Previous: chisl Up: ../linpack.html Next: chpdi

CHPCO

       SUBROUTINE CHPCO(AP,N,KPVT,RCOND,Z)
       INTEGER N,KPVT(1)
       COMPLEX AP(1),Z(1)
       REAL RCOND
 C
 C     CHPCO FACTORS A COMPLEX HERMITIAN MATRIX STORED IN PACKED
 C     FORM BY ELIMINATION WITH SYMMETRIC PIVOTING AND ESTIMATES
 C     THE CONDITION OF THE MATRIX.
 C
 C     IF  RCOND  IS NOT NEEDED, CHPFA IS SLIGHTLY FASTER.
 C     TO SOLVE  A*X = B , FOLLOW CHPCO BY CHPSL.
 C     TO COMPUTE  INVERSE(A)*C , FOLLOW CHPCO BY CHPSL.
 C     TO COMPUTE  INVERSE(A) , FOLLOW CHPCO BY CHPDI.
 C     TO COMPUTE  DETERMINANT(A) , FOLLOW CHPCO BY CHPDI.
 C     TO COMPUTE  INERTIA(A), FOLLOW CHPCO BY CHPDI.
 C
 C     ON ENTRY
 C
 C        AP      COMPLEX (N*(N+1)/2)
 C                THE PACKED FORM OF A HERMITIAN MATRIX  A .  THE
 C                COLUMNS OF THE UPPER TRIANGLE ARE STORED SEQUENTIALLY
 C                IN A ONE-DIMENSIONAL ARRAY OF LENGTH  N*(N+1)/2 .
 C                SEE COMMENTS BELOW FOR DETAILS.
 C
 C        N       INTEGER
 C                THE ORDER OF THE MATRIX  A .
 C
 C     OUTPUT
 C
 C        AP      A BLOCK DIAGONAL MATRIX AND THE MULTIPLIERS WHICH
 C                WERE USED TO OBTAIN IT STORED IN PACKED FORM.
 C                THE FACTORIZATION CAN BE WRITTEN  A = U*D*CTRANS(U)
 C                WHERE  U  IS A PRODUCT OF PERMUTATION AND UNIT
 C                UPPER TRIANGULAR MATRICES , CTRANS(U) IS THE
 C                CONJUGATE TRANSPOSE OF  U , AND  D  IS BLOCK DIAGONAL
 C                WITH 1 BY 1 AND 2 BY 2 BLOCKS.
 C
 C        KPVT    INTEGER(N)
 C                AN INTEGER VECTOR OF PIVOT INDICES.
 C
 C        RCOND   REAL
 C                AN ESTIMATE OF THE RECIPROCAL CONDITION OF  A .
 C                FOR THE SYSTEM  A*X = B , RELATIVE PERTURBATIONS
 C                IN  A  AND  B  OF SIZE  EPSILON  MAY CAUSE
 C                RELATIVE PERTURBATIONS IN  X  OF SIZE  EPSILON/RCOND .
 C                IF  RCOND  IS SO SMALL THAT THE LOGICAL EXPRESSION
 C                           1.0 + RCOND .EQ. 1.0
 C                IS TRUE, THEN  A  MAY BE SINGULAR TO WORKING
 C                PRECISION.  IN PARTICULAR,  RCOND  IS ZERO  IF
 C                EXACT SINGULARITY IS DETECTED OR THE ESTIMATE
 C                UNDERFLOWS.
 C
 C        Z       COMPLEX(N)
 C                A WORK VECTOR WHOSE CONTENTS ARE USUALLY UNIMPORTANT.
 C                IF  A  IS CLOSE TO A SINGULAR MATRIX, THEN  Z  IS
 C                AN APPROXIMATE NULL VECTOR IN THE SENSE THAT
 C                NORM(A*Z) = RCOND*NORM(A)*NORM(Z) .
 C
 C     PACKED STORAGE
 C
 C          THE FOLLOWING PROGRAM SEGMENT WILL PACK THE UPPER
 C          TRIANGLE OF A HERMITIAN MATRIX.
 C
 C                K = 0
 C                DO 20 J = 1, N
 C                   DO 10 I = 1, J
 C                      K = K + 1
 C                      AP(K) = A(I,J)
 C             10    CONTINUE
 C             20 CONTINUE
 C
 C     LINPACK. THIS VERSION DATED 08/14/78 .
 C     CLEVE MOLER, UNIVERSITY OF NEW MEXICO, ARGONNE NATIONAL LAB.
 C
 C     SUBROUTINES AND FUNCTIONS
 C
 C     LINPACK CHPFA
 C     BLAS CAXPY,CDOTC,CSSCAL,SCASUM
 C     FORTRAN ABS,AIMAG,AMAX1,CMPLX,CONJG,IABS,REAL