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cppsv (3)
  • >> cppsv (3) ( Solaris man: Библиотечные вызовы )
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    NAME
         cppsv - compute the solution to a complex system  of  linear
         equations  A * X = B,
    
    SYNOPSIS
         SUBROUTINE CPPSV( UPLO, N, NRHS, AP, B, LDB, INFO )
    
         CHARACTER UPLO
    
         INTEGER INFO, LDB, N, NRHS
    
         COMPLEX AP( * ), B( LDB, * )
    
    
    
         #include <sunperf.h>
    
         void cppsv(char uplo, int n, int nrhs, complex *cap, complex
                   *cb, int ldb, int *info) ;
    
    PURPOSE
         CPPSV computes the solution to a complex  system  of  linear
         equations
            A * X = B, where A is an N-by-N Hermitian positive defin-
         ite matrix stored in packed format and X and B are N-by-NRHS
         matrices.
    
         The Cholesky decomposition is used to factor A as
            A = U**H* U,  if UPLO = 'U', or
            A = L * L**H,  if UPLO = 'L',
         where U is an upper triangular matrix and L is a lower  tri-
         angular  matrix.   The  factored  form  of A is then used to
         solve the system of equations 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.
    
         AP        (input/output)    COMPLEX     array,     dimension
                   (N*(N+1)/2)
                   On entry, the upper or lower triangle of the  Her-
                   mitian  matrix  A,  packed  columnwise in a linear
                   array.  The j-th column of  A  is  stored  in  the
                   array  AP  as  follows:  if UPLO = 'U', AP(i + (j-
                   1)*j/2) = A(i,j) for 1<=i<=j; if UPLO = 'L',  AP(i
                   + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.  See below
                   for further details.
    
                   On exit, if INFO = 0, the factor U or L  from  the
                   Cholesky  factorization  A = U**H*U or A = L*L**H,
                   in the same storage format as A.
    
         B         (input/output) COMPLEX 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).
    
         INFO      (output) INTEGER
                   = 0:  successful exit
                   < 0:  if INFO = -i, the i-th argument had an ille-
                   gal value
                   > 0:  if INFO = i, the leading minor of order i of
                   A  is  not positive definite, so the factorization
                   could not be completed, and the solution  has  not
                   been computed.
    
    FURTHER DETAILS
         The packed storage scheme is illustrated  by  the  following
         example when N = 4, UPLO = 'U':
    
         Two-dimensional storage of the Hermitian matrix A:
    
            a11 a12 a13 a14
                a22 a23 a24
                    a33 a34     (aij = conjg(aji))
                        a44
    
         Packed storage of the upper triangle of A:
    
         AP = [ a11, a12, a22, a13, a23, a33, a14, a24, a34, a44 ]
    
    
    
    


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