259 Lecture 10 Spring 2013

Advanced Excel Topics – More User Defined Functions; Conditional Statements

Outline More User Defined Functions!

Perp_Bisector_Slope() Perp_Bisector_Intercept() Quadratic_1() Quadratic_2()

Pseudo Code IF…THEN…ELSE Statements

Modified Quadratic Function A Piecewise Defined Function

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Perp_Bisector_Slope() Example 1: Create a user defined

function Perp_Bisector_Slope() that will return the slope of the line that is the “perpendicular bisector” of the line segment determined by the points (x1,y1) and (x2,y2).

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Perp_Bisector_Slope() Given:

Points (x1,y1) and (x2,y2). Line L is the perpendicular bisector of the

line segment determined by the points (x1,y1) and (x2,y2).

Find: The slope of line L.

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Perp_Bisector_Slope() Pseudo Code:

(1) Find the slope of the line segment determined by the points (x1,y1) and (x2,y2), and then store the result in the variable m1. (2) Find the negative reciprocal of m1 and then store the result in the variable m2 . (3) Return the value stored in the variable m2 as the result of the user defined function.

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Perp_Bisector_Slope()Function Perp_Bisector_Slope(x1 As Double, y1 As Double,

x2 As Double, y2 As Double) As Double'Returns the slope of the line that is the '"perpendicular bisector" of the line segment'determined by points (x1,y1) and (x2,y2).'The function does NOT work for vertical linesDim m1 As Double, m2 As Doublem1 = (y2 - y1) / (x2 - x1)'negative reciprocal of m1m2 = -1 / m1Perp_Bisector_Slope = m2

End Function

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Perp_Bisector_Intercept() Example 2: Create a user defined

function Perp_Bisector_Intercept() that will return the y-intercept of the line that is the “perpendicular bisector” of the line determined by the points (x1,y1) and (x2,y2).

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Perp_Bisector_Intercept() Given:

Points (x1,y1) and (x2,y2). Line L is the perpendicular bisector of the

line segment determined by the points (x1,y1) and (x2,y2).

Find: The y-intercept of line L.

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Perp_Bisector_Intercept() Pseudo Code:

(1) Find the slope of the line by using the Perp_Bisector_Slope(x1, y1, x2, y2) function previously defined, and then store the result in the variable m.(2) Find the x-component of the midpoint of the line segment, and then store the result in the variable Midpoint_X.(3) Find the y-component of the midpoint of the line segment, and then store the result in the variable Midpoint_Y.(4) Return the y-intercept of line L, by substituting the coordinates of the midpoint into the expression y -m*x.

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Perp_Bisector_Intercept()Function Perp_Bisector_Intercept(x1 As Double, y1 As Double, x2 As Double,

y2 As Double) As Double'Returns the y-intercept of the line that is the 'perpendicular bisector" of the line segment'determined by points (x1,y1) and (x2,y2).'The function does NOT work for vertical linesDim m As DoubleDim Midpoint_X As Double, Midpoint_Y As Doublem = Perp_Bisector_Slope(x1, y1, x2, y2)Midpoint_X = (x1 + x2) / 2Midpoint_Y = (y1 + y2) / 2'b = y - m*x'put in a known point (Midpoint_X, Midpoint_Y) on the linePerp_Bisector_Intercept = Midpoint_Y - m * Midpoint_X

End Function

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Quadratic_1() Example 3: Create a user defined

function Quadratic_1() that will return the first real root of a quadratic equation Ax2 + Bx + C = 0.

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Quadratic_1() Given:

A, B, and C Roots of Ax2 + Bx + C = 0 are

and Find:

The first real root of a quadratic equation Ax2 + Bx + C = 0.

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AACBB

242 A

ACBB2

42

Quadratic_1() Pseudo Code: (1) Substitute the A, B, and C values

into the formula

and return the result of this expression.

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AACBB

242

Quadratic_1()Function Quadratic_1(A As Double, B As Double, C As Double)

As Double'Returns the first real root of a quadratic equation 'Ax^2+Bx+C=0'Does NOT return a complex rootQuadratic_1 = (-B + Sqr(B ^ 2 - 4 * A * C)) / (2 *

A)End Function

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Quadratic_2() Example 4: Create a user defined

function Quadratic_2() that will return the second real root of a quadratic equation Ax2 + Bx + C = 0.

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Quadratic_2() Given:

A, B, and C Roots of Ax2 + Bx + C = 0 are

and Find:

The second real root of a quadratic equation Ax2 + Bx + C = 0.

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AACBB

242 A

ACBB2

42

Quadratic_2() Pseudo Code: (1) Substitute the A, B, and C values

into the formula

and return the result of this expression.

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AACBB

242

Quadratic_2()Function Quadratic_2(A As Double, B As Double, C As Double)

As Double'Returns the first real root of a quadratic equation 'Ax^2+Bx+C=0'Does NOT return a complex rootQuadratic_1 = (-B - Sqr(B ^ 2 - 4 * A * C)) / (2 *

A)End Function

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IF…THEN…ELSE Statements Just like in Excel, we can create

conditional statements within VBA! One of the most useful conditional

statements in VBA is the IF…THEN…ELSE statement!

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IF…THEN…ELSE Syntax Syntax:

If condition_1 Then result_1

ElseIf condition_2 Then result_2 ...

ElseIf condition_n Then result_n

Else result_else

End If

How the command works: condition_1 to condition_n are

evaluated in the order listed. Once a condition is found to be

true, the IF…THEN…ELSE statement will execute the corresponding code and not evaluate the conditions any further.

result_1 to result_n is the code that is executed once a condition is found to be true.

If no condition is met, then the Else portion of the IF…THEN…ELSE statement will be executed.

Note that the ElseIf and Else portions are optional.

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Quadratic_1_Improved() Example 5: Modify the

Quadratic_1() user defined function to return the first root (real or complex).

For example x2+4x+8=0 should return (2+2i) and x2+5x+6=0 should return -2.

Then modify the VBA code for this new function to make a user defined function to find the other root!

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Quadratic_1_Improved() Given: A, B, and C

Roots of Ax2 + Bx + C = 0 are:

Find: The first root of a quadratic equation Ax2 + Bx + C = 0 .

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042

42

4 222

ACBifA

ACBBandA

ACBB

042

4

22

4

22

22

ACBifiA

ACB

ABandi

A

ACB

AB

Quadratic_1_Improved() Pseudo Code:

(1) If B^2 – 4AC 0, then substitute the A, B, and C values into the formula

and return the value of this expression.(2) Otherwise, put the A, B, and C values into the formula

and store the result in the variable Real_Part.(3) Substitute the A, B, and C values into the formula

and store the result in the variable Imaginary_Part.(4) Return the string value “{Real_Part} + {Imaginary_Part} i “ by substituting the actual numeric values for Real_Part and Imaginary_Part into {Real_Part} and {Imaginary_Part} .

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AACBB

242

AB2

A

ACB

2

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Quadratic_1_Improved()Function Quadratic_1_Improved(A As Double, B As Double, C As Double) As Variant

'Returns the first root of a quadratic equation Ax^2+Bx+C=0'Returns both real and complex rootsDim Real_Part As Double, Imaginary_Part As StringIf B ^ 2 - 4 * A * C >= 0 Then

Quadratic_1_Improved = (-B + Sqr(B ^ 2 - 4 * A * C)) / (2 * A)Else

Real_Part = -B / (2 * A)Imaginary_Part = Sqr(Abs(B ^ 2 - 4 * A * C)) / (2 * A)Quadratic_1_Improved = Str(Real_Part) + "+ " + Str(Imaginary_Part) +

"i"End If

End Function

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A piecewise “user defined function” f(x) Example 6: Use VBA IF statement(s)

to create the following piecewise “user defined function” f(x):

Plot a graph of this function!25

3300

3)( 2

3

xifxifxif

xxx

xf

A piecewise “user defined function” f(x)Function f(x As Double) As Double

'Returns x^3, if x<0'Returns x^2, if 0<=x<=3'Returns Sqr(x-3), if x>3If x<0 Thenf = x^3End IfIf (x >= 0) And (x <= 3) Thenf = x^2End IfIf (x>3) Thenf = Sqr(x-3)End If

End Function

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References User Defined Functions Notes – John

Albers IF…THEN…ELSE Statements (p. 20 of

this lecture) - http://www.techonthenet.com/excel/formulas/if_then.php