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ctbmv (3)
  • >> ctbmv (3) ( Solaris man: Библиотечные вызовы )
  • 
    NAME
         ctbmv - perform one of the matrix-vector operations    x  :=
         A*x, or x := A'*x, or x := conjg( A' )*x
    
    SYNOPSIS
         SUBROUTINE CTBMV ( UPLO, TRANS, DIAG, N, K, A, LDA, X,  INCX
                   )
    
         INTEGER INCX, K, LDA, N
    
         CHARACTER*1 DIAG, TRANS, UPLO
    
         COMPLEX A( LDA, * ), X( * )
    
    
    
         #include <sunperf.h>
    
         void ctbmv(char uplo, char trans, char diag, int n,  int  k,
                   complex *ca, int lda, complex *cx, int incx);
    
    PURPOSE
         CTBMV  performs one of the  matrix-vector  operations  x  :=
         A*x,  or  x  :=  A'*x, or x := conjg( A' )*x where x is an n
         element vector and  A is an n by n unit, or non-unit,  upper
         or lower triangular band matrix, with ( k + 1 ) diagonals.
    
    
    PARAMETERS
         UPLO      - CHARACTER*1.
                   On entry, UPLO specifies whether the matrix is  an
                   upper or lower triangular matrix as follows:
    
                   UPLO = 'U' or  'u'    A  is  an  upper  triangular
                   matrix.
    
                   UPLO = 'L'  or  'l'    A  is  a  lower  triangular
                   matrix.
    
                   Unchanged on exit.
    
         TRANS     - CHARACTER*1.
                   On entry, TRANS specifies the operation to be per-
                   formed as follows:
    
                   TRANS = 'N' or 'n'   x := A*x.
    
                   TRANS = 'T' or 't'   x := A'*x.
    
                   TRANS = 'C' or 'c'   x := conjg( A' )*x.
    
                   Unchanged on exit.
    
         DIAG      - CHARACTER*1.
                   On entry, DIAG specifies whether or not A is  unit
                   triangular as follows:
    
                   DIAG = 'U' or 'u'   A is assumed to be  unit  tri-
                   angular.
    
                   DIAG = 'N' or 'n'   A is not assumed  to  be  unit
                   triangular.
    
                   Unchanged on exit.
    
         N         - INTEGER.
                   On entry, N specifies the order of the  matrix  A.
                   N must be at least zero.  Unchanged on exit.
    
         K         - INTEGER.
                   On entry with UPLO = 'U' or 'u', K  specifies  the
                   number  of  super-diagonals  of  the matrix A.  On
                   entry with UPLO = 'L'  or  'l',  K  specifies  the
                   number  of  sub-diagonals of the matrix A.  K must
                   satisfy  0 .le. K.  Unchanged on exit.
    
         A         - COMPLEX          array of DIMENSION ( LDA, n ).
                   Before entry with UPLO = 'U' or 'u', the leading (
                   k  + 1 ) by n part of the array A must contain the
                   upper triangular band part of the matrix of  coef-
                   ficients,  supplied  column  by  column,  with the
                   leading diagonal of the matrix in row ( k + 1 ) of
                   the  array,  the  first super-diagonal starting at
                   position 2 in row k, and so on. The top left k  by
                   k  triangle of the array A is not referenced.  The
                   following program segment will transfer  an  upper
                   triangular  band  matrix  from  conventional  full
                   matrix storage to band storage:
    
                   DO 20, J = 1, N M = K + 1 - J DO 10, I = MAX( 1, J
                   - K ), J A( M + I, J ) = matrix( I, J ) 10    CON-
                   TINUE 20 CONTINUE
    
                   Before entry with UPLO = 'L' or 'l', the leading (
                   k  + 1 ) by n part of the array A must contain the
                   lower triangular band part of the matrix of  coef-
                   ficients,  supplied  column  by  column,  with the
                   leading diagonal of the matrix in  row  1  of  the
                   array, the first sub-diagonal starting at position
                   1 in row 2, and so on. The bottom  right  k  by  k
                   triangle  of  the  array A is not referenced.  The
                   following program segment will  transfer  a  lower
                   triangular  band  matrix  from  conventional  full
                   matrix storage to band storage:
    
                   DO 20, J = 1, N M = 1 - J DO 10, I = J, MIN( N,  J
                   +  K  )  A( M + I, J ) = matrix( I, J ) 10    CON-
                   TINUE 20 CONTINUE
    
                   Note that when DIAG = 'U' or 'u' the  elements  of
                   the array A corresponding to the diagonal elements
                   of the matrix are not referenced, but are  assumed
                   to be unity.  Unchanged on exit.
    
         LDA       - INTEGER.
                   On entry, LDA specifies the first dimension  of  A
                   as declared in the calling (sub) program. LDA must
                   be at least ( k + 1 ).  Unchanged on exit.
    
         X         - COMPLEX          array of dimension at least
                   ( 1 + ( n - 1 )*abs( INCX ) ).  Before entry,  the
                   incremented  array  X  must  contain the n element
                   vector x. On exit, X is overwritten with the tran-
                   formed vector x.
    
         INCX      - INTEGER.
                   On entry, INCX specifies  the  increment  for  the
                   elements  of  X. INCX must not be zero.  Unchanged
                   on exit.
    
    
    
    


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