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Интерактивная система просмотра системных руководств (man-ов)

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sgbsv (3)
  • >> sgbsv (3) ( Solaris man: Библиотечные вызовы )
  • 
    NAME
         sgbsv - compute the solution to  a  real  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 SGBSV( N, KL, KU, NRHS, AB, LDAB, IPIV,  B,  LDB,
                   INFO )
    
         INTEGER INFO, KL, KU, LDAB, LDB, N, NRHS
    
         INTEGER IPIV( * )
    
         REAL AB( LDAB, * ), B( LDB, * )
    
    
    
         #include <sunperf.h>
    
         void sgbsv(int n, int kl, int ku, int nrhs, float *sab,  int
                   ldab,  int *ipivot, float *sb, int ldb, int *info)
                   ;
    
    PURPOSE
         SGBSV computes the solution to a real system of linear equa-
         tions 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) REAL 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) REAL 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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