Multiplies a real band matrix in band storage mode by a real vector.

Required Arguments

A — Real 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 — Real vector of length NX.   (Input)

Y — Real 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 MURBV (A, NLCA, NUCA, X, Y [,…])

Specific:         The specific interface names are S_MURBV and D_MURBV.

FORTRAN 77 Interface

Single:            CALL MURBV (N, A, LDA, NLCA, NUCA, NX, X, IPATH, NY, Y)

Double:          The double precision name is DMURBV.

Description

If IPATH = 1, MURBV computes y = Ax, where A is a real band matrix and x and y are real vectors. If IPATH = 2, MURBV computes y = ATx.

Example

Multiply a real band matrix of order 6, with two upper codiagonals and two lower codiagonals stored in band mode, by a real vector of length 6. The output vector will be a real vector of length 6.

 

      USE MURBV_INT

      USE WRRRN_INT

 

      IMPLICIT   NONE

!                                 Declare variables

      INTEGER    LDA, N, NLCA, NUCA, NX, NY

      PARAMETER  (LDA=5, N=6, NLCA=2, NUCA=2, NX=6, NY=6)

!

      INTEGER    IPATH

      REAL       A(LDA,N), X(NX), Y(NY)

!                                 Set values for A (in band mode)

!                                 A = ( 0.0  0.0  1.0  2.0  3.0  4.0 )

!                                     ( 0.0  1.0  2.0  3.0  4.0  5.0 )

!                                     ( 1.0  2.0  3.0  4.0  5.0  6.0 )

!                                     (-1.0 -2.0 -3.0 -4.0 -5.0  0.0 )

!                                     (-5.0 -6.0 -7.0 -8.0  0.0  0.0 )

!

!                                 Set values for X

!                                 X = (-1.0  2.0 -3.0  4.0 -5.0  6.0 )

!

      DATA A/0.0, 0.0, 1.0, -1.0, -5.0, 0.0, 1.0, 2.0, -2.0, -6.0, &

          1.0, 2.0, 3.0, -3.0, -7.0, 2.0, 3.0, 4.0, -4.0, -8.0, 3.0, &

          4.0, 5.0, -5.0, 0.0, 4.0, 5.0, 6.0, 0.0, 0.0/

      DATA X/-1.0, 2.0, -3.0, 4.0, -5.0, 6.0/

!                                 Compute y = Ax

      IPATH = 1

      CALL MURBV (A, NLCA, NUCA, X, Y)

!                                 Print results

      CALL WRRRN ('y = Ax', Y, 1, NY, 1)

      END

Output

 

                     y = Ax
    1       2       3       4       5       6
-2.00    7.00  -11.00   17.00   10.00   29.00

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