**Throwback Thursday: Programs for the HP 49g+/50g from 2003-2007**

My first
Hewlett Packard calculator was an HP 48G+, which I bought in 2000. I really did not get serious into RPN and RPL
until I bought an HP 49g+ in 2003.
Despite keyboard problems, the 49g+ was my go-to calculator. The first 49g+ had a plus key that came
loose, the second one I had trouble with the ON button. Thankfully, by the time the HP 50g was released,
the keyboard was reliable. I bought my
first 50g I think in 2003 – not sure. It
was the standard black 50g with orange and white text. Several years later, I
ordered the blue 50g from Spain.
Recently, I traded the black 50g with a friend of mine (me getting a HP
42S in return).

During 2003 to
2006 (I wish I noted the dates when I programmed these things back then), I
made a library of programs that covered math, science, finance, and stats. After finding them still on the SD card,
today, I am going to list some of my favorite programs from that era.

All the
programs presented were done in User RPL and most of them, if not all of them,
should be able to be used on any of the HP 48 series. (no guarantees)

**QCKPLOT – Simplified Plot Screen**

(updated
2/19/2015)

QCKPLOT is
probably my favorite out of the bunch.
QCKPLOT allows the user to plot a single function y(x) in a familiar
graph set up screen input interface. The
plotting interface with the 49g+ and 50g took a while to get used to.

QCKPLOT:

<< ‘X’ PURGE

“Quick Function
Plot”

{ { “y(x)=” “Enter
y(x)” }

{ “xmin=” “x
minimum” }

{ “xmax=” “x
maximum” }

{ “ymin=” “y
minimum” }

{ “ymax=” “y
maximum” } }

{ 2 2 } { } { }
INFORM

IF 0 == THEN KILL
END

EVAL YRNG XRNG STEQ
‘X’ INDEP FUNCTION (0,0) AXES

ERASE DRAX DRAW PICT
{#0d #0d} “Y=” EQ →STR + 1

→GROB GOR PICTURE
>>

You can use RPN
to build expressions. However,
everything for the window variables must evaluate to numbers. For example, if you want to set xmax to 2π,
use 2 π * →NUM [ENTER]. Which brings me
to my next favorite…

**PCTXT: Puts text on the graph screen.**

PCTXT inserts a
text screen to any Cartesian point on the graph screen. The program does not immediately show the
graph screen upon completion, which allows for use as a subroutine. If PCTXT is used a standalone program, press
the left arrow button [ ← ] or hold [left shift] while pressing [ F3 ] to see
the results. (I am assuming you are in RPN mode).

Input:

2: coordinates

1: string

PCTXT:

<< 1 →GROB
PICT ROT C→PX ROT GXOR >>

**ZETA41: Zeta Function Approximation**

The HP 49g+/50g
does not have a built in Reimann Zeta function.
Using the standard definition of the zeta function takes forever.

Σ(I=1,
infinity, 1/X^Z)

What is presented here is a series that
converges faster than the standard definition. The upper limit of 250 is
arbitrary – you can increase the upper limit for better accuracy, but keep in
mind it there is a cost in calculation time. The accuracy increases as X
increases.

Input:

1: X

ZETA41:

<< → X
‘∑(I=1,250,(-1)^(I+1)/I^X)/(1-2^(1-X))’ >>

**FIB: nth Fibonacci Number**

FIB uses an
explicit formula to calculate the nth Fibonacci number, rather than use a
sequence loop.

Input:

1: N

FIB:

<< → N

<< 1 5 √ + 2 /
N ^ 1 5 √ - 2 / N ^

- 5 √ / EVAL 0 RND
>> >>

Test: FIB(8) = 21,
FIB(12) = 144

**CRDTRN Subroutine: (Coordinate Transformation)**

CRDTRN
transforms a coordinate (x, y) to a new coordinate (x’, y’) with new center
(xc, yc) and rotation angle θ. CRDTRN is
both a good standalone program and a useful subroutine.

Input:

5: XOLD

4: YOLD

3: XCTR

2: YCTR

1: θ

CRDTRN

<< → XOLD
YOLD XCTR YCTR θ

<< XOLD
YOLD R→C XCTR YCTR R→C – θ DUP COS →NUM SWAP NEG SIN →NUM R→C * >>
>>

Example: Let the original coordinate be (1,2) What would be the coordinates if the center
was moved to (-1, 3) and the plane was rotated 60⁰ (π/3 radians)?

In Raidian
Mode:

5: 1

4: 2

3: -1

2: 3

1: π/3

New
coordinate: (.13397456215,
-2.23205080757)

**QUADRES: Quadratic Regression (uses ∑DAT)**

(Update
2/19/2015)

QUADRES aims
to fulfill a missing statistical regression for the HP 49g+/50g series: quadratic regression.

Y = a*X^2 +
b*X + c

The program
uses the standard system statistics matrix ΣDAT. The coefficients are returned in a matrix:

[[ c ]

[ b ]

[ a ]]

Example:

ΣDAT =

[[ 2, .23 ]

[ 3, .58 ]

[ 4, .96 ]

[ 8 1.85 ]

[ 16 3.66 ]]

Results:

[[
-.302930140195 ]

[
.304114954514 ]

[
-3.55628308881E-3 ]]

Or Y = -3.55628308881E-3*X^2
+ .304114954514*X - .302930140195

QUADRES:

<< ∑DAT 1
COL- VANDERMONDE DUP SIZE OBJ→ DROP DROP 3 2 →LIST {1,1}

SWAP SUB LSQ
>>

**CSUM: Sum of each of the matrix’s columns**

**RSUM: Sum of each of the matrix’s rows**

An example for
CSUM and RSUM:

Matrix:

[[ 2, 3, -7 ]

[ 1, 8, 1 ]

[ -3, 4, 6 ]]

CSUM: [0, 15,
0]

RSUM: [-2, 10,
7]

Input: Matrix

CSUM:

<< →COL → S

<< 1 S START
AXL ∑LIST S ROLL NEXT

S →LIST AXL >>
>>

RSUM:

<< →ROW → S

<< 1 S START
AXL ∑LIST S ROLL NEXT

S →LIST AXL >>
>>

**LVEVAL: Evaluate (simplify) every element in a list or vector**

LVEVAL evaluates
and simplifies each component of a given list or vector. For example, LVEVAL turns a list consisting
of:

{‘e^2’, ‘π/2’, ‘5.273*LOG(3.44)’}
to:

In exact mode:

{‘e^2’, ‘π/2’, 2.82927266768}

Or in
approximate mode:

{7.38905609893,
1.5707963268, 2.82927266768}

Input:

1: list/vector

LVEVAL:

<< → LV

<< LV TYPE 5
IF ≠

THEN LV AXL ‘LV’ STO
1 SF END 1 LV SIZE

FOR I LV I GET EVAL
LV I 3 ROLL PUT ‘LV’

STO NEXT IF 1 FS?
THEN LV AXL ‘LV’ STO 1

CF END LV >>
>>

**Bezier Curve**

This program
draws a Bezier curve. I honestly don’t
quite remember what α0, β0, α1, and β1 represent – I think they are points that
are not on the curve be affect the path of the curve. (X0, Y0) and (X1, Y1) are
end points.

« 'T' PURGE
PARAMETRIC { T 0. 1. } INDEP "Bézier Curve" { "X0"
"Y0" "α0" "ß0" "X1" "Y1"
"α1" "ß1" } { 2. 4. } { } { } INFORM 0.

IF ==

THEN KILL

END OBJ→ DROP → X0 Y0 α0 ß0 X1 Y1 α1 ß1

« X0 X1 - 2. * α0 α1 + 3. * + 'T' 3. ^ * X1
X0 - 3. * α1 α0 2. * + 3. * - 'T' 2. ^ * + α0 3. * 'T' * + X0 + Y0 Y1 - 2. * ß0
ß1 + 3. * + 'T' 3. ^ * Y1 Y0 - 3. * ß1 ß0 2. * + 3. * - 'T' 2. ^ * + ß0 3. *
'T' * + Y0 + i * + 'XY1(T)' SWAP = DEFINE 'T' XY1 STEQ 'T' XY1 ERASE AUTO DRAX
DRAW PICTURE » »

**One Minute Marvels**

The document “One
Minute Marvels” by Richard Nelson and
Wlodek Mier-Jedrzejowicz is
a collection of short, very effective RPL programs for the HP 48 series. Programs include list operations (including rotate
a list’s elements, fill a list with zeroes, randomize a list), calendar
functions (including day of the week, stopwatch programs), and math and utility
programs (LCD, GCM, Ulad Principle, quick quadratic equation, and flag toggles
just to name a few). For owners of the
HP 48 series, including HP 49g+/50g, I consider this document an excellent addition
to your mathematics library.

Link to
download “One Minute Marvels”: http://www.hpcalc.org/details.php?id=1691

Cheers to the
HP 48 series and my trusty blue HP 50g!

Eddie

This blog is
property of Edward Shore – 2015.

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