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zpbsv (3)
  • >> zpbsv (3) ( Solaris man: Библиотечные вызовы )
  • 
    NAME
         zpbsv - compute the solution to a complex system  of  linear
         equations  A * X = B,
    
    SYNOPSIS
         SUBROUTINE ZPBSV( UPLO, N, KD, NRHS, AB, LDAB, B, LDB,  INFO
                   )
    
         CHARACTER UPLO
    
         INTEGER INFO, KD, LDAB, LDB, N, NRHS
    
         COMPLEX*16 AB( LDAB, * ), B( LDB, * )
    
    
    
         #include <sunperf.h>
    
         void zpbsv(char uplo, int n, int kd, int nrhs, doublecomplex
                   *zab,  int  ldab,  doublecomplex *zb, int ldb, int
                   *info) ;
    
    PURPOSE
         ZPBSV computes the solution to a complex  system  of  linear
         equations
            A * X = B, where A is an N-by-N Hermitian positive defin-
         ite band matrix 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 band matrix, and L is a lower
         triangular  band matrix, with the same number of superdiago-
         nals or subdiagonals as A.  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.
    
         KD        (input) INTEGER
                   The number of superdiagonals of the  matrix  A  if
                   UPLO  = 'U', or the number of subdiagonals if UPLO
                   = 'L'.  KD >= 0.
    
         NRHS      (input) INTEGER
                   The number of right hand sides, i.e.,  the  number
                   of columns of the matrix B.  NRHS >= 0.
    
         AB        (input/output)   COMPLEX*16    array,    dimension
                   (LDAB,N)
                   On entry, the upper or lower triangle of the  Her-
                   mitian  band  matrix  A,  stored in the first KD+1
                   rows of the array.  The j-th column of A is stored
                   in the j-th column of the array AB as follows:  if
                   UPLO = 'U', AB(KD+1+i-j,j) = A(i,j)  for  max(1,j-
                   KD)<=i<=j;  if UPLO = 'L', AB(1+i-j,j)    = A(i,j)
                   for  j<=i<=min(N,j+KD).   See  below  for  further
                   details.
    
                   On exit, if INFO = 0, the triangular factor U or L
                   from  the Cholesky factorization A = U**H*U or A =
                   L*L**H of the band matrix A, in the  same  storage
                   format as A.
    
         LDAB      (input) INTEGER
                   The leading dimension of the array  AB.   LDAB  >=
                   KD+1.
    
         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, 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 band storage scheme  is  illustrated  by  the  following
         example, when N = 6, KD = 2, and UPLO = 'U':
    
         On entry:                       On exit:
    
             *    *   a13  a24  a35  a46      *    *   u13  u24  u35  u46
             *   a12  a23  a34  a45  a56      *   u12  u23  u34  u45  u56
            a11  a22  a33  a44  a55  a66     u11  u22  u33  u44  u55  u66
    
         Similarly, if UPLO = 'L' the format of A is as follows:
    
         On entry:                       On exit:
    
            a11  a22  a33  a44  a55  a66     l11  l22  l33  l44  l55  l66
            a21  a32  a43  a54  a65   *      l21  l32  l43  l54  l65   *
            a31  a42  a53  a64   *    *      l31  l42  l53  l64   *    *
    
         Array elements marked * are not used by the routine.
    
    
    
    


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