NUMAL Section 1.1.9

BEGIN SECTION : 1.1.9 (April, 1974)

AUTHORS  : T.J. DEKKER, W. HOFFMANN.

CONTRIBUTORS: W. HOFFMANN, S.P.N. VAN KAMPEN.

INSTITUTE: MATHEMATICAL CENTRE.

RECEIVED: 731030.

BRIEF DESCRIPTION:

    THE PROCEDURE REASCL  NORMALIZES THE  (NON-NULL) COLUMNS  OF A TWO-
    DIMENSIONAL ARRAY IN SUCH A WAY THAT, IN EACH COLUMN, AN ELEMENT OF
    MAXIMUM  ABSOLUTE  VALUE  EQUALS  1.  THE  NORMALIZED  VECTORS  ARE
    DELIVERED IN THE CORRESPONDING COLUMNS OF THE ARRAY.

KEYWORDS:

    NORMALIZATION,
    VECTOR SCALING.

CALLING SEQUENCE:

    THE HEADING OF THE PROCEDURE IS:
    "PROCEDURE" REASCL(A, N, N1, N2); "VALUE" N, N1, N2;
    "INTEGER" N, N1, N2; "ARRAY" A;
    "CODE" 34183;

    THE MEANING OF THE FORMAL PARAMETERS IS:
    A:      <ARRAY IDENTIFIER>;
            A TWO-DIMENSIONAL ARRAY A[1:N,N1:N2];
            ENTRY: THE  N2 - N1 + 1  COLUMN VECTORS MUST BE GIVEN IN A;
            EXIT:  THE NORMALIZED  VECTORS (I.E. IN  EACH VECTOR AN
                   ELEMENT  OF MAXIMUM  ABSOLUTE  VALUE  EQUALS 1)  ARE
                   DELIVERED IN THE CORRESPONDING COLUMNS OF A;
    N:      <ARITHMETIC EXPRESSION>;
            THE NUMBER OF ROWS OF ARRAY A;
    N1, N2: <ARITHMETIC EXPRESSION>;
            THE LOWER AND UPPER BOUND OF THE COLUMN INDICES OF ARRAY A.

PROCEDURES USED: NONE.

RUNNING TIME: PROPORTIONAL TO N * (N2 - N1 + 1).

LANGUAGE:   ALGOL 60.

METHOD AND PERFORMANCE: SEE REF [1].

REFERENCES:
    [1].T.J. DEKKER AND W. HOFFMANN.
        ALGOL 60 PROCEDURES IN NUMERICAL ALGEBRA, PART 2.
        MC TRACT 23, 1968, MATH. CENTR., AMSTERDAM.

EXAMPLE OF USE:

    THE PROCEDURE REASCL IS USED IN REAEIG1, SECTION 3.3.1.2.2.

SOURCE TEXT(S) :

"CODE" 34183;