C                                                                1/15/81
C***********************************************************************
C  ODRV -- DRIVER FOR SPARSE MATRIX REORDERING ROUTINES
C***********************************************************************
        SUBROUTINE  ODRV
     *     (N, IA,JA,A, P,IP, NSP,ISP, PATH, FLAG)
C
C  DESCRIPTION
C
C    ODRV FINDS A MINIMUM DEGREE ORDERING OF THE ROWS AND COLUMNS OF A
C    SYMMETRIC MATRIX M STORED IN (IA,JA,A) FORMAT (SEE BELOW).  FOR THE
C    REORDERED MATRIX, THE WORK AND STORAGE REQUIRED TO PERFORM GAUSSIAN
C    ELIMINATION IS (USUALLY) SIGNIFICANTLY LESS.
C
C    IF ONLY THE NONZERO ENTRIES IN THE UPPER TRIANGLE OF M ARE BEING
C    STORED, THEN ODRV SYMMETRICALLY REORDERS (IA,JA,A), (OPTIONALLY)
C    WITH THE DIAGONAL ENTRIES PLACED FIRST IN EACH ROW.  THIS IS TO
C    ENSURE THAT IF M(I,J) WILL BE IN THE UPPER TRIANGLE OF M WITH
C    RESPECT TO THE NEW ORDERING, THEN M(I,J) IS STORED IN ROW I (AND
C    THUS M(J,I) IS NOT STORED);  WHEREAS IF M(I,J) WILL BE IN THE
C    STRICT LOWER TRIANGLE OF M, THEN M(J,I) IS STORED IN ROW J (AND
C    THUS M(I,J) IS NOT STORED).
C
C
C  STORAGE OF SPARSE MATRICES
C
C    THE NONZERO ENTRIES OF THE MATRIX M ARE STORED ROW-BY-ROW IN THE
C    ARRAY A.  TO IDENTIFY THE INDIVIDUAL NONZERO ENTRIES IN EACH ROW,
C    WE NEED TO KNOW IN WHICH COLUMN EACH ENTRY LIES.  THESE COLUMN
C    INDICES ARE STORED IN THE ARRAY JA;  I.E., IF  A(K) = M(I,J),  THEN
C    JA(K) = J.  TO IDENTIFY THE INDIVIDUAL ROWS, WE NEED TO KNOW WHERE
C    EACH ROW STARTS.  THESE ROW POINTERS ARE STORED IN THE ARRAY IA;
C    I.E., IF M(I,J) IS THE FIRST NONZERO ENTRY (STORED) IN THE I-TH ROW
C    AND  A(K) = M(I,J),  THEN  IA(I) = K.  MOREOVER, IA(N+1) POINTS TO
C    THE FIRST LOCATION FOLLOWING THE LAST ELEMENT IN THE LAST ROW.
C    THUS, THE NUMBER OF ENTRIES IN THE I-TH ROW IS  IA(I+1) - IA(I),
C    THE NONZERO ENTRIES IN THE I-TH ROW ARE STORED CONSECUTIVELY IN
C
C            A(IA(I)),  A(IA(I)+1),  ..., A(IA(I+1)-1),
C
C    AND THE CORRESPONDING COLUMN INDICES ARE STORED CONSECUTIVELY IN
C
C            JA(IA(I)), JA(IA(I)+1), ..., JA(IA(I+1)-1).
C
C    SINCE THE COEFFICIENT MATRIX IS SYMMETRIC, ONLY THE NONZERO ENTRIES
C    IN THE UPPER TRIANGLE NEED BE STORED.  FOR EXAMPLE, THE MATRIX
C
C             ( 1  0  2  3  0 )
C             ( 0  4  0  0  0 )
C         M = ( 2  0  5  6  0 )
C             ( 3  0  6  7  8 )
C             ( 0  0  0  8  9 )
C
C    COULD BE STORED AS
C
C            \ 1  2  3  4  5  6  7  8  9 10 11 12 13
C         ---+--------------------------------------
C         IA \ 1  4  5  8 12 14
C         JA \ 1  3  4  2  1  3  4  1  3  4  5  4  5
C          A \ 1  2  3  4  2  5  6  3  6  7  8  8  9
C
C    OR (SYMMETRICALLY) AS
C
C            \ 1  2  3  4  5  6  7  8  9
C         ---+--------------------------
C         IA \ 1  4  5  7  9 10
C         JA \ 1  3  4  2  3  4  4  5  5
C          A \ 1  2  3  4  5  6  7  8  9          .
C
C
C  PARAMETERS
C
C    N    - ORDER OF THE MATRIX
C
C    IA   - INTEGER ONE-DIMENSIONAL ARRAY CONTAINING POINTERS TO DELIMIT
C           ROWS IN JA AND A;  DIMENSION = N+1
C
C    JA   - INTEGER ONE-DIMENSIONAL ARRAY CONTAINING THE COLUMN INDICES
C           CORRESPONDING TO THE ELEMENTS OF A;  DIMENSION = NUMBER OF
C           NONZERO ENTRIES IN (THE UPPER TRIANGLE OF) M
C
C    A    - REAL ONE-DIMENSIONAL ARRAY CONTAINING THE NONZERO ENTRIES IN
C           (THE UPPER TRIANGLE OF) M, STORED BY ROWS;  DIMENSION =
C           NUMBER OF NONZERO ENTRIES IN (THE UPPER TRIANGLE OF) M
C
C    P    - INTEGER ONE-DIMENSIONAL ARRAY USED TO RETURN THE PERMUTATION
C           OF THE ROWS AND COLUMNS OF M CORRESPONDING TO THE MINIMUM
C           DEGREE ORDERING;  DIMENSION = N
C
C    IP   - INTEGER ONE-DIMENSIONAL ARRAY USED TO RETURN THE INVERSE OF
C           THE PERMUTATION RETURNED IN P;  DIMENSION = N
C
C    NSP  - DECLARED DIMENSION OF THE ONE-DIMENSIONAL ARRAY ISP;  NSP
C           MUST BE AT LEAST  3N+4K,  WHERE K IS THE NUMBER OF NONZEROES
C           IN THE STRICT UPPER TRIANGLE OF M
C
C    ISP  - INTEGER ONE-DIMENSIONAL ARRAY USED FOR WORKING STORAGE;
C           DIMENSION = NSP
C
C    PATH - INTEGER PATH SPECIFICATION;  VALUES AND THEIR MEANINGS ARE -
C             1  FIND MINIMUM DEGREE ORDERING ONLY
C             2  FIND MINIMUM DEGREE ORDERING AND REORDER SYMMETRICALLY
C                  STORED MATRIX (USED WHEN ONLY THE NONZERO ENTRIES IN
C                  THE UPPER TRIANGLE OF M ARE BEING STORED)
C             3  REORDER SYMMETRICALLY STORED MATRIX AS SPECIFIED BY
C                  INPUT PERMUTATION (USED WHEN AN ORDERING HAS ALREADY
C                  BEEN DETERMINED AND ONLY THE NONZERO ENTRIES IN THE
C                  UPPER TRIANGLE OF M ARE BEING STORED)
C             4  SAME AS 2 BUT PUT DIAGONAL ENTRIES AT START OF EACH ROW
C             5  SAME AS 3 BUT PUT DIAGONAL ENTRIES AT START OF EACH ROW
C
C    FLAG - INTEGER ERROR FLAG;  VALUES AND THEIR MEANINGS ARE -
C               0    NO ERRORS DETECTED
C              9N+K  INSUFFICIENT STORAGE IN MD
C             10N+1  INSUFFICIENT STORAGE IN ODRV
C             11N+1  ILLEGAL PATH SPECIFICATION
C
C
C  CONVERSION FROM REAL TO DOUBLE PRECISION
C
C    CHANGE THE REAL DECLARATIONS IN ODRV AND SRO TO DOUBLE PRECISION
C    DECLARATIONS.
C
C-----------------------------------------------------------------------
C