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C SPDX-FileCopyrightText: 2023 SAP SE
C
C SPDX-License-Identifier: Apache-2.0
C
SUBROUTINE SPRBS2 ( MSPAR , MTREES, MSIFA , SM , B ,
$ LDB , NRHS , RWORK , LPU , IERR )
C ------------------------------------------------------------------
IMPLICIT NONE
INTEGER LDB , NRHS , LPU , IERR
INTEGER MSPAR(*) , MTREES(*) ,
$ MSIFA(*)
DOUBLE PRECISION SM(*) , B(LDB,NRHS) ,
$ RWORK(*)
C ======================================================================
C S A M library routine : SPRBS2 GROUP 9 / PUBLIC
C ======================================================================
C
C Purpose
C -------
C
C --- To backward solve the NRHS right-hand sides stored
C column by column in B.
C
C Created : Jan. 11, 1994 (acd)
C Revisions : Aug. 24, 1998 (acd)
* MSPAR(50) -> MSPAR(*), and added superelement option.
* Jun. 01, 1999 (acd)
* Modification in order to account for evaluation of
* internal stiffness only.
C Feb. 25, 2003 (kmo)
C Suppress error messages if LPU < 0.
C Get pointers from MSPAR instead of recalculating them.
C Added internal permutation array PERI2E.
C Replaced SPRBS7 by SPRBS7 and SPRBS8.
C Replaced SPRBS9 by SPRZR0 and SPRZR1.
C Aug. 14, 2003 (kmo)
C Added MSPAR(57) in calls to SPRBS7 and SPRBS8.
C Sep. 22, 2004 (kmo)
C Changed the MSPAR(1) value from 7 to 8.
C Aug. 27, 2005 (kmo)
C Removed calls to SPRZR0 and SPRZR1 again.
C Instead NEQ is reset to LDB when MSPAR(57) = 1
C assuming the internal equations are ordered first.
C
C MSPAR - INTEGER(*)
C Entry : As output from SPRSMB.
C Exit : Not changed, except for MSPAR(1) that is set to 8
C in case of successful exit, and to -8 otherwise.
C MTREES - INTEGER(NTREES)
C Entry : As output from SPRSMB.
C Exit : Not changed.
C MSIFA - INTEGER(NMSIFA)
C Entry : As output from SPRSMB.
C Exit : Not changed.
C SM - DOUBLE PRECISION(NSM)
C Entry : As output from SPRFC1.
C Exit : Not changed.
C B - DOUBLE PRECISION(LDB,NRHS)
C Entry : The forward solved right-hand sides
C stored column by column.
C Exit : The solution stored column by column.
C LDB - INTEGER
C Entry : The leading dimension of B.
C Exit : Not changed.
C NRHS - INTEGER
C Entry : The number of right-hand sides stored in B.
C Exit : Not changed.
C LPU - INTEGER
C Entry : Output unit.
C Exit : Not changed.
C IERR - INTEGER
C Entry : Not defined
C Exit : Is set to zero if a successful call,
C = -1 if error from SPRFC1 is not cleared.
C = -2 if MTREES, MSIFA, SM and/or RWORK
C are not great enough.
C
C Working arrays
C --------------
C
C RWORK - DOUBLE PRECISION(NRWORK)
C Entry : Not defined.
C See below.
C Exit : Need not be saved.
C
C Procedures
C ----------
C
C SPRBS7
C SPRBS8
C SPRER1
C
C Intrinsic
C ---------
C
C None
C
C Include Blocks
C --------------
C
C None
C
C Common Blocks
C -------------
C
C None
C
C ------------------------------------------------------------------
INTEGER
$ NMSIFA, NRWORK, NSM , NTREES
INTEGER
$ DIAG , ELSEQ , IRHS , LINDX , LNZ ,
$ MFRONT, MLUSED, MTUSED, NB , NELACT, NEQ , NOFSUB, NSUPER,
$ NZEROL, PERI2E, RWUSED, SMUSED, STACK , SUPSUP, XBLOCK, XELSEQ,
$ XLINDX, XSUPER
EXTERNAL SPRBS7, SPRBS8, SPRER1
C ==================================================================
#if FT_DEBUG > 1
IF (LPU.GE.0) WRITE(LPU,*) 'ENTERING SPRBS2'
#endif
C --------------------
C GET INFO FROM MSPAR.
C --------------------
IF ( MSPAR(1) .LT. 0 ) THEN
MSPAR(1) = -8
IERR = -1
CALL SPRER1 ( 30, 'SPRBS2', 0, 0, 0, LPU, IERR )
RETURN
ELSE
MSPAR(1) = 8
IERR = 0
ENDIF
NEQ = MSPAR( 8)
NSUPER = MSPAR(11)
NB = MSPAR(12)
MFRONT = MSPAR(14)
NOFSUB = MSPAR(15)
NZEROL = MSPAR(16)
NELACT = MSPAR(19)
C
NMSIFA = MSPAR( 3)
NTREES = MSPAR( 4)
NSM = NZEROL + NEQ
NRWORK = MFRONT
C --------------------------------------------
C SET POINTERS TO MTREES AND CHECK ITS LENGTH.
C --------------------------------------------
XSUPER = MSPAR(45)
XLINDX = MSPAR(46)
* === SUPSUP-acd
SUPSUP = XLINDX + NSUPER + 1
ELSEQ = SUPSUP + NSUPER
XELSEQ = ELSEQ + NELACT
XBLOCK = XELSEQ + NB + 1
MTUSED = XBLOCK + NB
C -------------------------------------------
C SET POINTERS TO MSIFA AND CHECK ITS LENGTH.
C -------------------------------------------
PERI2E = 1
LINDX = MSPAR(47)
MLUSED = LINDX + NOFSUB - 1
C ----------------------------------------
C SET POINTERS TO SM AND CHECK ITS LENGTH.
C ----------------------------------------
DIAG = 1
LNZ = DIAG + NEQ
SMUSED = LNZ + NZEROL - 1
C -------------------------------------------
C SET POINTERS TO RWORK AND CHECK ITS LENGTH.
C -------------------------------------------
STACK = 1
RWUSED = STACK + MFRONT - 1
C Solve for only the first LDB (internal) equations when LDB < NEQ
IF ( MSPAR(57).EQ.1 .AND. LDB.LT.NEQ ) NEQ = LDB
IF ( MTUSED .GT. NTREES .OR.
$ MLUSED .GT. NMSIFA .OR. SMUSED .GT. NSM .OR.
$ RWUSED .GT. NRWORK .OR. LDB .LT. NEQ ) THEN
MSPAR(1) = -2
IF ( LPU .GE. 0 ) THEN
WRITE(LPU,'(/A)') ' *** ERROR FROM SPRBS2'
IF ( MTUSED .GT. NTREES ) THEN
WRITE(LPU,'(/A,I8,I8/)') 'MTREES TOO SHORT',NTREES,MTUSED
ENDIF
IF ( MLUSED .GT. NMSIFA ) THEN
WRITE(LPU,'(/A,I8,I8/)') 'MSIFA TOO SHORT',NMSIFA,MLUSED
ENDIF
IF ( SMUSED .GT. NSM ) THEN
WRITE(LPU,'(/A,I8,I8/)') 'SM TOO SHORT',NSM,SMUSED
ENDIF
IF ( RWUSED .GT. NRWORK ) THEN
WRITE(LPU,'(/A,I8,I8/)') 'RWORK TOO SHORT',NRWORK,RWUSED
ENDIF
IF ( LDB .LT. NEQ ) THEN
WRITE(LPU,'(/A,I8,I8/)') 'LDB < NEQ', LDB, NEQ
ENDIF
ENDIF
IERR = -2
CALL SPRER1 ( 37, 'SPRBS2', 0, 0, 0, LPU, IERR )
RETURN
ENDIF
C ==================================================================
DO 100 IRHS = 1, NRHS
C ----------------------------------------
C BACKWARD SOLVE IRHS BY A CALL TO SPRBS7.
C ----------------------------------------
IF ( MSPAR(58).GE.1 ) THEN
CALL SPRBS8 (NSUPER, NEQ, MFRONT, NOFSUB, NZEROL,
$ MSPAR(57), MTREES(XSUPER), MTREES(XLINDX),
$ MTREES(SUPSUP), MSIFA(LINDX), MSIFA(PERI2E),
$ B(1,IRHS), SM(LNZ), RWORK(STACK))
ELSE
CALL SPRBS7 (NSUPER, NEQ, MFRONT, NOFSUB, NZEROL,
$ MSPAR(57), MTREES(XSUPER), MTREES(XLINDX),
$ MTREES(SUPSUP), MSIFA(LINDX),
$ B(1,IRHS), SM(LNZ), RWORK(STACK))
ENDIF
100 CONTINUE
C ==================================================================
#if FT_DEBUG > 1
IF (LPU.GE.0) WRITE(LPU,*) 'LEAVING SPRBS2'
#endif
RETURN
C ------------------------------------------------------------------
C END OF MODULE SPRBS2
END
SUBROUTINE SPRBS7 ( NSUPER, NEQ , MFRONT, NOFSUB,
$ NZEROL, LPAR57, XSUPER, XLINDX, SUPSUP,
$ LINDX , GLBRHS, LNZ , LOCRHS )
C ------------------------------------------------------------------
IMPLICIT NONE
INTEGER NSUPER, NEQ , MFRONT, NOFSUB, NZEROL, LPAR57
INTEGER XSUPER(NSUPER+1) , XLINDX(NSUPER+1) ,
$ SUPSUP(NSUPER) , LINDX(NOFSUB)
DOUBLE PRECISION GLBRHS(NEQ) , LNZ(NZEROL) ,
$ LOCRHS(MFRONT)
C ------------------------------------------------------------------
C
C PURPOSE
C -------
C
C SPRBS7
C
C --- TO PERFORM AN IN-CORE MULTIFRONT BACKWARD SOLUTION STEP, THIS IS
C THE TOP LEVEL DRIVER.
C
C CREATED : JAN. 11, 1994 (ACD)
C REVISIONS : FEB. 25, 2003 (KMO)
C Replaced SPRBS8 by SPRBS9.
C AUG. 14, 2003 (KMO)
C Added input parameter LPAR57.
C AUG. 27, 2005 (KMO)
C Added NEQ in calls to SPRFB1 and SPRFB2.
C
C
C ON ENTRY
C --------
C
C NSUPER : INTEGER
C NUMBER OF SUPERNODES.
C NEQ : INTEGER
C NUMBER OF EQUATIONS.
C MFRONT : INTEGER
C LARGEST FRONT MATRIX.
C NOFSUB : INTEGER
C LENGTH OF LINDX.
C NZEROL : INTEGER
C LENGTH OF LNZ.
C LPAR57 : INTEGER
C IF (LPAR57.LE.0) DO A FULL SOLVE EVEN IF THE EQUATION
C SYSTEM IS PARTITIONED INTO INTERNAL AND RETAINED DOFS.
C XSUPER : INTEGER(NSUPER+1)
C THE SUPERNODE PARTITION.
C (XLINDX,
C LINDX) : INTEGER(NSUPER+1), INTEGER(NOFSUB)
C THE NON-ZERO STRUCTURE OF C.
C LNZ : DOUBLE PRECISION(NZEROL)
C CC' FACTOR MATRICES.
C
C INPUT/OUTPUT
C ------------
C
C GLBRHS : DOUBLE PRECISION(NEQ)
C ON ENTRY : FORWARD SOLVED VECTOR.
C ON EXIT : SOLUTION VECTOR.
C
C WORKING ARRAYS
C --------------
C
C LOCRHS : DOUBLE PRECISION(MFRONT)
C STORES ON A DENSE FORMAT ALL "SUBMATRIX" RHS'S.
C
C SUBPROGRAMS/FUNCTIONS
C ---------------------
C
C SPRFB1
C SPRBS9
C SPRFB2
C
C ------------------------------------------------------------------
INTEGER IPLNZ , JS , JSLEN , JSSTRT, SUPVAR, SUPSZE
EXTERNAL SPRFB1, SPRBS9, SPRFB2
C ==================================================================
IPLNZ = NZEROL + 1
C ==================================================================
DO 100 JS = NSUPER, 1, -1
SUPVAR = XSUPER(JS+1) - XSUPER(JS)
JSSTRT = XLINDX(JS)
JSLEN = XLINDX(JS+1) - JSSTRT
SUPSZE = (JSLEN*(JSLEN+1) - (JSLEN-SUPVAR)*(JSLEN-SUPVAR+1))/2
IPLNZ = IPLNZ - SUPSZE
IF ( SUPSUP(JS).LE.0 .OR. LPAR57.LE.0 ) THEN
C -----------------------------------------------------
C PERFORM SUPVAR STEPS OF ELIMINATION since this is not
* a retained supernode.
C -----------------------------------------------------
CALL SPRFB1 ( NEQ, JSLEN, LINDX(JSSTRT), GLBRHS, LOCRHS )
CALL SPRBS9 ( SUPVAR, JSLEN, LNZ(IPLNZ), LOCRHS )
CALL SPRFB2 ( NEQ, JSLEN, LINDX(JSSTRT), GLBRHS, LOCRHS )
ENDIF
100 CONTINUE
C ==================================================================
RETURN
C ------------------------------------------------------------------
C END OF MODULE SPRBS7
END
SUBROUTINE SPRBS8 ( NSUPER, NEQ , MFRONT, NOFSUB,
$ NZEROL, LPAR57, XSUPER, XLINDX, SUPSUP,
$ LINDX , PERI2E, GLBRHS, LNZ , LOCRHS )
C ------------------------------------------------------------------
IMPLICIT NONE
INTEGER NSUPER, NEQ , MFRONT, NOFSUB, NZEROL, LPAR57
INTEGER XSUPER(NSUPER+1) , XLINDX(NSUPER+1) ,
$ SUPSUP(NSUPER) , LINDX(NOFSUB) ,
$ PERI2E(NEQ)
DOUBLE PRECISION GLBRHS(NEQ) , LNZ(NZEROL) ,
$ LOCRHS(MFRONT)
C ------------------------------------------------------------------
C
C PURPOSE
C -------
C
C SPRBS8
C
C --- TO PERFORM AN IN-CORE MULTIFRONT BACKWARD SOLUTION STEP, THIS IS
C THE TOP LEVEL DRIVER. Identical to SPRBS7 except for the internal
C permutation array PERI2E.
C
C CREATED : JAN. 11, 1994 (ACD)
C REVISIONS : FEB. 25, 2003 (KMO)
C Made a new SPRBS8 from SPRBS7 by adding PERI2E, and
C using SPRFB3 and SPRFB4 instead of SPRFB1 and SPRFB2.
C AUG. 14, 2003 (KMO)
C Added input parameter LPAR57.
C AUG. 27, 2005 (KMO)
C Added NEQ in calls to SPRFB3 and SPRFB4.
C
C
C ON ENTRY
C --------
C
C NSUPER : INTEGER
C NUMBER OF SUPERNODES.
C NEQ : INTEGER
C NUMBER OF EQUATIONS.
C MFRONT : INTEGER
C LARGEST FRONT MATRIX.
C NOFSUB : INTEGER
C LENGTH OF LINDX.
C NZEROL : INTEGER
C LENGTH OF LNZ.
C LPAR57 : INTEGER
C IF (LPAR57.LE.0) DO A FULL SOLVE EVEN IF THE EQUATION
C SYSTEM IS PARTITIONED INTO INTERNAL AND RETAINED DOFS.
C XSUPER : INTEGER(NSUPER+1)
C THE SUPERNODE PARTITION.
C (XLINDX,
C LINDX) : INTEGER(NSUPER+1), INTEGER(NOFSUB)
C THE NON-ZERO STRUCTURE OF C.
C PERI2E : INTEGER(NEQ)
C Permutation from internal to external equation order.
C LNZ : DOUBLE PRECISION(NZEROL)
C CC' FACTOR MATRICES.
C
C INPUT/OUTPUT
C ------------
C
C GLBRHS : DOUBLE PRECISION(NEQ)
C ON ENTRY : FORWARD SOLVED VECTOR.
C ON EXIT : SOLUTION VECTOR.
C
C WORKING ARRAYS
C --------------
C
C LOCRHS : DOUBLE PRECISION(MFRONT)
C STORES ON A DENSE FORMAT ALL "SUBMATRIX" RHS'S.
C
C SUBPROGRAMS/FUNCTIONS
C ---------------------
C
C SPRFB3
C SPRBS9
C SPRFB4
C
C ------------------------------------------------------------------
INTEGER IPLNZ , JS , JSLEN , JSSTRT, SUPVAR, SUPSZE
EXTERNAL SPRFB3, SPRBS9, SPRFB4
C ==================================================================
IPLNZ = NZEROL + 1
C ==================================================================
DO 100 JS = NSUPER, 1, -1
SUPVAR = XSUPER(JS+1) - XSUPER(JS)
JSSTRT = XLINDX(JS)
JSLEN = XLINDX(JS+1) - JSSTRT
SUPSZE = (JSLEN*(JSLEN+1) - (JSLEN-SUPVAR)*(JSLEN-SUPVAR+1))/2
IPLNZ = IPLNZ - SUPSZE
IF ( SUPSUP(JS).LE.0 .OR. LPAR57.LE.0 ) THEN
C -----------------------------------------------------
C PERFORM SUPVAR STEPS OF ELIMINATION since this is not
* a retained supernode.
C -----------------------------------------------------
CALL SPRFB3 ( NEQ, JSLEN, LINDX(JSSTRT), PERI2E,
$ GLBRHS, LOCRHS )
CALL SPRBS9 ( SUPVAR, JSLEN, LNZ(IPLNZ), LOCRHS )
CALL SPRFB4 ( NEQ, JSLEN, LINDX(JSSTRT), PERI2E,
$ GLBRHS, LOCRHS )
ENDIF
100 CONTINUE
C ==================================================================
RETURN
C ------------------------------------------------------------------
C END OF MODULE SPRBS8
END
SUBROUTINE SPRBS9 ( SUPVAR, LENVAR, LNZ , LOCRHS )
C ------------------------------------------------------------------
IMPLICIT NONE
INTEGER SUPVAR, LENVAR
DOUBLE PRECISION LNZ(*) , LOCRHS(LENVAR)
C ------------------------------------------------------------------
C
C PURPOSE
C -------
C
C SPRBS9
C
C --- TO PERFORM A PARTIAL BACKWARD SOLVE FOR THE MULTIFRONTAL METHOD.
C
C CREATED : JAN. 11, 1994 (ACD)
C REVISIONS : FEB. 25, 2003 (KMO)
C Renamed from SPRBS8 to SPRBS9.
C
C
C ON ENTRY
C --------
C
C SUPVAR : INTEGER
C NUMBER OF VARIABLES TO SOLVE FOR IN CURRENT STEP.
C LENVAR : INTEGER
C ORDER OF THE ASSOCIATED FRONT MATRIX IN CURRENT STEP.
C LNZ : DOUBLE PRECISION(LENVARCSUPVAR-SUPVAR*(SUPVAR-1)/2)
C THE CURRENT FACTOR SUBMATRIX.
C
C ON EXIT
C -------
C
C LOCRHS : DOUBLE PRECISION(LENVAR)
C BACKWARD SOLVED LOCAL VECTOR.
C
C ------------------------------------------------------------------
INTEGER I , IPLNZ1, IPLNZ2, J , OFFSET
DOUBLE PRECISION RESULT
DOUBLE PRECISION ZERO
PARAMETER ( ZERO = 0.0D0 )
C ==================================================================
OFFSET(I,J) = (I*(J-1))-((J-1)*(J-2)/2)
C ==================================================================
C ---------------------
C SOLVING THE SUPERNODE
C USING STANDARD LOOP.
C ---------------------
DO 200 J = SUPVAR, 1, -1
IPLNZ1 = 1 + OFFSET(LENVAR,J)
IPLNZ2 = IPLNZ1
RESULT = ZERO
C -------------------------------------------------------------
C ------ THIS LOOP MAY BE SUBSTITUTED BY MACHINE ROUTINE FOR DOT PROD.
C -------------------------------------------------------------
DO 100 I = J + 1, LENVAR
IPLNZ2 = IPLNZ2 + 1
RESULT = RESULT + LOCRHS(I)*LNZ(IPLNZ2)
100 CONTINUE
LOCRHS(J) = ( LOCRHS(J) - RESULT ) / LNZ(IPLNZ1)
200 CONTINUE
C ==================================================================
RETURN
C ------------------------------------------------------------------
C END OF MODULE SPRBS9
END