This function computes the bilinear form xTAy.

Function Return Value

BLINF — The value of xTAy is returned in BLINF.   (Output)

Required Arguments

A — Real NRA by NCA matrix.   (Input)

X — Real vector of length NRA.   (Input)

Y — Real vector of length NCA.   (Input)

Optional Arguments

NRA — Number of rows of A.   (Input)
Default: NRA = size (A,1).

NCA — Number of columns of A.   (Input)
Default: NCA = 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).

FORTRAN 90 Interface

Generic:          BLINF (A, X, Y [,…])

Specific:          The specific interface names are S_BLINF and D_BLINF.

FORTRAN 77 Interface

Single:             BLINF(NRA, NCA, A, LDA, X, Y)

Double:           The double precision name is DBLINF.

Description

Given the real rectangular matrix A and two vectors x and y, BLINF computes the bilinear form xTAy.

Comments

The quadratic form can be computed by calling BLINF with the vector X in place of the vector Y.

Example

Compute the bilinear form xTAy, where x is a vector of length 5, A is a 5 ´ 2 matrix and y is a vector of length 2.

 

      USE BLINF_INT

      USE UMACH_INT

 

      IMPLICIT   NONE

!                                 Declare variables

      INTEGER    NCA, NRA

      PARAMETER  (NCA=2, NRA=5)

!

      INTEGER    NOUT

      REAL       A(NRA,NCA), VALUE, X(NRA), Y(NCA)

!                                 Set values for A

!                                 A = ( -2.0  2.0 )

!                                     (  3.0 -6.0 )

!                                     ( -4.0  7.0 )

!                                     (  1.0 -8.0 )

!                                     (  0.0 10.0 )

!                                 Set values for X

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

!                                 Set values for Y

!                                 Y = ( -6.0  3.0 )

!

      DATA A/-2.0, 3.0, -4.0, 1.0, 0.0, 2.0, -6.0, 7.0, -8.0, 10.0/

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

      DATA Y/-6.0, 3.0/

!                                 Compute bilinear form

      VALUE = BLINF(A,X,Y)

!                                 Print results

      CALL UMACH (2, NOUT)

      WRITE (NOUT,*) ' The bilinear form trans(x)*A*y = ', VALUE

      END

Output

 

The bilinear form trans(x)*A*y =     195.000

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