FIMAG
Computes the image transformation matrix.
Required Arguments
T — NF by NF transformation matrix. (Input)
TI — NF by NF image transformation matrix. (Output)
Optional Arguments
NF — Number of factors. (Input)
Default: NF = size (T,2).
Default: NF = size (T,2).
LDT — Leading dimension of T exactly as specified in the dimension statement in the calling program. (Input)
Default: LDT = size (T,1).
Default: LDT = size (T,1).
LDTI — Leading dimension of TI exactly as specified in the dimension statement in the calling program. (Input)
Default: LDTI = size (TI,1).
Default: LDTI = size (TI,1).
FORTRAN 90 Interface
Generic: CALL FIMAG (T, TI [, …])
Specific: The specific interface names are S_FIMAG and D_FIMAG.
FORTRAN 77 Interface
Single: CALL FIMAG (NF, T, LDT, TI, LDTI)
Double: The double precision name is DFIMAG.
Description
Routine FIMAG computes the image transformation matrix TI from the factor rotation matrix (T). The image transformation matrix takes the unrotated factor loadings into the factor structure matrix when the unrotated loadings are computed from a correlation matrix. It is computed as the inverse of the transpose of the factor rotation matrix T. When orthogonal rotations are used, (TT)−1 = T so there is no reason to compute the image transformation matrix.
Comments
1. Workspace may be explicitly provided, if desired, by use of F2MAG/DF2MAG. The reference is:
CALL F2MAG (NF, T, LDT, TI, LDTI, RWK, IWK)
The additional arguments are as follows:
RWK — Real work vector of length NF + NF(NF ‑ 1)/2.
IWK — Integer work vector of length NF.
2. Informational Error
Type | Code | Description |
|---|---|---|
3 | 1 | T is ill‑conditioned. The solution may not be accurate. |
Example
This example is a continuation of the example contained in the manual document for routine FROTA. The image transformation matrix is obtained from the orthogonal rotation matrix. Some small differences between the matrix TI when compared with the matrix T computed via routine FROTA can be seen. These differences are because of roundoff error since for orthogonal rotations, the image transformation matrix is the same as the rotation matrix.
USE FIMAG_INT
USE WRRRN_INT
IMPLICIT NONE
INTEGER LDT, LDTI, NF
PARAMETER (LDT=3, LDTI=3, NF=3)
!
REAL T(LDT,NF), TI(LDTI,NF)
!
DATA T/.7307, .6816, -.0382, -.5939, .6623, .4569, .3367, -.3112, &
.8887/
!
CALL FIMAG (T, TI)
!
CALL WRRRN ('TI', TI)
END
Output
TI
1 2 3
1 0.7307 -0.5938 0.3367
2 0.6816 0.6622 -0.3112
3 -0.0382 0.4569 0.8887
