CXML
duskyd
Unsymmetric sparse simple driver using skyline storage scheme
FORMAT
DUSKYD
(n, au, iaudiag, nau, al, ialdiag, nal, bx, ldbx, nbx, iparam, rparam,
iwrk, rwrk, ierror)
Arguments
n integer*4
On entry, the order of the matrix A.
On exit, n is unchanged.
au real*8
On entry, an array containing information on the matrix
A. If istore = 1 or 2, then au contains the upper
triangular part, including the diagonal, of the matrix
A, stored in the profile-in or diagonal-out mode,
respectively. Array AU is of length at least nau, where
nau is the envelope size of the upper triangular part
of A, including the diagonal. If istore = 3, then au
contains the matrix A, stored in the structurally
symmetric, profile-in storage mode. In this case, array
AU is of length at least nau, where nau is the envelope
size of the matrix A.
On exit, if istore = 1 or 2, au contains the factors
U and D of the L*D*U factorization of the matrix A. If
istore = 3, then au contains the factors L, U and D of
the L*D*U factorization of the matrix A. au must
remain unchanged between the call to the routine DUSKYD
and any routines that use the factors such as DUSKYS,
DUSKYC, and DUSKYR.
iaudiag integer*4
On entry, an array containing the pointers to the
locations of the diagonal elements in the arrays AU.
iaudiag is of length at least n for the profile-in and
the structurally symmetric profile-in storage modes.
iaudiag is of length at least (n+1) for the diagonal-
out storage mode.
On exit, iaudiag is unchanged.
nau integer*4
On entry, the number of elements stored in array AU.
If istore = 1 or 2, then nau is the envelope size of
the upper triangular part of the matrix A. If istore =
3, then nau is the envelope size of the matrix A. For
the profile-in and the structurally symmetric profile-
in storage modes, nau = IAUDIAG(n). For the
diagonal-out storage mode, nau = IAUDIAG(n+1) - 1.
On exit, nau is unchanged.
al real*8
On entry, an array containing information on the matrix
A. If istore = 1 or 2, then al contains the lower
triangular part, including the diagonal, of the matrix
A, stored in the profile-in or diagonal-out mode,
respectively. Storage is allocated for the diagonal
elements, though the elements themselves are not
stored. Array AL is of length at least nal, where nal
is the envelope size of the lower triangular part of A,
including the diagonal. If istore = 3, then al is a
dummy argument.
On exit, if istore = 1 or 2, al contains the factor L
of the L*D*U factorization of the matrix A. If
istore = 3, then al is undefined. al must remain
unchanged between the call to the routine DUSKYD and
any routines that use the factors such as DUSKYS,
DUSKYC, and DUSKYR.
ialdiag integer*4
On entry, an array containing the pointers to the
locations of the diagonal elements in the arrays AL and
ALF. ialdiag is of length at least n for the profile-
in storage mode. ialdiag is of length at least n+1 for
the diagonal-out storage mode. If istore = 3, then
ialdiag is a dummy argument.
On exit, ialdiag is unchanged.
nal integer*4
On entry, the number of elements stored in array AL.
If istore = 1 or 2, then nal is the envelope size of
the lower triangular part of the matrix A. For the
profile-in storage mode, nal = IALDIAG(n). For the
diagonal-out storage mode, nal = IALDIAG(n+1) - 1. If
istore = 3, then nal is a dummy argument.
On exit, nal is unchanged.
bx real*8
On entry, a two dimensional array BX of order nbx,
containing the nbx right sides.
On exit, bx contains the solutions for the nbx systems.
ldbx integer*4
On entry, the leading dimension of array BX. ldbx
>=n.
On exit, ldbx is unchanged.
nbx real*4
On entry, the number of right sides.
On exit, nbx is unchanged.
iparam integer*4
An array of length at least 100, containing the integer
parameters for the simple driver.
iparam(1): niparam
On entry, defines the length of the array IPARAM.
niparam >= 100.
On exit, iparam(1) is unchanged.
iparam(2): nrparam
On entry, defines the length of the array RPARAM.
nrparam >= 100.
On exit, iparam(2) is unchanged.
iparam(3): niwrk
On entry, defines the size of the integer work array,
IWRK. niwrk >= 4n.
On exit, iparam(3) is unchanged.
iparam(4): nrwrk
On entry, defines the size of the real work array,
RWRK. As the real work array is not used at present,
nrwrk can be unspecified.
On exit, iparam(4) is unchanged.
iparam(5): iounit
On entry, defines the I/O unit number for printing
error messages and information from the routine DUSKYD.
The I/O unit must be opened in the calling subprogram.
If iounit <= 0, no output is generated.
On exit, iparam(5) is unchanged.
iparam(6): iolevel
On entry, defines the message level that determines the
amount of information printed out to iounit, when
iounit > 0.
iolevel = 0 : fatal error messages only
iolevel = 1 : error messages and minimal information
iolevel = 2 : error messages and detailed information
On exit, iparam(6) is unchanged.
iparam(7): idefault
On entry, defines if the default values should be used
in arrays IPARAM and RPARAM. If idefault = 0, then the
following default values are assigned:
IPARAM(1) = niparam = 100
IPARAM(2) = nrparam = 100
IPARAM(6) = iolevel = 0
IPARAM(8) = istore = 1
IPARAM(9) = ipvt = 0
IPARAM(11) = itrans = 0
RPARAM(1) = pvt_sml = 10**(-12)
If idefault = 1, then you must assign values to the
above variables before the call to the DUSKYD routine.
On exit, iparam(7) is unchanged.
iparam(8): istore
On entry, defines the type of storage scheme used for
the skyline matrix. If istore = 1, the matrix A is
stored using the profile-in storage mode; if istore =
2, the matrix A is stored using the diagonal-out
storage mode. Default: istore = 1.
On exit, iparam(8) is unchanged.
iparam(9): ipvt
On entry, defines if the factorization should continue
when a small pivot, defined by RPARAM(1), is
encountered. If ipvt = 0 and the absolute value of the
pivot element is smaller than pvt_sml = RPARAM(1),
then the factorization process is stopped and control
returned to the calling subprogram. If ipvt = 1 and a
pivot smaller than RPARAM(1) in absolute value is
encountered in the factorization, the process
continues. If ipvt = 2 and a pivot smaller than
RPARAM(1) in absolute value is encountered in the
factorization, it is replaced by a predetermined value
pvt_new = RPARAM(2), and the factorization is
continued. Default: ipvt = 0.
On exit, iparam(9) is unchanged.
iparam(10): ipvt_loc
On entry, an unspecified variable.
On exit, iparam(10) contains the location of the first
pivot element smaller in absolute value than pvt_sml.
The pivot element is returned in pvt_val = RPARAM(3).
If iparam(10) = 0, then no such pivot element exists.
iparam(11): itrans
On entry, defines the form of matrix used in the
solution. If itrans = 0, the system solved is A*X =
B; if itrans = 1, the system solved is trans(A)*X = B.
Default: itrans = 0.
On exit, iparam(11) is unchanged.
rparam real*8
An array of length at least 100, containing the real
parameters for the simple driver.
rparam(1): pvt_sml
On entry, defines the value of the pivot element which
is considered to be small. If a pivot element smaller
than pvt_sml, in absolute value, is encountered in the
factorization process, then, depending on the value of
ipvt = IPARAM(9), the process either stops, continues
or continues after the pivot is set equal to pvt_new =
RPARAM(2). pvt_sml > 0. Recommended value: 10**(-15)
<= pvt_sml <= 1. Default: pvt_sml = 10**(-12).
On exit, rparam(1) is unchanged.
rparam(2): pvt_new
On entry, defines the value to which the pivot element
must be set if ipvt = 2 and the pivot element is less
than pvt_sml in absolute value. pvt_new should be
large enough to avoid overflow when calculating the
reciprocal of the pivot element.
On exit, rparam(2) is unchanged.
rparam(3): pvt_val
On entry, an unspecified variable.
On exit, rparam(3) contains the value of the first
pivot element smaller than pvt_sml in absolute value.
This element occurs at the location returned in
IPARAM(12). If no such pivot element is found, the
value of pvt_val is unspecified.
iwrk integer*4
On entry, an array of length at least 4n used for
integer workspace.
On exit, the first 4n elements of the array IWRK
contain information generated by the factorization
routine DUSKYF. This information is required by
routines that use the factorization, such as DUSKYS,
DUSKYC, and DUSKYR, and should remain unchanged
between the call to DUSKYD and any subsequent calls to
one of these routines.
rwrk real*8
On entry, an array used for real workspace.
On exit, rwrk is unchanged. Presently, rwrk is not
used by the routine DSSKYF. It can be a dummy
variable.
ierror integer*4
On entry, an unspecified variable.
On exit, ierror contains the error flag. A value of
zero indicates a normal exit from the routine DUSKYD.
Description
DUSKYD is a simple driver routine that factors and solves the system
A X = B
or
trans(A) X = B
where A is an unsymmetric matrix stored in a skyline form, using either the
profile-in storage mode, the diagonal-out storage mode, or the structurally
symmetric profile-in storage mode; B is a matrix of nbx right sides and X
is the matrix of the corresponding nbx solution vectors. On entry to the
routine DUSKYS, the array BX contains the nbx right sides; on exit, these
are overwritten by the solution vectors. The variable itrans determines
whether the matrix A or trans(A) is used in the solution process.
The matrix A is first factorized as A = L D U by a call to the routine
DUSKYF. L is a unit lower triangular matrix, U is a unit upper triangular
matrix, and D is a diagonal matrix. The routine DUSKYF does not perform any
pivoting to preserve the numerical stability of the L*D*U factorization. It
is therefore primarily intended for the solution of systems that do not
require pivoting for numerical stability, such as diagonally dominant
systems. Caution is urged when using this routine for problems that require
pivoting.
If a small pivot, in absolute value, pvt_sml, is encountered in the
process of factorization, you have the option of either stopping the
factorization process and returning to the calling program, continuing the
factorization process, or continuing after setting the pivot equal to some
predetermined value, pvt_new. The location of the first occurrence of a
small pivot is returned in ipvt_loc and its value in pvt_val.
After the factorization has been obtained without any errors, the routine
DUSKYD calls the solve routine, DUSKYS, to solve the system. The call to
the routine DUSKYD can be followed by a call to the routines DUSKYS,
DUSKYC, and DUSKYR, provided that the first 4n elements of the integer
workspace array IWRK remain unchanged between calls. The real work array
RWRK is not used at present.
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