eqblok Subroutine

Each breakpoint interval gives rise to a block in the linear system.
This block is determined by the K collocation equations in the interval
with the side conditions, if any, in the interval interspersed
appropriately, and involves the KPM B-splines having the interval in
their support.  Correspondingly, such a block has NROW = K + ISIDEL
rows, with ISIDEL = number of side conditions in this and the 
previous intervals, and NCOL = KPM columns.

Further, because the interior knots have multiplicity K, we can
carry out in SLVBLK K elimination steps in a block before pivoting
might involve an equation from the next block.  In the last block,
of course, all KPM elimination steps will be carried out in SLVBLK.

See the detailed comments in SLVBLK for further
information about the almost block diagonal form used here.

14 February 2007

Carl DeBoor

Carl DeBoor,
A Practical Guide to Splines,
Springer, 2001,
ISBN: 0387953663,
LC: QA1.A647.v27.

Input, real ( kind = 8 ) T(N+KPM), the knot sequence.

Input, integer ( kind = 4 ) N, the dimension of the approximating spline 
space, that is, the order of the linear system to be constructed.

Input, integer ( kind = 4 ) KPM, = K + M, the order of the approximating 
spline.

Input, integer ( kind = 4 ) LENBLK, the maximum length of the array BLOKS,
as allowed by the dimension statement in COLLOC.

Workspace, real ( kind = 8 ) WORK1(KPM,KPM), used in PUTIT.

Workspace, real ( kind = 8 ) WORK2(KPM,M+1), used in PUTIT.

Output, real ( kind = 8 ) BLOKS(*), the coefficient matrix of the
linear system, stored in almost block diagonal form, of size
KPM * sum ( INTEGS(1,1:NBLOKS) ).

Output, integer ( kind = 4 ) INTEGS(3,NBLOKS), describing the block 
structure.
INTEGS(1,I) = number of rows in block I;
INTEGS(2,I) = number of columns in block I;
INTEGS(3,I) = number of elimination steps which can be carried out in 
block I before pivoting might bring in an equation from the next block.

Output, integer ( kind = 4 ) NBLOKS, the number of blocks, equals number
of polynomial pieces.

Output, real ( kind = 8 ) B(*), the right hand side of the linear 
system, stored corresponding to the almost block diagonal form, 
of size sum ( INTEGS(1,1:NBLOKS) ).