# ztbmv (3) - Linux Manuals

ztbmv.f -

## SYNOPSIS

### Functions/Subroutines

subroutine ztbmv (UPLO, TRANS, DIAG, N, K, A, LDA, X, INCX)
ZTBMV

## Function/Subroutine Documentation

### subroutine ztbmv (characterUPLO, characterTRANS, characterDIAG, integerN, integerK, complex*16, dimension(lda,*)A, integerLDA, complex*16, dimension(*)X, integerINCX)

ZTBMV Purpose:

``` 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.
```

Parameters:

UPLO

```          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.
```

TRANS

```          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.
```

DIAG

```          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.
```

N

```          N is INTEGER
On entry, N specifies the order of the matrix A.
N must be at least zero.
```

K

```          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.
```

A

```          A is COMPLEX*16 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 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.
```

LDA

```          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 ).
```

X

```          X is (input/output) COMPLEX*16 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
tranformed vector x.
```

INCX

```          INCX is INTEGER
On entry, INCX specifies the increment for the elements of
X. INCX must not be zero.
```

Author:

Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

Date:

November 2011

Further Details:

```  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.
```

Definition at line 187 of file ztbmv.f.

## Author

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