside the sparsitry patterm will be zero.
- Return
- Expr.outer¶
Expression::t Expr::outer(Expression::t e, shared_ptr<ndarray<double,1>> a) Expression::t Expr::outer(shared_ptr<ndarray<double,1>> a, Expression::t e) Expression::t Expr::outer(Expression::t e, Matrix::t m) Expression::t Expr::outer(Matrix::t m, Expression::t e) Expression::t Expr::outer(Expression::t e, Parameter::t p) Expression::t Expr::outer(Parameter::t p, Expression::t e)
Return an expression representing the outer product \(xy^T\) of two vectors \(x,y\). If \(x\) has length
kand \(y\) has lengthnthen the result is of shape(k,n).- Parameters
e(Expression) – A vector expression.a(double[]) – A vector of constants.m(Matrix) – A one-dimensional matrix.p(Parameter) – A vector parameter.
- Return
- Expr.repeat¶
Expression::t Expr::repeat(Expression::t e, int n, int d) Expression::t Expr::repeat(Variable::t x, int n, int d)
Repeat an expression a number of times in the given dimension. This is equivalent to stacking \(n\) copies of the expression in dimension \(d\); see
Expr.stack.- Parameters
e(Expression) – The expression to repeat.n(int) – Number of times to repeat. Must be strictly positive.d(int) – The dimension in which to repeat. Must define a valid dimension index.x(Variable) – The variable to repeat.
- Return
- Expr.reshape¶
Expression::t Expr::reshape(Expression::t e, shared_ptr<ndarray<int,1>> newshape) Expression::t Expr::reshape(Expression::t e, int size) Expression::t Expr::reshape(Expression::t e, int dimi, int dimj)
Reshape the expression into a different shape with the same number of elements.
- Parameters
e(Expression) – The expression to reshape.newshape(int[]) – Reshape into an expression of this shape.size(int) – Reshape into a one-dimensional expression of this size.dimi(int) – The first dimension size.dimj(int) – The second dimension size.
- Return
- Expr.stack¶
Expression::t Expr::stack(int dim, shared_ptr<ndarray<Expression::t,1>> exprs) Expression::t Expr::stack(int dim, Expression::t e1, Expression::t e2) Expression::t Expr::stack(int dim, Expression::t e1, double a2) Expression::t Expr::stack(int dim, double a1, Expression::t e2) Expression::t Expr::stack(int dim, double a1, double a2, Expression::t e1) Expression::t Expr::stack(int dim, double a1, Expression::t e2, double a3) Expression::t Expr::stack(int dim, double a1, Expression::t e2, Expression::t e3) Expression::t Expr::stack(int dim, Expression::t e1, double a2, double a3) Expression::t Expr::stack(int dim, Expression::t e1, double a2, Expression::t e3) Expression::t Expr::stack(int dim, Expression::t e1, Expression::t e2, double a3) Expression::t Expr::stack(int dim, Expression::t e1, Expression::t e2, Expression::t e3) Expression::t Expr::stack(shared_ptr<ndarray<Expression::t,2>> exprs)
Stack a list of expressions along an arbitrary dimension. All expressions must have the same shape, except for dimension
dim. The arguments may be any combination of expressions, scalar constants and variables.For example, suppose \(A,B\) are two \(n\times m\) matrices. Then stacking them in the first dimension produces a matrix of shape
(2n,m):\[\begin{split}\left[\begin{array}{c}A\\ B\end{array}\right],\end{split}\]stacking them in the second dimension produces a matrix of shape
(n,2m):\[\left[\begin{array}{cc}A & B\end{array}\right],\]and stacking them in the third dimension produces a three-dimensional array of shape
(n,m,2).The version which takes a two-dimensional array of expressions constructs a block matrix with the given expressions as blocks. The dimensions of the blocks must be suitably compatible.
- Parameters
dim(int) – The dimension in which to stack.exprs(Expression[]) – A list of expressions.exprs(Expression[][]) – A list of expressions.e1(Expression) – An expression.e2(Expression) – An expression.a2(double) – A scalar constant.a1(double) – A scalar constant.a3(double) – A scalar constant.e3(Expression) – An expression.
- Return
- Expr.sub¶
Expression::t Expr::sub(Expression::t e1, Expression::t e2) Expression::t Expr::sub(Expression::t e1, shared_ptr<ndarray<double,1>> a1) Expression::t Expr::sub(Expression::t e1, shared_ptr<ndarray<double,2>> a2) Expression::t Expr::sub(shared_ptr<ndarray<double,1>> a1, Expression::t e2) Expression::t Expr::sub(shared_ptr<ndarray<double,2>> a2, Expression::t e2) Expression::t Expr::sub(Expression::t e1, double c) Expression::t Expr::sub(double c, Expression::t e2) Expression::t Expr::sub(Expression::t e1, Matrix::t m) Expression::t Expr::sub(Matrix::t m, Expression::t e2) Expression::t Expr::sub(Expression::t e1, NDSparseArray::t n) Expression::t Expr::sub(NDSparseArray::t n, Expression::t e2)
Computes the difference of two expressions. The expressions must have the same shape and the result will be also an expression of that shape. The allowed combinations of arguments are the same as for
Expr.add.- Parameters
e1(Expression) – An expression.e2(Expression) – An expression.a1(double[]) – An array of constants.a2(double[][]) – An array of constants.c(double) – A constant.m(Matrix) – A Matrix object.n(NDSparseArray) – An NDSparseArray object.
- Return
- Expr.sum¶
Expression::t Expr::sum(Expression::t expr) Expression::t Expr::sum(Expression::t expr, int dim)
Sum the elements of an expression. Without extra arguments, all elements are summed into a scalar expression of size 1.
With argument
dim, elements are summed along a specific dimension, resulting in an expression of reduced dimension. Note that the result of summing over a dimension of size 0 is 0.0. This means that for an expression of shape(2,0,2), summing over the second dimension yields an expression of shape(2,2)of zeros.For example, if the argument is an \(n\times m\) matrix then summing along the \(0\)-th dimension computes the \(1\times m\) vector of column sums, and summing along the \(1\)-st dimension computes the \(n\times 1\) vector of row sums.
- Parameters
expr(Expression) – An expression object.dim(int) – The dimension along which to sum.
- Return
- Expr.transpose¶
Expression::t Expr::transpose(Expression::t e)
Transpose a two-dimensional expression.
- Parameters
e(Expression) – Expression to transpose.- Return
- Expr.vstack¶
Expression::t Expr::vstack(shared_ptr<ndarray<Expression::t,1>> exprs) Expression::t Expr::vstack(Expression::t e1, Expression::t e2) Expression::t Expr::vstack(Expression::t e1, double a2) Expression::t Expr::vstack(double a1, Expression::t e2) Expression::t Expr::vstack(Expression::t e1, Expression::t e2, Expression::t e3) Expression::t Expr::vstack(Expression::t e1, Expression::t e2, double a3) Expression::t Expr::vstack(Expression::t e1, double a2, Expression::t e3) Expression::t Expr::vstack(Expression::t e1, double a2, double a3) Expression::t Expr::vstack(double a1, Expression::t e2, Expression::t e3) Expression::t Expr::vstack(double a1, Expression::t e2, double a3) Expression::t Expr::vstack(double a1, double a2, Expression::t e3) Expression::t Expr::vstack(double a1, double a2, double a3)
Stack a list of expressions vertically (i.e. along the first dimension). The expressions must have the same shape, except for the first dimension. The arguments may be any combination of expressions, scalar constants and variables.
For example, if \(y^1,y^2,y^3\) are three horizontal vectors of length \(n\) (and shape
(1,n)) then their vertical stack is the matrix\[\begin{split}\left[ \begin{array}{c}- y^1 - \\ - y^2 - \\ - y^3 - \end{array}\right]\end{split}\]of shape
(3,n).- Parameters
exprs(Expression[]) – A list of expressions.e1(Expression) – An expression.e2(Expression) – An expression.a2(double) – A scalar constant.a1(double) – A scalar constant.e3(Expression) – An expression.a3(double) – A scalar constant.
- Return
- Expr.zeros¶
Expression::t Expr::zeros(int size) Expression::t Expr::zeros(shared_ptr<ndarray<int,1>> shp)
Create an expression consisting of zeros.
- Parameters
size(int) – Length of the vector to be constructed.shp(int[]) – Defines the shape of the expression.
- Return
