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zsysv (3)
  • >> zsysv (3) ( Solaris man: Библиотечные вызовы )
  • 
    NAME
         zsysv - compute the solution to a complex system  of  linear
         equations  A * X = B,
    
    SYNOPSIS
         SUBROUTINE ZSYSV( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK,
                   LWORK, INFO )
    
         CHARACTER UPLO
    
         INTEGER INFO, LDA, LDB, LWORK, N, NRHS
    
         INTEGER IPIV( * )
    
         COMPLEX*16 A( LDA, * ), B( LDB, * ), WORK( LWORK )
    
    
    
         #include <sunperf.h>
    
         void zsysv(char uplo, int n, int  nrhs,  doublecomplex  *za,
                   int  lda, int *ipivot, doublecomplex *zb, int ldb,
                   int *info);
    
    PURPOSE
         ZSYSV computes the solution to a complex  system  of  linear
         equations
            A * X = B, where A is an N-by-N symmetric  matrix  and  X
         and B are N-by-NRHS matrices.
    
         The diagonal pivoting method is used to factor A as
            A = U * D * U**T,  if UPLO = 'U', or
            A = L * D * L**T,  if UPLO = 'L',
         where U (or L) is a product of permutation  and  unit  upper
         (lower)  triangular  matrices,  and D is symmetric and block
         diagonal with 1-by-1 and 2-by-2 diagonal blocks.   The  fac-
         tored  form  of  A is then used to solve the system of equa-
         tions A * X = B.
    
    
    ARGUMENTS
         UPLO      (input) CHARACTER*1
                   = 'U':  Upper triangle of A is stored;
                   = 'L':  Lower triangle of A is stored.
    
         N         (input) INTEGER
                   The number of linear equations, i.e., the order of
                   the matrix A.  N >= 0.
    
         NRHS      (input) INTEGER
                   The number of right hand sides, i.e.,  the  number
                   of columns of the matrix B.  NRHS >= 0.
    
         A         (input/output) COMPLEX*16 array, dimension (LDA,N)
                   On entry, the symmetric matrix A.  If UPLO =  'U',
                   the leading N-by-N upper triangular part of A con-
                   tains the upper triangular part of the  matrix  A,
                   and the strictly lower triangular part of A is not
                   referenced.  If UPLO =  'L',  the  leading  N-by-N
                   lower triangular part of A contains the lower tri-
                   angular part of the matrix  A,  and  the  strictly
                   upper triangular part of A is not referenced.
    
                   On exit, if INFO = 0, the block diagonal matrix  D
                   and the multipliers used to obtain the factor U or
                   L from the factorization  A  =  U*D*U**T  or  A  =
                   L*D*L**T as computed by ZSYTRF.
    
         LDA       (input) INTEGER
                   The leading dimension of  the  array  A.   LDA  >=
                   max(1,N).
    
         IPIV      (output) INTEGER array, dimension (N)
                   Details of the interchanges and the  block  struc-
                   ture  of D, as determined by ZSYTRF.  If IPIV(k) >
                   0, then rows and columns k and IPIV(k) were inter-
                   changed,  and  D(k,k)  is a 1-by-1 diagonal block.
                   If UPLO = 'U' and IPIV(k) = IPIV(k-1)  <  0,  then
                   rows  and  columns  k-1  and  -IPIV(k) were inter-
                   changed and D(k-1:k,k-1:k) is  a  2-by-2  diagonal
                   block.  If UPLO = 'L' and IPIV(k) = IPIV(k+1) < 0,
                   then rows and columns k+1 and -IPIV(k) were inter-
                   changed  and  D(k:k+1,k:k+1)  is a 2-by-2 diagonal
                   block.
    
         B         (input/output)   COMPLEX*16    array,    dimension
                   (LDB,NRHS)
                   On entry, the N-by-NRHS right hand side matrix  B.
                   On  exit,  if  INFO  =  0,  the N-by-NRHS solution
                   matrix X.
    
         LDB       (input) INTEGER
                   The leading dimension of  the  array  B.   LDB  >=
                   max(1,N).
    
         WORK      (workspace/output)  COMPLEX*16  array,   dimension
                   (LWORK)
                   On exit, if INFO = 0, WORK(1) returns the  optimal
                   LWORK.
    
         LWORK     (input) INTEGER
                   The length of WORK.  LWORK >= 1, and for best per-
                   formance  LWORK  >=  N*NB, where NB is the optimal
                   blocksize for ZSYTRF.
    
         INFO      (output) INTEGER
                   = 0: successful exit
                   < 0: if INFO = -i, the i-th argument had an  ille-
                   gal value
                   > 0: if INFO = i, D(i,i)  is  exactly  zero.   The
                   factorization  has  been  completed, but the block
                   diagonal matrix D  is  exactly  singular,  so  the
                   solution could not be computed.
    
    
    
    


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