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source: palm/trunk/SOURCE/spline_x.f90 @ 143

Last change on this file since 143 was 4, checked in by raasch, 18 years ago
Id keyword set as property for all *.f90 files
Property svn:keywords set to `Id`
File size: 18.9 KB

Rev	Line
[1]	1	SUBROUTINE spline_x( vad_in_out, ad_v, var_char )
	2
	3	!------------------------------------------------------------------------------!
	4	! Actual revisions:
	5	! -----------------
	6	!
	7	!
	8	! Former revisions:
	9	! -----------------
[3]	10	! $Id: spline_x.f90 4 2007-02-13 11:33:16Z raasch $
	11	! RCS Log replace by Id keyword, revision history cleaned up
	12	!
[1]	13	! Revision 1.8 2004/04/30 12:54:20 raasch
	14	! Names of transpose indices changed, enlarged transposition arrays introduced
	15	!
	16	! Revision 1.1 1999/02/05 09:15:59 raasch
	17	! Initial revision
	18	!
	19	!
	20	! Description:
	21	! ------------
	22	! Upstream-spline advection along x
	23	!
	24	! Input/output parameters:
	25	! ad_v = advecting wind speed component
	26	! vad_in_out = quantity to be advected, excluding ghost- or cyclic boundaries
	27	! result is given to the calling routine in this array
	28	! var_char = string which defines the quantity to be advected
	29	!
	30	! Internal arrays:
	31	! r = 2D-working array (right hand side of linear equation, buffer for
	32	! Long filter)
	33	! tf = tendency field (2D), used for long filter
	34	! vad = quantity to be advected (2D), including ghost- or cyclic
	35	! boundarys along the direction of advection
	36	! wrk_long = working array (long coefficients)
	37	! wrk_spline = working array (spline coefficients)
	38	!------------------------------------------------------------------------------!
	39
	40	USE advection
	41	USE grid_variables
	42	USE indices
	43	USE statistics
	44	USE control_parameters
	45	USE transpose_indices
	46
	47	IMPLICIT NONE
	48
	49	CHARACTER (LEN=*) :: var_char
	50
	51	INTEGER :: component, i, j, k, sr
	52	REAL :: overshoot_limit, sm_faktor, t1, t2, t3, ups_limit
	53	REAL, DIMENSION(:,:), ALLOCATABLE :: r, tf, vad, wrk_spline
	54	REAL, DIMENSION(:,:,:), ALLOCATABLE :: wrk_long
	55
	56	#if defined( __parallel )
	57	REAL :: ad_v(0:nxa,nys_x:nyn_xa,nzb_x:nzt_xa), &
	58	vad_in_out(0:nxa,nys_x:nyn_xa,nzb_x:nzt_xa)
	59	#else
	60	REAL :: ad_v(nzb+1:nzt,nys:nyn,nxl:nxr), &
	61	vad_in_out(nzb:nzt+1,nys-1:nyn+1,nxl-1:nxr+1)
	62	#endif
	63
	64	!
	65	!-- Set criteria for switching between upstream- and upstream-spline-method
	66	IF ( var_char == 'u' ) THEN
	67	overshoot_limit = overshoot_limit_u
	68	ups_limit = ups_limit_u
	69	component = 1
	70	ELSEIF ( var_char == 'v' ) THEN
	71	overshoot_limit = overshoot_limit_v
	72	ups_limit = ups_limit_v
	73	component = 2
	74	ELSEIF ( var_char == 'w' ) THEN
	75	overshoot_limit = overshoot_limit_w
	76	ups_limit = ups_limit_w
	77	component = 3
	78	ELSEIF ( var_char == 'pt' ) THEN
	79	overshoot_limit = overshoot_limit_pt
	80	ups_limit = ups_limit_pt
	81	component = 4
	82	ELSEIF ( var_char == 'e' ) THEN
	83	overshoot_limit = overshoot_limit_e
	84	ups_limit = ups_limit_e
	85	component = 5
	86	ENDIF
	87
	88	!
	89	!-- Initialize calculation of relative upstream fraction
	90	sums_up_fraction_l(component,1,:) = 0.0
	91
	92	#if defined( __parallel )
	93
	94	!
	95	!-- Allocate working arrays
	96	ALLOCATE( r(-1:nx+1,nys_x:nyn_x), vad(-1:nx+1,nys_x:nyn_x), &
	97	wrk_spline(0:nx,nys_x:nyn_x) )
	98	IF ( long_filter_factor /= 0.0 ) THEN
	99	ALLOCATE( tf(0:nx,nys_x:nyn_x), wrk_long(0:nx,nys_x:nyn_x,1:3) )
	100	ENDIF
	101
	102	!
	103	!-- Loop over all gridpoints along z
	104	DO k = nzb_x, nzt_x
	105
	106	!
	107	!-- Store array to be advected on work array and add cyclic boundary along x
	108	vad(0:nx,nys_x:nyn_x) = vad_in_out(0:nx,nys_x:nyn_x,k)
	109	vad(-1,:) = vad(nx,:)
	110	vad(nx+1,:) = vad(0,:)
	111
	112	!
	113	!-- Calculate right hand side
	114	DO j = nys_x, nyn_x
	115	DO i = 0, nx
	116	r(i,j) = 3.0 * ( &
	117	spl_tri_x(2,i) * ( vad(i,j) - vad(i-1,j) ) * ddx + &
	118	spl_tri_x(3,i) * ( vad(i+1,j) - vad(i,j) ) * ddx &
	119	)
	120	ENDDO
	121	ENDDO
	122
	123	!
	124	!-- Forward substitution
	125	DO j = nys_x, nyn_x
	126	wrk_spline(0,j) = r(0,j)
	127	DO i = 1, nx
	128	wrk_spline(i,j) = r(i,j) - spl_tri_x(5,i) * wrk_spline(i-1,j)
	129	ENDDO
	130	ENDDO
	131
	132	!
	133	!-- Backward substitution (Sherman-Morrison-formula)
	134	DO j = nys_x, nyn_x
	135	r(nx,j) = wrk_spline(nx,j) / spl_tri_x(4,nx)
	136	DO i = nx-1, 0, -1
	137	r(i,j) = ( wrk_spline(i,j) - spl_tri_x(3,i) * r(i+1,j) ) / &
	138	spl_tri_x(4,i)
	139	ENDDO
	140	sm_faktor = ( r(0,j) + 0.5 * r(nx,j) / spl_gamma_x ) / &
	141	( 1.0 + spl_z_x(0) + 0.5 * spl_z_x(nx) / spl_gamma_x )
	142	DO i = 0, nx
	143	r(i,j) = r(i,j) - sm_faktor * spl_z_x(i)
	144	ENDDO
	145	ENDDO
	146
	147	!
	148	!-- Add cyclic boundary to right hand side
	149	r(-1,:) = r(nx,:)
	150	r(nx+1,:) = r(0,:)
	151
	152	!
	153	!-- Calculate advection along x
	154	DO j = nys_x, nyn_x
	155	DO i = 0, nx
	156
	157	IF ( ad_v(i,j,k) == 0.0 ) THEN
	158
	159	vad_in_out(i,j,k) = vad(i,j)
	160
	161	ELSEIF ( ad_v(i,j,k) > 0.0 ) THEN
	162
	163	IF ( ABS( vad(i,j) - vad(i-1,j) ) <= ups_limit ) THEN
	164	vad_in_out(i,j,k) = vad(i,j) - dt_3d * ad_v(i,j,k) * &
	165	( vad(i,j) - vad(i-1,j) ) * ddx
	166	!
	167	!-- Calculate upstream fraction in % (s. flow_statistics)
	168	DO sr = 0, statistic_regions
	169	sums_up_fraction_l(component,1,sr) = &
	170	sums_up_fraction_l(component,1,sr) + 1.0
	171	ENDDO
	172	ELSE
	173	t1 = ad_v(i,j,k) * dt_3d * ddx
	174	t2 = 3.0 * ( vad(i-1,j) - vad(i,j) ) + &
	175	( 2.0 * r(i,j) + r(i-1,j) ) * dx
	176	t3 = 2.0 * ( vad(i-1,j) - vad(i,j) ) + &
	177	( r(i,j) + r(i-1,j) ) * dx
	178	vad_in_out(i,j,k) = vad(i,j) - r(i,j) * t1 * dx + &
	179	t2 * t1*2 - t3 t1**3
	180	IF ( vad(i-1,j) == vad(i,j) ) THEN
	181	vad_in_out(i,j,k) = vad(i,j)
	182	ENDIF
	183	ENDIF
	184
	185	ELSE
	186
	187	IF ( ABS( vad(i,j) - vad(i+1,j) ) <= ups_limit ) THEN
	188	vad_in_out(i,j,k) = vad(i,j) - dt_3d * ad_v(i,j,k) * &
	189	( vad(i+1,j) - vad(i,j) ) * ddx
	190	!
	191	!-- Calculate upstream fraction in % (s. flow_statistics)
	192	DO sr = 0, statistic_regions
	193	sums_up_fraction_l(component,1,sr) = &
	194	sums_up_fraction_l(component,1,sr) + 1.0
	195	ENDDO
	196	ELSE
	197	t1 = -ad_v(i,j,k) * dt_3d * ddx
	198	t2 = 3.0 * ( vad(i,j) - vad(i+1,j) ) + &
	199	( 2.0 * r(i,j) + r(i+1,j) ) * dx
	200	t3 = 2.0 * ( vad(i,j) - vad(i+1,j) ) + &
	201	( r(i,j) + r(i+1,j) ) * dx
	202	vad_in_out(i,j,k) = vad(i,j) + r(i,j) * t1 * dx - &
	203	t2 * t1*2 + t3 t1**3
	204	IF ( vad(i+1,j) == vad(i,j) ) THEN
	205	vad_in_out(i,j,k) = vad(i,j)
	206	ENDIF
	207	ENDIF
	208
	209	ENDIF
	210	ENDDO
	211	ENDDO
	212
	213	!
	214	!-- Limit values in order to prevent overshooting
	215	IF ( cut_spline_overshoot ) THEN
	216
	217	DO j = nys_x, nyn_x
	218	DO i = 0, nx
	219	IF ( ad_v(i,j,k) > 0.0 ) THEN
	220	IF ( vad(i,j) > vad(i-1,j) ) THEN
	221	vad_in_out(i,j,k) = MIN( vad_in_out(i,j,k), &
	222	vad(i,j) + overshoot_limit )
	223	vad_in_out(i,j,k) = MAX( vad_in_out(i,j,k), &
	224	vad(i-1,j) - overshoot_limit )
	225	ELSE
	226	vad_in_out(i,j,k) = MAX( vad_in_out(i,j,k), &
	227	vad(i,j) - overshoot_limit )
	228	vad_in_out(i,j,k) = MIN( vad_in_out(i,j,k), &
	229	vad(i-1,j) + overshoot_limit )
	230	ENDIF
	231	ELSE
	232	IF ( vad(i,j) > vad(i+1,j) ) THEN
	233	vad_in_out(i,j,k) = MIN( vad_in_out(i,j,k), &
	234	vad(i,j) + overshoot_limit )
	235	vad_in_out(i,j,k) = MAX( vad_in_out(i,j,k), &
	236	vad(i+1,j) - overshoot_limit )
	237	ELSE
	238	vad_in_out(i,j,k) = MAX( vad_in_out(i,j,k), &
	239	vad(i,j) - overshoot_limit )
	240	vad_in_out(i,j,k) = MIN( vad_in_out(i,j,k), &
	241	vad(i+1,j) + overshoot_limit )
	242	ENDIF
	243	ENDIF
	244	ENDDO
	245	ENDDO
	246
	247	ENDIF
	248
	249	!
	250	!-- Long-filter (acting on tendency only)
	251	IF ( long_filter_factor /= 0.0 ) THEN
	252
	253	!
	254	!-- Compute tendency
	255	DO j = nys_x, nyn_x
	256	DO i = 0, nx
	257	tf(i,j) = vad_in_out(i,j,k) - vad(i,j)
	258	ENDDO
	259	ENDDO
	260
	261	!
	262	!-- Apply the filter.
	263	DO j = nys_x, nyn_x
	264	wrk_long(0,j,1) = 2.0 * ( 1.0 + long_filter_factor )
	265	wrk_long(0,j,2) = ( 1.0 - long_filter_factor ) / wrk_long(0,j,1)
	266	wrk_long(0,j,3) = ( long_filter_factor * tf(nx,j) + &
	267	2.0 * tf(0,j) + tf(1,j) &
	268	) / wrk_long(0,j,1)
	269	DO i = 1, nx-1
	270	wrk_long(i,j,1) = 2.0 * ( 1.0 + long_filter_factor ) - &
	271	( 1.0 - long_filter_factor ) * wrk_long(i-1,j,2)
	272	wrk_long(i,j,2) = ( 1.0 - long_filter_factor ) / wrk_long(i,j,1)
	273	wrk_long(i,j,3) = ( tf(i-1,j) + 2.0 * tf(i,j) + &
	274	tf(i+1,j) - ( 1.0 - long_filter_factor ) * &
	275	wrk_long(i-1,j,3) ) / wrk_long(i,j,1)
	276	ENDDO
	277	wrk_long(nx,j,1) = 2.0 * ( 1.0 + long_filter_factor ) - &
	278	( 1.0 - long_filter_factor ) * wrk_long(nx-1,j,2)
	279	wrk_long(nx,j,2) = ( 1.0 - long_filter_factor ) / wrk_long(nx,j,1)
	280	wrk_long(nx,j,3) = ( tf(nx-1,j) + 2.0 * tf(nx,j) + &
	281	long_filter_factor * tf(0,j) - &
	282	( 1.0 - long_filter_factor ) * &
	283	wrk_long(nx-1,j,3) &
	284	) / wrk_long(nx,j,1)
	285	r(nx,j) = wrk_long(nx,j,3)
	286	ENDDO
	287
	288	DO i = nx-1, 0, -1
	289	DO j = nys_x, nyn_x
	290	r(i,j) = wrk_long(i,j,3) - wrk_long(i,j,2) * r(i+1,j)
	291	ENDDO
	292	ENDDO
	293
	294	DO j = nys_x, nyn_x
	295	DO i = 0, nx
	296	vad_in_out(i,j,k) = vad(i,j) + r(i,j)
	297	ENDDO
	298	ENDDO
	299
	300	ENDIF ! Long filter
	301
	302	ENDDO
	303
	304	#else
	305
	306	!
	307	!-- Allocate working arrays
	308	ALLOCATE( r(nzb+1:nzt,nxl-1:nxr+1), vad(nzb:nzt+1,nxl-1:nxr+1), &
	309	wrk_spline(nzb+1:nzt,nxl-1:nxr+1) )
	310	IF ( long_filter_factor /= 0.0 ) THEN
	311	ALLOCATE( tf(nzb+1:nzt,nxl-1:nxr+1), wrk_long(nzb+1:nzt,0:nx,1:3) )
	312	ENDIF
	313
	314	!
	315	!-- Loop over all gridpoints along y
	316	DO j = nys, nyn
	317
	318	!
	319	!-- Store array to be advected on work array and add cyclic boundary along x
	320	vad(:,:) = vad_in_out(:,j,:)
	321	vad(:,-1) = vad(:,nx)
	322	vad(:,nx+1) = vad(:,0)
	323
	324	!
	325	!-- Calculate right hand side
	326	DO i = 0, nx
	327	DO k = nzb+1, nzt
	328	r(k,i) = 3.0 * ( &
	329	spl_tri_x(2,i) * ( vad(k,i) - vad(k,i-1) ) * ddx + &
	330	spl_tri_x(3,i) * ( vad(k,i+1) - vad(k,i) ) * ddx &
	331	)
	332	ENDDO
	333	ENDDO
	334
	335	!
	336	!-- Forward substitution
	337	DO k = nzb+1, nzt
	338	wrk_spline(k,0) = r(k,0)
	339	ENDDO
	340
	341	DO i = 1, nx
	342	DO k = nzb+1, nzt
	343	wrk_spline(k,i) = r(k,i) - spl_tri_x(5,i) * wrk_spline(k,i-1)
	344	ENDDO
	345	ENDDO
	346
	347	!
	348	!-- Backward substitution (Sherman-Morrison-formula)
	349	DO k = nzb+1, nzt
	350	r(k,nx) = wrk_spline(k,nx) / spl_tri_x(4,nx)
	351	ENDDO
	352
	353	DO k = nzb+1, nzt
	354	DO i = nx-1, 0, -1
	355	r(k,i) = ( wrk_spline(k,i) - spl_tri_x(3,i) * r(k,i+1) ) / &
	356	spl_tri_x(4,i)
	357	ENDDO
	358	sm_faktor = ( r(k,0) + 0.5 * r(k,nx) / spl_gamma_x ) / &
	359	( 1.0 + spl_z_x(0) + 0.5 * spl_z_x(nx) / spl_gamma_x )
	360	DO i = 0, nx
	361	r(k,i) = r(k,i) - sm_faktor * spl_z_x(i)
	362	ENDDO
	363	ENDDO
	364
	365	!
	366	!-- Add cyclic boundary to the right hand side
	367	r(:,-1) = r(:,nx)
	368	r(:,nx+1) = r(:,0)
	369
	370	!
	371	!-- Calculate advection along x
	372	DO i = 0, nx
	373	DO k = nzb+1, nzt
	374
	375	IF (ad_v(k,j,i) == 0.0) THEN
	376
	377	vad_in_out(k,j,i) = vad(k,i)
	378
	379	ELSEIF ( ad_v(k,j,i) > 0.0) THEN
	380
	381	IF ( ABS( vad(k,i) - vad(k,i-1) ) <= ups_limit ) THEN
	382	vad_in_out(k,j,i) = vad(k,i) - dt_3d * ad_v(k,j,i) * &
	383	( vad(k,i) - vad(k,i-1) ) * ddx
	384	!
	385	!-- Calculate upstream fraction in % (s. flow_statistics)
	386	DO sr = 0, statistic_regions
	387	sums_up_fraction_l(component,1,sr) = &
	388	sums_up_fraction_l(component,1,sr) + 1.0
	389	ENDDO
	390	ELSE
	391	t1 = ad_v(k,j,i) * dt_3d * ddx
	392	t2 = 3.0 * ( vad(k,i-1) - vad(k,i) ) + &
	393	( 2.0 * r(k,i) + r(k,i-1) ) * dx
	394	t3 = 2.0 * ( vad(k,i-1) - vad(k,i) ) + &
	395	( r(k,i) + r(k,i-1) ) * dx
	396	vad_in_out(k,j,i) = vad(k,i) - r(k,i) * t1 * dx + &
	397	t2 * t1*2 - t3 t1**3
	398	IF ( vad(k,i-1) == vad(k,i) ) THEN
	399	vad_in_out(k,j,i) = vad(k,i)
	400	ENDIF
	401	ENDIF
	402
	403	ELSE
	404
	405	IF ( ABS( vad(k,i) - vad(k,i+1) ) <= ups_limit ) THEN
	406	vad_in_out(k,j,i) = vad(k,i) - dt_3d * ad_v(k,j,i) * &
	407	( vad(k,i+1) - vad(k,i) ) * ddx
	408	!
	409	!-- Calculate upstream fraction in % (s. flow_statistics)
	410	DO sr = 0, statistic_regions
	411	sums_up_fraction_l(component,1,sr) = &
	412	sums_up_fraction_l(component,1,sr) + 1.0
	413	ENDDO
	414	ELSE
	415	t1 = -ad_v(k,j,i) * dt_3d * ddx
	416	t2 = 3.0 * ( vad(k,i) - vad(k,i+1) ) + &
	417	( 2.0 * r(k,i) + r(k,i+1)) * dx
	418	t3 = 2.0 * ( vad(k,i) - vad(k,i+1) ) + &
	419	( r(k,i) + r(k,i+1) ) * dx
	420	vad_in_out(k,j,i) = vad(k,i) + r(k,i) * t1 * dx - &
	421	t2 * t1*2 + t3 t1**3
	422	IF ( vad(k,i+1) == vad(k,i) ) THEN
	423	vad_in_out(k,j,i) = vad(k,i)
	424	ENDIF
	425	ENDIF
	426
	427	ENDIF
	428	ENDDO
	429	ENDDO
	430
	431	!
	432	!-- Limit values in order to prevent overshooting
	433	IF ( cut_spline_overshoot ) THEN
	434
	435	DO i = 0, nx
	436	DO k = nzb+1, nzt
	437	IF ( ad_v(k,j,i) > 0.0 ) THEN
	438	IF ( vad(k,i) > vad(k,i-1) ) THEN
	439	vad_in_out(k,j,i) = MIN( vad_in_out(k,j,i), &
	440	vad(k,i) + overshoot_limit )
	441	vad_in_out(k,j,i) = MAX( vad_in_out(k,j,i), &
	442	vad(k,i-1) - overshoot_limit )
	443	ELSE
	444	vad_in_out(k,j,i) = MAX( vad_in_out(k,j,i), &
	445	vad(k,i) - overshoot_limit )
	446	vad_in_out(k,j,i) = MIN( vad_in_out(k,j,i), &
	447	vad(k,i-1) + overshoot_limit )
	448	ENDIF
	449	ELSE
	450	IF ( vad(k,i) > vad(k,i+1) ) THEN
	451	vad_in_out(k,j,i) = MIN( vad_in_out(k,j,i), &
	452	vad(k,i) + overshoot_limit )
	453	vad_in_out(k,j,i) = MAX( vad_in_out(k,j,i), &
	454	vad(k,i+1) - overshoot_limit )
	455	ELSE
	456	vad_in_out(k,j,i) = MAX( vad_in_out(k,j,i), &
	457	vad(k,i) - overshoot_limit )
	458	vad_in_out(k,j,i) = MIN( vad_in_out(k,j,i), &
	459	vad(k,i+1) + overshoot_limit )
	460	ENDIF
	461	ENDIF
	462	ENDDO
	463	ENDDO
	464
	465	ENDIF
	466
	467	!
	468	!-- Long filter (acting on tendency only)
	469	IF ( long_filter_factor /= 0.0 ) THEN
	470
	471	!
	472	!-- Compute tendency
	473	DO i = nxl, nxr
	474	DO k = nzb+1, nzt
	475	tf(k,i) = vad_in_out(k,j,i) - vad(k,i)
	476	ENDDO
	477	ENDDO
	478
	479	!
	480	!-- Apply the filter
	481	wrk_long(:,0,1) = 2.0 * ( 1.0 + long_filter_factor )
	482	wrk_long(:,0,2) = ( 1.0 - long_filter_factor ) / wrk_long(:,0,1)
	483	wrk_long(:,0,3) = ( long_filter_factor * tf(:,nx) + &
	484	2.0 * tf(:,0) + tf(:,1) ) / wrk_long(:,0,1)
	485
	486	DO i = 1, nx-1
	487	DO k = nzb+1, nzt
	488	wrk_long(k,i,1) = 2.0 * ( 1.0 + long_filter_factor ) - &
	489	( 1.0 - long_filter_factor ) * &
	490	wrk_long(k,i-1,2)
	491	wrk_long(k,i,2) = ( 1.0 - long_filter_factor ) / wrk_long(k,i,1)
	492	wrk_long(k,i,3) = ( tf(k,i-1) + 2.0 * tf(k,i) + &
	493	tf(k,i+1) - ( 1.0 - long_filter_factor ) * &
	494	wrk_long(k,i-1,3) ) / wrk_long(k,i,1)
	495	ENDDO
	496	wrk_long(:,nx,1) = 2.0 * ( 1.0 + long_filter_factor ) - &
	497	( 1.0 - long_filter_factor ) * &
	498	wrk_long(:,nx-1,2)
	499	wrk_long(:,nx,2) = ( 1.0 - long_filter_factor ) / wrk_long(:,nx,1)
	500	wrk_long(:,nx,3) = ( tf(:,nx-1) + 2.0 * tf(:,nx) + &
	501	long_filter_factor * tf(:,0) - &
	502	( 1.0 - long_filter_factor ) * &
	503	wrk_long(:,nx-1,3) ) / wrk_long(:,nx,1)
	504	r(:,nx) = wrk_long(:,nx,3)
	505	ENDDO
	506	DO i = nx-1, 0, -1
	507	DO k = nzb+1, nzt
	508	r(k,i) = wrk_long(k,i,3) - wrk_long(k,i,2) * r(k,i+1)
	509	ENDDO
	510	ENDDO
	511	DO i = 0, nx
	512	DO k = nzb+1, nzt
	513	vad_in_out(k,j,i) = vad(k,i) + r(k,i)
	514	ENDDO
	515	ENDDO
	516
	517	ENDIF ! Long filter
	518
	519	ENDDO
	520	#endif
	521
	522	IF ( long_filter_factor /= 0.0 ) DEALLOCATE( tf, wrk_long )
	523	DEALLOCATE( r, vad, wrk_spline )
	524
	525	END SUBROUTINE spline_x

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