IBM 5100 Apl Reference Manual

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lAN

M.

ENGEL

DEC -119

7T

o o

IBM

APL

5100

Reference Manual

Preface

This publication specific Portable Computer, the planning and procedures. about forms insertion and ribbon replacement

5103 printer. This publication

the 5100

information

and

is

a reference manual

about the

APL

the

APL

language.

that

provides

use

of

the IBM 5100

language, and installation

It

also provides

is

intended

information

for

Prerequisite Publication

IBM

5100 APL Introduction, SA21-9212

Related Publications

•

IBM

5100

APL Reference Card, GX21-9214

•

APL

Language, GC26-3847

for users

the

of

"

o

Third Edition (May

This

is a major

Newsletter

Changes have been made

Requests or

the

A

form gone, address Rochester,

©International

SN21-0258.

for

IBM

branch

for

readers'

MN

revision

of,

copies

of I BM

office

comments

your

comments

55901.

Business Machines

1976)

and obsoletes,

throughout,

publications

serving

your

is

at

to I BM

Corporation

the

so

this

should

locality.

the

back

Corporation,

be made

of

this

1975,

edition

SA21-9213-1

should

be reviewed

to

your

publication.

Publications,

1976

and

Technical

in

its

entirety.

I BM representative

If

the

form

Dept

is

245,

o

Contents

CHAPTER

IBM Display Screen Switches.

Power On or Restart Procedures Display Screen

Keyboard

Attention Hold Execute Command Positioning the Cursor and

Copy Display

I

ndicator

-,

I The

\l

i

t

-(

Process In

CHAPTER

System Overview System Command Descriptions

The The The )COPY The )DROP Command .

The) The) The)

The The The) The )PATCH Command The) The The The )Sf Command The The The The )WSI D Command

CHAPTER Variables.

Data Representation

Numbers. Scaled Representation (Scientific Character Constants

Logical Data

Scalar. Arrays 32

Generating Arrays

Finding the Shape Empty

Catenation Indexing .

1.

5100

Display Screen

OPERATION

Portable

Lights . 8 The /\

Process

)CLEAR )CONTINUE

)ERASE

F NS Command

LI B Command

LOA )MARK )MODE

OUTSE L Command

PCOPY Command )REWIND )SAVE

)SIV )SYMBOLS )V

ARS

Arrays

Computer

Control

Check

2. SYSTEM

Command

Command.

Command

D Command

Command.

Command

3.

DATA

of

Overview Primitive Scalar Functions .

.

Information

COMMANDS

An

Array

on the

Notation)

.

2 2 2 3

5 6 6 6 6

6 8

8 9

10 10 10 13 13 14 15 15 16

16 18 18 20 20 21 25 26 26 27 27 28 28 29

30 30 30 30 31 31 32 32

33 35 36 37 39

CHAPTER

Primitive Mixed

APL

Special Symbols .

4.

PRIMITIVE

+

Function:

The

Function:

The The x

Function:

The

-;-

Function:

r

Function:

The

L

Function:

The

I

Function:.

The

*

Function:

The The

~

Function:

The

0

Function:

The!

Function:

The?

Function:

The V The'"

Function:

The

AFunction:

The

VFunction:

The>

Function:

=

Function:

The

<

Function:

The

~

Function:

The The::;

Function:

~

Function:

The The p

Function:

The,

Function:

The /

Function:

The \

~

Function:

The

The 'f

Function:

"fhe t

Function:

The +

Function:

The 1

Function:

The ¢

Function:

The

~

Function:

The?

Function:

The

1.

Function:

The T

Function: Function:

The E The

[E

Function:

The

.t

Function:

The ~ Function:

Operators

Reduction Operator

I nner Product Operator ( • ) Outer Product Operator ( 0 Scan

Operator

Assignment

Arrow

Branch

Quad

D

Quad Quote

Comment R

Parentheses ( )

Conjugate, Negation, Minus Signum, Times

Reciprocal, Divide .

Ceiling, Floor, Magnitude, Residue 52

Exponential, Power

Natural Log, Pi

Factorial, Binomial Roll

And Or Not Nand. Nor Greater Than 67 Equal

Less

Greater Than

Less

Not

Functions.

Shape, Reshape (Structure)

Rpvel, Catenate, Laminate Compress

Expand. Grade Grade

Take.

Drop. Index Reverse, Rotate

Transpose, Generalized Transpose

Deal

Decode

Encode (Representation) Membership.

Matrix Execute

Format

(\

)

Arrow

-)-

[!]

(BUILT-IN)

Plus.

Maximum.

Minimum

Times, Circular

To

Than

or

Equal

(I)

Equal

To

Up Down'

Generator, Index

(Base

Inverse,

.)

+

FUNCTIONS.

Logarithm

or

Equal

To

Value)

Matrix

To

.

of

Divide

43 43 44 45 46 48 49 51

54

55 56 59 61 62 63 64 65 66

68 69 70 71 72 73 75

77

81 82 83 84 86 87 88 89 93 95 96

99 104 105

107

108 111 111 113 116 118 120

120. 121 121 122 122 122

I I

I

f

iii

I

CHAPTER

FUNCTIONS

System Variables

System

CHAPTER

Mechanics

Interactive

Arranging

Locked Function

Trace and

5.

SYSTEM

Comparison Index Printing Print Random

Line

Workspace Available: 0

Latent

Atomic

The The 0 FX The 0 EX The The 0 NC

Function Branching and Labels Loc"!l and

Requesting

Execution

Bare

Displaying Revising a User-Defined Reopening An

Example

Trace Stop

Tolerance: 0 CT

Origin:

010

Precision: 0

Width: 0 PW

Link:

Counter: 0 LC

Expression: 0

Vector: 0 AV

Functions

0 CR

Function: Function: Function:

0 N L

Function: Function:

6.

USER-DEFINED

of

Function

Header.

Global

Functions

Keyboard

.

the

Output

Functions

.

Editing

a User-Defined

Function

of

Stop

Controls

Control

Contro

I 154

VARIABLES

.

PP

.

0 R L

WA

LX

.

Canonical Representation Fix

. Expunge Name

List

Name Classification

FUNCTIONS

Definition

Names

Input

during

from

a User-Defined

.

Function

Definition

Function

Editing

AND

SYSTEM

Function

123

123 124 125 125 126 126 126 126 126

127

128 128 129 132 132 133

134

134 135 137 139 144

145 146 146

147

148 148 148 150 151

152

CHAPTER

THE

Data

5100

Tape Data Cartridge

CHAPTER How How

Thickness

How

CHAPTER

APPENDIX Environment

5100

Auxiliary Printer

APPENDIX

OVERSTRUCK

APPENDIX

IBM

GLOSSARY

INDEX

9.

MORE

5100

Security

Storage Capacity

Storage Considerations

10.

I nsert

Forms

Adjust

Replace a

11.

A.

Procedure .

Tape

Setup

Procedure

B.

C.

D.

THE

the

ERROR

SETUP

Unit

APL

CHARACTERS

ATOMIC

5100

to

Setup

APLSV

THINGS

Handling

5103

PRINTER

Copy

Control

Ribbon

.

MESSAGES

PROCEDURES

Setup

Procedure

CHARACTER

VECTOR

APL

COMPATIBI

TO

KNOW

and Care

Dial

SET

for

ABOUT

Forms

AND

LlTY

171 171

172

173 175

176

177

179 179

182

191

192

197

199

201

202

WITH

206

210

215

CHAPTER Suspension State I nd

CHAPTER

OUTPUT

Establishing a Opening a Data Transferring

Closing a Data Retracting Return An

iv

7.

SUSPENDED

icator

.

8.

TAPE

Variable

File

Data 163

Transferring

Operation) Transferring Transferring

Codes 166

Example

Data

. 163

Data

File

or

the

Variable

Using Tape and

FUNCTION

AND

PRINTER

to

be Shared .

or

Specifying

to

Tape

from to

the

Terminating

Name Being Shared .

Printer

(OUT

or

Tape (I N

Printer

(PRT

the

Printer I nputlOutput

EXECUTION

INPUT

AND

Output

ADD

Operation)

Printer

Output

155 155 155

158

159

164 164

165

167

(

\BNI

5100 pORi

ihe

5100 \ f

board. a

,V

to the s,/stem w'" perform.

fe.tures

munications adapter.

.w

mon\tors'.,-~eh~'ed,/,sbP~:;ds~~:~;:ches

pe

the user.

....

,

p.BLE

igur~t

I"

,I.b

CONlPUiER

1

~t::e~rt~~~c:;\~~:~'

un."

"

for the 5100 are

le

• d

O\lER\I\EIN

ind",cator

an

amdliarv

ih

5100 has a

e

.nd

an

adapter for

lights communicate informat,on

alloW

the user

t.pe

unit. • printer

displaV

to

control the operations

blOCk

••

screen.

KeV"

and

W~

ite

nd •

COm"

(

..

C

switches

\ndica

9

tOr

tl

Lights

~

switches Adapter for

\Nh

,'!

ite

I

SlacK

MonitorS

,ape

unit

and

'\

DISPLAY

Th~

display screen (Figure 2)

up

to

64

output

as

0)

of

the (flashing be displayed. If

ter,

the

input,

all lines

the

two

moved

SWITCHES

The

switches

restarting

SCREEN

characters

(processed

display

horizontal

flashing line

of

bottom

off

of

the

on

system,

lines again.

can

in

each

I ine.

information)

contain

the

display screen.

the

information

line) indicates

cursor

is

replaced

display are moyed

The

5100

console

and

controlling

display

moved

by

top

161ines

Input

(information

is

displayed.

entered

where

the

to a position

the

flashing

up

so

lines

of

(Figure 3) are used

how

of

information

The

from

the

that

character.

that

information

the

display

information

supplied

bottom

keyboard.

from

already

As

are lost as

for

turning

is

displayed.

at a time,

by

the

two

lines (lines 1

The

the

keyboard

contains

the

5100

can

be

the

power

with

user) as well

cursor

will

a charac-

processes

entered

on

lines are

on,

/ "

and

Power On

The starting

Lme

~

15 14

13

12

11 10

9

8

7

6·

5

4 3

2 5

o

or

Restart Procedures

following

switches

the

system

Numbers

...

.......

1-------64

3+2

_

-4-

~

are used

operation.

I

nput

Output Cursor

when

from

the

(flashing

character

turning

keyboard

horizontal

positions

power

line)

---------1.,.

on

to

the

system

or

re-

Normally, board of

the

Figure 2. The

2

to

distinguish

is

indented

display screen.

5100

and

Display Screen

input

output

from

is

displayed

output,

starting

input

from

at

the

left

key-

edge

BASIC/APL

(

Only dual-language machines have this switch. The switch setting determines which

language will be pressed. is

pressed,

Power

ON/OFF

When this switch system performs internal checks and becomes ready switch

is

Note:

The

this message

RESTART switch

RESTART

This switch restarts internal checks and becomes ready displayed when after

20

seconds, press RESTART again. If

after

several

in

operation

If

the

switch setting

the

language in

is

in

put

in

the

OF F position, no power

message CLEAR

is

not

displayed

is

discussed next).

the

system

attempts,

when power

is

changed

operation

the

ON position, power

WS

is

displayed when

after

20

system

call

operation.

in

is

ready. If

your

service representative.

is

turned

after

power

will

not

be changed.

is

supplied

is

supplied

seconds, restart

When it

15-20 seconds.

the

system does

the

system does

on

or

after

RESTART

is

turned

on

or

after

to

the

system. The

in

15-20 seconds. When

to

the

system.

the

system becomes ready. If

the

is

pressed,

The

system

not

operation

the

system performs

message CLEAR

display

not

the

become ready

is

RESTART

the

(the

WS

message

is

c

The primary uses malfunction has occurred language machines.

Note: Any

will be lost when RESTART

of

this switch are

information

and

you

to

change

had stored is

pressed.

restart

the

in

Display Screen Control

The following switches are used screen

is

displayed.

L32

64

R32

This three-position switch (positions 64, L32, and R32)

• 64 - Characters are displayed can be shown

• L32 - Characters are displayed the

left

• R32 - Characters are displayed the

right

32

characters

32

characters

on

each line.

of

to

control

in

adjacent positions,

in

alternate positions (blanks between);

the

64-character lines are shown.

in

alternate positions (blanks between); only

of

the

64-character lines are shown.

the

system

language

the

active workspace (see

how

the

operation

in

operation

information

operates

and

up

to

after

a system

on

dual-

Chapter

on

the

display

as follows:

64

characters

2)

only

3

~

tE'

"

r::::

~

Sol

-f

::s-

eD

~

8

n

0

~

CD

BRIGHTNESS

0

BASIC

~~~~~~G!£J(RENUM]~(REWIND](CalcRes~~~

APL

(l

LOAD)~~CIQ!JCI.:§D(lVARS)~~(lOUTSELHREWIND)~

L3264

R32

D

PROCESS

POWER

ON

D

POWER

OFF

IN

PROCESS

©

CHECK

COpy

DISPLAY

REVERSE

DISPLAY

D

[DELETE}(INSERT)

BASIC

D D

APL

RESTART

DISPLAY

D

NORMAL

REGISTERS

OGJCDCDGJCDCDmCJCJOCD

••

fI)(IJ(I)COCDCOOJCOwCDQO

CD

OJ

CD

Q (]]

CD

CD.GJ

rn

coO]

(]]

GJCDGJQCDCDCIJOOOJCD

( )

J

'I

Shift

Key

Alphameric Keys

Shift Key

•

888 GJ88

OCJGJ

( 0

aa

)0

Numeric Keys

_

G G

0

[:]

I"

'-

(

REVERSE

This switch on control

DISPLAY

determines

a dark background

may have

to

whether

or

be adjusted when

dark

the

display screen will display light characters

characters

on

a light

the

switch setting

background.

is

changed.

The brightness

DISPLAY

REGISTERS

This switch

Note: When

KEYBOARD

The

5100

keys are grouped

When

the

of

the

bottom

held,

the keys can be used tered

using symbols (+ - be entered using keys

The

keyboard performed of

the

APL language

chapter

(Chapter

is

for

the

service representative's use

you

use

your

keyboard

keys are pressed,

upper

the

by a typewriter.

(Figure 3) has alphameric and

together

two

lines)

symbol

numeric keys

-;-

x) located

contains

to

4)

on

enter

to

some keys

symbols

of

this

when

5100,

this switch must be in

numeric

and

are similar

the

characters entered

on

the

display screen.

the

key pressed

numbers; however, numbers can

on

the

on

the

top

the

right

of

that

These keys are discussed in

on

the

manual.

to

is

right side

row

of

the

numeric keys.

perform

keyboard

those

on a typewriter

appear

If

either

entered.

of

the

keyboard.

the

alphameric

operations

are discussed in

servicing

The

the

your

the

NORMAL position.

keys.

The

keyboard.

in

the

input

shift

key

is

top

row

of

be

conveniently en-

The

keyboard

in

addition

following text. Uses

the

APL language

5100.

alphameric

line (one

pressed

alphameric

arithmetic

can also

to

those

and

•

c

Attention.

Pressing ATTN

everything

Pressing ATTN during system start

Output displayed because causes

When ATTN outside a user-defined possible. Also, indicates where

operation

the

execution

that

the

(attention)

from

the

at

of

was being generated before

there

output

and

is

pressed twice during

the

message INTERRUPT,

the

statement

when

cursor

to

the

execution

the

end

of

a user-defined

is

a delay

the

actual display

function),

was

entering information

end

of

the

between

the

interrupted

of

line o .

any

expression

statement

function,

the

of

the

execution

the

or

currently

enter

-+-0

system

the

operation

execution

output.

of a statement

of

that statement, are displayed.

from

the

keyboard

user-defined

being processed.

LC.

stopped

of

the

statement

(either inside

statement

stops

and a caret

function

To

may

as

soon

(A)

that

erases

stops

re-

not

that

or as

be

5

Hold

•

When pressed once, HOLD causes all processing allows processing

the

display rapidly. When key

is

active.

to

resume.

information

the

hold

during

is

in

The

an

effect

primary output

Notes:

1.

Holding service personnel.

2. When

keys (+ - service personnel.

the

down

hold

-;-

x)

the

is

on

CMD

in

the

effect

key

and

(HOLD pressed once),

right side

of

Execute

When

this

key

is

processed

by

the

pressed, system. This

the

input

key

to

purpose

operation,

(HOLD pressed

pressing HOLD

the

keyboard

line

of

information

must

be pressed

stop;

when

of

HOLD

when

the

once),

only

is

restricted

the

use

of

are restricted

on

the

for

any

input

pressed again,

is

to

permit

display

is

changing

the

COpy

to

use

by

the

arithmetic

to

use

by

display screen

to

be processed.

it

reading

DISPLAY

the

is

Command

When

this

key

is

pressed and held, pressing an alphameric key in

causes

the

APL

command

in

the

input

line.

The

)FNS, )VARS, )COPY, )WSID, )OUTSEL,

Note: Holding

service personnel.

down

Positioning the Cursor and

The

following keys are used

screen:

Forward Space

this

the

is

key

held

•

is

pressed

down,

last position

on

the

When this

key reaches first position

keyword

command

the

CMD

Information

to

once,

the

cursor

on

other

input

one

or

keywords

key

and

position

the

cursor

continues

input

line.

character

pressing HOLD

above

that

key

are: ) LOAD, )SAVE, )CONT,

and

)REWIND.

is

restricted

on the Display Screen

the

cursor

and

information

moves

one

position

to

move

to

the

right. When

line (line 1

or

0),

it

wraps

to

the

around

top

be

entered.

to

use

on

the

right. When

row

)LlB,~

by

the

display

the

cursor

to

the

6

Insert

(

('

When

the

CMD characters to

the

The cursor does

Before the insert operation:

After

When these keys are

right and blank characters

Note: If

not

Backspace

right

work.

at

one

the

there

•

key

is

held

down

and

the

and

to

the

right

of

the

cursor position (flashing character) are moved position, and a blank character not

insert

is

a character

move.

operation:

both

For

example:

/ Flashing character

123V

123_567

held

down,

the

continue

in

position

to

forward space key

is

inserted

characters

be inserted.

64

of

line 0,

at

continue

the

insert

is

pressed once,

the

cursor position.

to

move

operation

to

the

will

•

When this key

it

is

held position 1 the

other

Delete

When

the

character

to

the

right are moved over

cursor

is

Before the delete operation:

After

When these keys are tinue

to

is

pressed once,

down,

the

cursor

on

one

input

line.

•

CMD

key

is

held

at

the

cursor position (flashing character)

not

moved. For example:

the

delete operation:

both

be deleted and all

the

cursor moves one position

continues

line (line 1

down

one

to

or

and

the

position

move

to

0), it wraps

backspace key

to

the

left

the left. When

around

is

deleted and

to

close

12344~

r--------.::::.

123456

held

down,

the

characters

to

the

at

the

right are moved

to

the

left. When

the

cursor reaches

to

the

last position on

is

pressed once,

all

characters

up

the

space.

Flash

ing

character

cursor position con-

to

the

left.

the

The

!I,IIIt,

(

./

7

Scroll Up •

This key (located above When

this

key

the

lines are moved

As

this

When

Scroll Down

This key (located above When

As screen. When

key

•

the

key

the

lines are moved

Copy Display

If

there

is a 5103

once,

all

the DISPLAY key

Note:

is

has been pressed

The

is

pressed

is

held

down,

is

pressed

this

key

CD

Printer,

information

operational

L32

64

R32 switch has

the

once,

up,

the

once, down, is

held

when

presently

even

once).

numeric

top

the

numeric

the down,

when

keys) can be used

each displayed line

line

is

lost as it

lines

continue

keys)

each displayed line

bottom

the

line

the

lines

CMD key

on

the

system

no

effect

is

moved

is

moved

to

move up.

can

be

used

is

moved

is

lost as it

continue

is

display screen

on

held

is

what

in

to

down

the

will be

only

off

only

is

moved

move

and

is

hold

in

execution

up

to

the

display screen.

in

execution

to

the

down.

this

key

printed.

state

printed.

COpy

(the

mode.

line.

mode.

lower line.

display

is

pressed

HOLD

INDICATOR LIGHTS

The

5100

console (Figure 3) has

Process

Check

When

on,

press

the

tion

cannot

sentative.

this light indicates

REST

ART

be

successfully restarted

switch

the

following

that a system

to

restart

the

after

indicator

malfunction

system

several

operation.

attempts,

lights:

has

occurred.

call

If

the

your

system

In this case,

opera-

service repre-

8

(

In

Process

When

the

IN

PROCESS light

put

and

flashing

Notes:

1.

For

some expressions generated cases, even goes

off

when

the

has

completed

2.

If

the

display screen

IN

PROCESS light

your

service representative.

system

before

though

and

system

is

processing

is

on.

cursor

th~

the

output

has finished processing

execution).

is

off,

input,

After

are displayed,

or

user-defined

expression

system

is

displayed.

blank (no

check

generally

the

input

and

functions

or

function

is

still processing

The

data

or

the

brightness

the

is

processed,

the

system

has

flashing

the

input

cursor

control

display screen

the

light goes

waits

for

(see

Chapter

completed

data,

the

cursor

(the

expression

is

present)

and

before calling

is

blank

off,

input.

5),

output

execution.

IN

PROCESS light

is

again displayed

or

the

and

the

out-

is

I n such

function

(/

"""":

(

-"-'

.......

-'

c

9

Chapter 2. System Commands

SYSTEM OVERVIEW

The

5100

contains an active workspace, which

the

user's data

is

turned active workspace saved

on

for

use

at contents tape.

The

tape

use. Before a

one

or

more files where tains information for a description

The

system

the

system,

and

off

or

tape

(stored workspace) and

a later

of

the

is

your

tape

commands, which are used are discussed next.

is

the

part

of

internal storage where

user-defined functions (programs) are stored. When

the

RESTART switch

is

lost. However,

time

(see System Command Descriptions

active workspace

library;

about

of

that

can be used,

data

can be stored. Each file has a file header, which con-

the

file. See

the

file header.

is,

is

the

~ontents

then

exist in

it

is

a place where

it

must be

the)

to

pressed

LI

on

the

5100,

of

the

active workspace can be

read back into

both

formatted. A formatted

B system

control

and

the

in

the

active workspace and

you

can store

command

provide information

this chapter).

the

power

all

the

data

in

the

active workspace

The

on

data

for later

tape

contains

in this

chapter

about

SYSTEM COMMAND DESCRIPTIONS

The

information

described

Commands

Command

)CLEAR

)COPY

)ERASE

)LOAD

)PCOPY

)SYMBOLS

)WSID

following list shows

about

in

detail later

that

Control

how

system

the

various parts

in

this chapter.

the

Active Workspace

Meaning

Clear

the

active workspace.

Copy

stored

Erase global objects (see note 1) from

Replace

Copy stored objects (see

tect

Change

the

objects

the

commands

of

objects (see

active workspace with a stored workspace.

in

the

number

active workspace 10.

are used

the

system. Each system

note

active workspace from being destroyed.

of symbols allowed

1) into

to

control and provide

command

the

active workspace.

the

active workspace.

the

active workspace and pro-

in

the

active workspace.

is

10

Commands

that

Control

the

Library (Tape)

(

{,'

Command

)CONTINUE

)DROP

)MARK

)SAVE

Commands

Command

)FNS

)LlB

)SI

)SIV

that

Provide I

Meaning

Write

the

workspace

Drop a tape

Format

Write

the

workspace

nformation

Meaning

Display

contents

can

contain

file.

the

tape.

contents

cannot

About

the

names

workspace

the

state

the

state

of

the

active

suspended

of

the

active

contain

the

System

of

the

user-defined

file headers.

indicator.

indicator

workspace

functions.

workspace

suspended

and

local names.

on

functions.

tape.

The

active

(

Other

)SYMBOLS

)VARS

)WSID

Commands

Command

)MODE

)OUTSEL

)PATCH

)REWIND

Notes:

1.

Objects

2.

The

system

)REWIND,

they

are used.

that

refers

commands

and

Display

workspace.

Display

Control

Meaning

Place

Select

Apply data

Rewind

to

both

)SAVE will

the

number

the

names

the

active

the

System

the

5100

printer

IMFs (internal

after a tape

the

tape.

user-defined

)CONTINUE, )COPY, )PCOPY,

blank

of

symbols

of

the

workspace

in

communications

output.

machine

error.

functions

the

top 8 or

allowed

global variables.

10.

fix)

and

variables.

9 lines

mode.

to

the

)DROP,

on

the

and

used in

system

or

)LOAD,

display screen

the

active

recover

)MARK,

when

c

11

All

system

a

right

parenthesis. Each

meters separated and cussed in

(required

cannot

commands

by

blanks.

be

used as

Chapter

or

optional

6).

(and

system

System

part

only

system

command

information)

commands

of a function

commands)

must

begin

for

the

cannot

be

definition

have as

system

used

(function

their

first

on

a new line. Para-

commands

within

APL

definition

character

must

be

instructions

is

dis-

System

1.

2.

The

any

used as

• Device/file

commands

The

system

keyboard.

The

system )WSID, the

CMD

command

parameters,

operation

parameters

unit

is

tape

fied

is

less presents most

three

tape

unit.

Device/File

only

02

can

be

command

commands

)OUTSEL

key

you

if required,

will

number

unit 1 and

than

the digits specify For

and

while pressing

want.

take

place. Following

for

system

specifies

four

digits,

file

number.

example:

Number

entered

can

)LOAD, )REWIND

must

commands:

the

auxiliary

tape

the

file

two

be

entered

the

be

tape

unit 1 is

If

number

Meaning

Tape

ways:

one

)SAVE,

entered

the

)CONT,

can

be

top-row

and

is

an

unit

and

tape

unit

assumed and

value specified

and

1, file 1

1, file 2

character

entered

key

the

explanation

file

is

the

at a time

)US,

)FNS,

in

one

just

below

EXECUTE key pressed

of

to

be

used.

tape

unit

the

is

four

leftmost

from

the

)VARS,

operation

the

label

terms

The

2. If value specified re-

digits,

digit specifies

by

of

and

built-in

the

value speci-

the

)COPY,

holding

the

symbols

right-

the

before

tape

12

2002

• Workspace (with

no

11

characters

• Password (with

no blanks). If

eight are used.

•

Object

is

Parameters

•

ID

is

any

combination

blanks);

is

a user-defined

enclosed

are

entered,

any

combination

however,

more

in

the

only

of

than

function

brackets

Tape

2,

of

up

first

character

the

first

up

to

eight

characters

or

variable name.

can

be

optional

file 2

to

11

are used.

alphabetic

must

be

are

entered,

in

certain

or

numeric

alphabetic.

or

numeric

only

cases.

characters

If

more

characters

the

first

than

..

The )CLEAR Command

(

The

no valid name The

When

Syntax

There

The

)CONTINUE

)CLEAR

workspace

I

ndex Workspace identification Comparison Printing Printing precision

Random Data

Symbols

the

)CLEAR

are no parameters.

command

and

origin

width

number

printed

command

contains

attributes

tolerance

seed

is

successfully

clears

are

Command

the

active workspace. A cleared workspace has

no user-defined variables

set

to:

CLEAR

1E

WS

13

or

functions

64

5

16807

ALL

125

completed,

CLEAR

WS

is

displayed.

and

no

data.

(~

(

c

The

)CONTI NUE

of

the

active workspace

this

command

be resumed later

successfully

The

)CONTI NUE

)SAVE

command

stores

completed,

command

on

IBM

Notes:

1.

A clear

2. A workspace )CONTINUE mand).

3.

)COPV

written

4.

A loaded

workspace.

5.

If

is available (see

workspace was

6.

If interrupted

stored

a

stored

loaded

ATTN

workspace

and

on

tape

workspace

into

workspace

into

is

command,

active

on

the

command

(except

APLSV.

with command

)PCOPV

using

a 5100 active workspace

another

the

DWA

written pressed during a )CONTINUE and

the

using

the

specified

onto

tape

without

status,

such as

same

or

a similar machine. When

CONTINUED device/file

on

the

as

noted

below)

cannot

suspended

be

(it

cannot

commands

the

)CONTINUE

written

that

was

5100

system

to

tape.

file

is

set

written functions

to

tape

written

with

variable

to

changing

suspended

5100

is

similar

and

on

can

be

written

cannot

specify

command.

using

that

to

a larger active

in

unused.

workspace I D,

the

functions,

number

in

function

is

distinguished

tape.

only

be

to

tape

stored

the

)CONTINUE

is

smaller

tape

using

workspace,

Chapter

operation,

stores

the

contents

active workspace. Primarily,

so an the workspace

written

using

workspaces

than

the

5)

is

the

operation

command

and from

on

the

command

the

)CONTINUE

the

same as

system

is

ID

is

format

the

)CONTI NUE

tape )SAVE

that

original active

workspace

operation

can

displayed.

to

the

using

the

com-

were

cannot

command

when

the

is

be

13'

7. Shared variable

execution

command. A subsequent)

media

is

restored

to

using )CONTI NUE

repositioned

or

placed

8. If a workspace stored with variable executed

or

a suspended function,

when

the

9. Workspaces are stored and loaded )CONTINUE

10. IMFs are the

stored workspace, it should be reapplied by

the

IMF

not

is

not

command

stored

already

Syntax

)CONTINUE [device/file number] [workspace 10] [:password]

where:

status

can be stored by using

LOAD allows

the

same

(that

is,

the

on a different

the

workspace

than

condition

tape

)CONTINUE

is

loaded.

using

the

as

containing

drive).

the 0 LX

int_o

the

)SAVE

user to, resume

when

command

system

active workspace faster using

by )CONTINUE. If an IMF

in

the

system) before

the

workspace was

the

shared variable

has an

command

command.

is

required for

the

)PATCH

workspace

the

)CONTINUE

execution

open

will

operation

comma~d

is

reloaded.

stored

cannot

shared

not

be

if

the

be

the

of

(if

device/file tape where vice/file

number

the

number

contents

workspace was loaded or specified by a previous )WSID

workspace I D (optional)

name must match

file

to

be used

on marked unused, to

this

workspace I

the

active workspace

:password (optional) characters must

(without

be matched when workspace. If no workspace I D ted

with

the

active workspace (if any) stored. with

If

just

the

active workspace

The )COPV Command

The

)COPY space written is

successfully

command

to

the

active workspace. Only objects

on

tape

with

completed,

(optional)

is

specified,

the

workspace I D

the

tape, unless

the

active workspace I D

D.

is

blanks), preceded by a colon. This sequence

workspace I D and

is

the

number

of

the

active workspace are

the

device/file

is

the

name

of

the

file

If

no name

is

specified

used.

any combination

the

stored workspace

or

password

no

is

not

used.

of

the

tape

unit and file

to

be written.

number

from which

the

command

the

workspace

both

the

is

marked unused.

and

tape file workspace I D are changed

in

of

up

to

is

entered,

is

assigned

password

to

be

stored. This

active workspace

If

the

command,

the

eight alphabetic

to

be read back into

the

password associa-

to

the

workspace being

is

entered, any password associated

is

and

or

of

copies all or specified global objects from a stored work-

in

the

)SAVE

COPI

command

ED

device/file

stored workspaces

can be copied. When

number

workspace I D

that

the

is

command

on

the

If

no de-

active

used.

the

file

is

name

of

numeric

characters

the

active

were

displayed.

14

Notes:

1.

If

the

into

the

2. If

interrupted is

unpredictable.

active workspace contains suspended functions, objects

it.

ATTN key

and

is

pressed during a )COPY

the

amount

of information copied into

operation,

the

cannot

system

be copied

operation

active workspace

is

Syntax

(~

(

)COpy

where:

device/file jects are copied from.

workspace I D

:password

command. specified by this

object the jects in

device/file

number

is

the

If no password was assigned previously, a password

name(s) (optional)

designated

the

designated

stored

The )DROP Command

The

)DROP marked unused, the

command

displayed.

command

the

is

successfully

number

is

the

security password assigned by a previous

command.

data

workspace

the

number

name

of

the

is

the

workspace. If

stored

workspace are copied.

marks a specified file unused.

in

the

file can

completed,

ID

:password

of

the

tape

unit

stored

workspace

name

of

the

global object(s)

this

parameter

no

longer be read

DROPPED device/file

[object

and

workspace file

on

tape.

is

omitted,

After

from

name(s)]

)WSI D or

cannot

to

all global ob-

the

file has been the

number

the

)SAVE

be

be copied

tape.

When

file

ID

ob-

from

is

....

(

/

c

Syntax

)DROP device/file

where:

file

number

device/file

file I D (optional)

the

If

The ) E RASE Command

The )ERASE space. There mand.

command

is

no

message displayed

Notes:

1. When a

is If

2.

able will

3. Even

part

issued.

the

object

after

of

penden\

be

the

function

being erased

retracted.

the

object

active workspace

number

is

the

is

the

name

specified

erases

is

erased,

[file ID]

number

(see

is

of

the

tape

of

the

stored

is a data

the

a shared variable (see

that

file,

any

named global objects

at

the

successful

Chapter

the

7)

is

name remains

contains

unit

and

the

workspace file

file

ID

specified

from

completion

erased,

all

the

Chapter

in

the

symbols used).

file

on

to

be

marked unused.

the

active work-

response

8),

the

symbol

the

is

ignored.

of

the

SI

DAMAGE

shared vari-

table (the

tape.

com-

15

Syntax

) ERASE

where:

object

name(s)

The )FNS Command

The)

FNS

command

active

workspace.

meter

is

specified,

or

character

Note: You

Syntax

)FNS

where:

characteds)

that

of

sequence.

can

[character(s)]

starts

with

characters

interrupt

(optional)

determines

name(s)

are

global

names

separated

displays The the

an

alphabetic

the

names

of

functions

names are displayed beginning

the

is

are listed alphabetically. If

)FNS

command

any

the

sequence

character

starting

of

point

by

blanks.

all global user-defined

the

with

the

by

alphabetic

and

contains

for

pressing

an

the

and

numeric

no

blanks. This

alphabetic

functions

character

specified

ATTN key.

listing.

character

characters

in

the

para-

sequence

The

)LIB

Command

The)

LIB

file

header

• File

• File I stored

• File

ng

i

File

00

01

02

03

command

contains

number.

D.

The

workspace,

type.

of

each

Type

displays

the

The

files

file I D can be

the

The

file

type

code:

Description

Unused file

Exchange

General

BASIC

the

following

on

tape

from 1 to

file ID

is

a 2-digit

exchange

source

file

headers

information:

are

numbered

is

the

same

code;

data

file (see

data

file

of

the

17

characters.

as

the

Chapter

file (see

files

on

sequentially,

If

stored

workspace

following

chart

8)

Chapter

tape

starting

the

8)

(library).

file

contains

ID.

gives

with

the

The

1.

a

mean-

16

File Type

Description

(

04

05

06

07

08

16

17

19

72

• Size storage.

•

Number

•

Number

displayed if

of

the

file.

of

unused

of

defective records

there

BASIC

workspace

BASIC keys file

continued

APL chapter)

APL saved file (see )SAVE

APL internal

tape

Patch,

Diagnostic file

IMF file

Storage

The

contiguous

are

files are

more

than

dump

file (see )CONTINUE

data

recovery,

file

formatted

1024-byte

(512-byte

nine defective records.

file

format

and

in

increments

blocks

blocks) in

command

file (see

tape

copy

of

storage in

the

command

in this

chapter)

Chapter

of

file; an asterisk

file

1024-byte

the

8)

file.

in

this

blocks

(*)

of

is

(

Note: This value can indicate

data

due

to

defective areas

Following

006

""

/

The

~

______

)LlB

is

an

example

FILE6

-

__

command

of

File

Size

Available storage

Number

FileID

File

operation

when

you

should

relocate a file

on

the

tape.

a file header:

07

Ol.O

type

-1

of

the

file~

_____

of

defective records

number

can be

interrupted

t

by pressing

.•

___

OO:l

---'

()

.....

the

to

avoid loss

ATTN key.

of

c

17

Syntax

) LIB [device/file number]

where:

device/file file number. All file headers from If

no

entry

are

currently display the file headers beginning currently

The )

LOAD

The

into active workspace. When device/file

Note: If

is

Command

) LOAD the

active

number

the

interrupted

Syntax

) LOAD device/file

where:

number

is

made,

positioned

command

workspace,

workspace 10

ATTN key

and

the

(optional)

the

at

loads

the

is

active workspace

number

is

the

display begins

at

on

tape

on

tape

unit

the

contents

completely

command

is

displayed.

pressed during a load

workspace

number

that

with

unit

with

the

2.

of a stored

replacing

is

successfully

is

cleared.

10

of

the

tape

file

to

the

end

the

first file following

1.

For

tape

first file following

workspace

the

contents

completed,

operation,

: password

of

unit

the

2,

that

the

and

the

tape

the

entry

the

file

from

were LOADED

system

starting

are displayed.

the

file

you

2000

will

you

are

the

tape

in

the

operation

device/file on

workspace

:password vious )WSID, )CONTINUE, viously assigned, a password to for

The

)MAR

The

)MARK can be saved to

a specified size. Additional files

additional )MARK

When

number

the

tape.

lOis

is

the

stored workspace

this

command,

K Command

command on

it. Each )MARK

the

operation

of

the

last file marked size

is

the

number

the

name

security password assigned

but

the

error

formats

commands.

is

successfully

of

the

or

)SAVE

cannot

is

not

message

the

tape

command

of

the

stored

command.

be specified. If a password was assigned

specified,

WS

so

different

completed,

of

the

tape

unit

and

workspace.

to

the

stored workspace by a pre-

If

or

if

it

LOCKED

that

the

formats

sizes can be

MAR KED

last file marked

is

active workspace

a specified

the

number

no

password was pre-

is

incorrectly specified

displayed.

number

formatted

is

displayed.

of

or

data

of

by using

the

files

file

18

(

CAUTION

file and

Syntax

Notes:

1.

The

ATTN key

2.

If

the

message was issued, specified file, to

continue.

If

an existing file

the

is

not

operative during

ALREADY

the

specified file already exists

enter

on

tape

existing files following

GO.

is

re-marked,

MARKED

If

the

is

file

is

not

the

re-marked file

the

)MARK

displayed

on

to

original

command

after

a )MARK

the

tape.

To

re-mark

be re-marked, press EXECUTE

information

cannot

in

be

used again.

operation.

command

the

re-marked

)MARK size

where:

is

size storage.

The

following

marked.

written

MAXSIZE= 3+f (CLEAR-ACTIVE)-;-1024, where:

• MAXSIZE blocks) to

• CLEAR

• ACTIVE are

The

formula

-see

Chapter

MAXSIZE= r

number

an integer specifying

The

to

tape

that

tape.

is

written

for a data

of

files

formulas

formula

with a )SAVE

is

the

would be required

the

th~

to

8) when all (WI!HOUT

for

maximum

value

tape.

can be used

of

file (data

to

mark starting file

the

size

of

each file in

to

determine

a workspace file (the

or

)CONTINUE

amount

DWA (see

of

DWA

of

the

-WITHH-1

data

to

write

Chapter

just

before

written

is 024,

of

to

contained

number

what

contents

command)

tape

storage

the

contents

5)

in

the

contents

tape

using an APL shared variable

in

where:

[device]

1024-byte

a clear workspace.

the

(1K) blocks

size a file

of

the

is

(number

of

the

of

the

active workspace

should

active

wo~kspace

of

1024-byte

active

workspace

active

workspace

of

be

is

(~i

• MAXSIZE blocks) required

• WITH

• WITHOUT

There is

written

required

type

by

Note:

fore, of

space.

stored

is

of

the

The

the

file plus

is

the

in

no

formula

to

depends

data

various

file

number

is

the

maximum

to

write

value

of

is

the

value

the

active workspace.

for

tape

as it

is

upon

how

is

used.

For

types

of

data,

header

for

of

bytes

0.5K.

amount

the

DWA (see

of

DWA

determining

entered

much

information

see Storage Considerations in

each

marked

of

tape

of

tape

data

to

tape.

Chapter

before

from

data

storage required

5) with

any

what

size

the

keyboard.

is

entered

on

how

file requires

storage

the

data

to

mark a

from

many

0.5K

for

(number

data

be

written

data

The

amount

the

bytes

each file

of

1024-byte

in

the

to

file

when

keyboard of

storage

Chapter

of

storage. There-

is

the

specified size

active work-

tape

was

the

data

of

tape

storage

and

what

are

required

9.

19

number specified size

of files

to

format.

mark

is

an integer specifying

the

number

of

files

of

the

starting is

device (optional,) specifies

An

made,

To

format a tape

following

)MARK

The

)MODE

The serial I/O

is

in

the

Communications Reference Manual, User's Manual,

file

number

to

start.

entry

of

1 specifies

tape

unit 1 is

for

commands

12

16

10

Command

)MODE

communications

command

adapter

SA21-9239,

program

four

are required:

4

2

3 7

mode,

feature

is

an integer specifying

the

tape

unit

tape

unit 1 and

assumed.

12K

files,

two

16K

5

-------~Starting

is

used

to

load

the

5100

from a tape

APL or

the

respectively.

mounted

is

no

longer available.

serial I/O

SA21-9215,

the

file

that

contains

2 specifies

files,

and

communications

in

tape

adapter

or

feature,

IBM

number

tape

drive 1. When

For

5100

the

unit

three

file

more

where

tape

2. If no

10K

number

program

information

see

IBM

Serial

formatting

to

be

files,

the

5100

I/O

formatted.

entry

is

the

or

5100

system

on

Adapter

Syntax

)MODE COM

The )OUTSEL Command

The

)OUTSEL

Syntax

)OUTSEL

where:

option

• When printed.

• When played,

• When it

is

one

ALL

OUT

OFF

is

assigned

command

[option]

of

the

is

specified, all

is

but

it

is

specified,

to

specified,

does

specifies which

following:

subsequent

only

not

go

to

none

an APL shared variable used

the

of

data

output

printer.

the

information

on

information

is

the

display will go

that

sent

to

the

displayed

by

the

is

displayed will be

printer;

is

printed,

printer

(see

to

the

input

Chapter

printer.

is

dis-

unless

7).

20

If no mand

parameter

or

when

is

specified,

the

machine

ALL

is

first

is

assumed.

turned

on,

After

the

a ) LOAD

ALL

option

or

)CLEAR com-

is

active.

The

)PA

TCH

Command

(

The following junction with

the

• Copy IMFs (internal machine fix), program

• Load IMFs for language available again.

• Display

• Recover

occur

1.

2. General exchange (file

3. BASIC source (file

4. APL internal

• Copy

is

a list

of

the

uses

with

specially devised programs

5100.

The

uses are described

onto

another

the

EC

data

on

during use

Exchange (file

the

contents

tape

system program into

version

of

tape

when

of

one

of

type

data

format

of

one

of

cartridge.

each interpreter module.

tape

read errors (ERROR

the

following files:

01)

type

03)

(file

tape

cartridge

this

command.

on

the

in

detail, following

the

Copy

the

02)

type

08)

to

This

command

customer

IMF

active workspace,

another

support

the

program, and

007

ddd-see

tape

cartridge.

is

used in con-

cartridge supplied

list:

the

Load IMF

then

make

Chapter 11)

the

APL

(/

•

c

The

customer

• File 1. interpreter module

• File 2.

• File 3.

• File 4. The

• File

tains

1.

2.

3.

4. !J.!J.SHARED-Displays

The

defined

do

not

support

The

5.

APL aids. This

the

following four functions:

!J. !J.

TRACE-Traces

!J.!J.

TRACEALL-

defined function currently

!J.!J.

TRACEOFF-

workspace.

!J.!J.

TRACE

function

require

cartridge

programs

EC

IMFs for

Tape Recovery program.

Tape

Copy program.

function

to

be traced enclosed

any

arguments.

contains

that

copy

versions.

the

5100

is

a saved work.space file (WSID=APLAIDS)

all

the

Traces

the

Turns

off

the

requires as its right argument

the

following files:

or load IMFs and

.

statements

first executable

in

the

all tracing.

shared variable names

in

a specified user-defined

active workspace.

in

single quotes.

the

program

statement

currently

the

The

that

of

each user-

in

name of

other

displays

that

con-

function.

the

active

the

user-

functions

21

This workspace file also contains the following five variables that describe the functions in the workspace:

DESCRIBE

1.

2.

DESCRIBE~~TRACE

3.

DESCRIBE~~TRACEALL

4.

DESCR

5.

DESCRJBE~~SHARED

These

)COPY command. For example,

workspace:

JBE~

~

TRACEOF F

functions and variables

can

be

copied

to

copy the

into

the active workspace using the

~

TRACE function

into

the active

)COPY 5 APLAIDS

Note: The )PATCH command

When

the )PATCH command

the following options

ENTER OPTION NO.

COpy

1.

LOAD

2.

DISP

3.

KEY-ENTER IMF

4.

END OF JOB

5.

TAPE RECOVERY

6.

TAPE

7.

-

..

are

displayed:

IMF TAPE

IMF'S

EC

VER.

COpy

PGM

AATRACE

is

not

is

used

with

required

for

using the functions in file

the tape cartridge inserted in tape drive

Flashing Cursor

5.

1,

22

To select an tape

drive 1).

tions will be displayed again. prompting messages might be displayed for

option,

If

an

enter

option

an

number

Option 1. Copy IMF Tape

option

Once

number other the

option

(the

tape

than

those displayed

number

the

selected

cartridge must be inserted

is

has been

option.

entered,

the

op-

additional

in

(

The

Copy IMF Tape

• File 1, which contains

EC

Version program.

• File 2, which contains

file as follows:

1.

Copy all IMFs

2.

COpy all IMFs for APL

3. Copy specific

4. Copy specified IMFs

used. being used, it

~

..

/

Note: The

the

copy

files should be marked.

The

to

respond

tape

operation

Copy IMF Tape program will issue

to

option

allows

the

Copy IMF program, Load IMF program, and Display

the

IMFs for

that

apply

to

APL.

that

apply

1M

Fs by problem number.

by

problem numbers

(I

f a problem

onto' which files 1 and 2 are

is

done. Use

each message.

is

not

number

copied.)

the

is

)LlB

following files

the

5100. The IMFs can be copied

to

specified

to

command

prompting

to

be copied

the

5100

being used.

that

apply

that

does

not

be copied

must

to

determine

messages and wait for

to

apply

be marked before

from

the

what

the

5100

to

the

size

the

tape:

from

being

5100

the

user

the

c

Copying IMFs allows

5100

to

be created.

tape

cartridges containing only

Option 2. Load tMFs

The Load IMFs makes

the

• Load all IMFs

• Load specified IMFs by problem numbers (If a problem is

not

The

Load IMFs program will issue

to

each message.

Note:

The

the

performance

to

your

5100

circumvented workspace until

option

allows IMFs

APL language available again. IMFs can be loaded as follows:

that

apply

to

the

loaded.)

IMFs

if

by

number

occupy

of

the

an APL

the

is

specified

storage (space)

your

5100

problem

statement

power

is

significantly; therefore, IMFs should

does

turned

to

be loaded into

5100 being used.

that

does

not

prompting

not

affect

or

off

messages and wait

in

the

active workspace and can also reduce

your

command.

or

RESTART

the

IMFs

the

system program and

apply

to

the

apply

to

the

operation

The

or

IMFs will remain in

is

pressed.

that

5100

for

if

the

apply

the

to

your

then

being used.

being used, it

user

to

not

be applied

problem can

the

respond

be

active

23

Option 3. Disp

The

Disp

option

will display a 4-digit

the

module identification

are

The

EC

respond

EC

Ver.

EC

Ver.

option

is

primarily

code

and

Version program will issue

to

each message.

for

for each

the

your

service representative's use. This

interpreter

two

digits are

messages

module.

the

and

wait

The

EC version.

for

first

the

two

user

digits

to

Option,4. Key-Enter

This

option

IMF

is

then

or

loaded

Option 5. End of

This

option

allows written

copied

Job

causes

IMF

the

from

the

Option 6. Tape Recovery

The

Tape

Recovery

tape

can

read errors

be used

data

on

type

which gram

• Exchange (file

• General exchange (file

• BASIC source (file

• APL internal

service representative

to

file 2

on

the

tape

the

tape.

APL language

option

allows

(ERROR

the

following files:

01)

type

03)

format

(file

the

007

02)

type

to

enter

IMFs

containing

to

be

available again.

user

to

ddd) are occurring.

08)

recover

the

data

from

the

IMFs.

The

from

a file

The

Tape Recovery Pro-

keyboard.

IMF can

or

files on

then

The

be

24

The

Tape

respond

The

Tape

the

data

the

data

Recovery program will issue

to

each message.

Recovery program will recover as

in

the

record where

that

precedes and follows

the

tape

that

read errors

prompting

record may also

much

messages

data

occur

and

wait

as possible

is

not

recoverable; some

not

be recoverable.

in

for

the

file; some

user

to

of

Option 7. Tape Copy Program

(

The

Tape Copy

tape)

of

drive, if available. Tape

Tape

copy

one

issues

option

cartridge

pro~pts

Syntax

) PATCH

There are no parameters.

The )PCOPV Command

The)

PCOPY space that

if a stored workspace. Therefore, from

being overlaid

written

When workspace

into

the

on

the

command

active workspace. It

objrct

name already exists in

tape

with

ID

is

displayed.

allows

you

to

another

copy

copies all

and

destroyed. Only objects

the

)SAVE

is

successfully

cartridge. Tape copy can utilize

also marks

and waits for you

or

specified global objects

is

the

object

command

completed,

copy

the

contents

the

tape

being copied

to

respond

same as

the

active workspace, it

in

the

active workspace

in

stored workspaces

can be copied.

COPI

ED

(up

to

from

)COPY

device/file

to

the

to.

each

prompt.

a stored work-

command,

is

not

is

number

end

of

marked

auxiliary

except

copied

protected

that

were

tape

from

('T

c

Syntax

where:

Notes:

1.

If

the

active workspace contains suspended functions, objects

into

it.

2. If

the

ATTN key interrupted unpred ictable.

3. If

the

specified NOT COPIED:object name

)PCOPY device/file

device/file

workspace I D

:password command. this

command.

object

name{s) (optional)

the

designated

stored

workspace are copied,

any).

is

and

the

object

number

is

If no password was assigned, a password

is

the

security password assigned by

stored

pressed during a )PCOPY operation,

amount

number

name

of

information ,copied

name already exists

is

also displayed.

workspace

the

number

workspace. If

of

is

the

stored

name

except

of

the

omitted,

those

in

the

ID

:password

tape

unit and

workspace on

the

of

the

global object(s)

all global objects in

already

into

active workspace,

[object

the

previous )WSID

cannot

in

the

cannot

the

system

the

active workspace

name(s)]

stored

tape.

be specified

to

active workspace (if

be copied

operation

the

message

workspace file.

or

)SAVE

by

be

copied

the

designated

is

from

25

The )REWIND Command

The

Syntax

)REWIND

at

the

successful

)REWIND [device number]

where:

device meter

number

is

omitted,

command

completion

(optional)

tape 1 is

The )SAVE Command

The

)SAVE

out

changing loaded individual global objects can be copied workspace. When this device/file th

is

or

copied

message

command

the

contents

on

number

is

displayed.

stores

a machine with a larger

command

workspace I D

rewinds

of

the

of

this

is

the

tape

rewound.

the

contents

the

active workspace.

is

successfully

is

specified tape.

command.

(on drive 1

of

the

or

a smaller active workspace. Also,

from

the

stored

completed,

displayed. Do

There

is

no message displayed

or

2)

to

be rewound. If

active workspace

The

stored workspace can be

workspace

SAVED

not

remove

the

onto

to

the

tape

active

until

the

with-

para-

Notes:

1.

A clear workspace tape

using

the

can be

written

2.

The

)COPV and )PCOPV

written

3. Depending

that

5100

4.

and

5. are stored with

6. IMFs are to the

on

tape

was

written

with a smaller active workspace.

If

ATTN

is

the

file

No

open shared variables are stored

not

reload

the

system) before

or

)SAVE

to

tape

only

on

the

amount

to

tape

pressed during a )SAVE

is

set

to

the

)CONTINUE

stored

IMF by using

the

a workspace with suspended

command;

using

commands

if

the

using

unused.

by

the

stored

however, a workspace with suspended

the

)CONTINUE

can specify

)SAVE

of

data

the

command.

)SAVE

the

)PATCH

workspace

command

in

the

)SAVE

operation,

in

operation.

was used.

stored workspace, a stored workspace

command

a )SAVE

command

is

reloaded.

function

command.

stored

workspaces

can be loaded into

the

system

operation.

If an IMF

(if

the

cannot

be

written

functions

that

were

another

operation

Open shared variables

is

required, it

IMF

is

not

is

interrupted

is

necessary

already in

on

26

Syntax

(

)SAVE [device/file

where:

devicelfile tape device/file

workspace

is

used.

workspace name to

b,e

unused, this active

:password (optional) characters must workspace. with

If

just

with

number

where

the number was loaded

I D (optional)

must

match

used

on

the

active workspace

workspace

(without

be

matched

the

active

the

workspace I D

the

active workspace

contents

the

tape

ID.

is

when

If

no

workspace

number ] [workspace I D]

(optional)

is

specified,

the

If

used.

is

blanks),

is

of

the

or

which

is

the

workspace

unless

the

and

no name

any

combination

preceded

the

stored

ID

(if any)

and

no

is

not

the

number

active workspace are

the

device/file

was specified by a previous

name

of

the

I D

of

both

file

is

marked

tape

file workspace I D will be

is

specified

by

workspace

or

password

is

assigned

password

used.

[:password]

of

the

tape

number

workspace

the

active

unused.

in

the

command,

of

up

to

eight

a colon. This

is

to

be read back

is

entered,

to

the

is

entered,

unit

and

file

to

be

written.

from

which )WSI D command

to

be

stored.

workspace

If

the

file

changed

the

name

alphabetic

sequence

the

workspace

any

password associated

of

into

password associated

being

on

the

If

no

the

active

This

and

the

is

marked

of

or

numeric

characters

the

stored.

file

to

the

active

(

The )SI Command

The

)SI

command

Syntax

The

functions by next

There

)SIV

The defined each recently suspended

(see State Indicator

an *,

with

most

~ecently

)SI

are

no

Command

)SI V command

functions

function.

suspended

parameters.

function,

the

displays

most

suspended

The

the

recently

displays

(see State Indicator in

suspended

function

and

names

of

the

suspended

in

Chapter

suspended

function,

the

functions

listed first, followed by

so

on.

and

names

7). function

so on.

of

the

Chapter

are indicated

and

The

suspended

listed first, followed

suspended

7)

and

by

the

pendent

functions

and

pendent

the

names local

an

*,

user-defined

are

indicated

by

user-

with

the

recently

the

to most

C

"

./

27

Syntax

There

The

)SYMBOLS

The

(variable names, number mand initially set

of

I N USE

allowed,

Note: When a

of workspace was

Syntax

)SIV

are

no

parameters.

Command

)SYMBOLS

of

has been issued. In a clear workspace,

symbols allowed,

is

WAS

symbols allowed in

)SYMBOLS [0]

command

function

symbols allowed can

to

125

by

displayed. When

the

former

stored

written

is

names,

the

5100.

IS

the

number

the

number

workspace

the

active workspace will

to

tape.

used

to

and

only

When

command

of

is

loaded into

of

change

symbols allowed

or

display

labels) allowed in

be changed immediately

the

command

symbols allowed,

is

used

the

number

the

active workspace.

number

be

of

is

used

number

to

change

is

displayed.

active workspace,

the

same as

of

symbols

after

a )CLEAR com-

symbols allowed

to

the

display

number

when

the

of

symbols used

of

the

number

the

stored

The

is

number

symbols

t.

)

where:

11.

(optional) symbols allowed in of

storage in

is

an integer equal

the

Notes:

1.

The

number

actual

2. When a symbol object active workspace reloaded, these of

symbols in use will be

The

total

3. space space can be changed as follows: a. Save b. Clear c.

Set

d. Copy

command.

of

number

is

erased or, in

number

to

tape

with a )SAVE

to

the

active workspace.

the

active workspace with

the

active workspace with

the

new

the

stored

to

or

greater

the

active workspace. Each symbol allowed requires eight

active workspace.

symbols allowed

allowed can be larger

is

used in

the

is

written

unused

number

names are removed

of

allowed symbols remains

of

workspace

is

the

active workspace, it remains

case

of

"VALUE

to

tape

the

same as

or

)CONTINUE

The

symbols with

to

the

than

26

that

assigned in blocks

than

the

number

ERROR",

with

the

)SAVE

from

the

number

the

)SAVE

the

)CLEAR

active

number

the

of

the

same

command

of

symbols in

command.

)SYMBOLS

workspace

specifies

of

21;

therefore

specified.

in

never existed. When

command

symbol table;

objects

in

after

and

reloading

the

command.

with

the

number

the

use even

the

writing

active workspace

though

and

subsequently

and

workspace.

the

)COPY

the

wcrk-

number

work-

of

bytes

the

28

(

The

)VARS

The space. included,

Syntax

where:

Command

)VARS

)VARS [character(s)]

character(s) (optional) starts with an used

command

The

variables are displayed alphabetically.

the

names are displayed beginning with

alphabetic

to

define

the

The )WSID Command

The

)WSID (workspace

number

file

written

be

mand

mand played. When workspace I D

if

is

also used

is

issued

and

workspace I D

either

without the

is

displayed.

displays

starting

a )SAVE

to

change

any parameters, device/file number workspace I D

)WSID

the

names

of

is

any

sequence

character

point

ID)

command

for

the

or a )CONTINUEcommand

or

assign

command

of

and

contains

for

an

alphabetic listing.

is

used

file where the active workspace

the

security password. When

is

issued

all global variables in

If

the

character

the

specified

alphabetic

to

with

and numeric

no blanks. This

change

or

display

is

used.

parameters, WAS device/file

the

active work-

parameter

character

characters

entry

the

tape contents

The

)WSID com-

the

is

sequence.

can be

device/

)WSI

D com-

is

dis-

that

will

number

c

Syntax

Note:

The

)WSI D command

to

change

any

information

)WSID [device/file number] [workspace ID] [:password]

where:

devicelfile where command

Note:

)CONTINUE

that

workspace

parameter

:password (optional) characters the tape.

number

the

active workspace will be is

issued.

If

this

parameter command

)SAVE

or

)CONTINUE

ID

(optional) will be

must

be

(without

security

password

only

affects

on

tape.

(optional)

entered

is

blanks), preceded

for

is

omitted,

will

not

command;

if

any

comoination

the

tape

an integer

work

the

other

the

active workspace; it

that

specifies

stored

when

either

the

device/file

unless a device/file

new name for

parameter

of

up

to

by

a colon. These characters will

file

when

the

active workspace

cannot

the

device/file

the

)SAVE

or

number

the

is

eight

is

cleared; a )SAVE

number

active workspace. This

used.

alphabetic

is

or

is

be used

number

)CONTI NUE

specified in

numeric

become

written

on

or

c

29

Chapter 3. Data

VARIABLES

You

can store items are called variables. Whenever data

associated with length with no blanks; characters can be

names longer

significant

to

data

in

the

5100

that

name. A variable

the

first

any

combination

than

77

characters can

APL.

The +-(assignment arrow)

by

character

LENGTHi··6

WIDTl-lfo8

AREA~LENGTHxWIDTH

To

display

the

value

of

a variable,

enter

assigning it

the

variable name

name

must be

of

alphabetic

be

used,

just

the

to

a variable name. These

is

used, APL supplies

can be

up

to

77

alphabetic

and numeric characters. Variable

but

only

is

used

variable name:

the

to

and

first

assign

the

77

data

stored

characters in

remaining

characters are

to

a variable:

the

6

8

4B

DATA

REPRESENTATION

Numbers

The character

the

as than

The can

LENGTH

WIDTH

I~I~EA

decimal digits 0

- , called

leftmost

zero:

negative sign,

be

used

character

O-lJ.

only

as

through 9 and

the

negative sign,

in

the

-,

is

distinct

part

of

the

decimal

is

used

representation

from

- (the symbol used

numeric

constant.

to

of

point

are used

denote

negative numbers. It appears

any

number

to

denote

in

the

whose value

subtraction)

usual way.

is

less

The

and

30

Scaled Representation (Scientific Notation)

(".

You can tiplying it representation in APL. by E and example:

The the must side

represent

Number

66700

.00284

E (E can

digits

be shifted.

of

it.

by

the

appropriate

then

an integer (the scale) representing

be

read times ten to the) in

to

the

right

There

Numeric Value Range

Numeric values in

7.237005577332262E75.

±.

5.397604346934028E -79.

numbers

the

by

The

of

the

can

be

5100 can range

The

stating a value

power

of

ten.

This

form

of

a scaled

Form

Scaled

t

6.67E4

•

2.84E3

E indicate

no

spaces

smallest numeric value

number

Multiplier

Scale

the

middle indicates

the

number

between

from

-7.237005577332262E75

in

some

type

the

the E and

convenient

of

notation

is a number

appropriate

of

places

the

5100 can use

range,

then

is

called scaled

(multiplier) followed

power

of

that

this

is

scaled

that

the

decimal

the

numbers

on

to

is

mul-

10.

point

either

For

form;

c

c:

Numeric Value Precision

Numbers in

digits.

the

5100 are carried internally with a precision

Character Constants

Zero

or

more characters enclosed in single

Appendix

(see

indicate functions, the

enclosing

B)

and

that

the. characters

but

represent only themselves. When

quotes

'ABCDEFG'

ABCDEFG

,

:1.23('~BC

123('~BC

M~'THE

M

THE

ANSWER

When a entered

quote

to

produce

is

required within

the

quotes,

blank characters (spaces),

keyed

do

not

represent numbers, variable names,

are

not

shown:

'

ANSWER

IS:'

IS:

the

character

single

quote

in

the

character

of

16

significant

including overstruck characters

is a character

character

constant,

constant.

constants

a pair

constant.

are displayed,

of

quotes

For

example:

The

must

quotes or

be

DON'T

'DON'

GIVE

'T

THE

GIVE

THE

ANSWER

AWAY

AWAY'

31

Logical

Data

Logical (Boolean)

(>

~

= <

true

and

to

the

Logical treated

SCALAR

A single item,

It has

ing

are

A

Scalars can be used

The

variable

~:;t)

generate logical

0 if

the

condition

logical

functions

data

can also be used

as numeric 1's

whether

no

coordinates;

examples

• A I

,,,'

name

of

data

and

that

scalars:

directly

for

the

consists

data

was false.

(/\I\vv",)

with

D's.

a single

is, it

in calculations

scalar can

of

only

as

their

to

check

the

number

can

be

then

ones

and

result;

The

output for

arithmetic

or

single

thought

or

be used

zeros.

The

the

result

can

then

be used as

certain

conditions

functions,

character

of

as a

can be assigned

in

constant,

geometric

the

calculations:

relational

is

1 if

in which case it

to

functions

the

condition arguments

being

true

is

called a

point.

The

a variable name.

or

false.

is

follow-

was

scalar.

I.>

c·

.J

ARRAYS

Array

is

the

items), vectors (strings dimensions arrays.

Indexing,

Some

2x3

l~f'2

Bi"~:~

(.·~+B

general

(multiple

for

term

of

tables). All primitive (built-in)

functions

example, can select

for

a collection

data),

matrices (tables

are designed specifically

certain

of

data,

elements

and includes scalars (single

of

data),

and

arrays

of

higher

functions

to

handle arrays

from

an array

are designed

rather

than

for

processing.

data

to

handle

scalars.

32

One

of

the

simplest kinds thought bers can be selected from a vector

sion.

variable names, present:

that

The

of

indicate

following

as a collection

the

Nand

of of

positions

example

C;

the

arrays,

the

vector, has only

elements

by

shows assigning a numeric

names are

arranged along a horizontal line.

of

elements

a single index, since a

then

in

an

array are called indices. An

entered

to

one

dimension; it

vector

has

only

and a character

display

the

values

can

The

one

vector

they

be

num-

element

dimen-

to

re-

two

(

N~5

N

6.2

-::5

C~"

·

~;

c

ABCDEFG

Generating Arrays

The

most

common

the

array

is

to

ments

of

the

function.

used

the

number

the

blank. right

'one dimension (is a vector) seven

be supplied

matter fewer seven entries in are used.

The

to

generate a n array

values for

for

each

coordinate.

The

values

argument

from

how

than

seven elements, its

The

way

have-that

new array.

symbol for

the

elements

coordinate

Each

of

(Y).

whatever

many

elements

the

new vector. If A has

following examples

6.2

-3

888

aB8

(y~;.

:1.2

ABCDEFG'

to

generate an array

is,

the

length

The

APL

function

the

reshape

is

X p

Y,

where X

of

the

array.

to

be generated;

number

the

The

in

the

left

elements instruction 7 p A means

values are

of

elements

A has, as long as it has at least

elements

show

95.12

is

to

of

each

coordinate;

that

function

the

found

are repeated as

generation

is

the

For

the

this

argument

new array are

in length,

stored

more

than

specify

the

forms

an

array

p.

The

format

shape

of

the

left

argument

number

that

indicates

must

be

whatever

the

array

and

that

under

the

one

often

seven elements,

of

some

following:

the

values

is

array and Y represents

(X),

separated

you

to

seven values are

name

element.

as needed

vectors:

the

of

the

reshape

of

the

function

you

enter

the

length

by

at

enter

be

generated has

A. It

does

If A has

to

provide

the

first seven

shape ele-

least as

a

of

one

the

to not

('

c

7(.>:1.

2 ]

:1.2:.3123:1.

2p12~5

123

:1.23

5(.)1

.

~5

1.3 1.3 1.3 1.3

An array with

two

Columns

coordinates

(rows

Rows

1.3

and

columns)

is

called a

matrix.

33

To

generate a matrix, lengths ordinate, coordinate, generated:

of

or

:1.

2 3

I.~

~;

the

number

or

(o1BCB

EFGH

ABC DEF

Note

that

the

right

argument

The required a

rank

(where N

providing

(planes, rows, 3-rank in

row

in

rank

of an

to

locate

of

1,

matrices have a

is

equal

as

the

arrays.

order:

I~IBCD

EFGH

I,.JKI...

you

two

coordinates.

number

M~2

specify X (left

of

rows, and

of

columns.

3pi

The

the

2 3 4 5 6

first

second

The

argument)

number

following

as

two

in X

is

the

example

numbers,

the

length length shows

which

of

the

of

the

how a matrix

t-1

6

t.1f-2

1+

r

I

ABCDEFGH

J

I

M

:1.

i-

2

:.3 p t1

Mi

values

in

the

right

argument

has

more

than

one

row

order.

array

is

the

number

any

element

to

the

left

argument a number

and

columns).

Note

that

A~'ABCDEFGHIJKLMNOPQRSTUVWXYZ'

;.~

:5

lJ.

P(.~I

\.

____

within

rank

of

rank). N-rank arrays, like matrices, are

The

following examples

the

elements

2-plane, 3-row,

row,

of

coordinates that

2,

and

indicating

taken

are arranged

the

elements

array. Scalars are N-rank arrays have a

from

in

are

it has,

the

length

show

the

right

4-column

row

taken

or

the

how

argument

array

order

from

number

rank

O.

rank

generated

for

each

to

in

the

of

Vectors have

from 3 to

coordinate

generate

are arranged

are

first co-

second

arrays. If

right

indices

by

the

is

63

34

MNDP

f~I~ST

UVWX

'+

AB

CD

EF

GH

IJ

1{1...

~1N

DP

GR

ST

UV

WX

3 2

\\-

f)l~

___

4-plane, 3-row,

2-column

array

Finding the Shape

of

An

Array

(

Once you each is

the name sult length (number is

always a vector:

The

have

coordinate)

of

is

one number

shape

of a matrix

A~111

~)

123

'+

5 6

2 3

12~3ll·

~5

6

·7

1 2 3

generated

by

the array.

of

(.1

M~2

an

array, you can

specifying p (shape function)

If A is

a vector

because A is

elements)

222

or

3p1

a one-dimensional array. The number

of

A's one dimension. The result

333

N-rank array

2 3

M

~)M

R~2

3

4pi

2 3

R

B

Lt·

1+

444

is

5 6

1+

find

its

with

six elements

555

found the

5 6 7 B

shape

with

666

same

(number

only

and

way:

of

elements in

a right argument which

you enter

is

6, the

of

the

shape

pA,

the

function

re-

~5

6

"7

B

3

2

1

~.)

Lt·

t)

"7

B

pR

'i

3 4

.:..

I n

some

cases,

it

might

be

necessary

nates (or

shape)

indice~)

and a right argument, which

of

Ai-lll

Bf·2

Ci-2

(jA

an

array. The rank

222

3p1

2

I.~~)

1

~3

6

ppA

1

,,,

(

/

2 3

pH

p(jB

2

pC

1+

3

2

ppC

3

to

know

can

is

the name

~5~53

4'+'+

3

~i

'+

,+

:~

3

just the rank, the number

be

found

by

entering pp

of

the array:

6

~)

of

(shape

coordi-

of

the

35

The

following

arrays:

Data

Type

Scalar

table

shows

Shape

No

dimension

what

pX

the

shapes

(indicated

and

ranks are

by

an

empty

for

the

vector).

various

Rank p pX

·0

types

of

Vector

Matrix

N-rank

arrays

Empty Arrays

Although exist.

An

when

creating lists (see Catenation in

defined

Following are

• Assign

function

-------------

0,

'-.

____________

most

arrays

array

with

(see

some

ways

10

to

a variable

EVECTOR-E"

[VECTOR

r:iEVECTOR

Number

number

Each

have

one

no

elements

Chapter

to

name

of

elements.

of

rows

is

or

more

is

6).

generate

to

generate

\.0

and

the

length

elements,

called an

this

chapter)

empty

An by a blank

The is

zero

number

empty

arrays:

an

empty

shape

of

of a coordinate.

arrays

array.

or

when

empty

vector:

array

display.

of

the

(zero

elements).

columns.

with

no Empty branching

is

indicated

empty

2

N

elements

arrays are useful

vector

also

in a user-

36

• Use a zero length

EMATRIX:l.~<3

EMATJ~IX:1.

~)EMAT

:3

0

• A

function

shape

of

a scalar:

might

coordinate

J~

I X

1.

generate

A

when

an

empty

blank

generating a

O~)

\

0-

vector

output

multidimensional

This and

A

blank

as its result;

display.

matrix

no

(0)

output

has

three

columns.

display

for

example,

array:

rows

finding

the

CATENATION

(~:

You can join function. The symbol or scalars and vectors,

fied,

as

together

the

following examples show:

A~~

1.

:~

5 6

Bi"'+

A,B

:l

:3

2

'+

1::'

\.1

B,A

q.

~:;

6

1.

2

:.:~

(4,2

:1.

2 3

3

1-

When catenating A,[I]B, where I defines

If

the

coordinate matrices and [I] is

[2],

the

show

how

'+

3/A

'1

r:M

3

last

coordinate

to

catenate

2

1+

two

is

not

[1],

two

arrays

to

make a single array by using

for

this

function

the

variables are joined

I.~

:3

is

6

q.

matrices

the

matrices:

or

N-rank arrays,

the

coordinate

specified,

first coordinate (number

(number

that

the

last coordinate

of

columns)

the

catenation

the

comma. When catenating vectors,

in

the

order

the

will be

is

function

expanded

is

used. When A

of

rows)

expanded.

in which

they

can

take

the

when A and

and

is

expanded; when [I]

The

following examples

are speci-

form

B are joined.

Bare

c~

(".,

-

./

("

1.0

20

~!50

'+0

~~

10

~7j

4·0

10

20

I.~O

~5

"")

I!.

1.1-

1::-1::'

..

J ,.J

1+'+

Ai"2

B~"2

A,B

30

60

A/[2:JB

()

30

0

60

A/[lJB

30

()

60

")

A-_

:3~1

66

:3~):1.

0

20

3(-1l.:1.

1:1.

'+'+

:1.1

'+'+

,')

Lot!.

55

22

55

")

22

33

66

33

66

,

:3

()

:3:3

4·0

1.1.

Graphic

A B

!!.!j

0

<~)

0

"':'I:!'

1

+

,.J ,.J

66

-

A

B

10

40

10 40

20 50

A

20 50

10

40

11

44

30 60

20 50

22

55

Representation

11

44

B

11

22

44

55

30 60

33 66

22 55

33 66

(~

37

A~-2

B~··2

(.1

:1.

0

20

1.1-0

~.:;O

LENGTH

~5(.)tO

'+.otl.

~

[2:JB

30

1.

:I.

1::·1::·

(~)

()

d,J

A,[lJB

ERr~DR

A~

[:I.J

Matrices ordinates not specified are ordinates not specified are following):

::.::~.~

l)(~)

20

30

:·5~3

~~2

:·5~~

77

of

unequal sizes can be catenated, providing ,that

1.,·0

~:;

0

,::.,:.-

,.J

,J

4·'+

'+'+

•

BB

B

60

61.)

the

same (see

not

the

77

the

first example following).

same, an error results (see

10

88

40

A

10

40

A

B

the

lengths

the

second example

20 50

10

40

11 55

30 60

of

20 50

22 66

If

the

co-

11 55

30 60

33 77

co-

11 55

22 66

44 88

22 66

33 77

44 88

B

44 88

A scalar can also be catenated catenated

to

a matrix. Notice

A~2

3pl0

A

10

20

30

'+0

~50

60

A,[2J99

1.0

20

30

99

l~O

50

60

99

A,[:LJ99

10

20

30

'+

0

~7j

()

6

()

9("/

99 99

A vector can also be catenated

matches

10

1.1·0

the

length

(.1,99

20

~50

of

the

88

::~()

99

ld)

8B

coordinate

•

to

that

20

to

an array.

the

scalar

30

~O

another

not

In

the

following example, a scalar

is

repeated

50

60

array, provided

specified. See

,

10

40

to

complete

the

following examples:

20

30

50

60

the

length of the vector

99

88

is

coordinate:

38

A/t:l]99

LENGTH E R

A/[l]

A

I~O

R

99

88

(

The

catenate function

necessary create a matrix named PHONE where each row will represent a 7-digit telephone number. First

at

PHONE with no (0) rows and seven colum-ns:

to

use an

you

a later time. The following instruction will establish

is

useful when creating lists

empty

array

to

start

want

to

establish

the

of

information. Sometimes it

a list. For example, suppose

matrix, then add

an

the

telephone

empty

array named

you

numbers

want

is

to

_---I:->H-O-N-E-:

o

'7

Now,

the

5336686

~:;:3366B6

45e)I+7'7l

2

\_7

INDEXING

PHDNE~"O

pPHONE

telephone

PHONE~PHONEIC1]'5336686'

7(.>·~

0

_______

numbers can be added as follows:

Blank display indicates an empty

PHONE

PHONE~PHONE/C1]'4564771'

PI··IONE

pPHONE

___________

The list of

now

contains

array.

telephone

two

numbers

rows.

c

You may

Referring

integers;

to

14 15 16 17. The result A [2] the

Here are some more examples

not to

d,nly certain elements

they

which

they

is

12 (assuming

index origin).

want

to

refer

are enclosed

apply. Assume

of

the

index origin

A~11

12 13

to

in

entering A

A[3]

A[~:;

:3 7 1]

15

13 17

11

Bi":~

~I.

'+

ACB]

13

1:1.

:1.4

16

B~'ABCDEFGHIJKLMNOPQRSTUVWXYZ

8[4

1

1~

DAN

AND

CI...A

I

I~

C~22

9

18

BEG]

VIRGINIA

the

whole array

is

called indexing. Index numbers must be

brackets and written after

that A is

is

of

indexing:

l4

15

6 Blank Character

but

just

to

certain elements.

the

name

of

the

variable

assigned a vector as follows: A+-11 12 13

the

whole vector, and

1; see Chapter 5

16

17

the

result

for

more information

of

1

·

27 1 14 4 27 3 12

7 9

14

9 1

1 9

18J

entering

on

39

If

you

use an index

instruction

cannot

that

be

executed

refers

to

A

11

12

13

1~

15

16

A[8]

INDEX

ERROR

ACBJ

A

You

cannot specified. For example, suppose then

error, since those elements

VALUE

an

index or

attempt

do

to

store

Z[3

I.J·]~":I.B

ErJ.rJ.D'~

Z

I::

3

I~.

::I

/'0.

anything else with an array until

values

do

not

~..

:1.

B

an

element

and

INDEX ERROR results:

that

does

not

exist in

17

after

the

that

no value has been assigned

in

certain elements within Z would result

exist:

'+6

I.).

b

to

the

array,

the

array has been

the

name Z;

in

an

/ '}

"

....

,

13

3 7 3

l..OOI(

Indices (whatever

those

expressions are finally evaluated,

indices for

the

is

array:

inside

the

brackets) can be expressions, provided

the

results are values

B

ABCDEFGH

I

,..II{

X~-1

2 3

I...MNO

P(~

4·

RSTUVWXYZ

~:=;

B[Xx2]

BDFH,J

X

1 2 3 ~ 5

B[1+Xx:~J

The

array from which elements are selected

example, a vector can be indexed as follows:

2 3 5 7 9 11

13 15

17

does

19[7

'ABCDEFGHIJKLMNOPQRSTUVWXYZ

PA

not

have

2 ~ 2]

'[12

that

represent valid

to

be a variable.

15

that

11

when

For

27

16

1]

,40

nDN r'i(.:,R\'

•

{i

BCD E F 0 H I

-~------

,"/1<

I...

r"'1

______

N

[I

P

(-).

F-~

STU \/

t·

.

.!

X '{

:?:

'I::

:::.:~

1+

(,1+

1

~.:.:.i

ll.j·

"':,":.1

......

I

:I.

:::~;

:I.

J D

::?

~.:.:.i

J

~~

~

The

shape

of

the

result

is

the

same as

the

index.

(

Indexing a matrix The index numbers for each coordinate are separated by semicolons. Suppose M a 3 by 4 matrix of consecutive integers:

M~3

or

N~rank

array requires an index number

4p1

2 3 4 5 6 7 8 9 10 11

f<;>r

each coordinate.

12

is

(

If you ask

1.

~5

9

1.0

If

you

want

If

you

want

..,

8

Similarly,

to

M

r)

~

6

to

see

the

~z

..

)

..,

(

11

to

refer

M[2;3J

to

refer

values

I.f.

8

r)

1

~

to

the

to

the third and

to

the

elements

of

M,

they

element

are displayed

in

row

2,

column 3,

fourth

elements

in

column 4, rows

in

the

usual matrix form:

you

would enter:

in

that

row,

1,2,

and 1,

you

would enter:

you

would enter:

("/

c

I.f.

8

L\.

You can use

matrix

of

those

enter:

MI:2

~)

6

9

1.0

If

you

do

not

array

that

you are indexing, APL assumes

For instance,

5 6 7 8

the

same procedure

elements

3;1.

c'

oJ

2

to

select a matrix within a matrix.

in

rows 2 and.3 and columns

1]

9

specify the index number for one or more of

that

you

want

to

get all of row 2,

you

would enter:

MC2j]

1,2,

and 1 of

the

coordinates

the

entire coordinate(s).

If

M,

you

want

would

of

the

41

Or

to

l.J.

B

:1.2

get all

M[

:I.

5

9

of

columns

i

'0I-

4 and 1,

l.

]

you

would

enter:

Note: You still have

The

number

of

semicolons required

of

semicolons

Mt<5

pM

3

L~

Mr.6Jf·9

R(~NK

You can change elements. (The rest

:I.

1+

....

t'

l

I.,.

7

")

4-

I::'

d

B

••

:1.0

ERROR

M[6]t-9

elements

A~3

A

3

b

'1

(:l[

2 i

f~

'i

::5

.'"0.

:~~

0

':~

B

to

enter

the

semicolon

is

not

specified, RANK

LI·p\:L2

within

an

array

of

the

array remains unchanged.)

3p1

2 3 4 5 6 7 8 9

::.~

:3]~-lO

20

to

make clear which

the

rank

of

the

ERROR

by

assigning new values

coordinate

array minus one.

results:

for

If

the

is

which.

the

correct

indexed

42

APL

functions language. User-defined functions are discussed called primitive functions, are supply

to

them.

are

of

two

types: user-defined and

denoted

by a symbol and

Chapter 4. Primitive (Built-In) Functions

those

that

are built

in

Chapter 6. Built-in functions,

operate

on

the

into

data

the

you

APL

(

The value two are said be single multiple tables defined

There are There functions are set

or

values

arguments, such

to

be monadic, such

data

items (scalars), strings

of

data

functions

two

are also

and

up

as

that

types operators

operators

they

would appear

you

supply are called arguments. Primitive functions

as

A";-

B,

are said

as";-

B,

(N-rank arrays). Arguments can also be expressions

result

in

a scalar, vector, matrix,

of

primitive functions: scalar functions and mixed functions.

that

operate

are provided

on

PRIMITIVE SCALAR FUNCTIONS

Scalar functions arrays

element

pend

on

the

lation

between

following table. Each scalar

Argument A

operate

by element.

shape and rank

tile

types

on

of

scalar arguments and arrays.

The

shape and rank (see

of

the

arguments.

arguments

function

Argument B

to

be dyadic;

which yields

of

data

(vectors), tables

on

the

primitive functions. Examples

throughout

the

display.

For

and

the

shape

is

described following

functions

the

reciprocal

this

chapter

Chapter

dyadic

of

that

use

of

B.

Arguments can

of

data

(matrices),

or

N-rank array.

for easy reference and

They

are

extended

3)

of

the

scalar functions,

the

result

is

shown

the

table:

Result

that

one

argument

or

of

to

result de-

the in

the

use

or

user-

the

re-

(~

('"

Scalar Scalar Scalar

Array Array with

shape as A shape

Scalar

or

one-

element

Array any

One-element One-element array array with

array shape same shape as

of

shape element array shape

Array

Scalar

different rank

the

same Array with

of

any

or

one-

the

rank with

from

the

of

A

arguments

Array with

argument B

Array with

One-element array

the

array with

greater rank

as

the

as

argument

the

shape

the

same

A

of

the

43

The + Function: Conjugate. Plus

[]

/

Monadic (One-Argument) Form:

The

conjugate

numeric scalar, vector,

of

the

argument:

c·

.J

If B

is

an

the

result

array,

is

the

B~2

function

A~"

'H~:;

+(.~

the

function

shape

3p-3

does

or

of

B:

B

H'~3

'''2 '-l.

(}

1-

2

+B

-2

'-1

Conjugate

not

other

array, and

is

extended

-2

change

-1

+8

the

argument.

the

shape

to

each

0 1 2

of

the

The

argument

the

result

elements

is

of

can be a

the

B.

same

The

as

that

shape

of

Dyadic (Two-Argument) Form:

The

plus

function

results in numeric scalars, vectors, one

of

the

same shape,

arguments

the

is

result has

3+~3

6

5.73

:1. :1.

Plus

the

or

other

a scalar

the

'W

:1.

A+B

sum

of

the

two

arguments. The arguments can be

arrays. Arguments must be

or

single-element array.

same shape as

N'

~3

+~.l.

the

arguments:

2

()

'+

the

If

the

arguments have

same shape, unless

the

44

(~

If

one as of

that

the

:l.

LI·

argument

of

multielement

...

)

......

5

the

Bf·2

B

~3

6

is

other

a scalar

input

array:

:.3

(.>:1.

or

single-element array, the shape

argument.

'")

,:..

The

.7.

I::·

,.I

,.)

4·

6

3+B

6

4-

~5

9

7 B

B+3

!5

6

'4·

·"1

(

9

8

The - Function: Negation, Minus Q

single element

is

applied

of

the

result

to

every

is

the

element

same

Monadic (One-Argument) Form: Negation

The

negation

numeric scalar, vector,

the

argument:

function

A~-·:J.

changes

or

·":3

other

the

sign

array.

A

···3

·":1.

····I~

If

the

argument

is

B~2

an array,

3p-3

the

-2

function

-:I. 0

B

-3

···2

-1

o

:J.

2

..

MB

:3

2

-1

:I.

-2

()

-8

of

The

is

the

argument.

shape

extended

:I.

2

of

the

to

The

result

each

argument

is

the

element

same

of

can be a

as

that

the

array:

of

45

Dyadic (Two-Argument) Form: Minus

A-B

The

minus function subtracts argument B from argument

numeric scalars, vectors,

one

of

the

less are

the

arguments

same shape, the result has

~:~""2

or

is

other

arrays.

a scalar

the

The

arguments must be

or

any single-element array. If

same shape as

:I.

1+····~5

'+'-

'''~:5

9

2 0

If

one same as element

argument

that

of

is

a scalar

of

the

the multielement array:

B~2

or

other

input argument.

3p1

2 3

a single-element array,

~

5 6

The

single element

B

:l

2

~5

1+

5 l)

:~"MB

2

:I.

0

"'1 '-2 "'3

B-'3

'-2

-':1.

0

1.

:?

:3

the

arguments:

-1+

the

shape

A.

The arguments can be

the

same shape un-

the

arguments

of

the

result

is

applied

to

every

/ "

I~.

)1

is

the

46

The x Function: Signum, Times (IJ

Monadic (One-Argument) Form: Signum

The

signum function indicates

- 1

is

the

result;

if

the

argument

tive, 1

is

the

result. The argument can be a numeric scalar, vector,

The

shape of

the

result

is

the

same

the

is

xB

sign

zero,

as

that

of

"':l 0 1

the

argument:

then 0 is

of

the

if

the

result; if

argument:

the

argument

the

is

argument

or

other

negative,

is

posi-

array.

If

the argument

is

an

array, the function

is

extended

to

each of the elements:

(

B~2

-~~

1 2

-1

3p-2

B

0

~5

-1

xB

"'1

-1

0

1

:I. :I.

Dyadic (Two-Argument) Form: Times

The times function result arguments can the same shape, unless one of the arguments Arguments of the same shape

be

numeric scalars, vectors, or other arrays. The arguments must

is

the product of argument A times argument

have

2x2.1

4·

. 2

2

1+

6.1

12.2

"'16

0 1 2 3

AxB

is

a scalar or any single-element array.

the same shape result:

-1+

B.

The

be

If

one argument

as

same element of the multielement array:

that of the other input argument. The

is

a scalar or a single-element array, the shape of the result

B~2

3p1

2 3 ~ 5 6

B

:I.

2 3

'+

5 6

3xB

369

:1.2 :1.5

18

single

element

is

applied

to

is

the

every

47

The"," Function: Reciprocal, Divide

CD

Monadic (One-Argument) Form: Reciprocal

The

reciprocal

a

numeric

the

argument:

O

If

the

I::'

....

,

argument

function

scalar, vector,

is

B~-2 2 ~)2 . ~5

result

or

an array,

is

other

the

reciprocal

array.

function

B

2 0 . 2 0 .

'~'H

o .

~:5

o .

!:j

~:;

~,:;

-;'-8

The

shape

is

extended

of

the

argument.

of

the

to

result

each

of

The

is

the

elements:

argument

same as

can be

that

of

Dyadic (Two-Argument) Form: Divide

The

divide

function

The

arguments can be numeric scalars, vectors,

be

the

same

shape unless

Arguments of

,.,

,:.,

:I.

•

~5

If

one

argument same as element

that

of

B~2

of

the

result

is

the

one

of

the

same shape have

is

a scalar

the

l)1ultielement array:

2p1

other

or

a single-element array,

input

10 20

argument.

B

:I.

10

20

lOO

~5+B

~3

o .

:J.~;

0.3

()

.

():~

A-;'-B

quotient

the

when

arguments

the

same shape result:

:1.00

argument.A or is

The

single

other

a scalar

the

element

is

divided by

arrays.

shape

The

arguments

or

a single-element array.

of

the

result

is

applied

to

argument

must

is

the

every

B,

\~,

48

(~

(

Note:

There

are

two

additional

When

zero

is

1.

2.

:1.

Any

()

value

..

:.

0

other

divided

than

by

zero

zero,

3+0

DOMAIN

ERROR

:'5'~"

0

,

....

The rFunction: Ceiling, Maximum

rules

that

the

cannot

OJ

apply

result

is

be divided

to

1 :

the

by

divide

zero:

function:

I

('

Monadic (One-Argument)

The

ceiling

function

is

rounded the array.

same

The

up),

as

shape

unless

the

argument.

of

'+

If

the

argument

:1.

2

2 2

B~2

B

1

is

an array,

Form:

result

the

2pl

the

result

1.3

is

argument

The

Ceiling r B

the

argument

is

the

same

the

function

1.5

1.

•

:'5

integer larger

is

an

integer. In

can

be a numeric

as

that

of

is

extended

2

than

the

argument:

to

each

the

argument

this

scalar, vector,

of

case,

the

elements:

(the

the

argument

result

or

other

is

Note:

The

result

Chapter 5 for

of

the

ceiling

information

on

function

the

OCT

depends

system

on

the

variable).

OCTsystem

variable (see

49

Dyadic (Two-Argument) Form: Maximum

The

maximum

numeric scalars, vectors,

one

less

same shape have

of

function

the

arguments

result

or

other

is

a scalar

the

same shape result:

is

the

arrays.

3

-·I.)r···:1.0

'''6

'-:1.

'-3 r

~:.=;

a single-element array,

~5

'+

If

one

argument same as of

that

the

multielement array:

:L

:3

2

r.:'

1+

,J

I.>

"7.

.J

::3

3

I::'

,J

6

'+

~j

•

:1.

is

of

the

Bi··2

B

~5r

B

a scalar

other

3p:1.

or

argument.

2

ArB

larger

of

the

The

arguments

or

any

single-element array.

• j.

The

I::'

,J

single

6

o

element

arguments.

must

"'4-

the

shape is

applied

The

arguments can be

be

the

same shape un-

Arguments

of

the

result

to

every

of

the

is

the

element

50

(

The L Function: Floor,

Monadic (One-Argument) Form:

The

floor

function

is

rounded

is

the

array.

down) unless

same as

The

shape

the

Minimum

result

argument.

of

the

result

3 "'3

LI.I·

If

the

argument

is

B~2

B

an array,

2pl

1-

1.6

LB

1 1

:1.

2

Floor

is

the

argument

The

is

the

function

1.5 1.6

:I

2

LB

integer smaller

is

already an integer.

argument

same as

is

2

.•

~5

than

the

argument In

this case,

can be a numeric scalar, vector,

that

of

the

argument:

extended

to

each

of

the

elements:

(the argument

the

result

or

other

c

Note: The result

Chapter 5 for information

Dyadic (Two-Argument) Form:

The

minimum

numeric scalars, vectors, less

one

of

the

same shape have

of

the

function

a~guments

the

same shape result:

1+1

..

6

1+

2

'-fo)

I..

"'10

"'1.0

5 . 1

-1,

5

.1

"'4·

floor

on

Minimum

result

or

other

is

a scalar

-:I.

function

the

is

the

'-:31

depends on

OCT system variable).

ALB

smaller

arrays.

or

..

5.1

of

The

any single-element array. Arguments

the

arguments.

arguments

OCT system variable (see

The

arguments can be

must

be

the

same shape un-

of

the

c

51

If

one same as of

the

t

1+

:t.

:05

argument

that

multielement

000)

,.

...

0

1::

,J

2

:3

is

of

the

Bioo::o~

B

ooz

'0)

I:>

:sl..

B

-1,

'\.0)

:3

a scalar

other

array:

3(.):1.

or

a single-element array,

argument.

2

:05

1+

The

1::.

'oJ

single

(:)

the

element

shape

is

applied

of

the

to

result

every

is

the

element

"~,

))1.

The I Function: Magnitude, Residue

Monadic (One-Argument) Form: Magnitude I B

The

magnitude

can

be

a numeric scalar, vector,

that

of

as

the

argument:

function

result

is

or

CD

the

absolute value

other

array~

100('.9

7.9

100.3

3

If

the

argument

B~2

is

an

2p-S.t

array,

the

-t

function

0

3.t4-

is

B

0.0~5

• 1

o

IB

~o:j

•

:I.

00.:1.

:.:~

. 1

'+

o

The

extended

of

the

shape

to

each

argument. of

the

result

of

the

The

argument

is

the

elements:

same

52

Dyadic (Two-Argument) Form: Residue A I B

The

residue

the

remainder when

apply

1.

function

when using

If

argument A is

result (when

argument B is

the

residue

equal

both

divided

function:

to

zero,

argument

then

016

6

by

argument

the

result

A and

is

argument

A.

The

equal

B are positive)

following rules

to

argument

is

B:

(

2.

If

argument A

argument A and zero (the result can be equal

argument A).

a.

When argument B from argument B until a value between argument A and zero

is

The

not

result

equal

to

zero,

is

obtained as follows:

is

positive,

:315

2

then

the

absolute value

result

to

'zero,

is

a value between

but

not

equal

of

argument A is

to

subtracted

is

reached:

(~

c

b. When argument B

argument B until a value between argument A

is

negative.

1

The

arguments can be numeric scalar, vectors,

be

the

same shape, unless

array. Arguments

one

of

the

same shape have

of

the

:317

:I.

:":~

1 6

0

61

:3

3

()

17

7

71

0

-"21

12.

~5

""":I.

.7

"-21

""":1.2.

~3

-0

.

~5

-'12.3

21

1

.7

1

12

.

~:~B~5

.

:3B~)

0

"""~?

•

1

:3B~:=j

•

6:1.~)

0

:1.

the

absolute value

arguments

the

of

argument A is

and

zero

or

other

arrays.

is

a scalar

same shape result:

or

any single-element

is

reached:

The

arguments must

added

to

c

C

If

one

argument

same

as

that

of

the

multielement array:

3

1 2

6

~5

'+

0

:I.

2

()

:1.

2

of

the

B'""2

B

31B

is

a scalar

other

:3(.>:1.

or

a single-element array, the shape

argument. The single element

'")

:'5

-:-

'+

/.)

~:)

is

applied

of

the

to

result

is

the

every element

53

The * Function: Exponential, Power

Monadic (One-Argument) Form: Exponential

The

exponential function result

to

the

power indicated by

vector, or other array.

The

is

the

Naperian base e (2.718281828459045) raised

the

argument. The argument can be a numeric scalar,

shape

of

the

*:1.

2.71.B:3

')f3

20.0B6

If

the

argument

is

an array,

Bi··~?

2pO

the

1.

function

2

:~

13

()

1

2 3

*B

~?.

1.

7.389:1.

Dyadic (Two-Argument) Form: Power A * 8

The power function result

B.

The

argument arguments must be

single-element array. Arguments

arguments can be numeric scalars, vectors,

is

the

same shape unless one

7:1.8~5

20

. 08l)

argument A raised

of

the

*8

result

is

the

same

is

extended

same shape have

to

of

to

the

power indicated by

the

arguments

as

that

of

each element

or

other is

a scalar,or any

the

same shape result:

the argument:

of

the

array:

arrays. The

0.25

1

3

o .

:I.~?'5

The

root

the

reciprocal

by

:I.

2

2~'3

...

-------2*-3

of a number can be found by raising

of

the

root. For example,

:1.

'+'

<j

:I.

6·)f··:··2

~5

'+

= 1/23 = 1/8 = .125

to

the

find

number

the

square root:

to

the

power indicated

54

(

("

The

If

one

argument

same

as

that

of

the

multielement array:

:L

2

~5

1+

of

the

B~"2

1-3

1.

is

a scalar

other

2(.>:1.

or

a single-element array, the shape

argument. The single element

2 3

4·

9

...

Function: Natural Log, Logarithm

The

~symbol

is

formed by overstriking

CD

the

0 symbol

of

is

applied

CD

and

the

* symbol.

the

result

to

every element

is

the

c

(""

Monadic (One-Argument) Form: Natural Log

The natural log function result

(2.718281828459045).

or

other

array. The shape

m2.7:1.B3

1.

m~.?O

. OBb

is

an array,

2(.>:1. 3 :1.0

If

..

.,

,:)

the

argument

Bfo2

is

the

log

The

argument can be a non-negative numeric scalar, vector,

of

the

result

the

function

20

B

:I.

3

to

20

wB

o

2.3026 2.9957

1.0986

~B

of

is

the

is

extended

the

argument B

same

as

that

to

of

each

to

the

argument:

element

Naperian base e

of

the

array:

Dyadic (Two-Argument) Form: Logarithm

The logarithm function result The

arguments can be numeric scalars, vectors,

be

the

same shape, unless

of

the

Arguments

same shape have

one

is

of

the

2m8

2 3

'+(+)8 9 :1.6

322

Ae

B

log

of

argument B

or

other

arguments

same shape result:

is

a scalar

to

the

base

of

argument A.

arrays.

The

arguments

or

any single-element array.

must

55

one

If same as of

the

1 2

:3

argument

that

multielement

is

of

the

B~··2

B

1+

a scalar

other

array:

2p1

or

a single-element array,

argument.

2

:3

ll·

The

single

the

element

shape

is

applied

of

the

to

result

every

is

the

element

o

0,1+771.2

The 0 Function:

Monadic (One-Argument) Form:

Thepi

times

argument the

same

3,

:1.

(7

,4·24·8

If

the

argument

1.

2

3

1+

Pi

function

can be a

as

that

of

01

1

+16

o:~

is

B~··2

B

(:)B

:~,

11+16

9,1+24·8

Times, Circular

result

numeric

the

argument:

an array,

2~):t

(),:5010~3

0,60206

CD

Pi

Times 0 B

is

the

value

of

scalar, vector,

the

function

2

:3

ll·

6,28:52

1.

2 ,

or

is

:::;66

pi

(3.141592653589793)

other

array.

The

extended

to

each

shape

element

times

of

the

of

the

B.

The

result

array:

is

56

Dyadic (Two-Argument) Form: Circular

The

circular

(argument

numeric

one

less

same shape result.

a positive

will result

function

A)

for

the

scalars, vectors,

is

a scalar

functions

in

or

The

performed.

argument

DOMAIN

result

is

the

specified radians

or

other

single-element array.

following

A negative

A;

any

values

ERROR:

Ao

B

value

of

(argument

arrays.

is

Arguments

a list

of

argument A is

for

argument A other

the

specified

B).

Arguments

the

values

trigonometric

The

arguments

must

be

the

of

the

same shape have

for

the A argument

the

mathematical than

function

can be

same shape, un-

and

inverse

the

following

the

Value

of

A

Operation Performed

(

('

008

loB

208

308

408

508

608

708

Cosine 8

Hyperbolic sine

Hyperbolic cosine of 8 (cosh 8)

Hyperbolic tangent of 8 (tanh 8)

Arcsin 8

Arccos 8

Arctan 8

of

B (sinh 8)

(~

(:

Arccosh 8

Arctanh 8

If

lent

0

8

is

45

here

is

how

to

,

to

pi

radians divided by 4):

B~"o":"1+

B

o I

7B~54·

o .

707:1.1.~.------_Sine

O.70711

1.

~.-----------Tangent

/,-------the

:loB

20B

..

·------Cosineof8

:~()B

solve for the' sine, cosine, and tangent of 8 (450 is

The

left argument specifies

trigonometric function.

of 8

equiva-

of 8

c'

57

If B is

the sine of an angle, then OoB yields the cosine of the same angle, and con-

if B is

versely,

0

,

30

which

o .

•

O

If

one argument

as

same

the cosine, OoB yields the sine. Suppose you wanted the sine of

is

equivalent

H'"':l

B

~3

~.-----------Sine

Oe)B

B660:3~>4---------Cosine

B~-20

B

BI.>603~.---------Cosine

Oc)B

t!!-~.

___________

\J~

is

that

of

the

to

pi

divided by 6:

()

(c)-~-6)

0

of

30

0

of

30

«)":--I.>

)

0

of

30

Sine of

30

0

a scalar or a single-element array, the shape of the result

other argument. The single element

is

applied

to

of the multielement array:

A'""2

2(.>:1. 2 :-5

Bt-t")--;·1+

4·

A

is

the

every element

()

.

7B~5'+

0.7071:1.

t

AoB

()

.7071

:1..2716

:1.

58

(~

The!

Function: Factorial, Binomial Q 0

The!

symbol

Monadic (One-Argument) Form: Factorial !B

The

factorial

the

number

vector,

or

is

function

value

other

formed

of

the

array.

by overstriking

result

is

the

argument.

The

shape

of

the

product

The

the

p+

24-

:l.X2x3X4-

24-

,')

.:..

l.

6

The

factorial

integers are

of

the

7.173~5

not

mathematical gamma

!1

2

function

! 3 . 1

:~

2

4-

1

.1.

120

also works with decimal numbers

allowed. When used

~'5

function

in

this way, factorial can be defined by use

- (!A)

'+

!O

1.

quotation

of

all

argument

result

is

equal

mark ( , ) and

the

positive integers from

can

be

a positive numeric scalar,

the

same as

to

that

and

zero,

gamma (A-1):

the

of

but

the

period (.).

one

argument:

negative

to

c

If

the

argument

()

I'Jr

.:..

1.

3

,')

:I.

..

'-

B

!B

...

is

2

an array,

2pO

the

1

function

")

.....

:~

:1.

6

is

extended

to

each

of

the

elements:

59

Dyadic (Two-Argument) Form: Binomial

The

binomial

that

can be

the

binomial expansion vectors, arguments

have

the

function

taken A at

or

other is

a scalar or any single-element array. Arguments of

same shape result:

2

arrays.

!l+

result

a time.

of

the

The

is

the

The

th

8

argument

f.)

2!6

1 1::'

.,J

~5

!

()

0

()

!

:3

1

2!3

3

If

one argument same as of

that

the

multielement array:

of

is

the

a scalar

other

or

a single-element array,

argument.

A!B

number

result

power.

must

w

The

of

different

of

A! 8 is

The

arguments can be numeric scalars,

be

the

x

>-

..

....------

single

element

combinations

also

the

(A+l)

th

same shape, unless

the

y

Z !

........

J-----Argument

The combinations argument 8 argument A(2)

the

shape of

is

applied

the

to

of

argumenf

coefficient

one

of

same shape

taken

result

is

the

every

element

B

of

the

B

of

at a time

'')

~5 ! ~5

:L

':N

0

1

~5

3

1

")

1

'+

0

1+

I.>

B~"2

:I, :I,

I+!

3

.:-

2~)0

1 2 3

1+

B

o 1

2 3

:I.

I.)

4,

I

~5

to

10

1+

7Qx(P-l)!

10

2 !

"',+

~5

10

7,87~:j

If noninteger arguments are used, this

follows: Beta (P,Q)

is

equal

function

P+Q-l

relates

to

the

beta

function

as

60

(

The?

Function: Roll

Monadic (One-Argument) Form: Roll ?8

The

roll

function

through

chance

other

8 (depending

of

being selected.

array.

The

('71

I~

result

on

shape

is a randomly

the

index origin). Each integer in

The

argument

of

the

result

7300

202

?:30

()

3

?~5

7 9

2

:I.

4·

'?6

6

1.1·

!5

6

76

6

If

the

argument

is

an

array,

the

function

selected integer

can be a positive integral scalar, vector,

is

the

same as

is

extended

from 0 through

the

that

of

the

to

each

element

range has an equal

argument:

of

8-1

the

or

1

array:

or

(~

('

B~2

B

1.:1.

2~?

33

",.1+

!7.i

!:5

6

t')

?B

2

:l7

:1.6

21+

:I.~~

,+

Dyadic (Two-Argument)

See

the

Deal

function

3pl1

Form

later

22

in

this

33

chapter

~4

under

55

66

Primitive Mixed Functions.

c

61

The A Function: And

Monadic (One-Argument) Form

is

There

Dyadic (Two-Argument) Form: And A/\ B

The value or

is

shape result:

no monadic form.

and function result

of

the

arguments must be either 0

other

arrays.

a scalar

or

any

CD

is

1 when A and B are

The

arguments must be

single-element array. Arguments

both

1; otherwise,

or

1.

The

arguments can be scalars, vectors,

the

same shape unless one

of

the

result

of

the

same shape have

is

O.

The

arguments

the

same

0

:1.

0

()

0

If

one

argument same as of

that

the

multielement array:

0

:1.

:I.

0

:J.

:1.

0

01\

:1.1\:1.

1AO

0

:I.

of

the

Bf·2

B

j.AB

:1.

0

is

a scalar

other

2pO

Operator

:tAO

:1.

1.

0

:I.

or

a single-element array,

argument. The single element

1-

1 0

the

And Table

'---

shape

of

is

applied

o

Argument B

the

result

to

every element

- Argument A

is

the

The v Function: Or

GJ

(:

Monadic (One-Argument) Form

There

is

no monadic form.

Dyadic (Two-Argument) Form: Or A v B

The

or

function result

result

is

O.

The values scalars, vectors, one

of

the

arguments

same shape have

is

a 1 when either

of

the

or

other

arrays.

is

a scalar

the

same shape result:

arguments must be 1 or

The

or

any single-element array. Arguments

1vO OvO

o

0 1

1vO

1 0 1

o 1 1 1

or

both

arguments are 1; otherwise,

O.

arguments must be

Operator

'"

The

arguments can be

the

same shape, unless

Or Table

v

the

of

the

......

I----Argument

A

c

C/

c

one

argument

If

same

as

that

of

the

multielement array:

0 1

()

1

j. j.

:1.

1

is

a scalar

of

the

other

B~··2

2pO

B

lvB

or

a single-element array,

argument. The single element

j.

0 1

the

shape is

applied

of

the

to

result

is

the

every element

63

The'"

Function:

Not

GJ

Monadic (One-Argument) Form:

The

not function result

ment must be 1 of

the

result

is

or

the

O.

The

same

is

as

1

o

If

the

argument

1 0

0

1

()

1

()

1 0

is

B~"2

H

1

NB

1

an array,

3(.>0

Not

'"

B

1 when B

argument can be a scalar, vector,

that

the

is

0 and 0 when B

of

the

argument:

function

is

extended

is

1.

to

each element

1

The

or

values of

other

array.

of

the

The

array:

argu-

shape

Dyadic (Two-Argument) Form

There

is

no dyadic form.

64

"'

..

The

A Function: Nand

OJ

CD

(

c

The A symbol

Monadic (One-Argument) Form

There

is

Dyadic (Two-Argument) Form: Nand

The

nand function result

The values other

arrays. The arguments must be

is

a scalar

shape result:

is

formed by overstriking

no monadic form.

is

0 when

of

the

arguments must 1

or

any single-element array. Arguments of

O~l

1

o

0 1

1XO

:I. 1 :I.

0

:I.

the

AAB

both

A and

or

O.

The arguments can be scalars, vectors,

the

same shape, unless

0 1

and

Bare

(/\)

and

1;

otherwise,

the

same shape have

Nand Table

the

not

one

(,...,)

symbols.

the

result

of

the

arguments

.----Argument

the

is

1.

same

or

A

c

If one argument same

as

that

of

the

multielement array:

B~"2

B

0

:I.

1

0

1XB

:I.

0

1.

is

the

a scalar

2pO

or

a single-element array,

other

argument. The single elemeht

:L

the

shape is

applied

of

the

to

result

is

the

every element

65

The V Function:

The

v symbol

Monadic (One-Argument) Form

There

is

Nor

IT)

is

formed

no monadic form.

OJ

by

overstriking

the

or

(v)

and

the

not(rv)

symbols.

/'

"

Dyadic (Two-Argument) Form:

The

nor

function result

values

of

the

arguments

other

arrays.

is

a scalar

shape result:

The

arguments

or

any single-element array. Arguments

o

O\jO

1

o

()

:1.

:I.

0 0 0

If

one

argument same as of

that

the

multielement array:

of

is

the

a scalar

other

Nor

A

vB

is 1 when must

:l(JO

argument.

A and B are

be 1

or

O.

must

be

the

:1.

0

1.

or

a single-element array,

The

both

0; otherwise,

The

arguments can be scalars, vectors,

same shape, unless

of

the

same shape have

the

shape

single element

is

the

one

of

Nor Table

of

the

applied

to

the

result

arguments

the

~---

result

every

element

is

O.

or

same

the

The

Argument

A

66

0

:I.

:1.

1

0

B~M2

B

OC:B

2?>O

1

The >Function: Greater Than [I)

Monadic (One-Argument) Form

is

no

There

monadic form.

(

Dyadic (Two-Argument) Form: Greater Than

The greater than function result otherwise the result arrays. The arguments must scalar or any single-element array. Arguments of the same shape shape result:

is

O.

is

The arguments can

be

the same shape, unless one of the arguments

A>B

1 when argument A

be

numeric scalars, vectors, or other

o

-'2>

0

o

.-

~.~

;:

....

~~

o

1

o

'-:1.

5,1

o o 1

If

one argument

same

as

tha,t

of the multielement array:

is

a scalar or a single-element array, the shape of the result

of the other argument. The

'-~3>~5,

1

single

o

'''1·1·

element

is

greater than argument

have

the same

is

applied

to

every element

B;

is

a

is

the

('~,

ll,

/

e

2

1+

~3

OCT

system variable).

~5

(.>

B~"2

.f.{

-x

••

c'

..

}

1

0 0

1

6

3>B

0

1 2

I~.

1

0

Note: The result of the > function depends on the

Chapter 5 for information on the

:1.

1'-

,'J

t.)

OCT

system variable

(see

67

The = Function: Equal To

Monadic (One-Argument) Form

There

is

no

monadic form.

Dyadic (Two-Argument) Form: Equal To A=B

[J

The equal to function result

of argument can be scalars, vectors, or other arrays. The arguments must be the same shape, unless one of the arguments of the

same

B;

otherwise, the result

shape

have

is

1 when the value of argument A equals the value

is

O.

The arguments (numeric or character)

is

a scalar or any single-element array. Arguments

the same shape result:

0::::5

()

1,65~321=1,65~321

1

1::::

I A I

o

.'

A

I::::

'B'

o

':1.

':::::1.

o

:I.

o

o 0

If

one argument

same

as

that of the other argument. The single element

of the multielement array.

is

a scalar or a single-element array, the shape of the result

is

applied to every element

is

the

68

'A':'ABACADAEAFAG'

101

Note:

OCT

system variable (see Chapter 5 for information on the

0

101

If

the arguments are numeric, the result of the = function depends on the

0 1 0 1 0

OCT

system variable).

(--

The < Function:

Monadic (One-Argument) Form

is

There

Less

Than

no monadic form.

CD

Dyadic (Two-Argument) Form:

The

less

than

function result

wise

the

result

is

O.

The arguments can be numeric scalars, vectors,

-'+

.

the

'+

The arguments must be any single-element array. Arguments

:L

.65<2

1

:I.

0-::

o

:I

.•

12~5<:I

o

5.1

o 1 0

If

one

argument

same

as

that

of

the

multielement array:

of

is

the

a scalar

other

Less

Than A < B

is

1 when argument A

same shape, unless one

of

the

.•

:1.23

or

a single-element array,

argument. The single element

is

of

same shape have

the

less

than

the

arguments

shape is

applied

argument

the

same shape result:

of

the

to

or

other

is

a scalar

result

every

8;

other-

arrays.

or

is

the

element

('

c

3p:L

f.u"2

B

I")

1

3

-:"

c'

l~

..J 6

~5<B

()

0

:L

1

:L

B<3

:L

l.

0

()

0

Note:

The

result

of

the

< function depends

Chapter 5 for information

~'5

~!

on

the

5 6

'+

OCT system variable).

on

the

OCT system variable (see

69

The

~

Function: Greater Than

or

Equal

To

[~)

Monadic (One-Argument) Form

There

is

no monadic form.

Dyadic (Two-Argument) Form: Greater Than

The

greater

or

equal scalars, vectors, of

the shape have

than

to

argument

arguments

the

same shape result:

1

or equal

B;

or

other

is

a scalar

65;::2

.

to

function result otherwise, arrays.

or

the

The

arguments must be

any single-element array. Arguments

0

"'2;::0

(I

:~~

;::

~~

1

~5

.

1.

:I.

1

If

one

same as of

the

argument

0

is

a scalar

that

of

the

other

multielement array:

or

a single-element array,

argument.

The

or

Equal To

is

1 when argument A

result

is

O.

The

single element

A~

B

is

greater

arguments can be numeric

the

same shape, unless

of

the

shape

of

the

result

is

applied

to

every element

than

same

is

the

l_;,

one

1

1+

:1.

()

Note:

5

for

Bf'2

B

'')

.:.,

3

!7j

6

3~:B

1 1

0

The

result of

information

3

I.f.

1::'

..J

;!.

3pl

the ~ function depends

on

the

OCT system variable).

6

on

the

OCT system variable (see Chapter

70

(

The,;

Monadic (One-Argument) Form

Function:

There

is

Less

no

monadic form.

Than

or

Equal

To

[~

)

Dyadic (Two-Argument) Form:

The less than

to

argument vectors, or other arrays. The arguments must arguments have

the same shape result:

or

equal to function result

B;

otherwise, the result

is

a scalar or any single-element array. Arguments of the same shape

Less

:I. :I. :I.

-::···"

.,.

JIO..

0

o

5.1-

o 0

1

If

one argument

as

same of the multielement array:

that of the other argument. The

is

a scalar or a single-element array, the shape of the result

Than

or

Equal To

is

1 when argument A

is

O.

The arguments can be numeric scalars,

single

A~

B

is

less

be

the same shape, unless one of the

element

is

applied to every element

than or equal

is

the

c

--"'

r.{~~·2

3p:J.

13

1

2 3

I.~

5 6

3~;B

0

1

:I.

1

1.

Note: The result of the

5 for information on the

2

~

function depends on the

OCT

system variable).

~5

I.)

ll·

:3

OCT

system variable

(see

Chapter

71

The F Function:

Monadic (One-Argument) Form

There

is

Not

Equal To

no monadic form.

CD

Dyadic (Two-Argument) Form:

The

not

equal to function result

otherwise, the result vectors, or other arrays. The arguments must be arguments

have

is

a scalar or any single-element array. Arguments

the

same shape result:

Not

Equal

is

O.

The arguments (numeric or character) can be scalars,

Ot-5

1

o

'A't-'A'

()

:I.

"':l

···:3t-~.:;,:I.

argument.

o 1

If

one

argument

same

as

that

of

the

multielement array:

~5

,

:I.

:1.

is

a scalar or a single element array, the shape of

of

the

other

To

A'/=B

1 when argument A

the

same shape unless one of

()

'"4·

The

single element

is

not

is

equal

of

the same shape

the

applied

to

argument

result

is

to

every element

8;

the

72

'A'¢'ABACADAEAFAG'

o

:I. 0 :I. 0 :I.

Note:

If

the arguments are numeric, the result of the

OCT system variable (see Chapter 5 for information on

The

not

equal to function can also be used

in

this manner,

the

Operator~---

0

value of

:I.

0 1 0

the

arguments must be either 0

Exclusive Or Table

:I.

as

an exclusive or function. When used

_Argument

~function

the

depends on the

OCT system variable).

or

1:

A

73

Dyadic

Mixed

Functions

AlB

or

A/[I]

B or

AlB

Name Result

Compress

The elements from B to

the

1's

in

A.

that

correspond

."

..

J

A\B

or

A

\[lJ B or

A~B

AtB

Ai-B

AlB

A¢B

or

A¢[I]

B by

orAsB

A~B

A?B Deal The

Expand

Take The number

Drop

Index

of

Rotate

General ized transpose specified

is

B by A; 1 B;

are

The are dropped from

The first occurrence

in

The elements

are rotated the

The

are randomly selected from selecting

expanded

in

A inserts an

a 0

in

A inserts a 0

taken

from

number

B.

A.

If A is

elements

coordinates

by

number

the

to

the

format

of

elements specified by A B.

of

elements specified

B.

in A of

of

B are rotated as specified

positive,

to

the

left.

of

B are

of

B interchanged as

A.

of

elements specified by A

same

number

specified

element

or

blank element.

the

elements

If A is

rotated

to

B,

twice.

from

by

A

elements

of

negative,

the

right.

without

B

74

A.LB

ATB

AEB

AffiB

AlB

Decode The value (base value)

Encode The representation ( representation)

Membership A 1 for each

Matrix Solution

divide equations with coefficient matrix

Format

the

argument A.

the

argument

found

not

(matrices) B and right-hand sides A the more sets

Argument B converted

array in

argument

of

argument B expressed

number

number system specified by

found.

least squares solution

system specified by

of

A.

element

in

B and a 0 for each

to

one

or

more sets

of

linear equations.

the

format

A.

specified

argument B in

of A that

element

of

to

one

to

a character

by

can be

linear

in

or

"I

Note:

The

mixed functions

(see

Operators

coordinate

index

entry

coordinate

index value row

coordinate

is

not

specified, overstruck with assumed (unless an index value was also used). When a plied

to

ments

in

later

in

of

an array. This

to

which

can be

from 1 to

(first coordinate) has an index value

of

2, and so on. A matrix, for example, has an index value

and an index value

the

last

the

function

a specific coordinate,

the

specified

reverse,

this chapter) reduction and

the

mixed

coordinate

coordinate.

is

done function

the

number

of

symbol

the

operation

rotate,

(columns)

For

compress,

by

using an index

or

operator

of

coordinates

2 for

the

or

operator

takes

example; assume

scan

is

of

1,

column

is

assumed. If a - (minus) symbol

symbol,

place

and

expand,

can be applied

entry

[I] which indicates

applied.

the

coordinate.

function

between

The

in

the

array;

the

first

you

have a 3-rank array:

and

the

operators

to

a specific

value

of

the

leftmost

has an

of

.1

for

the

If an index

coordinate

or

operator

corresponding ele-

is

entry

is

ap-

the

is

(~

('

• When

The p Function:

Monadic (One-Argument) Form:

The coordinate argument

the

first coordinate (planes)

corresponding elements

the

second

the

corresponding elements

the

third

tween

the

shape

function

of

can be any variable

coordinate

corresponding elements

Shape,

the

(J • ABeD ·

Reshape

result

argument, which indicates

1+

"'1

A-

••

(,J

:l

2

pl.

2 3

~3

A~"2

A

3

2

1

c·

l~

6

\J

pA

3

2

in

each plane.

(rows)

in

each row per plane.

(columns)

(Structure)

Shape

p B

is

the

shape

or

constant:

....

1-------

is

specified, the

is

specified,

is

specified,

in

each column

of

the

argument; it has

the

A Vector with

operation

the

per

length

operation

plane.

one

of

that

Four

takes

place

between

takes place between

takes

place be-

element

coordinate.

Elements

for each

The

('

The

shape

function

coordinates. An

p2

p'T'~

applied

empty

to

a scalar yields an

vector

is

indicated

Blank Result Lines

empty

vector, since a scalar has no

by

a blank result line:

75

The instruction p p B yields the rank (shape of the shape, or, number of coordinates)

B:

of

B~2

2 3p'CARBARFARARE'

B

CAR BAR

FAR

AI~E

pH

2

~5

ppB

:1

Dyadic (Two-Argument) Form:

The

reshape

element(s) from argument

array array, the elements are repeated. are required to Argument A must number rank, of the result. Argument B can elements of argument A are nonzero, then B cannot

in

row

of

elements

function forms

order.

fill

the array, only the required number of elements are used. be

Reshape

an

B.

If

there are not enough elements

a nonnegative integer or vector of nonnegative integers. The

in

argument A

(Structure) A p B

array of the shape specified

The elements of argument B are placed into the

If

there are more elements

is

equal to the number of coordinates, or the

be

2

:3

1

2

5 6

4·

2p'ABCDEFGH'

4·

AB

en

EF

GH

5(.)

• MOUSETRAP'

MOUSE

p

3

l+

:l.23

:1.2:3

1.23

123

:1.

23

12~5

:1.

2:'~

:I.

:~3

1,23

:1.23

1~~:3

12~5

A~~

2p1

2 3 ~ 5 6 7 8

A

1 2

3

4-

5 6

'7

B

by

argument A

in

argument B

in

any variable or constant.

be

an

empty array:

using

to

fill

the

argument B than

If

all

of the

76

1.

2 3

I.~

!7i

6

6p·

..

•

(

The,

Function: Ravel, Catenate, Laminate

Monadic (One-Argument) Form: Ravel

The

ravel

function results in a vector containing

argument B

in

row order. Argument B can be a scalar, vector, or

vector contains

1 2

~3

1+

is

an array,

the

A~2

A

the

elements

same number

2

2pl

5 6

'7

8

IA

:1.23'+5678

B~"2

:3

p • ABCDEF ·

B

ABC

DEF

IB

ABCDEF

o

,8

the

elements

in

the

vector are taken from argument B

other

of

elements as argument

2 3 ~ 5 6 7 8

of

argument

array. The resulting

B:

B.

If

(

c

Dyadic (Two-Argument) Form: Catenate

The function when

the

is

catenate when

[I] entry

is

a fraction.

the

or

[I]

Laminate

entry

(index entry)

A,

[I]

8

is

an integer and laminate

77

Catenate (The Index [I]

an existing coordinate. (See to

join

two

items along a new coordinate). The index

coordinate

array. If no index [I]

sizes can be joined, providing

same (see Catenation

is

expanded.

A~:I.

[u··7

AlB

-,

L~

1

9 A+-2

B+-2 A

3

1 2

5 6

'+

B

7

8

10

:L

1.

:1.2

AlB

2

1

L~

5

AI[1JB

1

2

L~

5

7

8 9

1.0

11.

:1.2

A,

,.)

1

.:-

.::'

4

\.I

A}[~.~]10

')

t:_

:1.

I'"

I.f-

,,)

10

:1.

0

20

30

I')

1

1:-

5

'+

Entry

1+

9

5

3p1 3p7

9

~3

10

6

:3

6

[2Jf.t

3

10

6

~5

10

6

20

:3

6

Is

an Integer):

the

The

is

specified,

in

Chapter 3):

~5

I)

t:"

8

7

8

II

..,

8

1:1.

20

30

..

The

catenate function joins

laminate function following

index

entry

must be a positive scalar

the

last coordinate

the

lengths

of

the

coordinate

1::'

t)

,.1

3 4

12

1.0

11.

9

12

9

1

r)

~-

C:I.JA

two

for

a description

[I],

if given, specifies which

or

one-element

is

used. Matrices

not

specified are

items along

of

unequal

the

how

/

,1

"~",

78

Laminate (The Index [I] Entry

creating a new coordinate, specified by

If

tive fraction. the

first coordinate; if

placed between existing coordinates 1 and 2 (the new coordinate

ways has a value (or length)

new coordinate 3 matrices are laminated:

the

in

is

a Fraction):

index

entry

the

index

of

the

shape vector (see

The

the

is

between 0 and 1,

entry

is

between 1 and 2, the new

2).

The

following chart shows

the

laminate function joins

index

entry

following examples) when

two

[I] which must be a posi-

the

new coordinate becomes

coordinate

that

is

the

positions

two

items by

added

of

3 by

is

al-

a

Index Value

.1

- .9

1.1

- 1.9

2.1 - 2.9

Lamination requires either of

the

arguments

:I.

2 3

'+

~.:;

7 B

:I.

1.

'+

77

:1.

LI·

is

a scalar:

A~3

B~3

I~

6,

9~

B

22

:3:~

~::; ~.:;

66

B8 ,99

C~"A}

.,

r

2 3

~5

I.>

3pl 3pl1

I:

I 8:1B

7 B 9

Positions Coordinate Vector

that

arguments A and B are

of

3

3 3

New

in

3 3

2 3 4 5 6 7 8 9

22

33

~~

55

the

Shape

3

the

same shape

66 77

88

99

or

that

one

c c

2

1.1

'4·4

77

3

22

1.':'1::'

\."J

B8

:3

(o)e

•

3:3

66

99

Shape Vector

79

1.

:1.:1.

7

."'''.'"1

( (

2

~3

3

C~··i~

C

2

:~

22

~5~5

B

<.»(.»

BB

(.)C

II

-----------Shape

~5

Cf-A,

...

r-

:I.

1.

,.)

r)

.-:'.A

..

2

··X

,:>

~3:~

I.f.

I+I.~

5~:.i

~5

6

c>6

77

7

BB

8

99

9

pC

,.)

II

k

3

}

I::

:1

..

~::.i:l

B

/

"'

9

Vector

[2.

:I.:lB

Shape Vector

The following examples show the result when the two matrices are catenated instead of laminated:

AI[lJB

1.

2

:5

1+

5

6

"7

8

9

:1.:1.

22

~53

1::'1::.

.J

•.

1

4-

"7

J

B8

A,[2JB

,.)

.:..

1:,"

.. I

8 9

66

99

:3

6

1

:1.

22

.::

.

.::.

I.I·I~

.

•• J ...

J

77

BB

33

66 99

4·4-

77

in

the preceding example

80

The I Function: Compress

CD

(

Monadic (One-Argument)

See Reduction later

Dyadic (Two-Argument) Form: Compress

The

compress function selects

to

1 's in

argument

values 0

must have

• One

•

When the (columns) rank

or

1.

the

of

the

Argument B is A

must

be

argument B is

coordinate

is

assumed. If

of

the

result

")

.....

1

3

Forra

in

this

chapter

elements

A.

Argument A must Argument same

arguments

the

that

:I.

()

B can be any scalar, vector,

number

a multidimensional array; same as

a multidimensional array,

is

the

0

:1.

(}

of

elements unless:

is

a scalar

the

length

acted on. If

the

AJ.B

same as

()

:l./l

2

")

OIl

..:..

the

~:~

:3

or

the

form

under

APL

Operators

A/Ul B or

from

be a logical scalar

single-element array.

of

the

index

is

rank of argument

2

AlB

argument B corresponding in sequence

then

the

argument B

the

[I] index

entry

is

used,

the

first

I.J.

..

or

AfB

or

other

number

coordinate

omitted,

coordinate

B:

/Blank

vector

having

the

array. Both arguments

of

elements

entry

the

in

being

acted

is

used

to

last

coordinate

is

assumed. The

argument

on.

specify

Display Line (empty array)

(".

e

C~'

1

c'

·_1

9

1.

<"i

2 3

6

:1.

0

:l

9 10

2

6

10

:I.

!5

9

")

.:-

(~)

j.O

...

)

..:..

10

"7

11.

t·)

.:-

:5

"7

11

2 3

I.)

10

[H<5

B

:3

"7

11

:I.

0

:5

j.l

0 1

0

1

3

11

0 1 1

liB

'7

:I.

:1.

OIB

I.J.

f>:I.

2

I.J.

B

:1.

:~

:l./[:I.::tB

I.J.

\

j

':>

.....

O/r:2::tB

:1.

\

liB

4·

j

')

......

O/S

4·

8

1

':>

....

:3

I.J.

,::-

,.J

I.>

"7

10

B 9

The the argument

Blank Display Line

:I.

II

first

coordinate

first

and

A, are selected .

second

A, are selected.

::.~

(rows)

third

rows, as specified by

coordinate

and

third

columns, as specified

(empty

is

specified;

(columns)

array)

is

specified;

by

81

The \ Function: Expand

Monadic (One-Argument) Form

CD

~I.

J

See Scan later

Dyadic (Two-Argument) Form: Expand A

The

result of

argument

in

this

the

expand function

A.

Each 1 in

chapter

argument

under

is

A selects an

APL

o in argument A inserts a 0 (or blank

must be a logical scalar scalar, vector, same number a multidimensional array, argument A must have length

When argument B that

is

assumed. If

If

argument B

the

number

array,

the

or

of

the argument B

acted on.

the

is

of

1's

rank

of

1.

")

.:..

3

0

1

B~"2

B

3

1.

2

1:."

1+

.J

6

t

"y

,:)

:L

~~

()

0

5 b

4·

l 1

")

3

0

.:..

1

c:-

I.~

O 6

.J

1

")

1

It:

••

3

{}

0 0

6

4-

5

other

1's as

is

an array,

If

the

A~B

is

a scalar

in

argument

the

result

:1.

0

3~)1

{}

l\[lJB

0

l\.B

0

or

vector having

array.

If

argument B

the

number

coordinate

index

used,

or

1

of

the

[I]

entry

is

then

the

single-element array, it

A.

If argument B

is

the

same

")

I:'.

0\1

I")

.,.

...

4-

3

\

1\[2JB

'\

Operators.

\[1]

B

or A \B

argument B expanded as indicated by

for

character data)

the

values 0

is

elements

being acted on.

index

entry

omitted,

first coordinate

as

the

or

A~B

element

a vector, argument A

the

rank

from argument B and each

in

the

result. Argument A

or

1. Argument B can be any

in

argument

the

is

used

last

is

not of

B.

same

number

to

specify

coordinate

is

assumed.

extended

a scalar

the

B argument.

If argument B

to

or

must

of

1's as

the

coordinate

(columns)

a length equal

single-element

3

5 6

The first coordinate (rows) expanded; a row tween

the

first and second row.

The second coordinate (columns) expanded; a column between

the

second and third columns.

have

the

is

the

is

to

is

inserted be-

is

inserted

is

82

The

4>

Function: Grade Up

The

~symbol

OJ

is

formed by overstriking

OJ

the

11

symbol and

the

I symbol.

Monadic (One-Argument) Form: Grade Up

The

grade up function result

argument B in ascending order. of

the

smallest smallest element in argument When

two

tion

in

the occurrence appears first in same as

"~)

.....

'+

element

or more elements

yector determines

the

number

1

.$3

C'

.J

of

1-

3

4tAt-6

-5

6

2

4-

ib:3

L~

:I.

6

The

following example shows

tor

into ascending order:

At-:l.~

A

11

12

1~

3

1

3

6

r>

5

.:-

[¢.AJ

15

is

in

argument

in

their

the

elements

I!!'

...

1 2

~5

2

:I.

:~

12

16

the

index values

That

B,

and so on. Argument B must be a numeric vector.

the

vector have

order

output).

in

the

I.f.

1+

:I.

::!

~5

how

the

18

:1.8

~B

that

would select

is,

the

first element

B,

the

in

the

result (the index value

The

number

argument:

:~

grade up function can be used

15

1:1.

of

the

is

the

index

same numeric value,

of

elements

the

result

in

the

elements

is

the

of

the

of

the

result

to

sort

of

index

posi-

first

is

the

a vec-

The result because for an example

Note:

ter 5 for

Dyadic (Two-Argument) Form

There

of

the

of

the

The

result

information

is

no

dyadic

grade up function

way equal elements are handled; see

uSing

the

of

the ~ function depends

on

form.

is

not

the

reverse

of

the

grade down function

The

'W

Function: Grade Down

grade up and grade down functions with equal elements.

on

the

010 system variable).

010 system variable (see

Chap~

83

The

'I'

Function:

The

1 symbol

Monadic (One-Argument) Form: Grade Down 1

The

grade down

of

the

numeric vector

of

the

result

the

index

be

a numeric vector. When numeric value, index value of

elements

~)

3

:5

:1.

5

2

in

of

the

1 5

:1.

Grade

is

the

their

the

~:'5

Lf.

\f1Af'6

6 2

~:3

~5

Down

formed

function

of

index

position in

first occurrence appears first

result

is

the

~:)

:I.

11

"M

"

......

4·

:3

6

LI·

6

(]]

by overstriking

result

Js

the argument 8 in of

the

largest

element

two

or

the

same

as

I')

1+

,.-..

1+

:l

5

1::'

,J

2

1-

CIJ

the

index values

descending order.

element

in

argument

more elements

vector determines

the

number

:3

Vsymbol and

that

would

in

argument

8,

and

in

the

their

in

the

output).

of

elements in

the

I symbol.

select

the

elements

That

is,

the

first

8,

the

so on. Argument 8

vector have

order

in

The

the

argument:

the

same

the

result (the

number

element

is

must

of

The

following example shows

vector in descending order:

A~14

f~d::

18

16

15

The following example shows up

and

grade

down

A~M!:;

A

r)

c'

...

1

7 3

A

••

B

12 16

~A:I

1Lf.

12

functions:

")

A.. 8

LI·

:1.0

,A

1+

1 6

3

7

B

6 1

how

the

grade

down

function

18

15

11

how

equal elements are handled when using

:5

7

:I.

1+

:5

2

If

:3-

8

:~

7

10

2

1

Positions 2

and

can be used

9 and 5

to

and

sort

the

10

grade

a

are equal.

84

(

Because first) not

the indices

for

both the grade down

the

reverse

of

the grade up function:

for

the equal elements

A[,A:J

10

8 7 5

1 2 2 3 3 4 5 7 8

~

3 3 2 2 1

A[~AJ

and

are

in the

same

grade

up function, the grade down

10

order

(first

occurrence function

is

(

Note: The result

for

ter 5

Dyadic (Two-Argument)

There

information on the 010 system variable).

is

no dyadic form.

of

the f function depends on the

Form

010

system variable

(see

Chap-

"

c

85

The + Function: Take

Monadic (One-Argument) Form

There

is

no monadic form.

CIJ

Dyadic (Two-Argument) Form: Take

The

take function result

from

argument

must be a scalar

be

a scalar. Argument A must be a vector with an

of

argument

are

taken; A specifies more elements is

padded with

value

of

B.

or

B.

When argument A

when argument A

O's

A:

:~

"':~t:l,

7t:l.

t

23'+5

"'7tt

00

1

:~34,5

B~3

is

the

Argument B can be a scalar, vector,

vector

of

integers.

is

than

(or blanks for character data). The shape

2

2 3

I",

00

2 3

'+

~pl

2 3 ~ 5 6 7 8 9

B

'")

:I.

!:5

5

9

:1,

'1

.:..

6

A"

6

10

3

'7

~5

"1

1.1

2

~5tB

'+

8

:1.2

At

8

number

is

positive,

negative,

the

number

~3

5

of

elements specified

If

argument B

the

last elements are taken.

of

is

element

the

first elements

elements

by

argument

or

other

array. Argument A

a vector, argument A must

for each coordinate

of

argument B

in

argument

of

the

10 11

If

argument

B,

result

12

A, taken

the

result

is

the

86

1-

'.~

7

10

1

7

1

2

5

'+

"1

1.0

1t

2

5

B

1:1,

3

6

8

Bf-2

B

3

6

9

:l2

1

")

.:..

1 2

"'1

9

:1,2

1-

,')

.:..

:L

1tB

3tB

2

3~)

tB

3tB

1.

2 3 4 5 6 7 8 9 10

:1.1

12

The + Function: Drop

Monadic (One-Argument) Form

There

is

no monadic form.

OJ

(~"

Dyadic (Two-Argument) Form:

The

drop function result

of

elements specified

other

array. Argument A must be a scalar if argument B

When argument B

nate

of

argument are dropped from dropped:

by

is

an array, argument A must have

B.

When argument A

the

result; when argument A

3J.l. 2 3

B~3

~p1

B

1+

:5

2

1

1::-

...

9

7

1l.

1

5

1 6

2

6

10

f.)

12

7

11 1

2.J.B

1

--1

a

~~

-2.J.B

Drop

A+B

is

the

remaining elements

argument A

is

dropped. Argument B can

is

positive,

of

the

is

negative,

argument

is

one

element

first elements

2 3 ~ 5 6 7 8 9 10 11

B after

be

a vector

a vector.

for

each coordi-

of

the

last elements are

12

the

number

or

argument

B

c

87

The 1 Function: Index Generator, Index

of

OJ

Monadic (One-Argument) Form: Index Generator

The index generator function result ing

with the index origin (see

be a nonnegative integer

that

is

a vector containing

010

system variable

is

either a scalar

\5

1.

2 3

Lf.

5

A~"

\ 6

A

12~3Lf.56

~:i

+

,5

..--

Each

of

the

generated integers

6 7 B 9 lO

Dyadic (Two-Argument) Form: Index

The

index

of

function result

the

element(s) in argument a scalar, vector, or array. The result in

argument B

is

ment

cannot

one greater than

be found

the

of

A 1 8

is

the index

B.

Argument A must be a vector. Argument B can be

in

largest index of A (010 + pA):

of

is

the same shape as argument

argument

18

the

in

Chapter 5). The argument can

or

a single-element array.

the

first occurrence

A,

the value

of

first B integers, start-

is

added

to

5.

in

argument A

B.

If

the

element

the

index for

that

of

ele-

2

.....

41-----------------

'ABCDEFG','C'

3

2

6

1 9 1

9

Note: The result of the 1 function depends on

5 for information on

8

1')

c·

\.J

.:..

:~

:1.

9 2

A

...

1

:I.

A\22

")

.:..

A."9

3pl

B~"2

B

A\S

22

:33

Lf.LI·

t)

B 2

8

9 8

1

the

010 system variable).

5~5

Lf.

B

C'

,J

2

Second Element

the

010

system variable (see Chapter

88

The

4>

Function: Reverse, Rotate

OJ

m

("

(

The ¢ symbol

form

of

symbol.

Monadic (One-Argument) Form: Reverse

The

reverse

expression.

is

formed by overstriking

the

function symbol

function reverses

is

9,

formed by overstriking

the

elements

<p

the

[I]

B

of

0 symbol and

or

<f>;B

or

aB

argument

B.

the

I symbol. A special

the

0 symbol and

Argument B can be

the

-

any

89

When argument B specify the coordinate ordinate (columns)

is

acted on:

I.J. 3 2 1

is

a multidimensional array, the index entry [I] can be used

is

<1>1

2 3

<I>'I...IVE'

EVIL

~5

2 1

f.)

5

I~.

A~2

A

SAVE

MUCH

M()I~E

TIME

(~r::I.]A

MORE TIME

SAVE

"

MUCH

(J>[2::tA

MUCH BAVE

TIME

"

MORE

(~[3]A

EVAS HCUM

\

EROM

Et1IT

(DA

EVAS HCUM

that

is

acted on.

2

'--------The

~-----The

If

the

1+

I+p

'SAVEMUCHMORETIME'

If

the index entry

sB

form

is

used, then the first coordinate

first coordinate (plane)

the planes are reversed.

second coordinate (rows)

the rows

specified; the columns

reversed.

The last coordinate

in

each plane are reversed.

third coordinate (columns)

is

omitted, the last co-

is

specified;

is

specified;

is

in

each plane are

acted on.

to

90

EROM EMIT

MORE TIME

SAVE MUCH

"

sA

"

'-------The

first coordinate

is

acted on.

Dyadic (Two-Argument) Form: Rotate A

<1>

[I]

Bar

A<1>B

or

AsB

(

c

The rotate function rotates the elements specified by argument argument B are rotated the

elements are rotated

can be any expression. The shape

When argument B specify the coordinate

ordinate (column) is

acted on.

If

argument B If argument-B argument A

the

number by 4 matrix (each row has four elements) and must have four elements:

3

4·

4-

5

31+~5:1.2

is is

is

a vector, the number

of

elements

2<1>:1.

5

'!2:1

:I.

2 3

'7(~:I.

B~3

A.

If

argument A

to

the left (rows), or upward (columns). If A

to

the

right (rows), or downward (columns). Argument B

is

a multidimensional array, the index entry

that

is

acted on. If the index entry

is

acted on. If the

a vector, then argument A must be a scalar a matrix, then argument A must be a scalar

in

the coordinate being rotated. For example, if B

2 3

4·

5..--

2 3

I.J.

5

2 3

I.~

5

4-p

1 2 3 ~ 5 6

B

:I.

2

:5

56'7

9

:1.0

52'7

9 6

1.

10

:I.

6

11

:1.2

:I.

6

:1.:1.

12

527

9

1 10 3

-1.

()

9

:I.

5

1.

1

o

2

"7

o

2 3

"7

:t.

6:1.1

A~"~"1

f~

"':1.

A(~[1]B

2 1.l B

6

0

1+ 8

:1.1

()

~:

2$r.1JB

1.1

~

3

2<1>[2:1B

:I.

:3

I.~

\

!7j

B

9

:1.0

2<J)B

:I.

5

L~'

B

9

:1.0

1

2eB

0

12

\"-----The

LI·

S

01.2

-2

3

12

'7

L~

i

'-------The

'------The

of is

positive, then the elements

of

the

result

AsB

form

of

elements

(2--1~

The first coordinate (rows) therefore, the rotation

therefore, the rotation

argument B the number

is

the same as

is

omitted, the last co-

is

used,

then

or

in

argument A must be

the

row coordinate

3 4 5

'7

8 9

10

r:: r 1

J

second coordinate (columns)

last coordinate

first coordinate

lOJJ

is

of

is

that

of

argument

[I]

can be used

the first coordinate

single-element array.

vector. When

is

specified, A

11

:1.2

is

between rows.

[:2

is

between columns.

acted on.

is

acted on.

positions

of

negative,

the

same

is

a 3

specified;

is

specified;

B.

to

as

91

If

argument B is

rank

that

be

the

same as argument B less

B~":5

~~

an N-rank array, argument A

is

one less

~3

p \

27

B

"1.

...

2

I!!'

.J

B

)

6

9

:1.2

:I.

~;

1.8

11.

2'+ 27

1-

'+

7

1,1-

10

:1.3

1'+

:L6

:1.7

19

20

22

23

2~5

26

pB

333

A~3

3pl

0 0 0 2 0 0 0 0

()

A

0

()...----

_____

The shape as

argument

1

o 2 o 0 0 acted on.

pA

3 3

A<lH:

1:lB

:1.0

4·

"7

19

13 16

1

'1

,.)

..

,

25

If

"7

1

10

:1.3

:1.6

19

")

.:

..

1")1::-

...

23

1:1.

17

20

1'+

21.)

:1.7

1:1.

1'+ 20 21

'1

I!.

2:5

....

1

26

2 3

8

c·

...

,

2

I::'

,J

8

'---

6

The first coordinate (planes) therefore,

9

1,2

15

:1.8

The first in each plane rotated between planes.

2l 2'+ 27

A<I>[2JB

3

6

L

9 The second coordinate (rows)

12

:I.

~5

:I.B

2'+

27

therefore,

1

0

than

the

rank

of

argument

the

coordinate

of

argument A must be

B less

the

coordinate being

the

rotation

element

is

one

position 0 2

the

rotation

/,------

R

otation

0

2 0

0

he first plane t

Rotation between rows

he second plane

t

Rotation

0

he

t

must

B.

The

being

the

is

specified;

is

between planes.

0 0

0

is

specified;

is

between

third

the

between rows

plane

be a scalar

acted

same

rows.

Argument A

or

an array with a

shape

of

argument A

on:

~ArgUment

The middle element

plane positions between planes.

of

in

is

rotated

must

A

each

two

92

(

The

lsi

The ~ symbol

Function: Transpose, Generalized Transpose m

is

formed

by

overstriking the 0 symbol and the \ symbol.

CTI

(

Monadic (One-Argument) Form: Transpose

The

transpose

any expression. the

function:

function

~'ABCD'

reverses

If

argument B

the coordinates

is

a scalar

ABeD

B~"2

B

2 3

...---------

c:.

,.I

6

~B

4

...

...----------

c:-

~

6

B-t

B

"

.:..

6

10

II

..

2

3

'7

:l

:1.

:L

'.~

1

2

3

~B

of

argument B. Argument B

or

vector, the argument

2-row 3-column matrix.

3-row 2-column matrix.

is

unchanged

can

by

be

("

/

('~'

c

2

6

10

3

7

1t

4-

8

12

1

~:;

jn

"

2:'5

~B

16

20

'1

2ll-

1'4·

1t3

22

1

4,

18

22

j

1::-

,

,J

~

:1.9

::.~3

16

20

24·

The coordinates are reversed.

93

Dyadic (Two-Argument) Form: Generalized Transpose

A~B

The generalized

specified by argument A. Argument B can be any expression. Argument A must

be a vector or a scalar, and must have an element for each coordinate also, argument A must contain all specified. For example, would be 2 1:

Hf·2

transpose

~3~)

:I.

function interchanges

the

integers between 1 and

to

transpose

the

rows and columns of a matrix, argument A

the

coordinates of argument B

of

the

largest integer

argument

H

:I.

2

:~

I::'

I.~

••

J

6

1"\

.:.:

:I.~B

I.J.

1

11

AM

5

3 6

To

transpose

would be 1 3 2:

1

t::"

\J

9

13 :1.7

21

:I.

2

3

l~

13

:1.4·

15

11.>

B~"2

B

I")

tI..

6

10

1

.1.

1B

22

1.

r:

..J

~)

7

B

17

:LB

19

20

the

rows and columns

I.J.

f) \ 2

~5

M1.

..

)

4·

"l

B

:I.

12

:1.

!7;

:1.1.>

20

19

21.1·

23

3

2~B

9

10

1:1.

12

2:1. 22

23

~~l~

of

a 3-rank (three-coordinate) array, argument A

1

.J.

An array with

The second and third coordinates have been interchanged, forming an array with columns.

two

planes, three rows, and four columns.

two

planes, four rows, and

three

as

B;

94

The?

Function: Deal

Monadic (One-Argument) Form

the

See

Dyadic (Two-Argument) Form: Deal A?B

The

(depending arguments must be single positive integers. Argument A must be less than to

Roll function earlier

deal

function randomly selects numbers from 0 through 8-1

on

the

argument

8;

CD

in

this chapter under

index origin),

argument A determines

without

Primitive

selecting the same number twice.

how

many numbers are selected.

Scalar

Functions.

or

1 through 8

80th

or

equal

I~'

(

..

/

c

95

The

.L

Function: Decode

Monadic (One-Argument) Form

There

is

no

monadic

form.

(Base

Value)

CD

Dyadic (Two-Argument) Form: Decode

The

decode

system specified by decimal

function

number

10

result

is

the

argument

system (base 10):

10

A.

1011

1776

The

following illustration shows

Argument A (number

10 10

,L..--+.L...--..Lt-----'--Ten

Argument B

is

7

system) specifies

10

equals one unit to

a vector with these values:

7

6

A.l

value

For

example,

how

it was done:

units

the

B

of

argument

7 7 6

the

in

each

left.

B expressed in

to

convert

following:

of

these positions

of

the

1776

to

its value

position

number

in

the

The result

x10x10x10

The

arguments

the

other

rank

of

the

is

the

same as doing

x10

x10x10

must

argument

larger

argument

the

following:

:1=

can be a scalar, vector,

6

=

70

=

700

~~The

=

1000

1776

be numeric. If

minus one.

one

The

units position always represents itself.

value

in

the

by

the

The

value

the

by and so on.

argument

or

other

rightmost value

in

the

two

rightmost values

is

a scalar or single-element array,

array.

in

The

result will have

argument A.

in

is

multiplied

is

multiplied

argument A,

the

96