MUCBV
Multiplies a complex band matrix in band storage mode by a complex vector.
Required Arguments
A — Complex NLCA + NUCA + 1 by N band matrix stored in band mode. (Input)
NLCA — Number of lower codiagonals in A. (Input)
NUCA — Number of upper codiagonals in A. (Input)
X — Complex vector of length NX. (Input)
Y — Complex vector of length NY containing the product A * X if IPATH is equal to 1 and the product trans(A) * X if IPATH is equal to 2. (Output)
Optional Arguments
N — Order of the matrix. (Input)
Default: N = SIZE (A,2).
LDA — Leading dimension of A exactly as specified in the dimension statement of the calling program. (Input)
Default: LDA = SIZE (A,1).
NX — Length of the vector X. (Input)
NX must be equal to N.
Default: NX = SIZE (X,1).
IPATH — Integer flag. (Input)
IPATH = 1 means the product Y = A * X is computed. IPATH = 2 means the product Y = trans(A) * X is computed, where trans(A) is the transpose of A.
Default: IPATH = 1.
NY — Length of vector Y. (Input)
NY must be equal to N.
Default: NY = SIZE (Y,1).
FORTRAN 90 Interface
Generic: CALL MUCBV (A, NLCA, NUCA, X, Y [, …])
Specific: The specific interface names are S_MUCBV and D_MUCBV.
FORTRAN 77 Interface
Single: CALL MUCBV (N, A, LDA, NLCA, NUCA, NX, X, IPATH, NY, Y)
Double: The double precision name is DMUCBV.
Description
If IPATH = 1, MUCBV computes y = Ax, where A is a complex band matrix and x and y are complex vectors. If IPATH = 2, MUCBV computes y = ATx.
Example
Multiply the transpose of a complex band matrix of order 4, with one upper codiagonal and two lower codiagonals stored in band mode, by a complex vector of length 3. The output vector will be a complex vector of length 3.
USE MUCBV_INT
USE WRCRN_INT
IMPLICIT NONE
! Declare variables
INTEGER LDA, N, NLCA, NUCA, NX, NY
PARAMETER (LDA=4, N=4, NLCA=2, NUCA=1, NX=4, NY=4)
!
INTEGER IPATH
COMPLEX A(LDA,N), X(NX), Y(NY)
! Set values for A (in band mode)
! A = ( 0.0+ 0.0i 1.0+ 2.0i 3.0+ 4.0i 5.0+ 6.0i )
! ( -1.0- 1.0i -1.0- 1.0i -1.0- 1.0i -1.0- 1.0i )
! ( -1.0+ 2.0i -1.0+ 3.0i -2.0+ 1.0i 0.0+ 0.0i )
! ( 2.0+ 0.0i 0.0+ 2.0i 0.0+ 0.0i 0.0+ 0.0i )
!
! Set values for X
! X = ( 3.0 + 4.0i 0.0 + 0.0i 1.0 + 2.0i -2.0 - 1.0i )
!
DATA A/(0.0,0.0), (-1.0,-1.0), (-1.0,2.0), (2.0,0.0), (1.0,2.0), &
(-1.0,-1.0), (-1.0,3.0), (0.0,2.0), (3.0,4.0), (-1.0,-1.0), &
(-2.0,1.0), (0.0,0.0), (5.0,6.0), (-1.0,-1.0), (0.0,0.0), &
(0.0,0.0)/
DATA X/(3.0,4.0), (0.0,0.0), (1.0,2.0), (-2.0,-1.0)/
! Compute y = Ax
IPATH = 2
CALL MUCBV (A, NLCA, NUCA, X, Y, IPATH=IPATH)
! Print results
CALL WRCRN ('y = Ax', Y, 1, NY, 1)
END
Output
y = Ax
1 2 3 4
( 3.00, -3.00) (-10.00, 7.00) ( 6.00, -3.00) ( -6.00, 19.00)
