NUMAL Section 3.3.1.1.3.2

BEGIN SECTION : 3.3.1.1.3.2 (November, 1976)

AUTHOR/CONTRIBUTOR: J.J.G. ADMIRAAL.

INSTITUTE: UNIVERSITY OF AMSTERDAM.

RECEIVED: 761101.

BRIEF DESCRIPTION:
    THE PROCEDURE ORTHOG ORTHOGONALIZES SOME ADJACENT MATRIX COLUMNS
    ACCORDING TO THE MODIFIED GRAM SCHMIDT METHOD (SEE [1]).

KEYWORDS:
    MATRIX COLUMNS,
    MODIFIED GRAM SCHMIDT ORTHOGONALIZATION.

CALLING SEQUENCE:

    THE DECLARATION OF THE PROCEDURE IN THE CALLING PROGRAM READS:

    "PROCEDURE" ORTHOG(N,LC,UC,X);
    "VALUE" N,LC,UC; "INTEGER" N,LC,UC;"ARRAY" X;
    "CODE" 36402;

    THE MEANING OF THE FORMAL PARAMETERS IS:
    N    :<ARITHMETIC EXPRESSION>;
          THE ORDER OF THE MATRIX X;
    LC   :<ARITHMETIC EXPRESSIOM>;
          THE LOWER COLUMN INDEX OF THE MATRIX COLUMNS;
    UC   :<ARITHMETIC EXPRESSION>;
          THE UPPER COLUMN INDEX OF THE MATRIX COLUMNS;
    X    :<ARRAY IDENTIFIER>;
          "ARRAY" X[1:N,LC:UC];
          ENTRY: THE MATRIX COLUMNS,TO BE
                 ORTHOGONALIZED;
          EXIT: THE ORTHOGONALIZED MATRIX COLUMNS.

PROCEDURES USED:
    TAMMAT = CP34014,
    ELMCOL = CP34023.

REQUIRED CENTRAL MEMORY: NO LOCAL ARRAYS ARE DECLARED.

RUNNING TIME: PROPORTIONAL TO N**3.

LANGUAGE: ALGOL 60.

METHOD AND PERFORMANCE:
    THE MODIFIED GRAM SCHMIDT METHOD (SEE [1],CHAPTER 4.54).

EXAMPLE OF USE: THE PROCEDURE ORTHOG IS USED IN SYMEIGIMP.
                (SECTION 3.3.1.1.3.3).

REFERENCES:
    [1]   J.H. WILKINSON.
          THE ALGEBRAIC EIGENVALUE PROBLEM.
          CLARENDON PRESS,OXFORD,1965.

SOURCE TEXT:
"CODE" 36402;