BLINF

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