LAPACK  3.5.0 LAPACK: Linear Algebra PACKage
cgbmv.f File Reference

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## Functions/Subroutines

subroutine cgbmv (TRANS, M, N, KL, KU, ALPHA, A, LDA, X, INCX, BETA, Y, INCY)
CGBMV More...

## Function/Subroutine Documentation

 subroutine cgbmv ( character TRANS, integer M, integer N, integer KL, integer KU, complex ALPHA, complex, dimension(lda,*) A, integer LDA, complex, dimension(*) X, integer INCX, complex BETA, complex, dimension(*) Y, integer INCY )

CGBMV

Purpose:
``` CGBMV  performs one of the matrix-vector operations

y := alpha*A*x + beta*y,   or   y := alpha*A**T*x + beta*y,   or

y := alpha*A**H*x + beta*y,

where alpha and beta are scalars, x and y are vectors and A is an
m by n band matrix, with kl sub-diagonals and ku super-diagonals.```
Parameters
 [in] TRANS ``` TRANS is CHARACTER*1 On entry, TRANS specifies the operation to be performed as follows: TRANS = 'N' or 'n' y := alpha*A*x + beta*y. TRANS = 'T' or 't' y := alpha*A**T*x + beta*y. TRANS = 'C' or 'c' y := alpha*A**H*x + beta*y.``` [in] M ``` M is INTEGER On entry, M specifies the number of rows of the matrix A. M must be at least zero.``` [in] N ``` N is INTEGER On entry, N specifies the number of columns of the matrix A. N must be at least zero.``` [in] KL ``` KL is INTEGER On entry, KL specifies the number of sub-diagonals of the matrix A. KL must satisfy 0 .le. KL.``` [in] KU ``` KU is INTEGER On entry, KU specifies the number of super-diagonals of the matrix A. KU must satisfy 0 .le. KU.``` [in] ALPHA ``` ALPHA is COMPLEX On entry, ALPHA specifies the scalar alpha.``` [in] A ``` A is COMPLEX array of DIMENSION ( LDA, n ). Before entry, the leading ( kl + ku + 1 ) by n part of the array A must contain the matrix of coefficients, supplied column by column, with the leading diagonal of the matrix in row ( ku + 1 ) of the array, the first super-diagonal starting at position 2 in row ku, the first sub-diagonal starting at position 1 in row ( ku + 2 ), and so on. Elements in the array A that do not correspond to elements in the band matrix (such as the top left ku by ku triangle) are not referenced. The following program segment will transfer a band matrix from conventional full matrix storage to band storage: DO 20, J = 1, N K = KU + 1 - J DO 10, I = MAX( 1, J - KU ), MIN( M, J + KL ) A( K + I, J ) = matrix( I, J ) 10 CONTINUE 20 CONTINUE``` [in] 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 ( kl + ku + 1 ).``` [in] X ``` X is COMPLEX array of DIMENSION at least ( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n' and at least ( 1 + ( m - 1 )*abs( INCX ) ) otherwise. Before entry, the incremented array X must contain the vector x.``` [in] INCX ``` INCX is INTEGER On entry, INCX specifies the increment for the elements of X. INCX must not be zero.``` [in] BETA ``` BETA is COMPLEX On entry, BETA specifies the scalar beta. When BETA is supplied as zero then Y need not be set on input.``` [in,out] Y ``` Y is COMPLEX array of DIMENSION at least ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n' and at least ( 1 + ( n - 1 )*abs( INCY ) ) otherwise. Before entry, the incremented array Y must contain the vector y. On exit, Y is overwritten by the updated vector y.``` [in] INCY ``` INCY is INTEGER On entry, INCY specifies the increment for the elements of Y. INCY must not be zero.```
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 188 of file cgbmv.f.

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