NUMAL Section 4.2.1.A
BEGIN SECTION : 4.2.1.A (July, 1974)
AUTHORS: C.J.ROOTHART.
CONTRIBUTORS: P.W.HEMKER.
INSTITUTE: MATHEMATICAL CENTRE.
RECEIVED: 730530.
BRIEF DESCRIPTION:
QADRAT COMPUTES THE DEFINITE INTEGRAL OF A FUNCTION OF ONE
VARIABLE OVER A FINITE INTERVAL.
KEYWORDS:
INTEGRATION,
QUADRATURE,
DEFINITE INTEGRAL.
CALLING SEQUENCE:
THE HEADING OF THE PROCEDURE READS:
"REAL" "PROCEDURE" QADRAT (X, A, B, FX, E);
"VALUE" A, B; "REAL" X, A, B, FX; "ARRAY" E;
"CODE" 32070;
QADRAT: DELIVERS THE COMPUTED VALUE OF THE DEFINITE INTEGRAL FROM
A TO B OF THE FUNCTION F(X);
THE MEANING OF THE FORMAL PARAMETERS IS:
X: <VARIABLE>;
INTEGRATION VARIABLE; X CAN BE USED AS A JENSEN-PARAMETER
DURING THE EVALUATIONS OF FX;
A,B: <ARITHMETIC EXPRESSION>;
(A,B) DENOTES THE INTERVAL OF INTEGRATION;
B < A IS ALLOWED;
FX: <ARITHMETIC EXPRESSION>;
FX DENOTES THE INTEGRAND F(X). THIS EXPRESSION WILL BE
DEPENDENT ON THE JENSEN-PARAMETER X.
E: <ARRAY IDENTIFIER>;
"ARRAY" E[1:3];
ENTRY: E[1]: THE RELATIVE ACCURACY REQUIRED;
E[2]: THE ABSOLUTE ACCURACY REQUIRED;
EXIT: E[3]: THE NUMBER OF ELEMENTARY INTEGRATIONS WITH
H < ABS(B-A) * E[1].
PROCEDURES USED: NONE.
REQUIRED CENTRAL MEMORY:
EXECUTION FIELD LENGTH: CIRCA 16 + 9 * RECURSION DEPTH.
RUNNING TIME: DEPENDS STRONGLY ON THE DEFINITE INTEGRAL TO COMPUTE.
LANGUAGE: ALGOL 60.
METHOD AND PERFORMANCE: SEE REF[1].
REFERENCES:
[1].C.J.ROOTHART AND H.FIOLET.
QUADRATURE PROCEDURES.
MATH.CENTRE, AMSTERDAM. REPORT MR 137/72.
EXAMPLE OF USE:
"BEGIN"
"ARRAY" E[1:3]; "REAL" T,Q;
EXECUTION FIELD LENGTH: CIRCA 16 + 26 * RECURSION DEPTH.
E[1]:= E[2]:= "-9;
Q:= QADRAT(T,0,3.141592653589 ,SIN(T),E);
OUTPUT(61,"("/,+.15D"+3D,3B,3ZD,/")",Q,E[3]);
"END"
DELIVERS:
+.200000000000033"+001 0
SOURCE TEXT(S):
"CODE" 32070;