Conditionally defined expression or function (2024)

Conditionally defined expression or function

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Syntax

pw = piecewise(cond1,val1,cond2,val2,...)

pw = piecewise(cond1,val1,cond2,val2,...,otherwiseVal)

Description

example

pw = piecewise(cond1,val1,cond2,val2,...) returns the piecewise expression or function pw whose value is val1 when condition cond1 is true, is val2 when cond2 is true, and so on. If no condition is true, the value of pw is NaN.

example

pw = piecewise(cond1,val1,cond2,val2,...,otherwiseVal) returns the piecewise expression or function pw that has the value otherwiseVal if no condition is true.

Examples

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Define and Evaluate Piecewise Expression

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Define the following piecewise expression by using piecewise.

$y = {\begin{cases} - 1 & x < 0 \\ 1 & x > 0 \end{cases}$

syms xy = piecewise(x < 0,-1,x > 0,1)

y = ${\begin{array}{cl} - 1 & if x < 0 \\ 1 & if 0 < x \end{array}$

Evaluate y at -2, 0, and 2 by using subs to substitute for x. Because y is undefined at x = 0, the value is NaN.

subs(y,x,[-2 0 2])

ans = $(\begin{array}{c} - 1 & NaN & 1 \end{array})$

Define Piecewise Function

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Define the following function symbolically.

$y (x) = {\begin{cases} - 1 & x < 0 \\ 1 & x > 0 \end{cases}$

syms y(x)y(x) = piecewise(x < 0,-1,x > 0,1)

y(x) = ${\begin{array}{cl} - 1 & if x < 0 \\ 1 & if 0 < x \end{array}$

Because y(x) is a symbolic function, you can directly evaluate it for values of x. Evaluate y(x) at -2, 0, and 2. Because y(x) is undefined at x = 0, the value is NaN. For details, see Create Symbolic Functions.

y([-2 0 2])

ans = $(\begin{array}{c} - 1 & NaN & 1 \end{array})$

Set Value When No Condition Is True

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Plot Piecewise Expression

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Plot the following piecewise expression by using fplot.

$y = {\begin{array}{c} - 2 & x < - 2 \\ x & - 2 < x < 2 \\ 2 & x > 2 \end{array} .$

syms xy = piecewise(x < -2,-2,-2 < x < 2,x,x > 2,2);fplot(y)

Assumptions and Piecewise Expressions

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On creation, a piecewise expression applies existing assumptions. Apply assumptions set after creating the piecewise expression by using simplify on the expression.

Assume x > 0. Then define a piecewise expression with the same condition x > 0. piecewise automatically applies the assumption to simplify the condition.

syms xassume(x > 0)pw = piecewise(x < 0,-1,x > 0,1)

pw = $1$

Clear the assumption on x for further computations.

assume(x,'clear')

Create a piecewise expression pw with the condition x > 0. Then set the assumption that x > 0. Apply the assumption to pw by using simplify.

pw = piecewise(x < 0,-1,x > 0,1);assume(x > 0)pw = simplify(pw)

pw = $1$

Clear the assumption on x for further computations.

assume(x,'clear')

Differentiate, Integrate, and Find Limits of Piecewise Expression

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Differentiate, integrate, and find limits of a piecewise expression by using diff, int, and limit respectively.

Differentiate the following piecewise expression by using diff.

$y = {\begin{cases} 1 / x & x < - 1 \\ \sin (x) / x & x \geq - 1 \end{cases}$

syms xy = piecewise(x < -1,1/x,x >= -1,sin(x)/x);diffy = diff(y,x)

diffy = ${\begin{array}{cl} - \frac{1}{x^{2}} & if x < - 1 \\ \frac{\cos (x)}{x} - \frac{\sin (x)}{x^{2}} & if - 1 < x \end{array}$

Integrate y by using int.

inty = int(y,x)

inty = ${\begin{array}{cl} \log (x) & if x < - 1 \\ sinint (x) & if - 1 \leq x \end{array}$

Find the limits of y at 0 by using limit.

limit(y,x,0)

ans = $1$

Find the right- and left-sided limits of y at -1. For details, see limit.

limit(y,x,-1,'right')

ans = $\sin (1)$

limit(y,x,-1,'left')

ans = $- 1$

Elementary Operations on Piecewise Expressions

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Add, subtract, divide, and multiply two piecewise expressions. The resulting piecewise expression is only defined where the initial piecewise expressions are defined.

syms xpw1 = piecewise(x < -1,-1,x >= -1,1);pw2 = piecewise(x < 0,-2,x >= 0,2);add = pw1+pw2

add = ${\begin{array}{cl} - 3 & if x < - 1 \\ - 1 & if x \in [- 1, 0) \\ 3 & if 0 \leq x \end{array}$

sub = pw1-pw2

sub = ${\begin{array}{cl} 1 & if x < - 1 \\ 3 & if x \in [- 1, 0) \\ - 1 & if 0 \leq x \end{array}$

mul = pw1*pw2

mul = ${\begin{array}{cl} 2 & if x < - 1 \\ - 2 & if x \in [- 1, 0) \\ 2 & if 0 \leq x \end{array}$

div = pw1/pw2

div = ${\begin{array}{cl} \frac{1}{2} & if x < - 1 \\ - \frac{1}{2} & if x \in [- 1, 0) \\ \frac{1}{2} & if 0 \leq x \end{array}$

Modify or Extend Piecewise Expression

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Modify a piecewise expression by replacing part of the expression using subs. Extend a piecewise expression by specifying the expression as the otherwise value of a new piecewise expression. This action combines the two piecewise expressions. piecewise does not check for overlapping or conflicting conditions. Instead, like an if-else ladder, piecewise returns the value for the first true condition.

Change the condition x < 2 in a piecewise expression to x < 0 by using subs.

syms xpw = piecewise(x < 2,-1,x > 0,1);pw = subs(pw,x < 2,x < 0)

pw = ${\begin{array}{cl} - 1 & if x < 0 \\ 1 & if 0 < x \end{array}$

Add the condition x > 5 with the value 1/x to pw by creating a new piecewise expression with pw as the otherwise value.

pw = piecewise(x > 5,1/x,pw)

pw = ${\begin{array}{cl} \frac{1}{x} & if 5 < x \\ - 1 & if x < 0 \\ 1 & if 0 < x \end{array}$

Input Arguments

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`cond` — Condition
symbolic condition | symbolic variable

Condition, specified as a symbolic condition or variable. A symbolic variable represents an unknown condition.

Example: x > 2

`val` — Value when condition is satisfied
number | vector | matrix | multidimensional array | symbolic number | symbolic variable | symbolic vector | symbolic matrix | symbolic multidimensional array | symbolic function | symbolic expression

Value when condition is satisfied, specified as a number, vector, matrix, or multidimensional array, or as a symbolic number, variable, vector, matrix, multidimensional array, function, or expression.

`otherwiseVal` — Value if no conditions are true
number | vector | matrix | multidimensional array | symbolic number | symbolic variable | symbolic vector | symbolic matrix | symbolic multidimensional array | symbolic function | symbolic expression

Value if no conditions are true, specified as a number, vector, matrix, or multidimensional array, or as a symbolic number, variable, vector, matrix, multidimensional array, function, or expression. If otherwiseVal is not specified, its value is NaN.

Output Arguments

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`pw` — Piecewise expression or function
symbolic expression | symbolic function

Piecewise expression or function, returned as a symbolic expression or function. The value of pw is the value val of the first condition cond that is true. To find the value of pw, use subs to substitute for variables in pw.

Tips

piecewise does not check for overlapping or conflicting conditions. A piecewise expression returns the value of the first true condition and disregards any following true expressions. Thus, piecewise mimics an if-else ladder.

Version History

Introduced in R2016b

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Conditionally defined expression or function (2024)

FAQs

What is an example of a conditional statement? ›

Example: We have a conditional statement If it is raining, we will not play. Let, A: It is raining and B: we will not play. Then; If A is true, that is, it is raining and B is false, that is, we played, then the statement A implies B is false.

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What is the conditional expression? ›

A conditional expression has the general form. where expr₁ is an expression that yields a true or false result. If the result is true, the value of the conditional expression is set to expr₂. If the result is false, the value of the conditional expression is set to expr₃.

How do you write conditional expressions? ›

Writing Conditional Expressions

Surround the expression in parentheses.
Surround strings or exact values (such as digits pressed) in quotation marks.
Enter variables without quotation marks.

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Show Me More ›

What does conditional expression mean in mathematica? ›

The ConditionalExpression has a value only when the condition evaluates to True . If the condition evaluates to False then the expression is undefined.

Get More Info Here ›

What are the 4 examples of conditional? ›

English Conditionals: Quick Summary

Zero conditional: If you jump in a pool, you get wet. First conditional: If you run a mile in the scorching heat, you will sweat. Second conditional: If I were you, I would apply for that job. Third conditional: If I had known you were coming, I would have made more food.

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What are 2 examples of conditional sentences? ›

Examples. If I were taller, I would buy this dress. If I were 20, I would travel the world. If I were you, I would give up smoking.

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How can you identify a conditional expression? ›

The major clue to identifying conditional statements is the if (and usually a then). Consider the following: If that is an owl, then it is the weirdest bird I have seen. If it is after sundown, then I should get home and feed my cats.

What are the 3 ways of writing conditional statements? ›

The converse statement is, "You will pass the exam if you study well" (if q, then p). The inverse statement is, "If you do not study well then you will not pass the exam" (if not p, then not q). The contrapositive statement is, "If you did not pass the exam, then you did not study well" (if not q, then not p).

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What are the 5 conditional statements? ›

5 Types of Conditional Sentences

Conditional sentence type	When to use	If-clause
Type Zero	Describing known facts	Simple present
Type 1	A possible situation and the result	Simple present
Type 2	A hypothetical condition and its possible result	Simple past
Type 3	An impossible past situation and its result in the past	Past perfect

1 more row

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How do you use conditional functions? ›

=if(condition,value_if_true,value_if_false)
=if(A2>3,32,”Number too small”)
=if (A2>20,”Number too large”, if (A2<10,”Number too small”, “Just right!”))
=countif(range,criteria)
=countif (F1:F230, “=red”)
=sumif(range,criteria,sum_range)
=sumif (D1:D230,”=television”, H1:H230)
=AND(condition, condition)

Discover More Details ›

What is a conditional expression also called? ›

The conditional expression is also known as the ternary operator. The ternary operator is a shorthand for an if-else statement and is represented by the symbol "?". It takes three operands: a condition, a value if the condition is true, and a value if the condition is false.

How is a conditional expression evaluated? ›

Expression is evaluated according to associativity of the operator. The associativity of the operator is a property that determines how operators of the same precedence are grouped in the absence of parenthesis.

What are the 3 conditional statements? ›

The conditional statements are also known as decision-making statements. They are of the type if statement , if-else , if else-if ladder , switch , etc. These statements determine the flow of the program execution.

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What is an example of one conditional statement? ›

Form: If + simple present, simple present Example 1: If it rains, I take an umbrella with me to work. Example 2: If I wake up early, I always read in bed. The first conditional uses the present tense in the if clause and the future tense in the result clause.

Tell Me More ›

What are examples of 3 conditionals? ›

Examples

If I'd known you were in hospital, I'd have visited you.
If I had known you were in hospital, I would have visited you.
I'd have bought you a present if I'd known it was your birthday.
I would have bought you a present if I had known it was your birthday.
If you'd given me your e-mail, I'd have written to you.

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Conditionally defined expression or function (2024)

Syntax

Description

Examples

Define and Evaluate Piecewise Expression

Define Piecewise Function

Set Value When No Condition Is True

Plot Piecewise Expression

Assumptions and Piecewise Expressions

Differentiate, Integrate, and Find Limits of Piecewise Expression

Elementary Operations on Piecewise Expressions

Modify or Extend Piecewise Expression

Input Arguments

`cond` — Condition
symbolic condition | symbolic variable

`val` — Value when condition is satisfied
number | vector | matrix | multidimensional array | symbolic number | symbolic variable | symbolic vector | symbolic matrix | symbolic multidimensional array | symbolic function | symbolic expression

`otherwiseVal` — Value if no conditions are true
number | vector | matrix | multidimensional array | symbolic number | symbolic variable | symbolic vector | symbolic matrix | symbolic multidimensional array | symbolic function | symbolic expression

Output Arguments

`pw` — Piecewise expression or function
symbolic expression | symbolic function

Tips

Version History

See Also

MATLAB-Befehl

Americas

Europe

Asia Pacific

FAQs

What is an example of a conditional statement? ›

What is a conditional expression also called? ›

References

Conditionally defined expression or function (2024)

Syntax

Description

Examples

Define and Evaluate Piecewise Expression

Define Piecewise Function

Set Value When No Condition Is True

Plot Piecewise Expression

Assumptions and Piecewise Expressions

Differentiate, Integrate, and Find Limits of Piecewise Expression

Elementary Operations on Piecewise Expressions

Modify or Extend Piecewise Expression

Input Arguments

cond — Condition symbolic condition | symbolic variable

val — Value when condition is satisfied number | vector | matrix | multidimensional array | symbolic number | symbolic variable | symbolic vector | symbolic matrix | symbolic multidimensional array | symbolic function | symbolic expression

otherwiseVal — Value if no conditions are true number | vector | matrix | multidimensional array | symbolic number | symbolic variable | symbolic vector | symbolic matrix | symbolic multidimensional array | symbolic function | symbolic expression

Output Arguments

pw — Piecewise expression or function symbolic expression | symbolic function

Tips

Version History

See Also

MATLAB-Befehl

Americas

Europe

Asia Pacific

FAQs

What is an example of a conditional statement? ›

What is a conditional expression also called? ›

References

`cond` — Condition
symbolic condition | symbolic variable

`val` — Value when condition is satisfied
number | vector | matrix | multidimensional array | symbolic number | symbolic variable | symbolic vector | symbolic matrix | symbolic multidimensional array | symbolic function | symbolic expression

`otherwiseVal` — Value if no conditions are true
number | vector | matrix | multidimensional array | symbolic number | symbolic variable | symbolic vector | symbolic matrix | symbolic multidimensional array | symbolic function | symbolic expression

`pw` — Piecewise expression or function
symbolic expression | symbolic function