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SUBROUTINE MATRF2(M,N,C,INDEX,ALPHA,NN,NZ,A,SNR,RNR,FEJLM)
C--------------------------------------------------------------------
C
C PURPOSE
C -------
C The subroutine generates sparse (rectangular or square) matrices.
C The dimensions of the matrix and the average number of nonzero
C elements per row can be specified by the user. Moreover, the user
C can also change the sparsity pattern and the condition number of the
C matrix. The non-zero elements of the desired matrix will be
C accumulated (in an arbitrary order) in the first NZ positions of
C array A. The column and the row numbers of the non-zero element
C stored in A(I), I=1,...,NZ, will be found in SNR(I) and RNR(I),
C respectively. The matrix generated by this subroutine is of the
C class F(M,N,C,R,ALPHA) (see reference).
C
C Note: If A is the sparse matrix of type F(M,N,C,R,ALPHA), then
C
C min|A(i,j)| = 1/ALPHA,
C
C max|A(i,j)| = max(INDEX*N - N,10*ALPHA).
C
C
C CONTRIBUTOR: Ernest E. Rothman
C Cornell Theory Center/Cornell National Supercomputer
C Facility.
C e-mail address: BITNET: eer@cornellf
C INTERNET: eer@cornellf.tn.cornell.edu
C
C minor modifications by Y. Saad. April 26, 1990.
C
C Note: This subroutine has been copied from the following reference.
C The allowable array sizes have been changed.
C
C REFERENCE: Zlatev, Zahari; Schaumburg, Kjeld; Wasniewski, Jerzy;
C "A testing Scheme for Subroutines Solving Large Linear Problems",
C Computers and Chemistry, Vol. 5, No. 2-3, pp. 91-100, 1981.
C
C
C INPUT PARAMETERS
C ----------------
C M - Integer. The number of rows in the desired matrix.
C N < M+1 < 9000001 must be specified.
C
C N - Integer. The number of columns in the desired matrix.
C 21 < N < 9000001 must be specified.
C
C C - Integer. The sparsity pattern can be changed by means of this
C parameter. 10 < C < N-10 must be specified.
C
C INDEX - Integer. The average number of non-zero elements per row in
C the matrix will be equal to INDEX.
C 1 < INDEX < N-C-8 must be specified.
C
C ALPHA - Real. The condition number of the matrix can be changed
C BY THIS PARAMETER. ALPHA > 0.0 MUST BE SPECIFIED.
C If ALPHA is approximately equal to 1.0 then the generated
C matrix is well-conditioned. Large values of ALPHA will
C usually produce ill-conditioned matrices. Note that no
C round-off errors during the computations in this subroutine
C are made if ALPHA = 2**I (where I is an arbitrary integer
C which produces numbers in the machine range).
C
C NN - Integer. The length of arrays A, RNR, and SNR (see below).
C INDEX*M+109 < NN < 9000001 must be specified.
C
C
C OUTPUT PARAMETERS
C -----------------
C NZ - Integer. The number of non-zero elements in the matrix.
C
C A(NN) - Real array. The non-zero elements of the matrix generated
C are accumulated in the first NZ locations of array A.
C
C SNR(NN) - INTEGER array. The column number of the non-zero element
C kept in A(I), I=1,...NZ, is stored in SNR(I).
C
C RNR(NN) - Integer array. The row number of the non-zero element
C kept in A(I), I=1,...NZ, is stored in RNR(I).
C
C FEJLM - Integer. FEJLM=0 indicates that the call is successful.
C Error diagnostics are given by means of positive values of
C this parameter as follows:
C FEJLM = 1 - N is out of range.
C FEJLM = 2 - M is out of range.
C FEJLM = 3 - C is out of range.
C FEJLM = 4 - INDEX is out of range.
C FEJLM = 5 - NN is out of range.
C FEJLM = 7 - ALPHA is out of range.
C
C
C
C
REAL*8 A, ALPHA, ALPHA1
INTEGER M, N, NZ, C, NN, FEJLM, M1, NZ1, RR1, RR2, RR3, K
INTEGER M2, N2
INTEGER SNR, RNR
DIMENSION A(NN), SNR(NN), RNR(NN)
M1 = M
FEJLM = 0
NZ1 = INDEX*M + 110
K = 1
ALPHA1 = ALPHA
INDEX1 = INDEX - 1
C
C Check the parameters.
C
IF(N.GE.22) GO TO 1
2 FEJLM = 1
RETURN
1 IF(N.GT.9000000) GO TO 2
IF(M.GE.N) GO TO 3
4 FEJLM = 2
RETURN
3 IF(M.GT.9000000) GO TO 4
IF(C.LT.11)GO TO 6
IF(N-C.GE.11)GO TO 5
6 FEJLM = 3
RETURN
5 IF(INDEX.LT.1) GO TO 12
IF(N-C-INDEX.GE.9)GO TO 13
12 FEJLM = 4
13 IF(NN.GE.NZ1)GO TO 7
8 FEJLM = 5
RETURN
7 IF(NN.GT.9000000)GO TO 8
IF(ALPHA.GT.0.0)GO TO 9
FEJLM = 6
RETURN
9 CONTINUE
C
C End of the error check. Begin to generate the non-zero elements of
C the required matrix.
C
DO 20 I=1,N
A(I) = 1.0d0
SNR(I) = I
20 RNR(I) = I
NZ = N
J1 = 1
IF(INDEX1.EQ.0) GO TO 81
DO 21 J = 1,INDEX1
J1 = -J1
DO 22 I=1,N
A(NZ+I) = dfloat(J1*J*I)
IF(I+C+J-1.LE.N)SNR(NZ+I) = I + C + J - 1
IF(I+C+J-1.GT.N)SNR(NZ+I) = C + I + J - 1 - N
22 RNR(NZ + I) = I
21 NZ = NZ + N
81 RR1 = 10
RR2 = NZ
RR3 = 1
25 CONTINUE
DO 26 I=1,RR1
A(RR2 + I) = ALPHA*dfloat(I)
SNR(RR2+I) = N - RR1 + I
RNR(RR2+I) = RR3
26 CONTINUE
IF(RR1.EQ.1) GO TO 27
RR2 = RR2 + RR1
RR1 = RR1 - 1
RR3 = RR3 + 1
GO TO 25
27 NZ = NZ + 55
29 M1 = M1 - N
ALPHA = 1.0d0/ALPHA
IF(M1.LE.0) GO TO 28
N2 = K*N
IF(M1.GE.N)M2 = N
IF(M1.LT.N)M2 = M1
DO 30 I=1,M2
A(NZ+I) = ALPHA*dfloat(K+1)
SNR(NZ + I) = I
30 RNR(NZ + I) = N2 + I
NZ = NZ + M2
IF(INDEX1.EQ.0) GO TO 82
J1 = 1
DO 41 J = 1,INDEX1
J1 = -J1
DO 42 I = 1,M2
A(NZ+I) = ALPHA*dFLOAT(J*J1)*(dfloat((K+1)*I)+1.0d0)
IF(I+C+J-1.LE.N)SNR(NZ+I) = I + C + J - 1
IF(I+C+J-1.GT.N)SNR(NZ+I) = C + I + J - 1 - N
42 RNR(NZ + I) = N2 + I
41 NZ = NZ +M2
82 K = K + 1
GO TO 29
28 CONTINUE
ALPHA = 1.0d0/ALPHA1
RR1 = 1
RR2 = NZ
35 CONTINUE
DO 36 I = 1,RR1
A(RR2+I) = ALPHA*dfloat(RR1+1-I)
SNR(RR2+I) = I
RNR(RR2+I) = N - 10 + RR1
36 CONTINUE
IF(RR1.EQ.10) GO TO 34
RR2 = RR2 + RR1
RR1 = RR1 + 1
GO TO 35
34 NZ = NZ + 55
ALPHA = ALPHA1
RETURN
END
SUBROUTINE DCN(AR,IA,JA,N,NE,IC,NN,IERR)
C-----------------------------------------------------------------------
C
C PURPOSE
C -------
C The subroutine generates sparse (square) matrices of the type
C D(N,C). This type of matrix has the following characteristics:
C 1's in the diagonal, three bands at the distance C above the
C diagonal (and reappearing cyclicly under it), and a 10 x 10
C triangle of elements in the upper right-hand corner.
C Different software libraries require different storage schemes.
C This subroutine generates the matrix in the storage by
C indices mode.
C
C
C Note: If A is the sparse matrix of type D(N,C), then
C
C min|A(i,j)| = 1, max|A(i,j)| = max(1000,N + 1)
C
C
C
C CONTRIBUTOR: Ernest E. Rothman
C Cornell Theory Center/Cornell National Supercomputer
C Facility.
C e-mail address: BITNET: eer@cornellf
C INTERNET: eer@cornellf.tn.cornell.edu
C
C
C REFERENCE
C ---------
C 1) Zlatev, Zahari; Schaumburg, Kjeld; Wasniewski, Jerzy;
C "A Testing Scheme for Subroutines Solving Large Linear Problems",
C Computers and Chemistry, Vol. 5, No. 2-3, pp. 91-100, 1981.
C 2) Osterby, Ole and Zletev, Zahari;
C "Direct Methods for Sparse Matrices";
C Springer-Verlag 1983.
C
C
C
C INPUT PARAMETERS
C ----------------
C N - Integer. The size of the square matrix.
C N > 13 must be specified.
C
C NN - Integer. The dimension of integer arrays IA and JA and
C real array AR. Must be at least NE.
C
C IC - Integer. The sparsity pattern can be changed by means of this
C parameter. 0 < IC < N-12 must be specified.
C
C
C OUTPUT PARAMETERS
C -----------------
C NE - Integer. The number of nonzero elements in the sparse matrix
C of the type D(N,C). NE = 4*N + 55.
C
C AR(NN) - Real array. (Double precision)
C Stored entries of a sparse matrix to be generated by this
C subroutine.
C NN is greater then or equal to, NE, the number of
C nonzeros including a mandatory diagonal entry for
C each row. Entries are stored by indices.
C
C IA(NN) - Integer array.
C Pointers to specify rows for the stored nonzero entries
C in AR.
C
C JA(NN) - Integer array.
C Pointers to specify columns for the stored nonzero entries
C in AR.
C
C IERR - Error parameter is returned as zero on successful
C execution of the subroutine.
C Error diagnostics are given by means of positive values
C of this parameter as follows:
C IERR = 1 - N is out of range.
C IERR = 2 - IC is out of range.
C IERR = 3 - NN is out of range.
C
C----------------------------------------------------------------------
C
real*8 ar(nn)
integer ia(nn), ja(nn), ierr
ierr = 0
c
c
c - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Check the input parameters:
c
if(n.le.13)then
ierr = 1
return
endif
if(ic .le. 0 .or. ic .ge. n-12)then
ierr = 2
return
endif
ne = 4*n+55
if(nn.lt.ne)then
ierr = 3
return
endif
c
c - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
c
c Begin to generate the nonzero elements as well as the row and column
c pointers:
c
do 20 i=1,n
ar(i) = 1.0d0
ia(i) = i
ja(i) = i
20 continue
ilast = n
do 30 i=1,n-ic
it = ilast + i
ar(it) = 1.0 + dfloat(i)
ia(it) = i
ja(it) = i+ic
30 continue
ilast = ilast + n-ic
do 40 i=1,n-ic-1
it = ilast + i
ar(it) = -dfloat(i)
ia(it) = i
ja(it) = i+ic+1
40 continue
ilast = ilast + n-ic-1
do 50 i=1,n-ic-2
it = ilast + i
ar(it) = 16.0d0
ia(it) = i
ja(it) = i+ic+2
50 continue
ilast = ilast + n-ic-2
icount = 0
do 70 j=1,10
do 60 i=1,11-j
icount = icount + 1
it = ilast + icount
ar(it) = 100.0d0 * dfloat(j)
ia(it) = i
ja(it) = n-11+i+j
60 continue
70 continue
icount = 0
ilast = 55 + ilast
do 80 i=n-ic+1,n
icount = icount + 1
it = ilast + icount
ar(it) = 1.0d0 + dfloat(i)
ia(it) = i
ja(it) = i-n+ic
80 continue
ilast = ilast + ic
icount = 0
do 90 i=n-ic,n
icount = icount + 1
it = ilast + icount
ar(it) = -dfloat(i)
ia(it) = i
ja(it) = i-n+ic+1
90 continue
ilast = ilast + ic + 1
icount = 0
do 100 i=n-ic-1,n
icount = icount + 1
it = ilast + icount
ar(it) = 16.0d0
ia(it) = i
ja(it) = i-n+ic+2
100 continue
c ilast = ilast + ic + 2
c if(ilast.ne.4*n+55) then
c write(*,*)' ilast equal to ', ilast
c write(*,*)' ILAST, the number of nonzeros, should = ', 4*n + 55
c stop
c end if
c
c - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
return
end
SUBROUTINE ECN(N,IC,NE,IA,JA,AR,NN,IERR)
C----------------------------------------------------------------------
C
C PURPOSE
C -------
C The subroutine generates sparse (square) matrices of the type
C E(N,C). This type of matrix has the following characteristics:
C Symmetric, positive-definite, N x N matrices with 4 in the diagonal
C and -1 in the two sidediagonal and in the two bands at the distance
C C from the diagonal. These matrices are similar to matrices obtained
C from using the five-point formula in the discretization of the
C elliptic PDE.
C
C
C Note: If A is the sparse matrix of type E(N,C), then
C
C min|A(i,j)| = 1, max|A(i,j)| = 4
C
C
C
C CONTRIBUTOR: Ernest E. Rothman
C Cornell Theory Center/Cornell National Supercomputer
C Facility.
C e-mail address: BITNET: eer@cornellf
C INTERNET: eer@cornellf.tn.cornell.edu
C
C
C REFERENCE
C ---------
C 1) Zlatev, Zahari; Schaumburg, Kjeld; Wasniewski, Jerzy;
C "A Testing Scheme for Subroutines Solving Large Linear Problems",
C Computers and Chemistry, Vol. 5, No. 2-3, pp. 91-100, 1981.
C 2) Osterby, Ole and Zletev, Zahari;
C "Direct Methods for Sparse Matrices";
C Springer-Verlag 1983.
C
C
C
C INPUT PARAMETERS
C ----------------
C N - Integer. The size of the square matrix.
C N > 2 must be specified.
C
C NN - Integer. The dimension of integer arrays IA and JA and
C real array AR. Must be at least NE.
C
C NN - Integer. The dimension of integer array JA. Must be at least
C NE.
C
C IC - Integer. The sparsity pattern can be changed by means of this
C parameter. 1 < IC < N must be specified.
C
C
C
C OUTPUT PARAMETERS
C -----------------
C NE - Integer. The number of nonzero elements in the sparse matrix
C of the type E(N,C). NE = 5*N - 2*IC - 2 .
C
C AR(NN) - Real array.
C Stored entries of the sparse matrix A.
C NE is the number of nonzeros including a mandatory
C diagonal entry for each row.
C
C IA(NN) - Integer array.(Double precision)
C Pointers to specify rows for the stored nonzero entries
C in AR.
C
C JA(NN) - Integer array.
C Pointers to specify columns for the stored nonzero entries
C in AR.
C
C IERR - Error parameter is returned as zero on successful
C execution of the subroutine.
C Error diagnostics are given by means of positive values
C of this parameter as follows:
C IERR = 1 - N is out of range.
C IERR = 2 - IC is out of range.
C IERR = 3 - NN is out of range.
C
C---------------------------------------------------------------------
C
C
real*8 ar(nn)
integer ia(nn), ja(nn), n, ne, ierr
ierr = 0
c
c - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
c
Check the input parameters:
c
if(n.le.2)then
ierr = 1
return
endif
if(ic.le.1.or.ic.ge.n)then
ierr = 2
return
endif
c
ne = 5*n-2*ic-2
if(nn.lt.ne)then
ierr = 3
return
endif
c
c - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
c
c Begin to generate the nonzero elements as well as the row and column
c pointers:
c
do 20 i=1,n
ar(i) = 4.0d0
ia(i) = i
ja(i) = i
20 continue
ilast = n
do 30 i=1,n-1
it = ilast + i
ar(it) = -1.0d0
ia(it) = i+1
ja(it) = i
30 continue
ilast = ilast + n - 1
do 40 i=1,n-1
it = ilast + i
ar(it) = -1.0d0
ia(it) = i
ja(it) = i+1
40 continue
ilast = ilast + n-1
do 50 i=1,n-ic
it = ilast + i
ar(it) = -1.0d0
ia(it) = i+ic
ja(it) = i
50 continue
ilast = ilast + n-ic
do 60 I=1,n-ic
it = ilast + i
ar(it) = -1.0d0
ia(it) = i
ja(it) = i+ic
60 continue
c ilast = ilast + n-ic
c if(ilast.ne.5*n-2*ic-2) then
c write(*,*)' ilast equal to ', ilast
c write(*,*)' ILAST, the no. of nonzeros, should = ', 5*n-2*ic-2
c stop
c end if
c
c - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
return
end
|
