.TH "BLAS/SRC/ztbmv.f" 3 "Version 3.12.0" "LAPACK" \" -*- nroff -*-
.ad l
.nh
.SH NAME
BLAS/SRC/ztbmv.f
.SH SYNOPSIS
.br
.PP
.SS "Functions/Subroutines"

.in +1c
.ti -1c
.RI "subroutine \fBztbmv\fP (uplo, trans, diag, n, k, a, lda, x, incx)"
.br
.RI "\fBZTBMV\fP "
.in -1c
.SH "Function/Subroutine Documentation"
.PP 
.SS "subroutine ztbmv (character uplo, character trans, character diag, integer n, integer k, complex*16, dimension(lda,*) a, integer lda, complex*16, dimension(*) x, integer incx)"

.PP
\fBZTBMV\fP 
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 ZTBMV  performs one of the matrix-vector operations

    x := A*x,   or   x := A**T*x,   or   x := A**H*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\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIUPLO\fP 
.PP
.nf
          UPLO is 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\&.
.fi
.PP
.br
\fITRANS\fP 
.PP
.nf
          TRANS is CHARACTER*1
           On entry, TRANS specifies the operation to be performed as
           follows:

              TRANS = 'N' or 'n'   x := A*x\&.

              TRANS = 'T' or 't'   x := A**T*x\&.

              TRANS = 'C' or 'c'   x := A**H*x\&.
.fi
.PP
.br
\fIDIAG\fP 
.PP
.nf
          DIAG is 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 triangular\&.

              DIAG = 'N' or 'n'   A is not assumed to be unit
                                  triangular\&.
.fi
.PP
.br
\fIN\fP 
.PP
.nf
          N is INTEGER
           On entry, N specifies the order of the matrix A\&.
           N must be at least zero\&.
.fi
.PP
.br
\fIK\fP 
.PP
.nf
          K is 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\&.
.fi
.PP
.br
\fIA\fP 
.PP
.nf
          A is COMPLEX*16 array, 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 coefficients, 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    CONTINUE
              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 coefficients, 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    CONTINUE
              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\&.
.fi
.PP
.br
\fILDA\fP 
.PP
.nf
          LDA is INTEGER
           On entry, LDA specifies the first dimension of A as declared
           in the calling (sub) program\&. LDA must be at least
           ( k + 1 )\&.
.fi
.PP
.br
\fIX\fP 
.PP
.nf
          X is COMPLEX*16 array, 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
           transformed vector x\&.
.fi
.PP
.br
\fIINCX\fP 
.PP
.nf
          INCX is INTEGER
           On entry, INCX specifies the increment for the elements of
           X\&. INCX must not be zero\&.
.fi
.PP
 
.RE
.PP
\fBAuthor\fP
.RS 4
Univ\&. of Tennessee 
.PP
Univ\&. of California Berkeley 
.PP
Univ\&. of Colorado Denver 
.PP
NAG Ltd\&. 
.RE
.PP
\fBFurther Details:\fP
.RS 4

.PP
.nf
  Level 2 Blas routine\&.
  The vector and matrix arguments are not referenced when N = 0, or M = 0

  -- Written on 22-October-1986\&.
     Jack Dongarra, Argonne National Lab\&.
     Jeremy Du Croz, Nag Central Office\&.
     Sven Hammarling, Nag Central Office\&.
     Richard Hanson, Sandia National Labs\&.
.fi
.PP
 
.RE
.PP

.PP
Definition at line \fB185\fP of file \fBztbmv\&.f\fP\&.
.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.