root / src / Step_GEDIIS.f90 @ 2
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| 1 |
! Geom = input parameter vector (Geometry), Grad = input gradient vector. |
|---|---|
| 2 |
! HEAT is Energy(Geom) |
| 3 |
SUBROUTINE Step_GEDIIS(Geom_new,Geom,Grad,HEAT,Hess,NCoord,FRST) |
| 4 |
|
| 5 |
use Io_module |
| 6 |
use Path_module, only : Nom, Atome, OrderInv, indzmat, Pi, Nat |
| 7 |
|
| 8 |
IMPLICIT NONE |
| 9 |
|
| 10 |
INTEGER(KINT) :: NCoord |
| 11 |
REAL(KREAL) :: Geom_new(NCoord), Grad(NCoord), Hess(NCoord*NCoord) |
| 12 |
REAL(KREAL), INTENT(IN) :: Geom(NCoord) |
| 13 |
REAL(KREAL) :: HEAT ! HEAT= Energy |
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LOGICAL :: FRST |
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|
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! MRESET = maximum number of iterations. |
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INTEGER(KINT), PARAMETER :: MRESET=15, M2=(MRESET+1)*(MRESET+1) !M2 = 256 |
| 18 |
REAL(KREAL), ALLOCATABLE, SAVE :: GeomSet(:), GradSet(:) ! MRESET*NCoord |
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REAL(KREAL), ALLOCATABLE, SAVE :: DX(:), GSAVE(:) !NCoord |
| 20 |
REAL(KREAL), SAVE :: ESET(MRESET) |
| 21 |
REAL(KREAL) :: ESET_tmp(MRESET), B(M2),BS(M2),BST(M2), B_tmp(M2) ! M2=256 |
| 22 |
LOGICAL DEBUG, PRINT, ci_lt_zero |
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INTEGER(KINT), SAVE :: MSET ! mth Iteration |
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REAL(KREAL) :: ci(MRESET), ci_tmp(MRESET) ! MRESET = maximum number of iterations. |
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INTEGER(KINT) :: NGEDIIS, MPLUS, INV, ITERA, MM, cis_zero, IXX, JXX, MSET_minus_cis_zero |
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INTEGER(KINT) :: I,J,K, JJ, KJ, JNV, II, IONE, IJ, INK,ITmp, IX, JX, KX, MSET_C_cis_zero |
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INTEGER(KINT) :: current_size_B_mat, MyPointer, Iat |
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REAL(KREAL) :: XMax, XNorm, S, DET, THRES, tmp, ER_star, ER_star_tmp |
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|
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DEBUG=.TRUE. |
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PRINT=.FALSE. |
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|
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IF (PRINT) WRITE(*,'(/,'' BEGIN GEDIIS '')') |
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|
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! Initialization |
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IF (FRST) THEN |
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! FRST will be set to False in SPACE_GEDIIS, so no need to modify it here |
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IF (ALLOCATED(GeomSet)) THEN |
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IF (PRINT) WRITE(*,'(/,'' In FRST, GEDIIS Dealloc '')') |
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DEALLOCATE(GeomSet,GradSet,DX,GSave) |
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RETURN |
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ELSE |
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IF (PRINT) WRITE(*,'(/,'' In FRST, GEDIIS Alloc '')') |
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ALLOCATE(GeomSet(MRESET*NCoord),GradSet(MRESET*NCoord),DX(NCoord),GSAVE(NCoord)) |
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END IF |
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END IF ! IF (FRST) THEN |
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|
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! SPACE_GEDIIS SIMPLY LOADS THE CURRENT VALUES OF Geom AND Grad INTO THE ARRAYS GeomSet |
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! AND GradSet, MSET is set to zero and then 1 in SPACE_GEDIIS at first iteration. |
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CALL SPACE_GEDIIS(MRESET,MSET,Geom,Grad,HEAT,NCoord,GeomSet,GradSet,ESET,FRST) |
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|
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IF (PRINT) WRITE(*,'(/,'' GEDIIS after SPACE_GEDIIS '')') |
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|
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! INITIALIZE SOME VARIABLES AND CONSTANTS: |
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NGEDIIS = MSET !MSET=mth iteration |
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MPLUS = MSET + 1 |
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MM = MPLUS * MPLUS |
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|
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! CONSTRUCT THE GEDIIS MATRIX: |
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! B_ij calculations from <B_ij=(g_i-g_j)(R_i-R_j)> |
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JJ=0 |
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INV=-NCoord |
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DO I=1,MSET |
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INV=INV+NCoord |
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JNV=-NCoord |
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DO J=1,MSET |
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JNV=JNV+NCoord |
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JJ = JJ + 1 |
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B(JJ)=0.D0 |
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DO K=1, NCoord |
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B(JJ) = B(JJ) + (((GradSet(INV+K)-GradSet(JNV+K))*(GeomSet(INV+K)-GeomSet(JNV+K)))/2.D0) |
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END DO |
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END DO |
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END DO |
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|
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! The following shifting is required to correct indices of B_ij elements in the GEDIIS matrix. |
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! The correction is needed because the last coloumn of the matrix contains all 1 and one zero. |
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DO I=MSET-1,1,-1 |
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DO J=MSET,1,-1 |
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B(I*MSET+J+I) = B(I*MSET+J) |
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END DO |
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END DO |
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|
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! for last row and last column of GEDIIS matrix |
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DO I=1,MPLUS |
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B(MPLUS*I) = 1.D0 |
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B(MPLUS*MSET+I) = 1.D0 |
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END DO |
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B(MM) = 0.D0 |
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|
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DO I=1, MPLUS |
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!WRITE(*,'(10(1X,F20.4))') B((I-1)*MPLUS+1:I*(MPLUS)) |
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END DO |
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|
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! ELIMINATE ERROR VECTORS WITH THE LARGEST NORM: |
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80 CONTINUE |
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DO I=1,MM !MM = (MSET+1) * (MSET+1) |
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BS(I) = B(I) !just a copy of the original B (GEDIIS) matrix |
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END DO |
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|
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IF (NGEDIIS .NE. MSET) THEN |
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DO II=1,MSET-NGEDIIS |
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XMAX = -1.D10 |
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ITERA = 0 |
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DO I=1,MSET |
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XNORM = 0.D0 |
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INV = (I-1) * MPLUS |
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DO J=1,MSET |
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XNORM = XNORM + ABS(B(INV + J)) |
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END DO |
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IF (XMAX.LT.XNORM .AND. XNORM.NE.1.0D0) THEN |
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XMAX = XNORM |
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ITERA = I |
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IONE = INV + I |
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ENDIF |
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END DO |
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|
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DO I=1,MPLUS |
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INV = (I-1) * MPLUS |
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DO J=1,MPLUS |
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JNV = (J-1) * MPLUS |
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IF (J.EQ.ITERA) B(INV + J) = 0.D0 |
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B(JNV + I) = B(INV + J) |
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END DO |
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END DO |
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B(IONE) = 1.0D0 |
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END DO |
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END IF ! matches IF (NGEDIIS .NE. MSET) THEN |
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|
| 130 |
! SCALE GEDIIS MATRIX BEFORE INVERSION: |
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DO I=1,MPLUS |
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II = MPLUS * (I-1) + I ! B(II)=diagonal elements of B matrix |
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GSAVE(I) = 1.D0 / DSQRT(1.D-20+DABS(B(II))) |
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!Print *, 'GSAVE(',I,')=', GSAVE(I)
|
| 135 |
END DO |
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GSAVE(MPLUS) = 1.D0 |
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DO I=1,MPLUS |
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DO J=1,MPLUS |
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IJ = MPLUS * (I-1) + J |
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B(IJ) = B(IJ) * GSAVE(I) * GSAVE(J) |
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END DO |
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END DO |
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|
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! INVERT THE GEDIIS MATRIX B: |
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DO I=1, MPLUS |
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!WRITE(*,'(10(1X,F20.4))') B((I-1)*MPLUS+1:I*(MPLUS)) |
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END DO |
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|
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CALL MINV(B,MPLUS,DET) ! matrix inversion. |
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|
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DO I=1, MPLUS |
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!WRITE(*,'(10(1X,F20.16))') B((I-1)*MPLUS+1:I*(MPLUS)) |
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END DO |
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|
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DO I=1,MPLUS |
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DO J=1,MPLUS |
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IJ = MPLUS * (I-1) + J |
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B(IJ) = B(IJ) * GSAVE(I) * GSAVE(J) |
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END DO |
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END DO |
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|
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! COMPUTE THE NEW INTERPOLATED PARAMETER VECTOR (Geometry): |
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ci=0.d0 |
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ci_tmp=0.d0 |
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|
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ci_lt_zero= .FALSE. |
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DO I=1, MSET |
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DO J=1, MSET ! B matrix is read column-wise |
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ci(I)=ci(I)+B((J-1)*(MPLUS)+I)*ESET(J) !ESET is energy set, yet to be fixed. |
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END DO |
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ci(I)=ci(I)+B((MPLUS-1)*(MPLUS)+I) |
| 172 |
!Print *, 'NO ci < 0 yet, c(',I,')=', ci(I)
|
| 173 |
IF((ci(I) .LT. 0.0D0) .OR. (ci(I) .GT. 1.0D0)) THEN |
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ci_lt_zero=.TRUE. |
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EXIT |
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END IF |
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END DO !matches DO I=1, MSET |
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|
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IF (ci_lt_zero) Then |
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cis_zero = 0 |
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ER_star = 0.D0 |
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ER_star_tmp = 1e32 |
| 183 |
|
| 184 |
! B_ij calculations from <B_ij=(g_i-g_j)(R_i-R_j)>, Full B matrix created first and then rows and columns are removed. |
| 185 |
JJ=0 |
| 186 |
INV=-NCoord |
| 187 |
DO IX=1,MSET |
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INV=INV+NCoord |
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JNV=-NCoord |
| 190 |
DO JX=1,MSET |
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JNV=JNV+NCoord |
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JJ = JJ + 1 |
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BST(JJ)=0.D0 |
| 194 |
DO KX=1, NCoord |
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BST(JJ) = BST(JJ) + (((GradSet(INV+KX)-GradSet(JNV+KX))*(GeomSet(INV+KX)-GeomSet(JNV+KX)))/2.D0) |
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END DO |
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END DO |
| 198 |
END DO |
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|
| 200 |
DO I=1, (2**MSET)-2 ! all (2**MSET)-2 combinations of cis, except the one where all cis are .GT. 0 and .LT. 1 |
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ci(:)=1.D0 |
| 202 |
! find out which cis are zero in I: |
| 203 |
DO IX=1, MSET |
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JJ=IAND(I, 2**(IX-1)) |
| 205 |
IF(JJ .EQ. 0) Then |
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ci(IX)=0.D0 |
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END IF |
| 208 |
END DO |
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|
| 210 |
ci_lt_zero = .FALSE. |
| 211 |
! B_ij calculations from <B_ij=(g_i-g_j)(R_i-R_j)>, Full B matrix created first and then rows and columns are removed. |
| 212 |
DO IX=1, MSET*MSET |
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B(IX) = BST(IX) !just a copy of the original B (GEDIIS) matrix |
| 214 |
END DO |
| 215 |
|
| 216 |
! Removal of KXth row and KXth column in order to accomodate cI to be zero: |
| 217 |
current_size_B_mat=MSET |
| 218 |
cis_zero = 0 |
| 219 |
! The bits of I (index of the upper loop 'DO I=1, (2**MSET)-2'), gives which cis are zero. |
| 220 |
DO KX=1, MSET ! searching for each bit of I (index of the upper loop 'DO I=1, (2**MSET)-2') |
| 221 |
IF (ci(KX) .EQ. 0.D0) Then !remove KXth row and KXth column |
| 222 |
cis_zero = cis_zero + 1 |
| 223 |
|
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! First row removal: (B matrix is read column-wise) |
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JJ=0 |
| 226 |
DO IX=1,current_size_B_mat ! columns reading |
| 227 |
DO JX=1,current_size_B_mat ! rows reading |
| 228 |
IF (JX .NE. KX) Then |
| 229 |
JJ = JJ + 1 |
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B_tmp(JJ) = B((IX-1)*current_size_B_mat+JX) |
| 231 |
END IF |
| 232 |
END DO |
| 233 |
END DO |
| 234 |
|
| 235 |
DO IX=1,current_size_B_mat*(current_size_B_mat-1) |
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B(IX) = B_tmp(IX) |
| 237 |
END DO |
| 238 |
|
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! Now column removal: |
| 240 |
JJ=0 |
| 241 |
DO IX=1,KX-1 ! columns reading |
| 242 |
DO JX=1,current_size_B_mat-1 ! rows reading |
| 243 |
JJ = JJ + 1 |
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B_tmp(JJ) = B(JJ) |
| 245 |
END DO |
| 246 |
END DO |
| 247 |
|
| 248 |
DO IX=KX+1,current_size_B_mat |
| 249 |
DO JX=1,current_size_B_mat-1 |
| 250 |
JJ = JJ + 1 |
| 251 |
B_tmp(JJ) = B(JJ+current_size_B_mat-1) |
| 252 |
END DO |
| 253 |
END DO |
| 254 |
|
| 255 |
DO IX=1,(current_size_B_mat-1)*(current_size_B_mat-1) |
| 256 |
B(IX) = B_tmp(IX) |
| 257 |
END DO |
| 258 |
current_size_B_mat = current_size_B_mat - 1 |
| 259 |
END IF ! matches IF (ci(KX) .EQ. 0.D0) Then !remove |
| 260 |
END DO ! matches DO KX=1, MSET |
| 261 |
|
| 262 |
! The following shifting is required to correct indices of B_ij elements in the GEDIIS matrix. |
| 263 |
! The correction is needed because the last coloumn and row of the matrix contains all 1 and one zero. |
| 264 |
DO IX=MSET-cis_zero-1,1,-1 |
| 265 |
DO JX=MSET-cis_zero,1,-1 |
| 266 |
B(IX*(MSET-cis_zero)+JX+IX) = B(IX*(MSET-cis_zero)+JX) |
| 267 |
END DO |
| 268 |
END DO |
| 269 |
|
| 270 |
! for last row and last column of GEDIIS matrix |
| 271 |
DO IX=1,MPLUS-cis_zero |
| 272 |
B((MPLUS-cis_zero)*IX) = 1.D0 |
| 273 |
B((MPLUS-cis_zero)*(MSET-cis_zero)+IX) = 1.D0 |
| 274 |
END DO |
| 275 |
B((MPLUS-cis_zero) * (MPLUS-cis_zero)) = 0.D0 |
| 276 |
|
| 277 |
DO IX=1, MPLUS |
| 278 |
!WRITE(*,'(10(1X,F20.4))') B((IX-1)*MPLUS+1:IX*(MPLUS)) |
| 279 |
END DO |
| 280 |
|
| 281 |
! ELIMINATE ERROR VECTORS WITH THE LARGEST NORM: |
| 282 |
IF (NGEDIIS .NE. MSET) THEN |
| 283 |
JX = min(MSET-NGEDIIS,MSET-cis_zero-1) |
| 284 |
DO II=1,JX |
| 285 |
XMAX = -1.D10 |
| 286 |
ITERA = 0 |
| 287 |
DO IX=1,MSET-cis_zero |
| 288 |
XNORM = 0.D0 |
| 289 |
INV = (IX-1) * (MPLUS-cis_zero) |
| 290 |
DO J=1,MSET-cis_zero |
| 291 |
XNORM = XNORM + ABS(B(INV + J)) |
| 292 |
END DO |
| 293 |
IF (XMAX.LT.XNORM .AND. XNORM.NE.1.0D0) THEN |
| 294 |
XMAX = XNORM |
| 295 |
ITERA = IX |
| 296 |
IONE = INV + IX |
| 297 |
ENDIF |
| 298 |
END DO |
| 299 |
|
| 300 |
DO IX=1,MPLUS-cis_zero |
| 301 |
INV = (IX-1) * (MPLUS-cis_zero) |
| 302 |
DO J=1,MPLUS-cis_zero |
| 303 |
JNV = (J-1) * (MPLUS-cis_zero) |
| 304 |
IF (J.EQ.ITERA) B(INV + J) = 0.D0 |
| 305 |
B(JNV + IX) = B(INV + J) |
| 306 |
END DO |
| 307 |
END DO |
| 308 |
B(IONE) = 1.0D0 |
| 309 |
END DO |
| 310 |
END IF ! matches IF (NGEDIIS .NE. MSET) THEN |
| 311 |
|
| 312 |
! SCALE GEDIIS MATRIX BEFORE INVERSION: |
| 313 |
DO IX=1,MPLUS-cis_zero |
| 314 |
II = (MPLUS-cis_zero) * (IX-1) + IX ! B(II)=diagonal elements of B matrix |
| 315 |
GSAVE(IX) = 1.D0 / DSQRT(1.D-20+DABS(B(II))) |
| 316 |
END DO |
| 317 |
GSAVE(MPLUS-cis_zero) = 1.D0 |
| 318 |
DO IX=1,MPLUS-cis_zero |
| 319 |
DO JX=1,MPLUS-cis_zero |
| 320 |
IJ = (MPLUS-cis_zero) * (IX-1) + JX |
| 321 |
B(IJ) = B(IJ) * GSAVE(IX) * GSAVE(JX) |
| 322 |
END DO |
| 323 |
END DO |
| 324 |
|
| 325 |
! INVERT THE GEDIIS MATRIX B: |
| 326 |
CALL MINV(B,MPLUS-cis_zero,DET) ! matrix inversion. |
| 327 |
|
| 328 |
DO IX=1,MPLUS-cis_zero |
| 329 |
DO JX=1,MPLUS-cis_zero |
| 330 |
IJ = (MPLUS-cis_zero) * (IX-1) + JX |
| 331 |
B(IJ) = B(IJ) * GSAVE(IX) * GSAVE(JX) |
| 332 |
END DO |
| 333 |
END DO |
| 334 |
|
| 335 |
DO IX=1, MPLUS |
| 336 |
!WRITE(*,'(10(1X,F20.4))') B((IX-1)*MPLUS+1:IX*(MPLUS)) |
| 337 |
END DO |
| 338 |
|
| 339 |
! ESET is rearranged to handle zero cis and stored in ESET_tmp: |
| 340 |
JJ=0 |
| 341 |
DO IX=1, MSET |
| 342 |
IF (ci(IX) .NE. 0) Then |
| 343 |
JJ=JJ+1 |
| 344 |
ESET_tmp(JJ) = ESET(IX) |
| 345 |
END IF |
| 346 |
END DO |
| 347 |
|
| 348 |
! DETERMINATION OF nonzero cis: |
| 349 |
MyPointer=1 |
| 350 |
DO IX=1, MSET-cis_zero |
| 351 |
tmp = 0.D0 |
| 352 |
DO J=1, MSET-cis_zero ! B matrix is read column-wise |
| 353 |
tmp=tmp+B((J-1)*(MPLUS-cis_zero)+IX)*ESET_tmp(J) |
| 354 |
END DO |
| 355 |
tmp=tmp+B((MPLUS-cis_zero-1)*(MPLUS-cis_zero)+IX) |
| 356 |
IF((tmp .LT. 0.0D0) .OR. (tmp .GT. 1.0D0)) THEN |
| 357 |
ci_lt_zero=.TRUE. |
| 358 |
EXIT |
| 359 |
ELSE |
| 360 |
DO JX=MyPointer,MSET |
| 361 |
IF (ci(JX) .NE. 0) Then |
| 362 |
ci(JX) = tmp |
| 363 |
MyPointer=JX+1 |
| 364 |
EXIT |
| 365 |
END IF |
| 366 |
END DO |
| 367 |
END IF |
| 368 |
END DO !matches DO I=1, MSET-cis_zero |
| 369 |
!Print *, 'Local set of cis, first 10:, MSET=', MSET, ', I of (2**MSET)-2=', I |
| 370 |
!WRITE(*,'(10(1X,F20.4))') ci(1:MSET) |
| 371 |
!Print *, 'Local set of cis ends:****************************************' |
| 372 |
|
| 373 |
! new set of cis determined based on the lower energy (ER_star): |
| 374 |
IF (.NOT. ci_lt_zero) Then |
| 375 |
Call Energy_GEDIIS(MRESET,MSET,ci,GeomSet,GradSet,ESET,NCoord,ER_star) |
| 376 |
IF (ER_star .LT. ER_star_tmp) Then |
| 377 |
ci_tmp=ci |
| 378 |
ER_star_tmp = ER_star |
| 379 |
END IF |
| 380 |
END IF ! matches IF (.NOT. ci_lt_zero) Then |
| 381 |
END DO !matches DO I=1, (2**K)-2 ! all (2**K)-2 combinations of cis, except the one where all cis are .GT. 0 and .LT. 1 |
| 382 |
ci = ci_tmp |
| 383 |
END IF! matches IF (ci_lt_zero) Then |
| 384 |
|
| 385 |
Print *, 'Final set of cis, first 10:***********************************' |
| 386 |
WRITE(*,'(10(1X,F20.4))') ci(1:MSET) |
| 387 |
Print *, 'Final set of cis ends:****************************************' |
| 388 |
Geom_new(:) = 0.D0 |
| 389 |
DO I=1, MSET |
| 390 |
Geom_new(:) = Geom_new(:) + (ci(I)*GeomSet((I-1)*NCoord+1:I*NCoord)) !MPLUS=MSET+1 |
| 391 |
! R_(N+1)=R*+DeltaR: |
| 392 |
DO J=1, NCoord |
| 393 |
tmp=0.D0 |
| 394 |
DO K=1,NCoord |
| 395 |
!tmp=tmp+Hess((J-1)*NCoord+K)*GradSet((I-1)*NCoord+K) ! If Hinv=.False., then we need to invert Hess |
| 396 |
END DO |
| 397 |
Geom_new(J) = Geom_new(J) - (ci(I)*tmp) |
| 398 |
END DO |
| 399 |
END DO |
| 400 |
|
| 401 |
DX(:) = Geom(:) - Geom_new(:) |
| 402 |
|
| 403 |
XNORM = SQRT(DOT_PRODUCT(DX,DX)) |
| 404 |
IF (PRINT) THEN |
| 405 |
WRITE (6,'(/10X,''DEVIATION IN X '',F10.4,8X,''DETERMINANT '',G9.3)') XNORM, DET |
| 406 |
!WRITE(*,'(10X,''GEDIIS COEFFICIENTS'')') |
| 407 |
!WRITE(*,'(10X,5F12.5)') (B(MPLUS*MSET+I),I=1,MSET) |
| 408 |
ENDIF |
| 409 |
|
| 410 |
! THE FOLLOWING TOLERENCES FOR XNORM AND DET ARE SOMEWHAT ARBITRARY! |
| 411 |
THRES = MAX(10.D0**(-NCoord), 1.D-25) |
| 412 |
IF (XNORM.GT.2.D0 .OR. DABS(DET) .LT. THRES) THEN |
| 413 |
IF (PRINT)THEN |
| 414 |
WRITE(*,*) "THE GEDIIS MATRIX IS ILL CONDITIONED" |
| 415 |
WRITE(*,*) " - PROBABLY, VECTORS ARE LINEARLY DEPENDENT - " |
| 416 |
WRITE(*,*) "THE GEDIIS STEP WILL BE REPEATED WITH A SMALLER SPACE" |
| 417 |
END IF |
| 418 |
DO K=1,MM |
| 419 |
B(K) = BS(K) ! why this is reverted? Because "IF (NGEDIIS .GT. 0) GO TO 80", see below |
| 420 |
END DO |
| 421 |
NGEDIIS = NGEDIIS - 1 |
| 422 |
IF (NGEDIIS .GT. 0) GO TO 80 |
| 423 |
IF (PRINT) WRITE(*,'(10X,''NEWTON-RAPHSON STEP TAKEN'')') |
| 424 |
Geom_new(:) = Geom(:) ! Geom_new is set to original Geom, thus DX = Geom(:) - Geom_new(:)=zero |
| 425 |
END IF ! matches IF (XNORM.GT.2.D0 .OR. DABS(DET).LT. THRES) THEN |
| 426 |
|
| 427 |
!******************************************************************************************************************* |
| 428 |
Geom_new(:) = 0.D0 |
| 429 |
DO I=1, MSET |
| 430 |
Geom_new(:) = Geom_new(:) + (ci(I)*GeomSet((I-1)*NCoord+1:I*NCoord)) !MPLUS=MSET+1 |
| 431 |
! R_(N+1)=R*+DeltaR: |
| 432 |
DO J=1, NCoord |
| 433 |
tmp=0.D0 |
| 434 |
DO K=1,NCoord |
| 435 |
tmp=tmp+Hess((J-1)*NCoord+K)*GradSet((I-1)*NCoord+K) ! If Hinv=.False., then we need to invert Hess |
| 436 |
END DO |
| 437 |
Geom_new(J) = Geom_new(J) - (ci(I)*tmp) |
| 438 |
END DO |
| 439 |
END DO |
| 440 |
!******************************************************************************************************************* |
| 441 |
|
| 442 |
IF (PRINT) WRITE(*,'(/,'' END GEDIIS '',/)') |
| 443 |
|
| 444 |
END SUBROUTINE Step_GEDIIS |
| 445 |
|