an interactive matrix interpretive system for the ibm 360/67. · 2016. 6. 1. · unitedstates...

AN INTERACTIVE MATRIX INTERPRETIVE SYSTEMFOR THE IBM 360/67

Robert Douglas Little

United StatesNaval Postgraduate School

THESISAN INTERACTIVE MATRIX INTERPRETIVE SYSTEM

FOR THE IBM 360/67

by


June 1970

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An Interactive Matrix Interpretive SystemFor the IBM 360/67

by

Robert Douglas ^LittleLieutenant, United States Navy

B.S., United States Naval Academy, 19 63

Submitted in partial fulfillment of therequirements for the degree of

MASTER OF SCIENCE IN MECHANICAL ENGINEERING

from the

NAVAL POSTGRADUATE SCHOOLJune 1970

LIBRARYNAVAL POSTGRADUATE SCHOOL

MONTEREY, CALIF. 93940ABSTRACT

The Matrix Interpretive System devised by Wilson and

modified by Cantin has been transformed into an interactive

program operable under a time sharing system. Several new

commands have been added to extend the usefulness of the code

and give it the capability to offline read, write and punch

data, to plot graphs and contour maps and to integrate simple

polynomial expressions.

TABLE OF CONTENTS

I. INTRODUCTION 7

A. GENERAL DESCRIPTION 7

B. HISTORICAL BACKGROUND 8

C. OBJECTIVES 8

II. GENERAL PROGRAM FEATURES 9

A. MAIN PROGRAM AND SERVICE SUBROUTINES 9

1. Main Program 9

2. Main Working Subroutine 9

3. Listing of a Matrix 11

4. Printing of Error Messages 11

5. Locating a Matrix 11

6. Calculating Eigenvalues and Eigenvectors - 11

7. Formation of Matrix N 11

B. OPERATION SUBROUTINES 14

1. Inverting a Symmetric Matrix 14

2. Adding, Removing and Storing a Submatrix — 14

3. Formation of an N by 2 Matrix 14

4. Printing of Graphs 14

5. Determining the Coefficients of a BicubicPolynomial 15

6. Printing Contour Maps 15

7. Formation of a 2 by 2 Stiffness Matrix 16

8. Numerical Integration 17

9. Numerical Integration of a Set ofDifferential Equations 18

III. OPERATIONS 20

IV. LIMITATIONS 38

A. SIZE AND NUMBER OF MATRICES 38

3

B. MATRIX NAMES 38

C. PLOT . 38

D. INTEGRATION 39

E. POLYNOMIAL FIT AND CONTOUR MAP 39

V. HOW TO CALL THE MATRIX INTERPRETJVE SYSTEM 40

A. TIME SHARING 40

B. BATCH PROCESSING 40

VI. SAMPLE PROBLEMS 42

A. EIGEN VALUE — ' 42

B. CONTOUR MAP — 45

C. GRAPH 51

VII. IMPROVEMENTS - ' 57

APPENDIX A COMPUTER PROGRAM 58

LIST OF REFERENCES 95

INITIAL DISTRIBUTION LIST 96

ACKNOWLEDGEMENTS

The author wishes to express his gratitude to Professor

E. L. Wilson of the University of California, the originator

of the program. He is also grateful to Professor Gilles

Cantin of the Naval Postgraduate School, his advisor, for

his constructive supervision and encouragement throughout

this work.

The Naval Postgraduate School Computer Center provided

facilities and technical advice for this work.

I. INTRODUCTION

A. GENERAL DESCRIPTION

Many engineering problems in such fields as steady-state

temperature distribution [Ref. 1] , stress in elastic structures

[Ref. 2], and fluid flows [Ref. 3] can be formulated as problems

of numerical linear algebra. Until the advent of modern

digital computers, all but the simplest of these problems had

to be reserved to specialists for solutions. Even problems of

moderate size required a considerable computational effort.

The computer changed all of this. All of the simple matrix

operations like multiplication, transposition, solution of eigen

systems can be coded to solve individual problems. The computer

program described in this report integrates a number of stand-

ard subprograms of linear algebra [Refs. 4,5,6,7] into a

problem oriented computer language. This program, heretofore

called: Matrix Interpretive System was coded in FORTRAN IV.

The resulting matrix operations sub-language has a syntax and

rules of its own as well as a certain number of diagnostic

messages that can be automatically returned to the user of the

language. The basic specification for the design of the

language structure was that it had to be simple enough to be

used by persons unfamiliar with computer programming. As

written, the language could be used to solve stacks of problems

sequentially; if an error is found in one of the problems a

message is printed and a solution for the next problem is

attempted. To be effective in a conversational mode at a

remote station, the program had to be heavily modified so as

to leave effective control of the flow of operations to the

user. This version of the code is called: Interactive Matrix

Interpretive System.

The Interactive Matrix Interpetive System is a general

program written in FORTRAN IV [Ref . 8] , it is a problem oriented

sub-language. The entire program is coded in double precision

arithmetic. The only subroutines which are used but are not

contained in the program are a square root and a natural log

subroutine. The program uses 160,000 bytes of core storage.

B. HISTORICAL BACKGROUND

The original program was developed by Professor E. L. Wilson

of the University of California in April 1963 for an IBM 7094.

It was later adapted by Professor G. Cantin of the Naval

Postgraduate School for a CDC 1604 in February 1966 and for

the IBM 360/67 in August 1968.

C. OBJECTIVES

The objectives of the author's work have been to:

1. transform the program into an interactive system

operable under time sharing from a remote typewriter station;

2. add operations to extend the capabilities of the

program;

3. create a "USER'S MANUAL" to facilitate the use of

the program.

II. GENERAL PROGRAM OPERATION

The Interactive Matrix Interpretive System will be referred

to as IMIS in this and following sections of this report. IMIS

is written in FORTRAN IV language for the IBM 360/67 time

sharing system available at the Naval Postgraduate School

(CP/CMS) . A different version called DSMIS is used for batch

processing. All operations are performed in double precision

arithmetic. Matrices are stored internally in a single

dimensional array, A, that is 10,000 double words in size.

Matrix names are stored in an array called NAME. Arrays, NROW

and NCOL, are used to store the number of rows and columns of

each matrix.

The following is a brief description of the function and

operation of most of the subroutines of IMIS. Some of the

subroutines are straightforward and will not be discussed. A

flow diagram of the program is presented in Figure 1.

A. MAIN PROGRAM AND SERVICE SUBROUTINES

1. Main Program

The Main program is used only to initialize internal

variables and to call the main service subroutine, SMIS1.

2. Main Working Subroutine (SMIS1)

SMIS1 is the general working subroutine* Some of the

operations such as duplication of a matrix and envelope of

a matrix are carried out in SMIS1. The other operations are

carried out in subroutines which are called from SMIS1. Most

of the error messages are called from SMIS1.

MAIN PROGRAM

ITGRAL

APRINT

FORMK *

PLOT *

SYMINV

MULT *

TRANS

INVERT

RESPON *

DELETE <-

SMIS 1

CONTUR

*| POLFIT

0©

* EIG

JACVAT

ILOAD

STOSM

ERRER H

B ) (C STJ

MFIND

IFigure 1. Functional Flow Diagram

10

3. Listing of a Matrix (MLIST)

MLIST stores each matrix by name, number of rows and

columns and starting position in the array, A. It checks the

name of a new matrix to be stored against the names of pre-

viously stored matrices to see if the name has been used before.

If there is another matrix with the same name, the previously

stored matrix will be deleted before the new matrix is stored.

4

.

Printing of Error Messages (ERRER)

When an error is made in an operational command, ERRER

is called. It prints out an error message, deletes the current

operational command and returns control to the typewriter.

5. Locating a Matrix (MFIND)

Locates the matrix or matrices to be used in an

operation. It finds the number of rows and columns of a matrix

and the starting position in the array A.

6 » Calculating Eigenvalues and Eigenvectors (JACVAT)

Determines all of the eigenvalues and eigenvectors of

a matrix. It uses the threshold cyclic Jacobi rotation method

[Ref. 4].

7. Formation of Matrix N (P)

The bicubic polynomial,

r3+C X 3Y 2+C X 3Y +C X 3+C

2 3 4 5P=C X 3Y 3+C X 3Y 2+C X 3Y +C X 3+C X 2Y 3+C X 2Y 2+C X 2Y +C X 2+

C XY 3+C XY 2+C XY+C X+C Y 3+C Y 2+C Y+C9 10 11 12 13 14 15 16

is used in the polynomial fit operation. This polynomial

can be written as

11

p = < F± > { C }

i=l ,2,. ..,16

where <F.> = <

X

3Y3

# X3Y2

/ X3Y / X

3/ X

2Y 3

,X2Y2,X

2Y ,X

2,

XY 3 ,XY 2 ,XY,X,Y 3 ,Y 2 ,Y,1 >

and {Ci > = <

C

l7 C 2 / . . . /C16>T

. In the POLFIT operation, values

of P at all of the sixteen nodal points of the grid shown in

Figure 2 must be used to solve for all of the unknown co-

efficients of the polynomial using the following matrix

equation:

{P± } = [N] {C

i >

i—

1

r 2 ,

,

. . , 16

where

[N]

<F<D>i

<F< 2)>

1

< F (16)>1

Subroutine P forms matrix N for use in the POLFIT operation.

The bicubic polynomial, P, will be referred to as CUPOL in the

following sections.

12

0.3 1,3 2,3 3,3

©•a 1,3 2,2 2,3

0,1 1,1 2,1 3,1

0,0 1,0 2,0 .

y x

Figure 2. Grid For Subroutine P

13

B. OPERATION SUBROUTINES

1

.

Inverting a Symmetric Matrix (SYMINV)

SYMINV inverts a symmetric matrix, A, by Gauss

elimination [Ref . 4] . If the matrix is not symmetric, it takes

the average of the two numbers, A (i , j ) , A( j , i) , and replaces

both by the average value and prints a warning that the matrix

was not symmetric.

2

.

Adding, Removing and Storing a Submatrix (STOSM)

STOSM is called to do three operations.

a) Store a submatrix at an indicated position in a

matrix when called by the command, STOSM.

b) The command, RMVSM, calls STOSM to remove a sub-

matrix from the original matrix.

c) ADDSM calls STOSM to add a submatrix to a matrix

at an indicated position.

3. Function Generation (FUNGN)

This subroutine takes a function described by a set

of points (X^,Y.) , not necessarily equally spaced, andi=l , 2 , . . . ,n

calculates, by straight line interpolation, ordinates at equally

spaced values of X.

4. Printing of Graphs (PLOT)

PLOT prints a 10 inch by 10 inch graph of 1 to 4

curves. It automatically scales the graph to the maximum and

minimum values of X and Y. The axes are plotted as

a) X X

b) Y Y

14

with the characters, X and Y, appearing at every inch on their

respective axes. When all of the points are plotted on one side

of either axis, an offset axis replaces the real axis and is

indicated by

a) A A offset X axis

b) B B offset Y axis

The origin of the axes and the X and Y scale factors are cal-

culated and printed below the graph.

5

.

Determining the Coefficients of a Bicubic Polynomial(POLFIT)'

The 16 unknown coefficients of a bicubic polynomial

surface can be determined in terms of 16 known values of the

polynomial at 16 known values of the independent variables.

POLFIT solves the matrix equation,

[N] {C} = [P]

for the matrix of unknown coefficients, C, where matrix N is

formed by the subroutine P. Matrix P is a matrix of the values

of CUPOL at each nodal point and is the input to POLFIT.

6. Printing Contour Maps (CONTUR)

CONTUR prints a contour map of CUPOL. There are 21

possible contour lines which are represented by the alphabetic

letters, A through J, 0, Q through Z. The input is either the

coefficients of CUPOL with the upper and lower limits of X and

Y or the values of the function at the grid points used for

POLFIT. In the latter case, POLFIT is called and the coeffi-

cients of CUPOL are calculated.

15

CUPOL is then scanned over the ranges of X and Y to

determine the maximum and minimum Z ordinate. The range of Z

is divided into 42 equal parts represented by alphabetic

characters and blanks assigned to alternating contour values.

CUPOL is then evaluated at each point on a line, the correct

character inserted and the line printed.

7. Formation of a 2 by 2 Stiffness Matrix (FORMK)

FORMK forms the stiffness matrix [Ref. 9],

[K] =

kll

k 12

k21

k22

for a simply supported beam having length, L, Young's Modulus,

E, moment of inertia, I, shear modulus, G, and effective shear

area, A.

The stiffness coefficients are:

11

12

2EI

[ 1+2$J

K

2EI / 1^3L 1 1+3

= k

22

21

where

$ =6EI

L2AG

16

The matrix equation,

M-

M<

= [K]

relates end moments, M, , M~ # to their corresponding rotations,

V as shown in Figure 3

.

Figure 3. Simple Beam

8 . Numerical Integration (ITGRAL)

The subroutine, ITGRAL, is capable of performing

numerical integration of one and two dimensional functions

described by discrete sets of points, either by Simpson's rule,

or, if the function to be integrated is known, by Gaussian quad-

rature .

17

9 . Numerical Integration of a Set of DifferentialEquations (RESPON )

In the study of vibrations of systems with many

degrees of freedom, the following system of ordinary differential

equations governs the problem:

[M] {X} + [C] (X) + [K] (X> = {p} (1)

where

[M] is the mass matrix,

[C] is the damping matrix

and

[K] is the stiffness matrix.

In general, if

{X} = [V] {x}(2)

where matrix [V] is the matrix of undamped mode shapes and {x}

is the vector of the time dependent amplitude function for each

mode, we get after substitution of (2) into (1)

:

[M] [V] {x} + [C] [V] {x} + [K] [V] {x} = {P} (3)

After premultiplication by [V] T and the use of the orthogonality

properties of normal modes:

[V] T [M] [V] = [-m^]

[V]T [K] [V] = [-W| = [-a,2m<J

[V] T [C] [V] = [-c^] = [-2Aa)m>J < a >

(a)'Such an orthogonality condition imposes somerestrictions on the form of the damping matrix [C]

.

18

where

x.Ci

21X1-^ o)j_

and using the notation

[V]T {P} = {p}

we get

[^m^] {x} + [--2Au)nwJ {x} + [^w 2nuj {x} = {p} (4)

or

{x} + [-2X0)^] (x) + [~-w 2^] {x} = {p*} (5)

where p* = p./m.

.

l i i

This last set of equations is completely decoupled

and can easily be numerically integrated. The subroutine

RESPON performs this task.

19

III. OPERATIONAL COMMANDS

The following is a list of the operations that IMIS con-

tains. The operations must conform to the standard format

shown in Figure 4. OPERATION stands for any of the symbolic

command names mentioned below. A, B, C and D are matrices used

as arguments of the operation. Nl, N2 , N3 and N4 are four

integer arguments that must always be right justified. SI and

S2 are two floating point arguments . The arguments can be

input or output values and are not all necessary for each

command

.

There are two versions of the matrix interpretive system

in use at the Naval Postgraduate School. One is for time

sharing and one for batch processing. The commands denoted by

a "*" can only be used in conjunction with the time sharing

option. The READ, WRITE and PUNCH commands make use of

sequential input/output files which are available with the

FORTRAN IV language [Ref . 8] .

^

b)

The READ command uses the file FT04F001. This file is

used to load matrices into IMIS from punched cards and is read

into the computer prior to executing IMIS. Any data stored in

the file is automatically erased when new data is read into the

file.

File FT0 8F001 is used to store any output which the user

wants to print offline. This file is not automatically erased

(k)A certain knowledge of the CP/CMS time sharing systemis needed when using a remote terminal of the computer. It ispresumed that the reader is already familiar with this system[Refo 10].

20

•p

6uo

H

Cfd

P

•Hp4

21

when new data is read into the file. New data is appended to

the data that is already stored in the file. Therefore, the

file must be erased before executing IMIS. To erase the file,

the command,

ERASEbFILEbFT0 8F001

is used. After exiting from IMIS, the command,

OFFLINEbPRINTCCbFILEbFT08F001

will cause the file to be printed on the offline printer.

The command, PUNCH, uses file FT07F001 to store data to

be punched onto cards. This file appends new data at the end

of old data so the file must be erased before using IMIS. The

command,

ERASEbFILEbFT07F001

erases the file. To offline punch the data stored in the file,

the command

,

OFFLINEbPUNCHbFILEbFT07F001

is issued after exiting from IMIS. Examples of the use of

these files are given in the sample problems. The operational

commands are

:

START This command causes the elimination of

all matrices which are in core storage

and must be the first command used in

the solution of a problem. If an error

is found during execution of a command,

an error message is printed on the

22

typewriter, the current command

eliminated and control returned to the

typewriter. If an error is found

during the execution of a problem with

DSMIS, the current problem is auto-

matically deleted and the remaining

cards scanned until a new START or

STOP command is found.

LOAD Matrix Load:

A = Name of matrix to be loaded.

Nl = Number of rows of matrix A.

N2 = Number of columns of matrix A.

N3 = Format control indicator for the

data.

The elements of the matrix are

typed or punched on cards row-wise

after the LOAD command according

to one of the options determined

by the value of N3:

a. if N3= 1 or blank, the format is

(12F6.0). A maximum of twelve

numbers per line, using as many

lines as required to write the

entire matrix must be used. If

the decimal point is omitted, it is

assumed to be at the extreme right

of the field.

23

PRINT

REMARK

STOP

ZERO

b. if N3= 2, (6F12.0), 6 numbers per

line in fields of 12 columns.

c. if N3= 3, (4F18.0), 4 numbers per


d. if N3= 4, (3F24.0), 3 numbers per


Matrix Print:

A = Name of matrix to be printed.

Nl= Number of lines, which follow the

PRINT command, to be printed as a

label for the matrix. Column 13

of the command card is used for

carriage control in DSMIS only.

A one in column 13 will cause the

matrix to be printed on a separate

output page.

This operation causes the number of

lines designated by Nl, which follow

the operation, to be printed as

remarks

.

This operation ends a run of problems

and is the last command to be issued

in a stack of problems. It can be

used only once per run.

Formation of a Null Matrix:

A = Name of null matrix.

24

ADD

SUB

MULT

TRANS

INVERT

SYMINV

STOSM

Nl= Number of rows of matrix A.

N2= Number of columns of matrix A.

Matrix Addition - [A] + [B] = [A]

Matrix A is replaced by the sum of

matrices A and B.

Matrix Subtraction - [A] - [B] = [A]

Matrix A is replaced matrix A minus

matrix B.

Matrix Multiplication - [A] • [B] = [C]

The product of matrix A times matrix

B is generated and defined by matrix C.

rn

Matrix Transpose - [B] = [A]

The transpose of matrix A is generated

and defined by matrix B.

Matrix Inversion - [A] = [A]

Matrix A is replaced by the inverse

of itself.

Symmetric Matrix Inversion - [A] = [A]

Symmetric matrix A is replaced by the

inverse of itself.

Store Submatrix in a Matrix:

A = Name of large matrix.

B = Name of submatrix to be stored.

Nl= Row number in large matrix of

first element of submatrix.

N2= Column number in large matrix of


-1

25

STODG

SCALE

ADDSM

RMVSM

Elements of A are replaced by

elements of B in designated area.

Store Row Matrix on Diagonal of Matrix:

A = Name of square matrix.

B = Name of row matrix to be stored on

diagonal of matrix A.

Diagonal elements of A are replaced by

elements of B.

Scalar Multiplication - [A] = SI* [A]

Add Submatrix to a Large Matrix:


B = Name of submatrix to be added

into large matrix.





Extracts Submatrix [B] from [A]

:


B = Name of submatrix defined as matrix.





N3= Number of rows in submatrix.

N4= Number of columns in submatrix.

Matrix A is not modified.

26

LOG

MSCALE

RMVDG

EIGEN

The Log of each Element

Each element in the matrix A is

replaced by the natural log of the

element.

Scalar Multiplication


replaced by B times the element where

B has previously been defined as a

1 by 1 matrix.

Extracts Row Matrix B from Diagonal

of Square matrix A.

A = Name of square matrix.

B = Name of row matrix composed of the

diaconal elements of matrix A.

Matrix A is not modified.

Eigenvalues and Eigenvectors:

The eigenvalues and eigenvectors of

the system, [A] [X]=X [B] [X] , are

determined where [A] is a symmetrical

matrix and [B] is a diagonal matrix

of positive elements stored as a row

matrix.

A = Name of matrix A.

B = Name of matrix B.

C = Name of matrix of eigenvectors

stored row-wise.

27

SQREL

INVEL

DELETE

D = Name of row matrix of eigenvalues,

X.

Nl= The number of eigenvectors to be

calculated. The ordering of

eigenvectors and eigenvalues is

determined by the sign of Nl as

follows

:

a. If Nl is positive, eigenvalues are

arranged in descending order.

b. If Nl is negative, eigenvalues are

arranged in ascending order.

N2= Eigenvector normalizing.

a. If N2 is blank:

Eigenvectors are normalized so

that [C] [B] [C]T

= [I]

b. If N2 is 1:

Eigenvalues are normalized so

that [A] = [C]T MU.] [C]

Square Root of Each Element


replaced by the square root of itself.

Inversion of Each Element


replaced by the reciprocal of itself.

Matrix Deletion

The matrix A is eliminated from core

storage

.

28

DUPL

ENVEL

RESPON

Matrix Duplication:

A = Name of matrix to be duplicated.

B = Name of matrix defined to be

identical with matrix A.

Envelope Value of Matrix

The maximum absolute value in each

row of matrix A is printed along with

its column number times an interval.

A = Name of matrix A.

Sl= Interval between columns.

Numerical Integration of a Set of

Differential Equations:

{x}+2X t-aj^] {x} + [-u>2^] {x}={S}P (t)

with initial conditions, x(0)=x(0)=0.

A = Name of a row matrix containing

the diagonal elements of matrix

h-o)^] . The dimension of A must

be (lxn) where n is the number of

equations in the set.

B = Name of a column matrix containing

the elements of {S}. The dimension

of B must be (nxl)

.

C = Name of a row matrix containing

the values of the function P(t)

evaluated at equal intervals, At:

P (0) ,P (At), P (2At) , . . . ,P (mAt)

29

The dimension of C depends on the

choice of At which must be small

for accurate results. The size of

At should be determined by actual

numerical experimentation with

the command.

D = Name of the output matrix contain-

ing the calculated values of the

variables as shown in Figure 5.

Nl= Output interval i. The values of

the n unknowns, {x} , are printed

at iAt,2iAt, 3iAt, . . . ; if i=l,

all of the values are printed.

Sl= Value of the damping ratio, A.

S2= Time increment, At, used in the

numerical integration.

x^(iAt) ,x1(2iAt) ,x

1(3iAt) ,

x2(iAt) ,x

2(2iAt) ,x

2(3iAt) ,

xn (iAt) ,xn

(2iAt) ,xn(3iAt) , . . .

Fig. 5. OUTPUT MATRIX, D, FOR RESPON

30

FUNGN

FORMK

Function Generation:

A = Name of matrix which defines a

function in terms of line segments

X1/Y1 ;X2 ,Y2; •**;Xn ,Yn . (Nx2)

B = Name of matrix to be formed which

is composed of the y ordinates at

equal x ordinate intervals of the

function defined by matrix A.

Nl= Number of y ordinates to be

generated. The first ordinate

will be equal to Y .

Sl= X ordinate interval.

Forms a 2x2 Element Stiffness Matrix:

A = Name of matrix to be formed.

The line following the command is as

follows

:

a. Columns 1-12 Moment of inertia of

member, I.

b. Columns 13-24 Effective shear

area of member, A.

c. Columns 25-36 Length of member, L.

d. Columns 37-4 8 Modulus of

elasticity of member, E.

The shear modulus, G, is assumed to be

equal to E/2.4.

31

PUNCH

* READ

* CONT

* WRITE

Punches Matrix onto Cards:

A = Name of matrix to be punched.

Nl= Number of comment cards to be

punched as a heading for matrix A.

After the PUNCH command is issued, the

next line contains the format elected

by the user as follows:

(NNTRR.SS)

where

NN= Number of elements per card.

RR= Field width per element.

SS= Number of significant digits.

T = Type of data field. T must be a

standard F or D Fortran format.

Loads Matrices from file FT04F001

The load operation card must have a

1. in SI. The last card must be a

Continue Operation card.

Continue Operation

Sl= 1.

Indicates that all matrices in file

FT04F001 have been loaded into IMIS.

Writes Matrix into File FT08F001:

A = Name of matrix to be written.

Nl= Number of lines of remarks to be

32

written as a label for the matrix

A.

N2 must be equal to 1.

PLOT Plots One to Four Curves Described by

Sets of Points Contained in Matrices

A, B, C, D:

A = First matrix to be plotted on one

graph. Plotted as a "+"

.

B = Second matrix to be plotted on

one graph. Plotted as a "*".

C = Third matrix to be plotted on one

graph. Plotted as a "0".

D = Fourth matrix to be plotted on one

graph. Plotted as a " ."

.

* " N3= 1. Offline print indicator. Graph

will be stored in file FT08F001

N4= Number of lines of remarks to be

printed at bottom of graph.

Matrices to be plotted do not have to

have the same number of points. They

have to be entered as N by 2 matrices

with the first column the X co-ordin- -_.

ates and the second column the Y co-

ordinates. When plotting more than

one curve on the same graph, a conflict

may arise if more than one curve passes

33

through the same point. The symbol

printed at that point is determined by

the following order: D, C, B and A.

POLFIT Determines the Coefficients of CUPOL:

A = Input matrix. (18x1)

B = Output matrix of coefficients of

CUPOL, (C lr C 2 , . . . ,C 16 )

where

A(l) = Hx

A(2) = H„

i .A3 A4 A5 A6 >XH

T-A7 A8 A9 A10

All A12 — A13 A14

Ii

ii

A15 A16 A17 A18

I

and

3 3 3 2 3 3CUPOL=C!X Y +C 2X Y +C3X Y+C4X +

C5X2Y 3+C

6X 2Y 2+C

7X 2Y+C

gX 2+

C9XY 3+C10XY

2+C1]L

XY+C12X+

C13y3+C14y2+C15Y+C16

34

CONTUR Contour Maps CUPOL:

N2= Number of lines of comments.

N3= Input type indicator.

a. N3= Blank or 1.

A = Input matrix. Same as for

POLFIT command. (18x1)

B = Output matrix of coefficients

of CUPOL. (16x1)

b. N3= 2

A = Input matrix. (20x1)

A(l) = Lower bound of X.

A (2) = Upper bound of X.

A (3) = Lower bound of Y.

A (4) = Upper bound of Y.

A (5) through A (20) are the

coefficients of CUPOL.

* N4= Offline print indicator. Stores

contour map in file FT09F001.

ITGRAL Integration of Functions Represented

by Discrete Values or Polynomials:

A = Input matrix. (Rxl)

N3= Integration type indicator:

a. If N3= 1, Simpson's Rule for one

dimension. R must be even.

A(l) = Hx

A (2) through A(R) are evenly

spaced values of function.

35

b. If N3 = 2, Simpson's Rule for two

dimensions

.

A(l) = Hx

A(2) = Hy

A (3) through A(R) are values of

function entered row-wise as for

POLFIT.

R = N 2+2, N must be odd.

There must be the same number of

values in both directions. Hx and

Hy can be unequal.

c. If N3= 3, Gauss Quadrature for one

dimension.



A (3) through A (14) are the co-

efficients of an 11th degree

polynomial

:

A3X11+A

4X10+A

5X 9+A

6X 8+A

7X 7+A

8X6+

a9x 5+a

10x 4+a

i;lx 3+a

12x 2+a13x+a14

d. If N3 = 4, Gauss Quadrature for two

dimensions

.



A (3) = Lower bound of Y.

36

A (4) = Upper bound of Y.

A (5) through A (20) are coefficients

of CUPOL.

37

IV. LIMITATIONS

A. SIZE AND NUMBER OF MATRICES

The storage available for all of the matrices in any

problem is 80,000 bytes or 10,000 double words. This limit

is arbitrary and controlled only by the total core storage

available at any installation. For the naval Postgraduate

School installation, 10,000 double words was selected in order

to reduce turn around time in batch processing and reduce the

size of the data set required for time sharing. The total

number of matrices which can be stored is 100.

B. MATRIX NAMES

Each matrix is referred to by its name composed of one to

six alphameric characters including blanks. The name is select-

ed by the user when the matrix is first loaded or generated by

an operation. If the name for a previously defined matrix is

used later as a name of a new matrix, the former matrix is

deleted before the operation is executed and is replaced by the

new matrix. This is done so that there is only one matrix with

a certain name at any one time

.

C

.

PLOT

There are 200 points in the Y direction on the graph. The

X direction has 130 points for the remote terminal printing and

160 points for the offline printer. The difference is due to

the different number of lines per inch. The accuracy of the

position of a point depends on the range in both the X and Y

direction. The maximum error in the Y direction is the range

of Y divided by 200. The maximum error in the X direction is

38

the range of X divided by either 130 for the remote terminal or

160 for the offline printer. If the X and Y ordinates of two

or more points fall on the same nodal point on the graph, only

one point will be plotted. If the points are from different

matrices, the matrix hierarchy (see page 34) determines which

will be plotted.

D. INTEGRATION

Integration by Simpson's Rule is restricted to equally

spaced points in any one direction. The error is of the order

of H£ for integration in one dimension and of the order of H£

times H^ for two dimensions. Hx does not have to equal H but

there has to be an odd number of points in any one direction.

Integration by Gauss Quadrature for six Gauss ordinates is

exact for all polynomials of degree eleven or less in one dimen-

sion and for CUPOL in two dimensions [Ref. 11]

E. POLFIT AND CONTUR

The polynomial, CUPOL, will pass through the values of

the function at the nodal points of the grid but may not be a

true representation in the space between nodal points. If the

range of values of the function is less than 10", a contour

map will not be printed.

39

V. HOW TO CALL THE MATRIX INTERPRETIVE SYSTEM

A. TIME SHARING (IMIS VERSION)

At the Naval Postgraduate School, IMIS is stored in a

library (AED) with the name, LIT, so that any number of users

can use the system at any one time. In order to call LIT, it

must be called as a subroutine. A Fortran program called IMIS

has to be written as follows:

CALL LIT

STOP

END

There are two other libraries which must be loaded along

with AED library in order to use LIT. This can be done with an

executive program called SMIS as follows:

FORTRAN IMIS

GLOBAL LOADER TXTLIB AEDLIB SYSLIB

LOAD IMIS

START

SMIS is then executed with the command, $ SMIS. The

computer will then type out the executive program with each

command preceded by a time. Next it will type

EXECUTION BEGINS . .

.

At this time you are in IMIS and ready to begin the first

problem. The first command will be START.

B. BATCH PROCESSING (DSMIS VERSION)

The first card must be a job card for the batch processing

system as follows:

40

//aaaznnmbJOB(nnnn,ssssFP,TTTT) , 'IDENTIFICATION'

where

aaa = The first three letters of the user's last name.

z = Job sequence number

nnnn= User's number.

ssss= Project number.

TTTT= Student section or faculty number.

The next six cards are control cards. Card five is used

only when using the punch command. The cards are as follows

stating in column one:

//JOBLIBbDDbDSNAME=DSMIS.F59CI / UNIT=2 314 ,DISP= (OLD, KEEP)

,

//bbbbbbbbbbbbbV0LUME=SER=MARY

//bbEXECbPGM=DSMIS , REGION=160K

//FT06F001bDDbSYSOUT=A

//FT07F001bDDbSYSOUT=B

//FT05F001bDDb*

The ", " is where blanks are left,b

The problem deck follows with the first command a START

command and the last a STOP command. The last card of the

deck is a standard delimiter card:

/*

On the job request card, check the item marked DISK PACK

under the SPECIAL INPUT heading and write in "MARY". If the

punch command is being used, under the heading SPECIAL OUTPUT

check the item marked PUNCHED CARDS.

41

VI. SAMPLE PROBLEMS

A. THE EIGEN SYSTEM

The matrix equation

[A] {X} = X[B] {X}

where

0.0 -1.0 0.01.0 2.0 -1.00.0 -1.0 2.0

[A] =

and

[B] =

is to be solved. The entire sequence of events is as shown

below. Everything written in lower case was typed by the

operator. The computer response is in upper case.

1.5 0.0 0.00.0 2.0 0.00.0 0.0 2.5

42

CO

ro

oCM

OrH

I

O•

O

ro

co

Q

W CM w T*

UP O D^ • ^O H OU 1 U u

ro ro CQo• ino •

CM J3

< - CQ ^ < Uin o CO

H 3: • £o S H« Q O H Q o • W s<C rd < X> < (fl o U HFH O O H «

+J en J ro tl r- d W ro -P CMu T3 13 (D ccrj id O CO in en •H-M • • •rH 5-1

(0 H O rH rH d) &

H O rHO O OPOPCTi CO <tf

in 00 o^ O CM

ro vd ON <&in CM Oo CO <J\

• • •

001

rH CM1

o H rHo o o

1 1

QI 1

Q Q<T\ r- oro <x> ^<rH V£> CM

CM VO o inCO o\ COrH ^r ro

• • •

rH in vo

H rH OO

1

O O1

Q Q QrH r^ ^r- rH <£>

CM rH rorH -^ *£> rj\

l> CM *£>

r^ KD O• • •

roI

^T rH1

rH CM CO

rHO

I

DCMCOin

co inCO

•

CMI

OI

QCOCM

CO

in

oo

CM

Tj H•P 04c•Hua,

rHinoin

43

w

3ou

Eh

XPu fO

EHU CO Q x u

PU TJ X U X

Eh HO X » X U U <:

W & O X Eh>z O O Q p EH P EH 2

u a X rt Ph x o ^ U J fO HPh H Eh D P #

W Eh n co tnco S S P 04

C -n p P CA3 M H H •HU 0) -p 3 3 HP N w e £ D.

co o o!-H o oQ P Qco o oCO o or- o o

co cm o oo o oC\ o o

• • •

r-\ rH CM1

O1

o oO o oQ Q Qo o oo o oo o o

CM O o oO o oo o o

• • •

fH CM iH

ro o coHOHi

1

Q Q QCO o 00CM o CMCO o CM

rH rH o CMr> o o•^r o (T>

I I

H CM CO

a,opw

oEn

44

B. CONTOUR MAP

A contour map for a surface described by the ordinates at

the sixteen nodal points of the grid shown on page 4 7 is

desired.

[A] =

10.0 12.0 8.0 10.012.0 11.0 9.0 8.08.0 9.0 11.0 12.0

10.0 8.0 12.0 10.0

and

Hx"Hy- 1

The results are as follows

45

c^

CO

CO

a\

CO(NH

o orH iH

• CMWOOH|DA •

O CN •

U H CO

m

o o£1

wH 5 DOS Q O • CM Eh

<C fC <£ Pi rH rH «J 2Eh O H O

p W i-5 CO 3 Un H3 rH -Pn rrj c+> • rH oW rH rH rH u

46

r- © m <oO O o cc>

i o m hin o 4- 0'• • • •

CD O f* CM

a.

t/>

l-zoa

or

t~

OUJ(9<a

a

UJxt-

o o o oo o o oo o o oo o o oo o o oo o o o• • • •

O 00 CM O

1 « c uCM >©

4 CD ft •-I

3 => o Do o © oo o o oo o o oo o o oo o o oo o © o

H II HUJ -9 => 1^

0- r-« 4 f-00 00 t- O

—• 4 o <0 CMCM r- •-< <o

CM • • • *

o 0D a<-<

CMi-l

c<00D•-1

aCM H N n II

f-1 o >— »- V00 O- f-> CM

U II II II

—• If

5 5 3 3

o CO rf) CO1^ «0 irt •*

lf> fl l>- coo- 4- 00 fO

t>- O- O CM

o oo oo oo oo oo o

o oo ©o ©o o© oo o

N H a B

z> z>

o oo oo oo oo oo o

II II

O 4"»H r*=> Z3

o oo oo oo oo oo o

oir>

4-r-l II ll •I II

00 u X 1/1 Xot»•

oCM 4- r~ ©lf> «* CO ro•o CM CD <*

M <o w> u% oUl • • • 1

o I'- V~ o CM? f* i-l

<

O CM 00 © u

XI-

a * 1 M f\ CO vD a f—CO <0 CO CM 9-* f-<

v-< u. O- fl 4 e'- C*l a lf>

z> 3 => 3 <«• en 00 CM t-

t-< • • • •

00 l»- 00 o r->

o «-« —

•

*o

II II

o >

47

•v-ieu ui o o or ««r«t««i cccr u O Hi u IS X »•" o a i/> K 3 > 3 xx >->->->->- x 3 > 3Ki/>aO-5MjCli C O 03 -3«J«»I<-3.«a tt <_-' O U u C X I- O Or *>5 I- 3 > 3 X >->>->->->-> X 3 > Kl/'aO

UO o o? «i<i«3«i*r<<i<r<j ir o O u u o X h- O a f5 K 3 > 3 x >->->->->->>->->- x 3 >3UiO o ec <<<r <<< ec o c a.' u O X -- o a o K 3 > 3 x >->-> >>->- x 3 >3

u in o mc «t«« <«< cc u o u u is 1 •« o a f> K 3 > 3 x >->->- >>->• xx 3 3Ku 111 C«j crcr <«< «« er c O Ui u O X f o a m K 3 > 3 x >->- >>- xx 3> 31-

o o a «j-- <».«* at o o id u e x •- o a v k 3 > 3 x >-> >->- x 3 >uiO o a <«» «r«i cc o C id u C X •- o a L'1 I- 3 > 3 x >-> >-> x 3 >3

o a «t CCO «< ec 00 O ui u I -- O a -*> I- 3 > 33 x >->- f**k-k- >- XI00 or *i< ccroc «r«i oc 00 o u- u o X ^- o a v* K 3 > 13 x >-> kkjisjkik >-> x 3>o o? «J< CDCOOC «-,« or<r o O u u o X •- o a f K 3 > 3 xx >> nkkn^n >->- x I

o «b «« coooco <« cccr o co u> u x " o a i" H 3 >> * xx >->- *jmm*.isii» >->- x 3t£ «J" CCCCCCC «l«l CC OO ID U O I »~ G a -*> K 3 > 3 X >> KKKKKNK >- XIT «J< DOCODCCC1 «l«r OC OOUUIUCX*— O tt »° K 33 > 5 X >->- *-^r*ji^rv.*~t^fv. >>- X

or <«a OCCCCCC «j«s< tfff 00 r u. u O I *- OolV> K 3 > 33 xx >->->- ^kmkkjkk >->- x<< COCOCDOD «a«3 CCCO o C Ui u C I •"-• O a -*" K 3 > 3 XX >->- ^rsirsir^^JMhjr^ >->-

«< COCCDOO 4-*< 03 o DO UU u C X •- -3-3 O tf M K S >> 3 X >->->- fsiiNiiîsjfvi^-j >->-<] < COOOOO << O3C0 to O UI IL C9 X "- "1"3 O a V3 K 3 > 33 XX >->- »wr*jM-vKjf»j >->-«< fjCCCO «j«-«l OC o O U1U1 u O X •- —J-5 O a 3 X >>->- MvNnk >>-

«« 00 <<« a ec 00 00 uj u u e X «-> -5-5 o a. v> n- 3 >> 33 xx >>>- nn >->-

«j« <j<r< ercr t_>o D 111 u IS I —>-> o or <f> y- r> > 33 xx >->->- >->•<<< «<« ecec 00 o u lu u. 00 x *" -5-5 c- a f>v t- ziz> > >i xx >>-> >>>«<« «K«3 ate uo OO ui u is X «- -5-^ 00c v K r> >> 33 xx >>->- >->>-<<<<o <<<<< CCOD i_>ci o ui uu e> x I-1 n-5 o oc I/I hh o > 33 xx >>>>>- >->->->>-<a««<<<<<«<i<i< arec i_>t cio u.ui u o xx •- ->-> o oca </> ^ 33 >> 33 xx >->->->->->->->->->•>->-<

«

<i<j <i<r < « < odot 00 00 ui u. ec x •-* -51 o ot wv> t~ z> >> 33 xx >>>->>>>>>a< araa tJ(_> O Ujui uu CIS I »- -1-5 O oc iot^ t-K- 33 > 33 XXX >>

eceocc «_•(_> 00 lu u ts X •- ->-> o a <fl I- 3 >> 33 xxxx«r> cffxooreo utu OO uiui uu bo xx #-- -»-» OO oca i«v> l-K 33 >> 333 xxxxx Xorecff>o:ica3o:ereDOD <_>o«J CO uiui u OO XI •-•- ->-j OO aa v)V> V- 33 >> 333 xxxxxxxxxxececitDsacc ooid uuu cc uiui uu c I •-•- ->•» 00 a <« t-t- 33 >> 333 xxxxxxx

0000 000 ujui u-u ois 1 -^ •?•) 00 a </>i/> ki- 33 >>> 3333U UUUOUUU OOO Uiui UU CC II •- -5-> o aa trivi »-t- 33 >» 3333333 3UUOUjUUU COO UIUj UU OC II —~ "5-5 OO aa V>ts> l-K 33 >>> 33333333OOC O uiuiui U-Ulu CC II •-•-• -5-5 OO aa \nv> t-t-t- 333 >>>>OOOOOO uju id uuu. cc XI •-•-• -5-5 OO aa ISKSI KKK 333 >>>>>>cooooco uûiuj uuu. ccc 11 "•- -5-5 00 aa </m«</> kkk 333 >>>>>>>

ii'Uiimijui uuu coc in •-•-< ->^ 00 aaa wvhsi (-»-»- 33333lUUUnulUltill UlUlUIUI UUU-U CCC HI •-»- -n OO aaa vnnvi KH-I- 33333333333ujuuiu-ui uuuuu ccc xxx •-->- -5-5 000 aaa </»/></> »—•—»—»- »— 33333u-uuuuuu coco xxx ^.-^ -5-5-5-5 ooo aaa i/x/iirtio kkkhhkk-UUUUUUUUU CCCCC XIII ^.»-»- -5-5-5-5 OOO acratt (/.(rttrtviio l-KH-l-l-H-hccccccc nil ^*-.»«h- -5-5-5-5 0000 aaaa »/>oov>i/h/>i/>*/>cccccccccccc XXIXI .,!-.,- -5-5-5-5 00000 aaaaa vi\nvn/vnxn\fnrnnuiv>vi

IXIIIII --.-.-^. -5-5-5-> 00000 aaaaaaaIIIIIIIIIXXII +.**—+-*.*.+* -5-5-5-5-5-5 OOOCOOO aâ q a a. a a ct a a a a a.

IIIXXXX ^- t-<»-^-4^,^-»-^^, -5-5-5-5-^-5-5-7 OOOOOOOOO aaaaaaa.~^. _»-,-._. ,_»-*-*-»— ^-^»— -5-5-^-5-5-5-5-5-5-5 OOOOOOOOOOOOOO

n u n -»-n-«»-l 11 n n iwh -5-5-5-5-5-5-5-5-5-5-5-5-5-5-5-5 OOOOOOOOOOOOOO-5"5-5 -> -5 -5 -3 "5-5 -5 -5-5^ -5 -5 "5 -5 -5-5 -5 -5 -5 -5 -5 -5 "5 -7 -5 -5 -5-5 —>

-5-5 -5—. "5 "5 "5 -5 -5"5 -5 -5 "5 -5 -5-5^-5 -5 -5 -5 "5-5 -5 "5 -5T5 -5 "5"5 "5-5 -5 -5"5 -5 -5 -5 -5-5"5^-5 -5"5 -5 -5-5 "5 "5 "5 -5 "5-5 -5 -5 -5T5 -5-5 "5 -5-5-5 -3 -5"5 "5 "5-5 "5-3 -5T5 -5-^-5-5-5^-5-5-5-5-5-5-5-5-5-5-5-5-5-5-5-5-3-5-5-5-5-5-^-5-5-5-5-5-5

OOOOOOOOOOOOOO -5-5-5-5-5-5-5-5-3T5-5-5-5-5-5 ^-^^•- >« (-.„^.^,>-^1^,^ >-.OOOOOOOOOOOOOO -5-5-5-5-5-5-3-5-5-5 ..-._,-.,-._-,-.__.-.--aaaaaaa 000000000 -5-5-5-5-5-5-3-3 „,-^-^.^.,-.i-.^.,- xxiiiixaaaaaaaaaaaaa 0000000 -ni-ni ...-^.m.-. iixiiiiiiixiiaaaaaaa 00000 -5-5-3-5 *»____ xilixxx>siinv.v.v\vw>viviviis,v, aaaaa 00000 -5-5-5-5 _____ xxxn cccccccccccc

tovi««v)u><^v> aaaa 0000 -5-5-5-3 ____ IIXX OCCCCCCl-l-l-Kf-l-t-i-K tnisivnsiifi aaaa 000 -5-5-3-5 »«-•_ IIIX ccccc uuuuuuuuu

l-l-t-H-l-l- «nv3ioco aaa OOo IIT) ^.-- XII CCCC u-uuuuuu33333 Ki-i-i-i- «•>(/></> aaa 000 -5-5 .«_ xxx ccc uuuuu ujuiuiu'uj33333333333 t— I— I- »— tnviio aaa OO -3-5 __ III CCC UUUU IDID Ulin IUIUUIUIUI UIUI33333 Kt- 1- vtviv, aaa 00 -5-5 _.-. ill ccc uuu uiumduiui»>>>>> 333 i-l-K VHfivt ecec OO ->-> -h XI CCC UUU UIUIUI OOOOOOO>>>>>> 333 i-n- vnn aa 00 -5-5 __ 11 cc uuil uiuiui 000000

>>>> 333 KKK «rtli5 aa OO ->-) __ IX CO UUU UiUlUJ OOOO33333333 >>> 33 l-K l/n/> aa OO -5-3 _- XI OO UU uju OOO UUUOUUuU3 3333333 >>> 33 l-K VHn aa O -5*5 _ II CO UU UJUI OOO OOOOOOO O3333 >>> 33 KK viVi a OO "5-5 _»- I OO U-U UIUI OOO OOOOXXXXXXX 333 >> 33 KK VI ec OO -3-3 --. I O UU UIUI OO OOO CD CO ff> OC CD CD 0?xxxxxxxxxx 333 >> 33 K «/></> aa OO -5-5 __ ii oo u uiuj OO ooo erajeooDojajeooccffiX XXXXX 333 >> 33 KK VIV> CCCC OO "5"5 __ IX OC UU UlUI OO OOO 030003030? SXXXX 33 >> 3 K VI OC O "5-5 _ I O u- ID OO OO 03030303

>->- XXX 33 > 33 KK «/></> a O -3-5 _ I CO UU UIUI O OO OOOCOD <«I>->->->->->-V>->- XX 33 >> 3 K 1/5*0 a O "5-3 _ I CO U UI OO OO COCC <«<««!<«

>->•>>->->•>->->->->->• XX 33 >> 33 K vi ecec O -5-5 _ XI c U UIUI OO OO OOOD <«<<«<<<«I<<-I>->->->>- >->•>>> XX 33 > 3 KK VI eC O "5-5 _ I C UU. UI O OO 0303 <<<•»< <<<<«*>->->- >->->- XX 33 >> 3 K VI>» >->>- XX 33 > 33 K V)l/7» >->->- XX 33 > 3 K VIV> *jm >->->- XX 33 >> 3 KK V)>-> misiisikjM >->->- X 3 > 33 K v>>->- nnnnnn >->- XX 33 > 3 K v>>> isiKjtxNjr^rsiM >>->- X 3 » 3 K V)>> NNMKJMIMNOJ >" >- XX 3 > 3 K VI

X >> NNNNNMK 3- 3-> XX 33 > 3 K VX >->- kj-jivh-ji-jnj^jivi >->• X 3 > 33 K VX > *JK.»vlKJKJ*JhJ >-> X 3 > 3 K V3 X >->- K1NMMMKJ VJ- XX 3 >> 3 K V3 X >-> *jivi-*t~j*j(si >->- XX 3 > 3 K V>* X >-> i^kiimMivi >->- X 33 > 3 K V3 X y- isimivi >-v X 3 3 > 3 K V

3> 3 X >->- >->- X 3 > 3 K V> 3 X >->- >-> X 3 > 3 K v

K3 >3 XX j->- >->- X 3 > 3 K VK3 3 XX >->->- >->->- X 3 > 3 K 1/

3> 3 X >>->- VV3- X 3 > 3 K </

3> 3 X >->->->-v >->->->- X 3 > 3 K VOa-OK > 3 X >>>->>->->- X 3 > 3 K V->Oav)K3 > 3 X >->->->->- XX 3 > 3 K V

-5-5 •- I o u Ul OO OO C0O3 «< <<«' -5-5 - I OO U- UIUJ o OO 0303 <<«! <<<' -5-5 X o u Ul o OO 0303 «« «1 "5-5 >-. I o uu ID OO OO coec <<< oo «I -5-5 I O U- UIUJ o o 03 <<< ooooo «1 -5-5 * r c u ui O KJ^J 0000 << OOOOOO <«t1 "5-5 - X O u Ul OO o 03 «t<< coooooo <<O _ I C U Ul o o coco «< oooooooo 4<o I o U Ul O OO coco <<< OOOOOOO 4X< CO

o I o u UIUI o o 03 <•* OOOOOOOO << CO

ol"

o II. Ul o o 03 « OOOOOOO t cco o u. ID oo o 0303 << OOOOOO « 00 oo I o IL Ul o o coco <« OOOOOO «< CO oo I o u ID o OO 00 «< OOOOO « 00 OOo I IS u Ul o OO 03 « OOO < 03 Oo X o u. Ul o o 03 « << CC O OUIo I o IL Ul o o CD « «a< cc o oo I o IL ID o o CO << <r< coco oo ujuo I o IL ID o o OD «<« <« COCO O UJUo I o IL Ul o o CO <«< <a<< CO o OILo I o IL Ul o o 00 <<<<<!<<<< 03 O OIDo I o U- Ui o o 00 <<<<<<< 03 O O UOI—o •— X o u ID c o CO 00 <<<<< CC O O UJU.CIH-)

48

CQ

u ~ a£) 2 co oD • E-i

jC p^ in COU >-i CUC «HP ^ •Pa — (0

49

The command

offline punch file ft07f001

will cause the matrix B to be punched onto cards with the

indicated format of four numbers per card with a field width

of 15 and 8 significant figures.

If the input for the contour map had been the coefficients

of CUPOL, the first page of output would have been as follows:

THIS IS THE FIRST PAGE OUTPUT COEFFICIENTS AS INPUT.

0.333300 X3Y3

1.500000 X2Y3

•2.833000 XY3

2.000000 Y3

1.500000 X3Y2

-6.750000 X2Y2

12.750000 XY2

-9.000000 Y2

-2.833000 X3Y

12.750000 X2Y

•18.750000 XY

9.000000 Y

2.000000 X3

-9.000000 X2

9.000000 X

10.000000

0= 7.0837699378

A= 7.3776 B =

F= 8.8465 G=

0= 10.3154 P =

V= 11.7843 W=

RANGE( 0. 708377D 01

7.6713 C= 7.9651

9.1402 H= 9.4340

10.60 c 2 S= 10.9029

12.0781 X= 12. 3^19

0.1295 940 02 »

0= 8.2589 E= 8.5527

1 = 9.7278 J= 10.0216

T = 11.1967 U= 11.4905

Y = 12.6656 Z= 12.°594

50

C. GRAPH

A plot of the function

x = e"15t sin(54.99t)

is desired from t = 0.0 to t = 0.3. The values were calculated

in a separate program and the values of X were punched onto

cards. They were prepared for offline reading into file

FT04F001.

The first card is a standard CP67 offline read card as

follows starting in column one.

CP67USERIDbbGUxxssssbbbbbbTTTT

where

xx = Terminal number user will be using.

ssss= User's account number.

TTTT= User's name.

The second card is as follows:

OFFLINEbREADbFILEbFT04F001

The next card is a LOAD command card with a 1. in SI.

LOAD A 80 2 1.

The matrix is punched onto cards row-wise with the same

format as one of the options under IMIS and these cards follow

the LOAD card. As many matrices as desired may be loaded in

this manner. The last card is a continue card as follows:

CONT 1

.

This card indicates that all matrices have been read

from file FT04F001. The deck is then loaded into the computer.

51

After logging onto the time sharing system, the command to read

the file is as follows:

offline read *

OFFLINE READ READ FILE FT04F001

IMIS is then executed and the sequence is as follows:

52

<J •> <! <Cw

H & wPi Q O Eh Eh

< <« (dH moEh O « hh"

-p CO J O Q) & Pmu T) CO +J -P(0 fd -H+> 0) U HW ^ S &

53

-X + *K - -X * + —

O

54

o4J

W

o

55

The command

OFFLINE PRINTCC FILE FT0 8F001

will cause the matrix A to be printed on the offline printer

56

VII. IMPROVEMENTS

This system is an open ended system, i.e., any matrix

operation with fewer than four matrix arguments, four integer

arguments and two scalar arguments can be coded as a new

command and added to the system. As coded this program is

sequential. Each command is executed once after it is read,

no facilities for automatic repetitive execution of one or more

commands is included. Such a feature would be very useful if

it could be implemented without introducing extraneous

complexities to the language.

57

APPENDIX A COMPUTER PROGRAM

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LIST OF REFERENCES

1. Holman, J. P., Heat Transfer , 2nd ed., p. 55, McGraw-Hill, 1968.

2. Crandall, S. H. , Engineering Analysis , pp. 1-405,McGraw-Hill, 1956.

3. Schlichting, H., Boundary Layer Theory , 6th ed., pp. 181-184, McGraw-Hill, 1968.

4. Wilkinson, J. P., The Algebraic Eigenvalue Problem ,

pp. 189-483, Oxford University Press, 1965.

5. Clenshaw, C. W. , and others, Modern Computing Methods ,

2nd ed., pp. 1-136, John Wright & Sons, 1961.

6. Forsythe, G. E. and Moler, C. B., Computer Solution ofLinear Algebraic Systems , pp. 1-136, Prentice-Hall, 1967.

7. Fox, L. , An Introduction to Numerical Linear Algebra ,

pp. 60-99, Oxford University Press, 1965.

8. IBM System/360, "FORTRAN IV LANGUAGE," Form C-28-6515-5,IBM Corp., Poughkeepsie, N. Y.

9. Przemieniecki , J. S., Theory of Matrix Structural Analysis ,

pp. 70-82, McGraw-Hill, 1968.

10. USERS MANUAL , 1st ed. , pp. 4-1 - 4-9, Naval PostgraduateSchool Computer Center, 1970.

11. Stroud, A. H. and Secrest, D. , Gaussian QuadratureFormulas

,

p. 7, Prentice-Hall, 1966.

95

INITIAL DISTRIBUTION LIST

No. Copies

1. Defense Documentation Center 2

Cameron StationAlexandria, Virginia 22314

2. Library, Code 0212 2

Naval Postgraduate SchoolMonterey, California 93940

3. Director, Computer Facility, Code 0211 5


4. Professor Gilles Cantin, Code 59Ci 5

Department of Mechanical EngineeringNaval Postgraduate SchoolMonterey, California 93940

5. LT R. D. Little, USN 2

Ship Repair Facility, GuamFPO San Francisco, California 96630

96

Security Classification

DOCUMENT CONTROL DATA -R&D/Security classification o( title, body ol abstract and indexing annotation must be entered when the overall report Is classllied)

I ORIGINATING activity (Corporate author)


2«, REPORT SECURITY CLASSIFICATION

Unclassified26. GROUP

3 REPOR T TITLE

An Interactive Matrix Interpretive System For theIBM 360/67

4. DESCRIPTIVE NOTES (Type ol report and, inclusive dates)

Master's Thesis; June 1970S au THORlS) (First name, middle initial, last name)


«. REPOR T D A TE

June 1970

7a. TOTAL NO. OF PAGES

97

7b. NO. OF REFS

11(a. CONTRACT OR GRANT NO.

b. PROJEC T NO.

0a. ORIGINATOR'S REPORT NUMBERIS)

9b. OTHER REPORT NO(S) (Any other numbers that may be assignedthis report)

10. DISTRIBUTION STATEMENT

This document has been approved for public release and sale;its distribution is unlimited.

11. SUPPLEMENTARY NOTES 12. SPONSORING MILITARY ACTIVITY


13. ABSTR AC T

The Matrix Interpretive System devised by Wilson and modified by

Cantin has been transformed into an interactive program operable under

a time sharing system. Several new commands have been added to extend

the usefulness of the code and give it the capability to offline read,

write and punch data, to plot graphs and contour maps and to integrate

simple polynomial expressions.

DD, F

r."..1473 lPAGE "S/N 0101 -807-681 1 97 Security Classification

A-S1408

Security Classification

KEY WO R DS

Problem Oriented Computer Sublanguage

Matrix Interpretive System

Numerical Linear Algebra

FORMNOV 6 51473 (BACK)

107-68? I 98 Security Classification A- 31 409

.

2 7 12 7

thesL712

An interactive Matrix Interpretive Syste

3 2768 002 12709 4DUDLEY KNOX LIBRARY

an interactive matrix interpretive system for the ibm 360/67. · 2016. 6. 1. · unitedstates...

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