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Computes the image transformation matrix.
T — NF by NF transformation matrix. (Input)
TI — NF by NF image transformation matrix. (Output)
NF — Number of
factors. (Input)
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).
LDTI — Leading
dimension of TI
exactly as specified in the dimension statement in the calling
program. (Input)
Default: LDTI = size (TI,1).
Generic: CALL FIMAG (T, TI [,…])
Specific: The specific interface names are S_FIMAG and D_FIMAG.
Single: CALL FIMAG (NF, T, LDT, TI, LDTI)
Double: The double precision name is DFIMAG.
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.
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
3 1 T is ill-conditioned. The solution may not be accurate.
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
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
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