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|
subroutine intmb03od(fname)
INCLUDE '../stack.h'
character fname*(*)
logical createvar, getrhsvar, checklhs, checkrhs
c
integer A,RCOND,RANK,SVAL,JPVT,TAU,R,Q,DWORK
integer ptrA,ptrRCOND,ptrJPVT,ptrSVAL,ptrTAU,ptrRANK
integer ptrDWORK,ptrR,ptrQ
double precision RCONDdef,SLVMAX
character*(1) JOBQR
double precision ZERO
parameter ( ZERO = 0.0D0)
c [Q,R,JPVT,RANK,SVAL]=rankqr(A,[RCOND,JPVT])
minrhs=1
maxrhs=3
minlhs=1
maxlhs=5
if(.not.checklhs(fname,minlhs,maxlhs)) return
if(.not.checkrhs(fname,minrhs,maxrhs)) return
JOBQR='Q'
SLVMAX=0.0d0
RCONDdef=0.0d0
A=1
RCOND=2
JPVT=3
SVAL=4
TAU=5
RANK=6
R=7
Q=8
DWORK=9
if(.not.getrhsvar(A,'d',M,N,ptrA)) return
if(rhs.eq.1) then
c rankqr(A)
c create RCOND=0.0,JPVT=[0,..,0]
if(.not.createvar(RCOND,'d',1,1,ptrRCOND)) return
stk(ptrRCOND)=RCONDdef
if(.not.createvar(JPVT,'i',1,N,ptrJPVT)) return
call icopy(N,0,0,istk(ptrJPVT),1)
elseif(rhs.eq.2) then
c rankqr(A,RCOND)
c get RCOND, create JPVT=[0,..,0]
if(.not.getrhsvar(RCOND,'d',mR,nR,ptrRCOND)) return
if(mR*nR.ne.1) then
buf=fname//': 2nd parameter (RCOND) has wrong dimension'
call error(998)
return
endif
if(.not.createvar(JPVT,'i',1,N,ptrJPVT)) return
call icopy(N,0,0,istk(ptrJPVT),1)
elseif(rhs.eq.3) then
c rankqr(A,RCOND,JPVT)
c get RCOND, JPVT
if(.not.getrhsvar(RCOND,'d',mR,nR,ptrRCOND)) return
if(mR*nR.ne.1) then
buf=fname//': 2nd parameter (RCOND) has wrong dimension'
call error(998)
return
endif
if(.not.getrhsvar(JPVT,'i',mJ,nJ,ptrJPVT)) return
if(mJ*nJ.ne.N) then
buf=fname//': JPVT must have same column dim. as A'
call error(998)
return
endif
endif
c Creating SVAL,TAU,RANK,R,Q,DWORK
if(.not.createvar(SVAL,'d',1,3,ptrSVAL)) return
if(.not.createvar(TAU,'d',1,min(M,N),ptrTAU)) return
if(.not.createvar(RANK,'i',1,1,ptrRANK)) return
if(.not.createvar(R,'d',M,N,ptrR)) return
if(.not.createvar(Q,'d',M,M,ptrQ)) return
LDWORKMIN=max(1,3*N)
LDWORK=maxvol(DWORK,'d')
if(LDWORK.le.LDWORKMIN) then
buf=fname//': not enough memory (use stacksize)'
call error(998)
return
endif
if(.not.createvar(DWORK,'d',1,LDWORK,ptrDWORK)) return
LDA=max(1,M)
call MB03OD(JOBQR, M, N, stk(ptrA), LDA, istk(ptrJPVT),
& stk(ptrRCOND), SLVMAX, stk(ptrTAU), istk(ptrRANK),
& stk(ptrSVAL), stk(ptrDWORK), INFO)
if(INFO.ne.0) then
call errorinfo(fname,INFO)
return
endif
c Save R (=current A)
call dcopy(M*N,stk(ptrA),1,stk(ptrR),1)
c Set to zero lower trapezoidal part of R:
IRANK=istk(ptrRANK)
IR=IRANK-M
do 10 K=1,N
II=II+1
NB=M-IRANK
IR=IR+M
NB1=NB
IR1=IR
if(K.lt.IRANK) then
IR1=IR-(IRANK-K)
NB1=NB+(IRANK-K)
endif
call dcopy(NB1,ZERO,0,stk(ptrR+IR1),1)
10 continue
c Make Q
if(M.le.N) then
c A is fat
CALL DORGQR( M, M, M, stk(ptrA), LDA, stk(ptrTAU),
& stk(ptrDWORK), LDWORK, INFO )
call dcopy(M*M,stk(ptrA),1,stk(ptrQ),1)
else
c A is tall => Q=[A,0]
call dcopy(M*N,stk(ptrA),1,stk(ptrQ),1)
call dcopy(M*(M-N),0.d0,0,stk(ptrQ+M*N),1)
CALL DORGQR( M, M, min(M,N), stk(ptrQ), LDA, stk(ptrTAU),
& stk(ptrDWORK), LDWORK, INFO )
endif
if(INFO.ne.0) then
call errorinfo(fname,INFO)
return
endif
c [Q,R,JPVT,RANK,SVAL]=rankqr(A,[RCOND,JPVT])
lhsvar(1)=Q
lhsvar(2)=R
lhsvar(3)=JPVT
lhsvar(4)=RANK
lhsvar(5)=SVAL
end
subroutine intzb03od(fname)
INCLUDE '../stack.h'
character fname*(*)
logical createvar, getrhsvar, checklhs, checkrhs
c
integer A,RCOND,RANK,SVAL,JPVT,TAU,R,Q,RWORK,DWORK
integer ptrA,ptrRCOND,ptrJPVT,ptrSVAL,ptrTAU,ptrRANK
integer ptrDWORK,ptrR,ptrQ,ptrRWORK
double precision RCONDdef,SLVMAX
character*(1) JOBQR
complex*16 ZERO
parameter( ZERO=(0.0D0,0.0D0) )
c [Q,R,JPVT,RANK,SVAL]=rankqr(A,[RCOND,JPVT])
minrhs=1
maxrhs=3
minlhs=1
maxlhs=5
if(.not.checklhs(fname,minlhs,maxlhs)) return
if(.not.checkrhs(fname,minrhs,maxrhs)) return
JOBQR='Q'
RCONDdef=0.0d0
SLVMAX=0.0d0
A=1
RCOND=2
JPVT=3
SVAL=4
TAU=5
RANK=6
R=7
Q=8
RWORK=9
DWORK=10
if(.not.getrhsvar(A,'z',M,N,ptrA)) return
if(rhs.eq.1) then
c rankqr(A)
c create RCOND=0.0,JPVT=[0,..,0]
if(.not.createvar(RCOND,'d',1,1,ptrRCOND)) return
stk(ptrRCOND)=RCONDdef
if(.not.createvar(JPVT,'i',1,N,ptrJPVT)) return
call icopy(N,0,0,istk(ptrJPVT),1)
elseif(rhs.eq.2) then
c rankqr(A,RCOND)
c get RCOND, create JPVT=[0,..,0]
if(.not.getrhsvar(RCOND,'d',mR,nR,ptrRCOND)) return
if(mR*nR.ne.1) then
buf=fname//': 2nd parameter (RCOND) has wrong dimension'
call error(998)
return
endif
if(.not.createvar(JPVT,'i',1,N,ptrJPVT)) return
call icopy(N,0,0,istk(ptrJPVT),1)
elseif(rhs.eq.3) then
c rankqr(A,RCOND,JPVT)
c get RCOND, JPVT
if(.not.getrhsvar(RCOND,'d',mR,nR,ptrRCOND)) return
if(mR*nR.ne.1) then
buf=fname//': 2nd parameter (RCOND) has wrong dimension'
call error(998)
return
endif
if(.not.getrhsvar(JPVT,'i',mJ,nJ,ptrJPVT)) return
if(mJ*nJ.ne.N) then
buf=fname//': JPVT must have same column dim. as A'
call error(998)
return
endif
endif
c Creating SVAL,RANK,R,Q,RWORK,DWORK
if(.not.createvar(SVAL,'d',1,3,ptrSVAL)) return
if(.not.createvar(TAU,'z',1,min(M,N),ptrTAU)) return
if(.not.createvar(RANK,'i',1,1,ptrRANK)) return
if(.not.createvar(R,'z',M,N,ptrR)) return
if(.not.createvar(Q,'z',M,M,ptrQ)) return
if(.not.createvar(RWORK,'d',1,2*N,ptrRWORK)) return
LDWORKMIN=max(2*min(M,N),N+1)
LDWORK=maxvol(DWORK,'z')
if(LDWORK.le.LDWORKMIN) then
buf=fname//': not enough memory (use stacksize)'
call error(998)
return
endif
if(.not.createvar(DWORK,'z',1,LDWORK,ptrDWORK)) return
LDA=max(1,M)
call ZB03OD(JOBQR, M, N, zstk(ptrA), LDA, istk(ptrJPVT),
& stk(ptrRCOND), SLVMAX, zstk(ptrTAU), istk(ptrRANK),
& stk(ptrSVAL), zstk(ptrDWORK), LDWORK, stk(ptrRWORK), INFO)
if(INFO.ne.0) then
call errorinfo(fname,INFO)
return
endif
c Save R (=current A)
call zcopy(M*N,zstk(ptrA),1,zstk(ptrR),1)
c Set to zero lower trapezoidal part of R:
IRANK=istk(ptrRANK)
IR=IRANK-M
do 10 K=1,N
II=II+1
NB=M-IRANK
IR=IR+M
NB1=NB
IR1=IR
if(K.lt.IRANK) then
IR1=IR-(IRANK-K)
NB1=NB+(IRANK-K)
endif
call zcopy(NB1,ZERO,0,zstk(ptrR+IR1),1)
10 continue
c Make Q
if(M.le.N) then
c A is fat
CALL ZUNGQR( M, M, M, zstk(ptrA), LDA, zstk(ptrTAU),
& zstk(ptrDWORK), LDWORK, INFO )
call zcopy(M*M,zstk(ptrA),1,zstk(ptrQ),1)
else
c A is tall => Q=[A,0]
call zcopy(M*N,zstk(ptrA),1,zstk(ptrQ),1)
call zcopy(M*(M-N),ZERO,0,zstk(ptrQ+M*N),1)
CALL ZUNGQR( M, M, min(M,N), zstk(ptrQ), LDA, zstk(ptrTAU),
& zstk(ptrDWORK), LDWORK, INFO )
endif
if(INFO.ne.0) then
call errorinfo(fname,INFO)
return
endif
c [Q,R,JPVT,RANK,SVAL]=rankqr(A,[RCOND,JPVT])
lhsvar(1)=Q
lhsvar(2)=R
lhsvar(3)=JPVT
lhsvar(4)=RANK
lhsvar(5)=SVAL
end
subroutine intmucomp(fname)
c [bound,D,G] = mucomp(Z,K,T)
c [bound,D] = mucomp(Z,K,T)
c bound = mucomp(Z,K,T)
include '../stack.h'
logical getrhsvar,createvar
logical checklhs,checkrhs
character fname*(*)
minrhs=3
maxrhs=3
minlhs=1
maxlhs=3
c
if(.not.checkrhs(fname,minrhs,maxrhs)) return
if(.not.checklhs(fname,minlhs,maxlhs)) return
if(.not.getrhsvar(1,'z', M, N, lZ)) return
if(M.ne.N) then
buf='mucomp'//': the matrix must be square'
call error(998)
return
endif
if(N.eq.0) then
if(lhs.eq.1) then
if(.not.createvar(2,'d', N, 1, lBOUND)) return
lhsvar(1) = 2
return
else if(lhs.eq.2) then
if(.not.createvar(2,'d', N, 1, lBOUND)) return
if(.not.createvar(3,'d', N, 1, lD)) return
lhsvar(1)=2
lhsvar(2)=3
return
else if(lhs.eq.3) then
if(.not.createvar(2,'d', N, 1, lBOUND)) return
if(.not.createvar(3,'d', N, 1, lD)) return
if(.not.createvar(4,'d', N, 1, lG)) return
lhsvar(1)=2
lhsvar(2)=3
lhsvar(3)=4
return
endif
endif
if(.not.getrhsvar(2,'i', M1, N1, lK)) return
if(.not.getrhsvar(3,'i', M2, N2, lT)) return
if(M1*N1.ne.M2*N2) then
buf='mucomp'//': K and T must have equal lengths'
call error(998)
return
endif
M = M1*N1
if(.not.createvar(4,'d', 1, 1, lBOUND)) return
if(.not.createvar(5,'d', N, 1, lD)) return
if(.not.createvar(6,'d', N, 1, lG)) return
if(.not.createvar(7,'d', 2*N-1, 1, lX)) return
if(.not.createvar(8,'i', 4*N-2, 1, lIWORK)) return
LRWRK = 2*N*N*N + 9*N*N + 44*N - 11
if(.not.createvar(9,'d', LRWRK, 1, lRWORK)) return
LZWRKMIN = 6*N*N*N + 12*N*N + 12*N - 3
LZWRK=maxvol(10,'z')
if(LZWRK.le.LZWRKMIN) then
buf='mucomp'//': not enough memory (use stacksize)'
call error(998)
return
endif
if(.not.createvar(10,'z',1,LZWRK,lZWORK)) return
call AB13MD( 'N', N, zstk(lZ), N, M, istk(lK), istk(lT),
$ stk(lX), stk(lBOUND), stk(lD), stk(lG), istk(lIWORK),
$ stk(lRWORK), LRWRK, zstk(lZWORK), LZWRK, INFO )
c SUBROUTINE AB13MD( FACT, N, Z, N, M, NBLOCK, ITYPE, X,
c $ BOUND, D, G, IWORK, DWORK, LDWORK, ZWORK, LZWORK,
c $ INFO )
if(info.ne.0) then
call errorinfo("mucomp",info)
return
endif
if(lhs.eq.1) then
lhsvar(1) = 4
else if(lhs.eq.2) then
lhsvar(1)=4
lhsvar(2)=5
else if(lhs.eq.3) then
lhsvar(1)=4
lhsvar(2)=5
lhsvar(3)=6
endif
c
end
SUBROUTINE ZB03OD( JOBQR, M, N, A, LDA, JPVT, RCOND, SVLMAX, TAU,
$ RANK, SVAL, WORK, LWORK, RWORK, INFO )
*
* .. Scalar Arguments ..
CHARACTER*1 JOBQR
INTEGER INFO, LDA, LWORK, M, N, RANK
DOUBLE PRECISION RCOND, SVLMAX
* ..
* .. Array Arguments ..
INTEGER JPVT( * )
DOUBLE PRECISION SVAL(3), RWORK( * )
COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * )
* ..
*
* Purpose
* =======
*
C
C RELEASE 4.0, WGS COPYRIGHT 2001.
C
C PURPOSE
C
C To compute (optionally) a rank-revealing QR factorization of a
C real general M-by-N matrix A, which may be rank-deficient,
C and estimate its effective rank using incremental condition
C estimation.
C
C The routine uses a QR factorization with column pivoting:
C A * P = Q * R, where R = [ R11 R12 ],
C [ 0 R22 ]
C with R11 defined as the largest leading submatrix whose estimated
C condition number is less than 1/RCOND. The order of R11, RANK,
C is the effective rank of A.
C
C ZB03OD does not perform any scaling of the matrix A.
*
* Arguments
* =========
*
C Mode Parameters
C
C JOBQR CHARACTER*1
C = 'Q': Perform a QR factorization with column pivoting;
C = 'N': Do not perform the QR factorization (but ssumes
C that it has been done outside).
*
* M (input) INTEGER
* The number of rows of the matrix A. M >= 0.
*
* N (input) INTEGER
* The number of columns of the matrix A. N >= 0.
*
* A (input/output) COMPLEX*16 array, dimension (LDA,N)
* On entry, the M-by-N matrix A.
* On exit, A has been overwritten by details of its
* complete orthogonal factorization.
*
* LDA (input) INTEGER
* The leading dimension of the array A. LDA >= max(1,M).
*
* LDB (input) INTEGER
* The leading dimension of the array B. LDB >= max(1,M,N).
*
* JPVT (input/output) INTEGER array, dimension (N)
* On entry, if JPVT(i) .ne. 0, the i-th column of A is permuted
* to the front of AP, otherwise column i is a free column.
* On exit, if JPVT(i) = k, then the i-th column of A*P
* was the k-th column of A.
*
* RCOND (input) DOUBLE PRECISION
* RCOND is used to determine the effective rank of A, which
* is defined as the order of the largest leading triangular
* submatrix R11 in the QR factorization with pivoting of A,
* whose estimated condition number < 1/RCOND.
*
C
C TAU (output) COMPLEX*16 array, dimension ( MIN( M, N ) )
C On exit with JOBQR = 'Q', the leading min(M,N) elements of
C TAU contain the scalar factors of the elementary
C reflectors.
C Array TAU is not referenced when JOBQR = 'N'.
C
* RANK (output) INTEGER
* The effective rank of A, i.e., the order of the submatrix
* R11. This is the same as the order of the submatrix T11
* in the complete orthogonal factorization of A.
*
C SVAL (output) DOUBLE PRECISION array, dimension ( 3 )
C The estimates of some of the singular values of the
C triangular factor R:
C SVAL(1): largest singular value of R(1:RANK,1:RANK);
C SVAL(2): smallest singular value of R(1:RANK,1:RANK);
C SVAL(3): smallest singular value of R(1:RANK+1,1:RANK+1),
C if RANK < MIN( M, N ), or of R(1:RANK,1:RANK),
C otherwise.
C If the triangular factorization is a rank-revealing one
C (which will be the case if the leading columns were well-
C conditioned), then SVAL(1) will also be an estimate for
C the largest singular value of A, and SVAL(2) and SVAL(3)
C will be estimates for the RANK-th and (RANK+1)-st singular
C values of A, respectively.
C By examining these values, one can confirm that the rank
C is well defined with respect to the chosen value of RCOND.
C The ratio SVAL(1)/SVAL(2) is an estimate of the condition
C number of R(1:RANK,1:RANK).
C
* WORK (workspace/output) COMPLEX*16 array, dimension (LWORK)
* On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
*
* LWORK (input) INTEGER
* The dimension of the array WORK.
*
* If JOBQR = 'Q':
* The unblocked strategy requires that:
* LWORK >= MAX( 2*MN, N+1 )
* where MN = min(M,N).
* The block algorithm requires that:
* LWORK >= MAX( 2*MN, NB*(N+1) )
* where NB is an upper bound on the blocksize returned
* by ILAENV for the routines ZGEQP3 and ZUNMQR.
*
* LDWORK = max( 1, 2*min( M, N ) ), if JOBQR = 'N'.
*
* If LWORK = -1, then a workspace query is assumed; the routine
* only calculates the optimal size of the WORK array, returns
* this value as the first entry of the WORK array, and no error
* message related to LWORK is issued by XERBLA.
*
* RWORK (workspace) DOUBLE PRECISION array, dimension (2*N)
*
* INFO (output) INTEGER
* = 0: successful exit
* < 0: if INFO = -i, the i-th argument had an illegal value
*
C METHOD
C
C The routine computes or uses a QR factorization with column
C pivoting of A, A * P = Q * R, with R defined above, and then
C finds the largest leading submatrix whose estimated condition
C number is less than 1/RCOND, taking the possible positive value of
C SVLMAX into account. This is performed using the LAPACK
C incremental condition estimation scheme and a slightly modified
C rank decision test.
C
C CONTRIBUTOR
C
C Complex version of MB03OD
C
*
* =====================================================================
*
* .. Parameters ..
INTEGER IMAX, IMIN
PARAMETER ( IMAX = 1, IMIN = 2 )
DOUBLE PRECISION ZERO, ONE
PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
COMPLEX*16 CZERO, CONE
PARAMETER ( CZERO = ( 0.0D+0, 0.0D+0 ),
$ CONE = ( 1.0D+0, 0.0D+0 ) )
* ..
* .. Local Scalars ..
LOGICAL LJOBQR, LQUERY
INTEGER I, ISMAX, ISMIN, J, LWKOPT, MN,
$ NB, NB1, NB2
DOUBLE PRECISION SMAX, SMAXPR, SMIN, SMINPR
COMPLEX*16 C1, C2, S1, S2
* ..
* .. External Subroutines ..
EXTERNAL XERBLA, ZGEQP3, ZLAIC1
* ..
* .. External Functions ..
LOGICAL LSAME
INTEGER ILAENV
EXTERNAL ILAENV, LSAME
* ..
* .. Intrinsic Functions ..
INTRINSIC ABS, DBLE, DCMPLX, MAX, MIN
* ..
* .. Executable Statements ..
*
LJOBQR = LSAME( JOBQR, 'Q' )
MN = MIN( M, N )
ISMIN = 1
ISMAX = MN + 1
*
* Test the input arguments.
*
INFO = 0
NB1 = ILAENV( 1, 'ZGEQRF', ' ', M, N, -1, -1 )
NB2 = ILAENV( 1, 'ZUNMQR', ' ', M, N, NRHS, -1 )
NB = MAX( NB1, NB2 )
LWKOPT = MAX( 1, 2*N+NB*( N+1 ) )
WORK( 1 ) = DCMPLX( LWKOPT )
LQUERY = ( LWORK.EQ.-1 )
C
IF( .NOT.LJOBQR .AND. .NOT.LSAME( JOBQR, 'N' ) ) THEN
INFO = -1
ELSE IF( M.LT.0 ) THEN
INFO = -2
ELSE IF( N.LT.0 ) THEN
INFO = -3
ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
INFO = -5
ELSE IF( RCOND.LT.ZERO ) THEN
INFO = -7
ELSE IF( SVLMAX.LT.ZERO ) THEN
INFO = -8
ELSE IF( LWORK.LT.( MAX( 2*MN, N+1 ) ) .AND. .NOT.
$ LQUERY ) THEN
INFO = -13
END IF
*
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'ZB03OD', -INFO )
RETURN
END IF
*
* Quick return if possible
*
IF( MN.EQ.0 ) THEN
SVAL( 1 ) = ZERO
SVAL( 2 ) = ZERO
SVAL( 3 ) = ZERO
RANK = 0
RETURN
END IF
C
IF( LJOBQR ) THEN
*
* Compute QR factorization with column pivoting of A:
* A * P = Q * R
*
CALL ZGEQP3( M, N, A, LDA, JPVT, TAU, WORK, LWORK,
$ RWORK, INFO )
*
* complex workspace: MN+NB*(N+1). real workspace 2*N.
* Details of Householder rotations stored in WORK(1:MN).
END IF
*
* Determine RANK using incremental condition estimation
*
WORK( ISMIN ) = CONE
WORK( ISMAX ) = CONE
SMAX = ABS( A( 1, 1 ) )
SMIN = SMAX
IF( SMAX.EQ.ZERO .OR. SVLMAX*RCOND.GT.SMAX) THEN
RANK = 0
SVAL( 1 ) = SMAX
SVAL( 2 ) = ZERO
SVAL( 3 ) = ZERO
ELSE
RANK = 1
SMINPR = SMIN
*
10 CONTINUE
IF( RANK.LT.MN ) THEN
I = RANK + 1
CALL ZLAIC1( IMIN, RANK, WORK( ISMIN ), SMIN, A( 1, I ),
$ A( I, I ), SMINPR, S1, C1 )
CALL ZLAIC1( IMAX, RANK, WORK( ISMAX ), SMAX, A( 1, I ),
$ A( I, I ), SMAXPR, S2, C2 )
*
IF( SVLMAX*RCOND.LE.SMAXPR ) THEN
IF( SVLMAX*RCOND.LE.SMINPR ) THEN
IF( SMAXPR*RCOND.LE.SMINPR ) THEN
DO 20 I = 1, RANK
WORK( ISMIN+I-1 ) = S1*WORK( ISMIN+I-1 )
WORK( ISMAX+I-1 ) = S2*WORK( ISMAX+I-1 )
20 CONTINUE
WORK( ISMIN+RANK ) = C1
WORK( ISMAX+RANK ) = C2
SMIN = SMINPR
SMAX = SMAXPR
RANK = RANK + 1
GO TO 10
END IF
END IF
END IF
END IF
SVAL( 1 ) = SMAX
SVAL( 2 ) = SMIN
SVAL( 3 ) = SMINPR
END IF
WORK( 1 ) = DCMPLX( LWKOPT )
C
RETURN
C *** Last line of ZB03OD ***
END
subroutine intricc2(fname)
c [X,RCOND,FERR]=ricc(A,C,D,'type','method')
c [X,RCOND]=ricc(A,C,D,'type','method')
c X = riccsl(A,C,D,'type','method')
c 'type' is 'continuous' or 'discrete'
c 'method' is 'schr' or 'sign' for continuous-time systems
c and 'schr' or 'invf' for discrete-tyme systems
include '../stack.h'
logical getrhsvar,createvar
logical checklhs,checkrhs
character fname*(*)
character*4 TYPE, METHOD
logical WANTC, WANTD, WSCHUR, WSIGN, WINVF
minrhs=4
maxrhs=5
minlhs=1
maxlhs=3
c
if(.not.checkrhs(fname,minrhs,maxrhs)) return
if(.not.checklhs(fname,minlhs,maxlhs)) return
if(.not.getrhsvar(1,'d', MA, NA, lA)) return
if(MA.ne.NA) then
buf='ricc'//': the matrix A must be square'
call error(998)
return
endif
if(.not.getrhsvar(2,'d', MD, ND, lD)) return
if(MD.ne.ND) then
buf='ricc'//': the matrix D must be square'
call error(998)
return
endif
if(.not.getrhsvar(3,'d', MC, NC, lC)) return
if(MC.ne.NC) then
buf='ricc'//': the matrix C must be square'
call error(998)
return
endif
if(MA.ne.MC .or. MC.ne.MD .or. MA.ne.MD) then
buf='ricc'//
$ ': the matrices A, C and D must have the same order'
call error(998)
return
endif
N = MA
if(.not.getrhsvar(4,'c', M1, N1, lTYPE)) return
TYPE(1:4) = cstk(lTYPE:lTYPE+4)
WANTC = (TYPE(1:4).eq.'cont' .or. TYPE(1:4).eq.'CONT')
WANTD = (TYPE(1:4).eq.'disc' .or. TYPE(1:4).eq.'DISC')
if(.not.WANTC .and. .not.WANTD) then
buf='ricc'//': type must be continuous or discrete'
call error(998)
return
endif
k = 5
WSCHUR = .TRUE.
if(rhs.eq.5) then
if(.not.getrhsvar(5,'c', M1, N1, lMETHOD)) return
METHOD(1:4) = cstk(lMETHOD:lMETHOD+4)
if(WANTC) then
WSCHUR = (METHOD(1:4).eq.'schr' .or. METHOD(1:4).eq.'SCHR')
WSIGN = (METHOD(1:4).eq.'sign' .or. METHOD(1:4).eq.'SIGN')
if(.not.WSCHUR .and. .not.WSIGN) then
buf='ricc'//': method must be schur or sign'
call error(998)
return
endif
else
WSCHUR = (METHOD(1:4).eq.'schr' .or. METHOD(1:4).eq.'SCHR')
WINVF = (METHOD(1:4).eq.'invf' .or. METHOD(1:4).eq.'INVF')
if(.not.WSCHUR .and. .not.WINVF) then
buf='ricc'//': method must be schur or invf'
call error(998)
return
endif
endif
k = 6
endif
if(.not.createvar(k,'d', N, N, lX)) return
if(.not.createvar(k+1,'d', N, 1, lWR)) return
if(.not.createvar(k+2,'d', N, 1, lWI)) return
if(.not.createvar(k+3,'d', 1, 1, lRCOND)) return
if(.not.createvar(k+4,'d', 1, 1, lFERR)) return
if(.not.createvar(k+5,'i', 1, max(2*N,N*N), lIWORK)) return
if(.not.createvar(k+6,'i', 1, 2*N, lBWORK)) return
if(WANTC) then
if(WSCHUR) then
LWORKMIN = 9*N*N + 4*N + max(1,6*N)
else if(WSIGN) then
LWORKMIN = 9*N*N + 7*N + 1
endif
else
if(WSCHUR) then
LWORKMIN = 12*N*N + 22*N + max(16,4*N)
else if(WINVF) then
LWORKMIN = 28*N*N + 2*N + max(1,2*N)
endif
endif
LWORK=maxvol(k+7,'d')
if(LWORK.le.LWORKMIN) then
buf='ricc'//': not enough memory (use stacksize)'
call error(998)
return
endif
if(.not.createvar(k+7,'d',1,LWORK,lDWORK)) return
if(WANTC) then
if(WSCHUR) then
call RICCSL( 'N', N, stk(lA), N, 'U', stk(lC), N, stk(lD),
$ N, stk(lX), N, stk(lWR), stk(lWI), stk(lRCOND),
$ stk(lFERR), stk(lDWORK), LWORK, istk(lIWORK),
$ istk(lBWORK), INFO )
c SUBROUTINE RICCSL( TRANS, N, A, LDA, C, LDC, D, LDD, X, LDX,
c $ WR, WI, RCOND, FERR, WORK, LWORK, IWORK, BWORK, INFO )
else if(WSIGN) then
call RICCMS( 'N', N, stk(lA), N, 'U', stk(lC), N, stk(lD),
$ N, stk(lX), N, stk(lWR), stk(lWI), stk(lRCOND),
$ stk(lFERR), stk(lDWORK), LWORK, istk(lIWORK), INFO )
c SUBROUTINE RICCMS( TRANS, N, A, LDA, C, LDC, D, LDD, X, LDX,
c $ WR, WI, RCOND, FERR, WORK, LWORK, IWORK, INFO )
endif
else
if(WSCHUR) then
call RICDSL( 'N', N, stk(lA), N, 'U', stk(lC), N, stk(lD),
$ N, stk(lX), N, stk(lWR), stk(lWI), stk(lRCOND),
$ stk(lFERR), stk(lDWORK), LWORK, istk(lIWORK),
$ istk(lBWORK), INFO )
c SUBROUTINE RICDSL( TRANS, N, A, LDA, C, LDC, D, LDD, X, LDX,
C $ WR, WI, RCOND, FERR, WORK, LWORK, IWORK, BWORK, INFO )
else if (WINVF) then
call RICDMF( 'N', N, stk(lA), N, 'U', stk(lC), N, stk(lD),
$ N, stk(lX), N, stk(lWR), stk(lWI), stk(lRCOND),
$ stk(lFERR), stk(lDWORK), LWORK, istk(lIWORK), INFO )
c SUBROUTINE RICDMF( TRANS, N, A, LDA, C, LDC, D, LDD, X, LDX,
C $ WR, WI, RCOND, FERR, WORK, LWORK, IWORK, INFO )
endif
endif
if(info.ne.0) then
call errorinfo("ricc",info)
return
endif
if(lhs.eq.1) then
lhsvar(1)=k
else if(lhs.eq.2) then
lhsvar(1)=k
lhsvar(2)=k+3
else if(lhs.eq.3) then
lhsvar(1)=k
lhsvar(2)=k+3
lhsvar(3)=k+4
endif
c
end
subroutine inthinf(fname)
c [Ak,Bk,Ck,Dk,RCOND]=hinf(A,B,C,D,ncon,nmeas,gamma)
include '../stack.h'
logical getrhsvar,createvar
logical checklhs,checkrhs
character fname*(*)
double precision GAMMA, TOL, EPS
integer N, M, R, Q
double precision dlamch
external dlamch
c
minrhs=7
maxrhs=7
minlhs=4
maxlhs=5
c
if(.not.checkrhs(fname,minrhs,maxrhs)) return
if(.not.checklhs(fname,minlhs,maxlhs)) return
if(.not.getrhsvar(1,'d', MA, NA, lA)) return
if(MA .ne. NA) then
buf='hinf'//': A must be a square matrix'
call error(998)
return
endif
if(.not.getrhsvar(2,'d', MB, NB, lB)) return
if(MA .ne. MB) then
buf='hinf'//': A and B must have equal number of rows'
call error(998)
return
endif
if(.not.getrhsvar(3,'d', MC, NC, lC)) return
if(NA .ne. NC) then
buf='hinf'//': A and C must have equal number of columns'
call error(998)
return
endif
if(.not.getrhsvar(4,'d', MD, ND, lD)) return
if(NB .ne. ND) then
buf='hinf'//': B and D must have equal number of columns'
call error(998)
return
endif
if(MC .ne. MD) then
buf='hinf'//': C and D must have equal number of rows'
call error(998)
return
endif
N = MA
M = NB
R = MC
if(N.eq.0 .or. M.eq.0 .or. R.eq.0) then
if(.not.createvar(5,'d', 0, 0, lAK)) return
if(.not.createvar(6,'d', 0, 0, lBK)) return
if(.not.createvar(7,'d', 0, 0, lCK)) return
if(.not.createvar(8,'d', 0, 0, lDK)) return
if(.not.createvar(9,'d', 0, 0, lRCOND)) return
lhsvar(1) = 5
lhsvar(2) = 6
lhsvar(3) = 7
lhsvar(4) = 8
lhsvar(5) = 9
return
endif
if(.not.getrhsvar(5,'i', M1, N1, lNCON)) return
if(M1.ne.1 .or. N1.ne.1 ) then
buf='hinf'//': NCON must be a scalar'
call error(998)
return
endif
NCON = istk(lNCON)
if(.not.getrhsvar(6,'i', M2, N2, lNMEAS)) return
if(M2.ne.1 .or. N2.ne.1 ) then
buf='hinf'//': NMEAS must be a scalar'
call error(998)
return
endif
NMEAS = istk(lNMEAS)
if(.not.getrhsvar(7,'d', M3, N3, lGAMMA)) return
if(M3.ne.1 .or. N3.ne.1 ) then
buf='hinf'//': GAMMA must be a scalar'
call error(998)
return
endif
GAMMA = stk(lGAMMA)
EPS = dlamch('eps')
TOL = sqrt(EPS)
if(.not.createvar(8,'d', N, N, lAK)) return
if(.not.createvar(9,'d', N, NMEAS, lBK)) return
if(.not.createvar(10,'d', NCON, N, lCK)) return
if(.not.createvar(11,'d', NCON, NMEAS, lDK)) return
if(.not.createvar(12,'d', 4, 1, lRCOND)) return
LINTWORK = max(2*max(N,M-NCON,R-NMEAS,NCON),N*N)
if(.not.createvar(13,'i', LINTWORK, 1, lIWORK)) return
if(.not.createvar(14,'i', 2*N, 1, lBWORK)) return
Q = MAX( M - NCON, NCON, R - NMEAS, NMEAS )
LWORKMIN = 2*Q*( 3*Q + 2*N ) +
$ MAX( 1, ( N + Q )*( N + Q + 6 ),
$ Q*( Q + MAX( N, Q, 5 ) + 1 ), 2*N*( N + 2*Q ) +
$ MAX( 1, 4*Q*Q +
$ MAX( 2*Q, 3*N*N +
$ MAX( 2*N*Q, 10*N*N + 12*N + 5 ) ),
$ Q*( 3*N + 3*Q +
$ MAX( 2*N, 4*Q + max( N, Q ) ) ) ) )
LWORK=maxvol(15,'d')
if(LWORK.le.LWORKMIN) then
buf='hinf'//': not enough memory (use stacksize)'
call error(998)
return
endif
if(.not.createvar(15,'d',1,LWORK,lDWORK)) return
CALL SB10FD( N, M, R, NCON, NMEAS, GAMMA, stk(lA), N,
$ stk(lB), N, stk(lC), R, stk(lD), R, stk(lAK),
$ N, stk(lBK), N, stk(lCK), NCON, stk(lDK),
$ NCON, stk(lRCOND), TOL, istk(lIWORK),
$ stk(lDWORK), LDWORK, istk(lBWORK), INFO )
if(info.ne.0) then
call errorinfo("hinf",info)
return
endif
lhsvar(1) = 8
lhsvar(2) = 9
lhsvar(3) = 10
lhsvar(4) = 11
if(lhs.eq.5) lhsvar(5) = 12
c
end
subroutine intdhinf(fname)
c [Ak,Bk,Ck,Dk,RCOND]=dhinf(A,B,C,D,ncon,nmeas,gamma)
include '../stack.h'
logical getrhsvar,createvar
logical checklhs,checkrhs
character fname*(*)
double precision GAMMA, TOL, EPS
integer N, M, R, Q
double precision dlamch
external dlamch
c
minrhs=7
maxrhs=7
minlhs=4
maxlhs=5
c
if(.not.checkrhs(fname,minrhs,maxrhs)) return
if(.not.checklhs(fname,minlhs,maxlhs)) return
if(.not.getrhsvar(1,'d', MA, NA, lA)) return
if(MA .ne. NA) then
buf='dhinf'//': A must be a square matrix'
call error(998)
return
endif
if(.not.getrhsvar(2,'d', MB, NB, lB)) return
if(MA .ne. MB) then
buf='dhinf'//': A and B must have equal number of rows'
call error(998)
return
endif
if(.not.getrhsvar(3,'d', MC, NC, lC)) return
if(NA .ne. NC) then
buf='dhinf'//': A and C must have equal number of columns'
call error(998)
return
endif
if(.not.getrhsvar(4,'d', MD, ND, lD)) return
if(NB .ne. ND) then
buf='dhinf'//': B and D must have equal number of columns'
call error(998)
return
endif
if(MC .ne. MD) then
buf='dhinf'//': C and D must have equal number of rows'
call error(998)
return
endif
N = MA
M = NB
R = MC
if(N.eq.0 .or. M.eq.0 .or. R.eq.0) then
if(.not.createvar(5,'d', 0, 0, lAK)) return
if(.not.createvar(6,'d', 0, 0, lBK)) return
if(.not.createvar(7,'d', 0, 0, lCK)) return
if(.not.createvar(8,'d', 0, 0, lDK)) return
if(.not.createvar(9,'d', 0, 0, lRCOND)) return
lhsvar(1) = 5
lhsvar(2) = 6
lhsvar(3) = 7
lhsvar(4) = 8
lhsvar(5) = 9
return
endif
if(.not.getrhsvar(5,'i', M1, N1, lNCON)) return
if(M1.ne.1 .or. N1.ne.1 ) then
buf='dhinf'//': NCON must be a scalar'
call error(998)
return
endif
NCON = istk(lNCON)
if(.not.getrhsvar(6,'i', M2, N2, lNMEAS)) return
if(M2.ne.1 .or. N2.ne.1 ) then
buf='dhinf'//': NMEAS must be a scalar'
call error(998)
return
endif
NMEAS = istk(lNMEAS)
if(.not.getrhsvar(7,'d', M3, N3, lGAMMA)) return
if(M3.ne.1 .or. N3.ne.1 ) then
buf='dhinf'//': GAMMA must be a scalar'
call error(998)
return
endif
GAMMA = stk(lGAMMA)
EPS = dlamch('eps')
TOL = sqrt(EPS)
if(.not.createvar(8,'d', N, N, lAK)) return
if(.not.createvar(9,'d', N, NMEAS, lBK)) return
if(.not.createvar(10,'d', NCON, N, lCK)) return
if(.not.createvar(11,'d', NCON, NMEAS, lDK)) return
if(.not.createvar(12,'d', N, N, lX)) return
if(.not.createvar(13,'d', N, N, lZ)) return
if(.not.createvar(14,'d', 8, 1, lRCOND)) return
LINTWORK = max(2*max(NCON,N),M,NCON+NMEAS,N*N)
if(.not.createvar(15,'i', LINTWORK, 1, lIWORK)) return
if(.not.createvar(16,'i', 2*N, 1, lBWORK)) return
Q = MAX( M - NCON, NCON, R - NMEAS, NMEAS )
LWORKMIN = max((N+Q)*(N+Q+6),13*N*N + M*M + 2*Q*Q + N*(M+Q) +
$ max(M*(M+7*N),2*Q*(8*N+M+2*Q)) + 6*N +
$ max(14*N+23,16*N,2*N+max(M,2*Q),3*max(M,2*Q)))
LWORK=maxvol(17,'d')
if(LWORK.le.LWORKMIN) then
buf='dhinf'//': not enough memory (use stacksize)'
call error(998)
return
endif
if(.not.createvar(17,'d',1,LWORK,lDWORK)) return
CALL SB10DD( N, M, R, NCON, NMEAS, GAMMA, stk(lA), N,
$ stk(lB), N, stk(lC), R, stk(lD), R, stk(lAK),
$ N, stk(lBK), N, stk(lCK), NCON, stk(lDK),
$ NCON, stk(lX), N, stk(lZ), N, stk(lRCOND), TOL,
$ istk(lIWORK), stk(lDWORK), LDWORK, istk(lBWORK),
$ INFO )
if(info.ne.0) then
call errorinfo("dhinf",info)
return
endif
lhsvar(1) = 8
lhsvar(2) = 9
lhsvar(3) = 10
lhsvar(4) = 11
if(lhs.eq.5) lhsvar(5) = 14
c
end
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