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zgbsv (3)
  • >> zgbsv (3) ( Solaris man: Библиотечные вызовы )
  • 
    NAME
         zgbsv - compute the solution to a complex system  of  linear
         equations  A  *  X  = B, where A is a band matrix of order N
         with KL subdiagonals and KU superdiagonals, and X and B  are
         N-by-NRHS matrices
    
    SYNOPSIS
         SUBROUTINE ZGBSV( N, KL, KU, NRHS, AB, LDAB, IPIV,  B,  LDB,
                   INFO )
    
         INTEGER INFO, KL, KU, LDAB, LDB, N, NRHS
    
         INTEGER IPIV( * )
    
         COMPLEX*16 AB( LDAB, * ), B( LDB, * )
    
    
    
         #include <sunperf.h>
    
         void zgbsv(int n, int kl, int ku,  int  nrhs,  doublecomplex
                   *zab,  int  ldab,  int *ipivot, doublecomplex * b,
                   int ldb, int *info) ;
    
    PURPOSE
         ZGBSV computes the solution to a complex  system  of  linear
         equations  A  *  X  = B, where A is a band matrix of order N
         with KL subdiagonals and KU superdiagonals, and X and B  are
         N-by-NRHS matrices.
    
         The LU decomposition with partial pivoting  and  row  inter-
         changes  is used to factor A as A = L * U, where L is a pro-
         duct of permutation and unit lower triangular matrices  with
         KL subdiagonals, and U is upper triangular with KL+KU super-
         diagonals.  The factored form of A is then used to solve the
         system of equations A * X = B.
    
    
    ARGUMENTS
         N         (input) INTEGER
                   The number of linear equations, i.e., the order of
                   the matrix A.  N >= 0.
    
         KL        (input) INTEGER
                   The number of subdiagonals within the band  of  A.
                   KL >= 0.
    
         KU        (input) INTEGER
                   The number of superdiagonals within the band of A.
                   KU >= 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 matrix A in band  storage,  in  rows
                   KL+1  to 2*KL+KU+1; rows 1 to KL of the array need
                   not be set.  The j-th column of A is stored in the
                   j-th   column   of   the   array  AB  as  follows:
                   AB(KL+KU+1+i-j,j)   =    A(i,j)    for    max(1,j-
                   KU)<=i<=min(N,j+KL)  On  exit, details of the fac-
                   torization: U is stored  as  an  upper  triangular
                   band matrix with KL+KU superdiagonals in rows 1 to
                   KL+KU+1, and the multipliers used during the  fac-
                   torization   are   stored   in   rows  KL+KU+2  to
                   2*KL+KU+1.  See below for further details.
    
         LDAB      (input) INTEGER
                   The leading dimension of the array  AB.   LDAB  >=
                   2*KL+KU+1.
    
         IPIV      (output) INTEGER array, dimension (N)
                   The pivot  indices  that  define  the  permutation
                   matrix  P;  row  i  of the matrix was interchanged
                   with row IPIV(i).
    
         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, U(i,i) is  exactly  zero.   The
                   factorization has been completed, but the factor U
                   is exactly singular, and the solution has not been
                   computed.
    
    FURTHER DETAILS
         The band storage scheme  is  illustrated  by  the  following
         example, when M = N = 6, KL = 2, KU = 1:
    
         On entry:                       On exit:
    
             *    *    *    +    +    +       *    *    *   u14   u25
    
         u36
             *    *    +    +    +    +       *    *   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
            a21  a32  a43  a54  a65   *      m21  m32  m43  m54   m65
         *
            a31  a42  a53  a64   *    *      m31  m42  m53   m64    *
         *
    
         Array elements marked * are not used by  the  routine;  ele-
         ments marked + need not be set on entry, but are required by
         the routine to  store  elements  of  U  because  of  fill-in
         resulting from the row interchanges.
    
    
    
    


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