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Интерактивная система просмотра системных руководств (man-ов)

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zhpsv (3)
  • >> zhpsv (3) ( Solaris man: Библиотечные вызовы )
  • 
    NAME
         zhpsv - compute the solution to a complex system  of  linear
         equations  A * X = B,
    
    SYNOPSIS
         SUBROUTINE ZHPSV( UPLO, N, NRHS, AP, IPIV, B, LDB, INFO )
    
         CHARACTER UPLO
    
         INTEGER INFO, LDB, N, NRHS
    
         INTEGER IPIV( * )
    
         COMPLEX*16 AP( * ), B( LDB, * )
    
    
    
         #include <sunperf.h>
    
         void zhpsv(char uplo, int n, int nrhs,  doublecomplex  *zap,
                   int  *ipivot,  doublecomplex  *zb,  int  ldb,  int
                   *info) ;
    
    PURPOSE
         ZHPSV computes the solution to a complex  system  of  linear
         equations
            A * X = B, where A is an N-by-N Hermitian  matrix  stored
         in packed format and X and B are N-by-NRHS matrices.
    
         The diagonal pivoting method is used to factor A as
            A = U * D * U**H,  if UPLO = 'U', or
            A = L * D * L**H,  if UPLO = 'L',
         where U (or L) is a product of permutation  and  unit  upper
         (lower) triangular matrices, D is Hermitian and block diago-
         nal with 1-by-1 and 2-by-2 diagonal  blocks.   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*16    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, the block diagonal matrix D and the  mul-
                   tipliers used to obtain the factor U or L from the
                   factorization A = U*D*U**H or A = L*D*L**H as com-
                   puted  by  ZHPTRF,  stored  as a packed triangular
                   matrix in the same storage format as A.
    
         IPIV      (output) INTEGER array, dimension (N)
                   Details of the interchanges and the  block  struc-
                   ture  of D, as determined by ZHPTRF.  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).
    
         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.
    
    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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