NUMAL Section 3.1.1.1.1.2.2

BEGIN SECTION : 3.1.1.1.1.2.2 (February, 1979)

CONTRIBUTORS: S.P.N. VAN KAMPEN, J. KOK.       

INSTITUTE: MATHEMATICAL CENTRE.      

RECEIVED: 731015.

BRIEF DESCRIPTION: 

    THIS SECTION CONTAINS TWO PROCEDURES:      
    CHLDETERM2, FOR THE CALCULATION OF THE DETERMINANT OF A
    SYMMETRIC POSITIVE DEFINITE MATRIX WHOSE CHOLESKY MATRIX IS  GIVEN       
    IN THE UPPER TRIANGLE OF A TWO-DIMENSIONAL ARRAY;    
    CHLDETERM1, FOR THE CALCULATION OF THE DETERMINANT OF A
    SYMMETRIC POSITIVE DEFINITE MATRIX WHOSE CHOLESKY MATRIX IS  GIVEN       
    COLUMNWISE IN A ONE-DIMENSIONAL ARRAY.     

KEYWORDS:

    DETERMINANT, 
    POSITIVE DEFINITE SYMMETRIC MATRIX,
    CHOLESKY DECOMPOSITION.


SUBSECTION: CHLDETERM2.    

CALLING SEQUENCE:

    THE HEADING OF THE PROCEDURE IS: 
    "REAL" "PROCEDURE" CHLDETERM2(A, N); "VALUE" N; "INTEGER" N;   
    "ARRAY" A; "CODE" 34312; 

    CHLDETERM2  := THE  DETERMINANT  OF THE  SYMMETRIC  POSITIVE   
    DEFINITE MATRIX OF WHICH THE CHOLESKY MATRIX IS STORED IN A;   

    THE MEANING OF THE FORMAL PARAMETERS IS:   
    A:      <ARRAY IDENTIFIER>;      
            "ARRAY" A[1:N,1:N];      
            ENTRY: THE  UPPER-TRIANGULAR PART OF THE  CHOLESKY MATRIX
                   AS  PRODUCED BY CHLDEC2 (SECTION  3.1.1.1.1.2.1) OR       
                   CHLDECSOL2 (SECTION  3.1.1.1.1.2.3)  MUST  BE GIVEN       
                   IN THE UPPER TRIANGLE OF A; 
            EXIT:  THE CONTENTS OF A ARE NOT CHANGED;    
    N:      <ARITHMETIC EXPRESSION>; 
            THE ORDER OF THE MATRIX. 

PROCEDURES USED: NONE.     

REQUIRED CENTRAL MEMORY: NO EXTRA ARRAYS ARE DECLARED.   

RUNNING TIME: PROPORTIONAL TO N.     

METHOD AND PERFORMANCE:    

    THE PROCEDURE CHLDETERM2  SHOULD BE CALLED AFTER A  SUCCESSFUL CALL      
    OF CHLDEC2 OR CHLDECSOL2, I.E. IF AUX[3] = N;
    CHLDETERM2  SHOULD  NOT  BE CALLED  IF OVERFLOW IS TO BE  EXPECTED.      

EXAMPLE OF USE:  

    SEE EXAMPLE OF USE OF CHLDECINV2 (SECTION 3.1.1.1.1.2.4)       


SUBSECTION: CHLDETERM1.    

CALLING SEQUENCE:

    THE HEADING OF THE PROCEDURE IS: 
    "REAL" "PROCEDURE" CHLDETERM1(A, N); "VALUE" N; "INTEGER" N;   
    "ARRAY" A; "CODE" 34313; 

    CHLDETERM1  := THE  DETERMINANT  OF THE  SYMMETRIC  POSITIVE   
    DEFINITE MATRIX OF WHICH THE CHOLESKY MATRIX IS STORED IN A;   

    THE MEANING OF THE FORMAL PARAMETERS IS:   
    A:      <ARRAY IDENTIFIER>;      
            "ARRAY" A[1 : (N + 1) * N // 2];   
            ENTRY: THE  UPPER-TRIANGULAR PART OF THE  CHOLESKY MATRIX
                   AS  PRODUCED BY CHLDEC1 (SECTION  3.1.1.1.1.2.1) OR       
                   CHLDECSOL1 (SECTION  3.1.1.1.1.2.3)  MUST  BE GIVEN       
                   COLUMNWISE IN ARRAY A;      
            EXIT:  THE CONTENTS OF A ARE NOT CHANGED;    
    N:      <ARITHMETIC EXPRESSION>; 
            THE ORDER OF THE MATRIX. 

PROCEDURES USED: NONE.     

REQUIRED CENTRAL MEMORY: NO EXTRA ARRAYS ARE DECLARED.   

RUNNING TIME: PROPORTIONAL TO N.     

METHOD AND PERFORMANCE:    

    THE PROCEDURE CHLDETERM1  SHOULD BE CALLED AFTER A  SUCCESSFUL CALL      
    OF CHLDEC1 OR CHLDECSOL1, I.E. IF AUX[3] = N;
    CHLDETERM1  SHOULD  NOT  BE  CALLED  IF OVERFLOW IS TO BE EXPECTED.      

EXAMPLE OF USE:  

    SEE EXAMPLE OF USE OF CHLDECINV1, SECTION 3.1.1.1.1.2.4.       

SOURCE TEXT(S) : 

"CODE" 34312;

"CODE" 34313;