Arithmetic Operations¶

Elementary Arithmetic¶

zeros¶

Syntax

zeros
zeros(dimensions…)
zeros(dimensions…, assumedType)

Description

Returns an array containing all zero elements.

When called with no arguments, zeros will return the scalar value 0.
If dimensions are provided, they must contain non-negative integers supplying the dimensions of the array to be returned.
If called with a scalar, zeros(n), this operator will return a square n x n matrix filled with zeros.
If assumedType is provided, it creates an array of zeros of the given data type. When single type is provided, no conversion to single precision is performed, it remains a double precision value.

ones¶

Syntax

ones
ones(dimensions…)
ones(dimensions…, assumedType)

Description

Returns an array whose elements all contain the scalar value one.

When called with no arguments, ones will return the scalar value 1.
If dimensions are provided, they must contain non-negative integers supplying the dimensions of the array to be returned.
If called with a scalar, ones(n), this operator will return a square n x n matrix filled with ones.
If assumedType is provided, it creates an array of ones of the given data type. When single type is provided, no conversion to single precision is performed, it remains a double precision value.

uplus¶

Syntax

uplus(x)
+x

Description

Unary plus returns the value of the operand x.

uminus¶

Syntax

uminus(x)
-x

Description

Unary minus returns the negation of the operand, x.

plus¶

Syntax

x + y
plus(x,y)

Description

Perform elementwise addition of two operands, x and y. If both x and y are arrays, their dimensions must agree. If either input is a scalar, it gets expanded into an appropriately sized array before addition. Note that x and y may be symbolic.

minus¶

Syntax

x - y
minus(x,y)

Description

Perform elementwise subtraction of two operands, x and y. If both x and y are arrays, their dimensions must agree. If either input is a scalar, it gets expanded into an appropriately sized array before subtraction. Note that x and y may be symbolic.

times¶

Syntax

x .* y
times(x,y)

Description

Multiply each element in x by the corresponding element in y. If both x and y are arrays, their dimensions must agree. If either input is a scalar, it gets expanded into an appropriately sized array before multiplication. Note that x and y may be symbolic.

mod¶

Syntax

mod(x,y)

Description

The modulo operation returns the remainder of x after division by operand y. Both inputs are required to be real.

Note that the dividend x and divisor y may be symbolic. However, whenever the divisor is symbolic the resulting expression will be non-linear. You will need to configure Grackle to use a solver that supports non-linear equations, see Constraint Solving.

ldivide¶

Syntax

a .\ b
ldivide(a,b)

Description

The left array division operator will divide each element in a by the corresponding element in b. If both a and b are arrays, their dimensions must agree. If either input is a scalar, it gets expanded into an appropriately sized array before division.

If the divisor is symbolic, you will need to configure Grackle to use a solver that supports non linear equations, see Constraint Solving.

rdivide¶

Syntax

b ./ a
rdivide(b,a)

Description

The right array division operator will divide each element in b by the corresponding element in a. If both a and b are arrays, their dimensions must agree. If either input is a scalar, it gets expanded into an appropriately sized array before division.

If the divisor is symbolic, you will need to configure Grackle to use a solver that supports non-linear equations, see Constraint Solving.

mtimes¶

Syntax

x * y
mtimes(x,y)

Description

Multiplication of two matrices, x and y. The number of columns in x must be equal to the number of rows in y for the matrices to multiply properly.

If either input is a scalar, the resulting operation is equivalent to times or .*. Note that x and y may be symbolic.

mldivide¶

Syntax

a \ b
mldivide(a,b)

Description

The matrix left division operator will divide each element in b by the scalar value, a. It does not currently support solving a system of linear equations of the form a*x = b for x.

Since mldivide suports division by a scalar value only, the resulting operation is equivalent to ldivide or .\.

mrdivide¶

Syntax

b / a
mrdivide(b,a)

Description

The matrix right divide operator will divide each element in b by the scalar, a. It does not currently support solving a system of linear equations of the form x*a = b for x.

Since mrdivide suports division by a scalar value only, the resulting operation should be equivalent to rdivide or ./.

mpower¶

Syntax

x ^ y
mpower(x,y)

Description

Raises the square matrix x to the power of y. mpower additionally requires the exponent y to be a natural number.

ceil¶

Syntax

ceil(x)

Description

Rounds to the nearest integer greater than or equal to x. If x is an array, it will take the ceiling of each element within x. Note that x may be symbolic.

floor¶

Syntax

floor(x)

Description

Rounds to the nearest integer less than or equal to x. If x is an array, it will take the floor of each element within x. Note that x may be symbolic.

round¶

Syntax

round(x)

Description

Rounds to the nearest integer. When two integers are equi-distant from the operand, as the case where x contains a fractional part of 0.5, x is rounded away from 0. Note that x may be symbolic.

Complex Numbers¶

i¶

Syntax

Description

i is the imaginary unit. It can be used to construct complex numbers.

imag¶

Syntax

imag(x)

Description

Returns the imaginary part of a complex value. For example, imag(a + bi) returns b.

real¶

Syntax

real(x)

Description

Returns the real part of a complex number. For example, real(a + bi) returns a.

abs¶

Syntax

abs(x)

Description

Returns the absolute value of x. If x is an array, it will evaluate the absolute value of each element. For complex numbers, x=a+bi, it returns the complex magnitude, sqrt(a^2 + b^2).

The result of abs operation may be irrational. In those cases, Grackle will switch to floating point precision to represent the result.

Exponents¶

The operations in this section may generate results that are irrational. In these cases, Grackle will switch to floating point precision to represent the result.

exp¶

Syntax

exp(x)

Description

Returns the exponential of the operand, e^x. If x is an array, it will evaluate the exponential of each element in x. For complex elements, x=a+bi it returns the complex exponential, (e^a)(cos(b) + i*sin(b)).

log¶

Syntax

log(x)

Description

Returns the natural logarithm of a non-zero input, x. If x is an array, it will evaluate the natural log of each element in x. For negative and complex elements, x=a+bi, the complex logarithm returns log(abs(x)) + i*atan2(b,a).

logarithm returns log(abs(x))/log(2) + i*atan2(b,a)/log(2).

log2¶

Syntax

log2(x)

Description

Returns the logarithm base 2 of a non-zero input. The value of log2(x) is equivalent to log(x)/log(2).

log10¶

Syntax

log10(x)

Description

Returns the logarithm base 10 of a non-zero input. The value of log10(x) is equivalent to log(x)/log(10).

sqrt¶

Syntax

sqrt(x)

Description

Returns the principal square root of an input, x. If the input is an array, it will evaluate the square root of each element in x.

If the input is symbolic the resulting expression will be non-linear. You will need to configure Grackle to use a solver that supports non-linear equations, see Constraint Solving.

Trigonometric¶

Operations in this section may generate results that are irrational. In these cases, Grackle will switch to double precision floating point to evaluate the functions and represent the result. Furthermore, symbolic input is permitted, however, very few solvers support them. See Constraint Solving.

atan2¶

Syntax

atan2(y,x)

Description

Returns the arctangent of y/x with a range of [-pi,pi]; this corresponds to the angle in radians between the positive x-axis and the line from the origin (x,y). If x and y are arrays, it will evaluate the inverse tangent for each pair of elements in the arrays. The dimensions of the input arrays must agree.

The inputs to atan2 are required to be real.

cos¶

Syntax

cos(x)

Description

Returns the cosine of the operand in radians. If x is an array, it will evaluate the cosine of each of its elements. For complex elements, x=a+bi it returns the sine for complex numbers, cos(a+bi) = cos(a)cosh(b) - i*sin(a)sinh(b) where cosh and sinh are the hyperbolic cosine and hyperbolic sine functions respectively.

hypot¶

Syntax

hypot(x)

Description

Returns the square root of sum of squares, sqrt(abs(x)^2 + abs(y)^2).

If both x and y are arrays, their dimensions must agree. If either input is a scalar, it gets expanded into an appropriately sized array before computing the result.

pi¶

Syntax

pi

Description

Returns the floating point representation of π.

sin¶

Syntax

sin(x)

Description

Returns the sine of the operand in radians. If x is an array, it will evaluate the sine of each of its elements. For complex elements, x=a+bi it returns the sine for complex numbers, sin(a+bi) = sin(a)cosh(b) + i*cos(a)sinh(b) where cosh and sinh are the hyperbolic cosine and hyperbolic sine functions respectively.

tan¶

Syntax

tan(x)

Description

Returns the tangent of the operand in radians, where tan(x)=sin(x)/cos(x). If x is an array, it will evaluate the tangent of each of its elements.