C
C Program SMPOWER to compute matrix SM2, which is POWER-th power of C input symetric matrix SM1. C C Version: 6.20 C Date: 2008, June 12 C C Coded by Petr Bulant C Department of Geophysics, Charles University Prague, C Ke Karlovu 3, 121 16 Praha 2, Czech Republic, C C....................................................................... C C Description of data files: C C Input data read from the standard input device (*): C The data are read by the list directed input (free format) and C consist of a single string 'SEP': C 'SEP'...String in apostrophes containing the name of the input C SEP parameter or history file with the input data. C No default, 'SEP' must be specified and cannot be blank. C C C Input data file 'SEP': C File 'SEP' has the form of the SEP C parameter file. The parameters, which do not differ from their C defaults, need not be specified in file 'SEP'. C Data specifying dimensions of the matrices: C M1='string'... Name of the file containing a single integer number C specifying the number of rows (and columns) of symmetric C matrices A and R. C Default: M1=' ' means that the number is 1. C Filenames of the matrix header files: C SM1='string' ... Name of the header file of the symmetric C matrix SM1. C No default, 'SM1' must be specified and cannot be blank. C SM2='string' ... Name of the header file of the symmetric C matrix SM2=SM1**POWER. C No default, 'SM2' must be specified and cannot be blank. C Recent version of the program cannot deal with sparse matrices. C For general description of the files with matrices refer to file C forms.htm. C Form of the output data file with matrix SM1: C FORMM='string' ... Form of the output files with matrices. Allowed C values are FORMM='formatted' and FORMM='unformatted'. C Data specifying the power: C POWER=real ... Power of the matrix SM1. C Default: POWER=1. C C----------------------------------------------------------------------- C Subroutines and external functions required: EXTERNAL SMBLO,SMPOW,IND,ERROR,RSEP1,RSEP3T,RSEP3R,RMAT,WMAT,EIGEN INTEGER IND C SMBLO,SMPOW,IND ... This file. C ERROR ... File error.for. C RSEP1,RSEP3T,RSEP3R ... C File sep.for. C RMAT,WMAT ... File C mat.for. C EIGEN ... eigennr.for. C C Common block /RAMC/: INCLUDE 'ram.inc' C ram.inc INTEGER IRAM(MRAM) EQUIVALENCE (IRAM,RAM) C CHARACTER*80 FILSEP,FILE1,FILE2 INTEGER M1,N,NN,NB,LU1,I1,I2,I3,I4,IBMI,IBMA PARAMETER (LU1=1) REAL POWER C C----------------------------------------------------------------------- C C Reading a name of the file with the input data: WRITE(*,'(A)') '+SMPOWER: Enter input filename: ' FILSEP=' ' READ(*,*) FILSEP C C Reading all the data from the SEP file into the memory: IF (FILSEP.NE.' ') THEN CALL RSEP1(LU1,FILSEP) ELSE C SMPOWER-01 CALL ERROR('SMPOWER-01: SEP file not given') ENDIF C C Reading the dimension of the matrices: CALL RSEP3T('M1',FILE1,' ') IF (FILE1.EQ.' ') THEN M1=1 ELSE OPEN(LU1,FILE=FILE1,STATUS='OLD') READ(LU1,*) M1 CLOSE(LU1) ENDIF N=M1 NN=M1*(M1+1)/2 MAXRAM=MRAM-2*N IF (3*NN+N*N+N+N+1+N+N.GT.MRAM) THEN C SMPOWER-02 CALL ERROR('SMPOWER-02: Small dimension MRAM of array RAM') C If possible, enlarge the dimension MRAM of array RAM in include C file ram.inc. ENDIF C C Reading the names of the files with the matrices: CALL RSEP3T('SM1',FILE1,' ') CALL RSEP3T('SM2',FILE2,' ') IF (FILE1.EQ.' ') THEN C SMPOWER-03 CALL ERROR('SMPOWER-03: Input file with matrix SM1 not given') ENDIF IF (FILE2.EQ.' ') THEN C SMPOWER-04 CALL ERROR('SMPOWER-04: Output file with matrix SM2 not given') ENDIF C C Reading input matrix: CALL RMAT(LU1,FILE1,M1,0,RAM(MAXRAM-NN+1)) C Reading the power: CALL RSEP3R('POWER',POWER,1.) C WRITE(*,'(A)') '+SMPOWER: Working... ' C C Identification of blocks: CALL SMBLO(RAM(MAXRAM-NN+1),N,NN,NB,IRAM(MAXRAM-NN-N)) C C Preparing array for results: DO 5, I1=MAXRAM-2*NN-N,MAXRAM-NN-N-1 RAM(I1)=0. 5 CONTINUE C C Computing the power: DO 20, I1=1,NB C Current block: IBMI=IRAM(MAXRAM-NN-N+I1-1)+1 IBMA=IRAM(MAXRAM-NN-N+I1) C Moving the block to RAM(1): I4=0 DO 10, I2=IBMI,IBMA DO 8, I3=IBMI,I2 I4=I4+1 RAM(I4)=RAM(MAXRAM-NN+IND(I3,I2)) 8 CONTINUE 10 CONTINUE I2=IBMA-IBMI+1 I3=I2*(I2+1)/2 C Computing the power: CALL SMPOW(RAM,I2,I3,POWER) C Moving the block to RAM(MAXRAM-NN-N-1-NN+1): I4=0 DO 14, I2=IBMI,IBMA DO 12, I3=IBMI,I2 I4=I4+1 RAM(MAXRAM-2*NN-N-1+IND(I3,I2))=RAM(I4) 12 CONTINUE 14 CONTINUE 20 CONTINUE C C Writing output matrix SM2: IF (FILE2.NE.' ') THEN CALL WMAT(LU1,FILE2,M1,0,RAM(MAXRAM-2*NN-N)) ENDIF WRITE(*,'(A)') '+SMPOWER: Done. ' C STOP END C C======================================================================= C SUBROUTINE SMPOW(SM,N,NN,POWER) C C======================================================================= C Computes the POWER-th power of symmetric matrix SM. INTEGER N,NN REAL SM(NN+N*N+N),POWER C Input: SM ... input symmetric matrix C N ... number of rows (and columns) of the matrix C NN ... N*(N+1)/2 C POWER ... the power C Output: SM ... the input matrix powered to POWER INTEGER I,J,I1,I2,I3 REAL AUX,SMMAX C----------------------------------------------------------------------- CALL EIGEN(SM,SM(NN+1),N,0) SMMAX=SM(1) DO 21 I=2,N SMMAX=AMAX1(SM(I*(I+1)/2),SMMAX) 21 CONTINUE DO 22 I=1,N AUX=SM(I*(I+1)/2) IF(AUX.LE.0.) THEN IF(ABS(AUX).GT.0.000001*SMMAX * .OR.(SMMAX.EQ.0..AND.POWER.LE.0.)) THEN C SMPOWER-05 CALL ERROR('SMPOWER-05: Eigenvalue not positive') ENDIF IF(POWER.LE.0.) THEN AUX=0.000001*SMMAX ELSE AUX=0. END IF END IF SM(NN+N*N+I)=AUX**POWER 22 CONTINUE DO 25 I=1,NN SM(I)=0. 25 CONTINUE DO 28 I3=1,N AUX=SM(NN+N*N+I3) J=NN+N*(I3-1) I=0 DO 27, I2=J+1,J+N DO 26, I1=J+1,I2 I=I+1 SM(I)=SM(I)+SM(I1)*SM(I2)*AUX 26 CONTINUE 27 CONTINUE 28 CONTINUE RETURN END C C======================================================================= C SUBROUTINE SMBLO(SM,N,NN,NB,IB) C C======================================================================= C Subroutine to find blocks of a symmetric matrix INTEGER N,NN,NB,IB(0:N) REAL SM(NN) C Input: SM ... symmetric matrix C N ... number of rows (and columns) of the matrix C NN ... N*(N+1)/2 C Output: NB ... number of blocks of the matrix C IB ... array with numbers of lines (and rows), at which C the blocks finish INTEGER I1,I2 EXTERNAL IND INTEGER IND C----------------------------------------------------------------------- C Initiating first block: NB=1 IB(0)=0 IB(1)=1 I1=0 10 CONTINUE C Loop for lines of the matrix: I1=I1+1 DO 20, I2=N,IB(NB)+1,-1 C Loop for rows of the line I1: IF (SM(IND(I1,I2)).NE.0.) THEN C The block is larger: IB(NB)=I2 GOTO 21 ENDIF 20 CONTINUE 21 CONTINUE IF (IB(NB).EQ.N) THEN C End of the search for blocks. RETURN ENDIF IF (IB(NB).EQ.I1) THEN C Block finished, continuing with the next block. NB=NB+1 IB(NB)=I1+1 ENDIF GOTO 10 END C======================================================================= INTEGER FUNCTION IND(I,J) INTEGER I,J C I ... Index of a line. C J ... Index of a row. IND=J*(J-1)/2+I RETURN END C C======================================================================= C INCLUDE 'error.for' C error.for INCLUDE 'sep.for' C sep.for INCLUDE 'forms.for' C forms.for INCLUDE 'length.for' C length.for INCLUDE 'mat.for' C mat.for INCLUDE 'indexi.for' C indexi.for INCLUDE 'eigennr.for' C eigennr.for INCLUDE 'indexx.for' C indexx.for of Numerical Recipes INCLUDE 'tred2.for' C tred2.for of Numerical Recipes INCLUDE 'tqli.for' C tqli.for of Numerical Recipes INCLUDE 'pythag.for' C pythag.for of Numerical Recipes C C======================================================================= C