NUMAL Section 3.1.2.1.1.2.1.2

BEGIN SECTION : 3.1.2.1.1.2.1.2 (June, 1974)

CONTRIBUTOR :    J. KOK.

INSTITUTE   :    MATHEMATICAL CENTRE.

RECEIVED    :    731001.

BRIEF DESCRIPTION  :

    THIS SECTION CONTAINS ONE PROCEDURE,
    CHLDETERMBND, FOR THE CALCULATION OF THE DETERMINANT OF A SYMMETRIC
    POSITIVE DEFINITE BAND MATRIX.

KEY WORDS  :

    DETERMINANT,
    SYMMETRIC POSITIVE DEFINITE MATRIX,
    BAND MATRIX.

CALLING SEQUENCE  :

    THE HEADING OF THE PROCEDURE IS :

    "REAL""PROCEDURE" CHLDETERMBND(A, N, W); "VALUE" N, W;
    "INTEGER" N, W; "ARRAY" A;
    "CODE" 34331;

    CHLDETERMBND DELIVERS THE DETERMINANT OF THE SYMMETRIC POSITIVE
    DEFINITE BAND MATRIX WHOSE CHOLESKY MATRIX IS STORED IN A.

    THE MEANING OF THE FORMAL PARAMETERS IS :

    A, N, W :   SEE 'CALLING SEQUENCE' OF CHLDECBND
                (SECTION 3.1.2.1.1.2.1.1.);
                THE CONTENTS OF A ARE AS PRODUCED BY CHLDECBND OR
                CHLDECSOLBND (SECTION 3.1.2.1.1.2.1.3.).

PROCEDURES USED :    NONE.

RUNNING TIME :    PROPORTIONAL TO N.

LANGUAGE    :    ALGOL 60.

METHOD AND PERFORMANCE :

    CHLDETERMBND CAN BE CALLED AFTER CHLDECBND OR CHLDECSOLBND ONLY IF
    THE CHOLESKY DECOMPOSITION WAS SUCCESSFUL, I.E. IF
    AUX[3] = N.
    THE FUNCTION VALUE OF CHLDETERMBND IS THE SQUARE OF THE DETERMINANT
    OF THE CHOLESKY MATRIX.
    CHLDETERMBND SHOULD NOT BE CALLED WHEN OVERFLOW CAN BE EXPECTED.

EXAMPLE OF USE :

    SEE EXAMPLES OF USE OF CHLSOLBND AND CHLDECSOLBND.

SOURCE TEXT(S) :
"CODE" 34331;