MXTXF
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.
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).
Default: NRA = SIZE (A,1).
NCA — Number of columns in A. (Input)
Default: NCA = SIZE (A,2).
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).
Default: LDA = SIZE (A,1).
NB — Order of the matrix B. (Input)
NB must be equal to NCA.
Default: NB = SIZE (B,1).
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).
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
