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;