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5.2 Matrix Arithmetic Operators

Stan supports the basic matrix operations using infix, prefix and postfix operations. This section lists the operations supported by Stan along with their argument and result types.

5.2.1 Negation Prefix Operators

vector operator-(vector x)
The negation of the vector x.

row_vector operator-(row_vector x)
The negation of the row vector x.

matrix operator-(matrix x)
The negation of the matrix x.

5.2.2 Infix Matrix Operators

vector operator+(vector x, vector y)
The sum of the vectors x and y.

row_vector operator+(row_vector x, row_vector y)
The sum of the row vectors x and y.

matrix operator+(matrix x, matrix y)
The sum of the matrices x and y

vector operator-(vector x, vector y)
The difference between the vectors x and y.

row_vector operator-(row_vector x, row_vector y)
The difference between the row vectors x and y

matrix operator-(matrix x, matrix y)
The difference between the matrices x and y

vector operator*(real x, vector y)
The product of the scalar x and vector y

row_vector operator*(real x, row_vector y)
The product of the scalar x and the row vector y

matrix operator*(real x, matrix y)
The product of the scalar x and the matrix y

vector operator*(vector x, real y)
The product of the scalar y and vector x

matrix operator*(vector x, row_vector y)
The product of the vector x and row vector y

row_vector operator*(row_vector x, real y)
The product of the scalar y and row vector x

real operator*(row_vector x, vector y)
The product of the row vector x and vector y

row_vector operator*(row_vector x, matrix y)
The product of the row vector x and matrix y

matrix operator*(matrix x, real y)
The product of the scalar y and matrix x

vector operator*(matrix x, vector y)
The product of the matrix x and vector y

matrix operator*(matrix x, matrix y)
The product of the matrices x and y

5.2.3 Broadcast Infix Operators

vector operator+(vector x, real y)
The result of adding y to every entry in the vector x

vector operator+(real x, vector y)
The result of adding x to every entry in the vector y

row_vector operator+(row_vector x, real y)
The result of adding y to every entry in the row vector x

row_vector operator+(real x, row_vector y)
The result of adding x to every entry in the row vector y

matrix operator+(matrix x, real y)
The result of adding y to every entry in the matrix x

matrix operator+(real x, matrix y)
The result of adding x to every entry in the matrix y

vector operator-(vector x, real y)
The result of subtracting y from every entry in the vector x

vector operator-(real x, vector y)
The result of adding x to every entry in the negation of the vector y

row_vector operator-(row_vector x, real y)
The result of subtracting y from every entry in the row vector x

row_vector operator-(real x, row_vector y)
The result of adding x to every entry in the negation of the row vector y

matrix operator-(matrix x, real y)
The result of subtracting y from every entry in the matrix x

matrix operator-(real x, matrix y)
The result of adding x to every entry in negation of the matrix y

vector operator/(vector x, real y)
The result of dividing each entry in the vector x by y

row_vector operator/(row_vector x, real y)
The result of dividing each entry in the row vector x by y

matrix operator/(matrix x, real y)
The result of dividing each entry in the matrix x by y

5.2.4 Elementwise Arithmetic Operations

vector operator.*(vector x, vector y)
The elementwise product of y and x

row_vector operator.*(row_vector x, row_vector y)
The elementwise product of y and x

matrix operator.*(matrix x, matrix y)
The elementwise product of y and x

vector operator./(vector x, vector y)
The elementwise quotient of y and x

vector operator./(vector x, real y)
The elementwise quotient of y and x

vector operator./(real x, vector y)
The elementwise quotient of y and x

row_vector operator./(row_vector x, row_vector y)
The elementwise quotient of y and x

row_vector operator./(row_vector x, real y)
The elementwise quotient of y and x

row_vector operator./(real x, row_vector y)
The elementwise quotient of y and x

matrix operator./(matrix x, matrix y)
The elementwise quotient of y and x

matrix operator./(matrix x, real y)
The elementwise quotient of y and x

matrix operator./(real x, matrix y)
The elementwise quotient of y and x

vector operator.^(vector x, vector y)
The elementwise power of y and x

vector operator.^(vector x, real y)
The elementwise power of y and x

vector operator.^(real x, vector y)
The elementwise power of y and x

row_vector operator.^(row_vector x, row_vector y)
The elementwise power of y and x

row_vector operator.^(row_vector x, real y)
The elementwise power of y and x

row_vector operator.^(real x, row_vector y)
The elementwise power of y and x

matrix operator.^(matrix x, matrix y)
The elementwise power of y and x

matrix operator.^(matrix x, real y)
The elementwise power of y and x

matrix operator.^(real x, matrix y)
The elementwise power of y and x