Computes the transpose product of a matrix, ATA.

Required Arguments

A — Real NRA by NCA rectangular matrix.   (Input)
The transpose product of A is to be computed.

B — Real NB by NB symmetric matrix containing the transpose product ATA.   (Output)

Optional Arguments

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

NCA — Number of columns in 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).

NB — Order of the matrix B.   (Input)
NB must be equal to NCA.
Default: NB = size (B,1).

LDB — Leading dimension of B exactly as specified in the dimension statement of the calling program.   (Input)
Default: LDB = size (B,1).

FORTRAN 90 Interface

Generic:          CALL MXTXF (A, B [,…])

Specific:         The specific interface names are S_MXTXF and D_MXTXF.

FORTRAN 77 Interface

Single:            CALL MXTXF (NRA, NCA, A, LDA, NB, B, LDB)

Double:          The double precision name is DMXTXF.

Description

The routine MXTXF computes the real general matrix B = ATA given the real rectangular matrix A.

Example

Multiply the transpose of a 3 ´ 4 real matrix by itself. The output matrix will be a 4 ´ 4 real symmetric matrix.

 

      USE MXTXF_INT

      USE WRRRN_INT

 

      IMPLICIT   NONE

!                                 Declare variables

      INTEGER    NB, NCA, NRA

      PARAMETER  (NB=4, NCA=4, NRA=3)

!

      REAL       A(NRA,NCA), B(NB,NB)

!                                 Set values for A

!                                 A = ( 3.0  1.0  4.0  2.0 )

!                                     ( 0.0  2.0  1.0 -1.0 )

!                                     ( 6.0  1.0  3.0  2.0 )

!

      DATA A/3.0, 0.0, 6.0, 1.0, 2.0, 1.0, 4.0, 1.0, 3.0, 2.0, -1.0, &

          2.0/

!                                 Compute B = trans(A)*A

      CALL MXTXF (A, B)

!                                 Print results

      CALL WRRRN ('B = trans(A)*A', B)

      END

Output

 

         B = trans(A)*A
        1       2       3       4
1   45.00    9.00   30.00   18.00
2    9.00    6.00    9.00    2.00
3   30.00    9.00   26.00   13.00
4   18.00    2.00   13.00    9.00

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