public interface ggglm
GGGLM solves a general Gauss-Markov linear model (GLM) problem:
minimize || y ||_2 subject to d = Ax + By
x
where A is an N-by-M matrix, B is an N-by-P matrix, and d is a
given N-vector. It is assumed that M <= N <= M+P, and
rank(A) = M and rank( A B ) = N.
Under these assumptions, the constrained equation is always
consistent, and there is a unique solution x and a minimal 2-norm
solution y, which is obtained using a generalized QR factorization
of the matrices (A, B) given by
A = Q(R), B = QTZ.
(0)
In particular, if matrix B is square nonsingular, then the problem
GLM is equivalent to the following weighted linear least squares
problem
minimize || inv(B)(d-A*x) ||_2
x
where inv(B) denotes the inverse of B.
Subroutines
Arguments
| Type |
Intent | Optional | Attributes |
|
Name |
|
|
integer(kind=ilp),
|
intent(in) |
|
|
:: |
n |
|
|
integer(kind=ilp),
|
intent(in) |
|
|
:: |
m |
|
|
integer(kind=ilp),
|
intent(in) |
|
|
:: |
p |
|
|
complex(kind=sp),
|
intent(inout) |
|
|
:: |
a(lda,*) |
|
|
integer(kind=ilp),
|
intent(in) |
|
|
:: |
lda |
|
|
complex(kind=sp),
|
intent(inout) |
|
|
:: |
b(ldb,*) |
|
|
integer(kind=ilp),
|
intent(in) |
|
|
:: |
ldb |
|
|
complex(kind=sp),
|
intent(inout) |
|
|
:: |
d(*) |
|
|
complex(kind=sp),
|
intent(out) |
|
|
:: |
x(*) |
|
|
complex(kind=sp),
|
intent(out) |
|
|
:: |
y(*) |
|
|
complex(kind=sp),
|
intent(out) |
|
|
:: |
work(*) |
|
|
integer(kind=ilp),
|
intent(in) |
|
|
:: |
lwork |
|
|
integer(kind=ilp),
|
intent(out) |
|
|
:: |
info |
|
Arguments
| Type |
Intent | Optional | Attributes |
|
Name |
|
|
integer(kind=ilp),
|
intent(in) |
|
|
:: |
n |
|
|
integer(kind=ilp),
|
intent(in) |
|
|
:: |
m |
|
|
integer(kind=ilp),
|
intent(in) |
|
|
:: |
p |
|
|
real(kind=dp),
|
intent(inout) |
|
|
:: |
a(lda,*) |
|
|
integer(kind=ilp),
|
intent(in) |
|
|
:: |
lda |
|
|
real(kind=dp),
|
intent(inout) |
|
|
:: |
b(ldb,*) |
|
|
integer(kind=ilp),
|
intent(in) |
|
|
:: |
ldb |
|
|
real(kind=dp),
|
intent(inout) |
|
|
:: |
d(*) |
|
|
real(kind=dp),
|
intent(out) |
|
|
:: |
x(*) |
|
|
real(kind=dp),
|
intent(out) |
|
|
:: |
y(*) |
|
|
real(kind=dp),
|
intent(out) |
|
|
:: |
work(*) |
|
|
integer(kind=ilp),
|
intent(in) |
|
|
:: |
lwork |
|
|
integer(kind=ilp),
|
intent(out) |
|
|
:: |
info |
|
Arguments
| Type |
Intent | Optional | Attributes |
|
Name |
|
|
integer(kind=ilp),
|
intent(in) |
|
|
:: |
n |
|
|
integer(kind=ilp),
|
intent(in) |
|
|
:: |
m |
|
|
integer(kind=ilp),
|
intent(in) |
|
|
:: |
p |
|
|
real(kind=sp),
|
intent(inout) |
|
|
:: |
a(lda,*) |
|
|
integer(kind=ilp),
|
intent(in) |
|
|
:: |
lda |
|
|
real(kind=sp),
|
intent(inout) |
|
|
:: |
b(ldb,*) |
|
|
integer(kind=ilp),
|
intent(in) |
|
|
:: |
ldb |
|
|
real(kind=sp),
|
intent(inout) |
|
|
:: |
d(*) |
|
|
real(kind=sp),
|
intent(out) |
|
|
:: |
x(*) |
|
|
real(kind=sp),
|
intent(out) |
|
|
:: |
y(*) |
|
|
real(kind=sp),
|
intent(out) |
|
|
:: |
work(*) |
|
|
integer(kind=ilp),
|
intent(in) |
|
|
:: |
lwork |
|
|
integer(kind=ilp),
|
intent(out) |
|
|
:: |
info |
|
Arguments
| Type |
Intent | Optional | Attributes |
|
Name |
|
|
integer(kind=ilp),
|
intent(in) |
|
|
:: |
n |
|
|
integer(kind=ilp),
|
intent(in) |
|
|
:: |
m |
|
|
integer(kind=ilp),
|
intent(in) |
|
|
:: |
p |
|
|
complex(kind=dp),
|
intent(inout) |
|
|
:: |
a(lda,*) |
|
|
integer(kind=ilp),
|
intent(in) |
|
|
:: |
lda |
|
|
complex(kind=dp),
|
intent(inout) |
|
|
:: |
b(ldb,*) |
|
|
integer(kind=ilp),
|
intent(in) |
|
|
:: |
ldb |
|
|
complex(kind=dp),
|
intent(inout) |
|
|
:: |
d(*) |
|
|
complex(kind=dp),
|
intent(out) |
|
|
:: |
x(*) |
|
|
complex(kind=dp),
|
intent(out) |
|
|
:: |
y(*) |
|
|
complex(kind=dp),
|
intent(out) |
|
|
:: |
work(*) |
|
|
integer(kind=ilp),
|
intent(in) |
|
|
:: |
lwork |
|
|
integer(kind=ilp),
|
intent(out) |
|
|
:: |
info |
|
Module Procedures