* * tauto_cor.F * * * This software was developed by the Thermal Modeling and Analysis * Project(TMAP) of the National Oceanographic and Atmospheric * Administration's (NOAA) Pacific Marine Environmental Lab(PMEL), * hereafter referred to as NOAA/PMEL/TMAP. * * Access and use of this software shall impose the following * obligations and understandings on the user. The user is granted the * right, without any fee or cost, to use, copy, modify, alter, enhance * and distribute this software, and any derivative works thereof, and * its supporting documentation for any purpose whatsoever, provided * that this entire notice appears in all copies of the software, * derivative works and supporting documentation. Further, the user * agrees to credit NOAA/PMEL/TMAP in any publications that result from * the use of this software or in any product that includes this * software. The names TMAP, NOAA and/or PMEL, however, may not be used * in any advertising or publicity to endorse or promote any products * or commercial entity unless specific written permission is obtained * from NOAA/PMEL/TMAP. The user also understands that NOAA/PMEL/TMAP * is not obligated to provide the user with any support, consulting, * training or assistance of any kind with regard to the use, operation * and performance of this software nor to provide the user with any * updates, revisions, new versions or "bug fixes". * * THIS SOFTWARE IS PROVIDED BY NOAA/PMEL/TMAP "AS IS" AND ANY EXPRESS * OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED * WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE * ARE DISCLAIMED. IN NO EVENT SHALL NOAA/PMEL/TMAP BE LIABLE FOR ANY SPECIAL, * INDIRECT OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES WHATSOEVER * RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN ACTION OF * CONTRACT, NEGLIGENCE OR OTHER TORTUOUS ACTION, ARISING OUT OF OR IN * CONNECTION WITH THE ACCESS, USE OR PERFORMANCE OF THIS SOFTWARE. * * Ansley Manke * July 1999 * Update to use abstract axis 1-feb-2000 * * This function computes the autocorrelation for a x series. * Autocorelation formula computed directly for lags of 0, 1, ..., N-1 * Return on an abstract X axis. * * In this subroutine we provide information about * the function. The user configurable information * consists of the following: * * descr Text description of the function * * num_args Required number of arguments * * axis_inheritance Type of axis for the result * ( CUSTOM, IMPLIED_BY_ARGS, NORMAL, ABSTRACT ) * CUSTOM - user defined axis * IMPLIED_BY_ARGS - same axis as the incoming argument * NORMAL - the result is normal to this axis * ABSTRACT - an axis which only has index values * * piecemeal_ok For memory optimization: * axes where calculation may be performed piecemeal * ( YES, NO ) * * * For each argument we provide the following information: * * name Text name for an argument * * unit Text units for an argument * * desc Text description of an argument * * axis_influence Are this argument's axes the same as the result grid? * ( YES, NO ) * * axis_extend How much does Ferret need to extend arg limits relative to result * SUBROUTINE tauto_cor_init(id) INCLUDE 'ferret_cmn/EF_Util.cmn' INTEGER id, arg CHARACTER*110 fcn_desc c CALL ef_version_test(ef_version) * ********************************************************************** * USER CONFIGURABLE PORTION | * | * V WRITE (fcn_desc, 20) CALL ef_set_desc(id, fcn_desc) 20 FORMAT ( 'Compute autocorrelation of ', . ' series, lags of 0, ..., N-1' ) CALL ef_set_desc(id, fcn_desc) CALL ef_set_num_args(id, 1) CALL ef_set_axis_inheritance(id, IMPLIED_BY_ARGS, . IMPLIED_BY_ARGS, IMPLIED_BY_ARGS, ABSTRACT) CALL ef_set_piecemeal_ok(id, NO, NO, NO, NO) CALL ef_set_num_work_arrays(id, 3) arg = 1 CALL ef_set_arg_name(id, arg, 'A') CALL ef_set_arg_desc(id, arg, 'X- series variable') CALL ef_set_axis_influence(id, arg, YES, YES, YES, NO) * ^ * | * USER CONFIGURABLE PORTION | *********************************************************************** RETURN END * * In this subroutine we provide information about the lo and hi * limits associated with each abstract or custom axis. The user * configurable information consists of the following: * * lo_ss lo subscript for an axis * * hi_ss hi subscript for an axis * SUBROUTINE tauto_cor_result_limits(id) INCLUDE 'ferret_cmn/EF_Util.cmn' INCLUDE 'ferret_cmn/EF_mem_subsc.cmn' INTEGER id * ********************************************************************** * USER CONFIGURABLE PORTION | * | * V INTEGER nt, nt1 INTEGER arg_lo_ss(4,EF_MAX_ARGS), arg_hi_ss(4,EF_MAX_ARGS), . arg_incr(4,EF_MAX_ARGS) * Use utility functions to get context information about the argument. CALL ef_get_arg_subscripts(id, arg_lo_ss, arg_hi_ss, arg_incr) nt = arg_hi_ss(T_AXIS,ARG1) - arg_lo_ss(T_AXIS,ARG1) +1 C Autocorrelation returns corelations for lags of 1 to N. nt1 = 1 CALL ef_set_axis_limits(id, T_AXIS, nt1, nt) * ^ * | * USER CONFIGURABLE PORTION | * ********************************************************************** RETURN END * * In this subroutine we request an amount of storage to be supplied * by Ferret and passed as an additional argument. * SUBROUTINE tauto_cor_work_size(id) INCLUDE 'ferret_cmn/EF_Util.cmn' INCLUDE 'ferret_cmn/EF_mem_subsc.cmn' INTEGER id * ********************************************************************** * USER CONFIGURABLE PORTION | * | * * Set the work arrays, X/Y/Z/T dimensions * * ef_set_work_array_dims(id,array #,xlo,ylo,zlo,tlo,xhi,yhi,zhi,thi) * INTEGER npts, irr INTEGER arg_lo_ss(4,1:EF_MAX_ARGS), arg_hi_ss(4,1:EF_MAX_ARGS), . arg_incr(4,1:EF_MAX_ARGS) CALL ef_get_arg_subscripts(id, arg_lo_ss, arg_hi_ss, arg_incr) npts = 1 + arg_hi_ss(T_AXIS,ARG1) - arg_lo_ss(T_AXIS,ARG1) * partial means pmean irr = 1 CALL ef_set_work_array_dims (id, irr, 1, 1, 1, 1, npts, 1, 1, 1) * partial variances pvar irr = 2 CALL ef_set_work_array_dims (id, irr, 1, 1, 1, 1, npts, 1, 1, 1) * box sizes BOX irr = 3 CALL ef_set_work_array_dims (id, irr, 1, 1, 1, 1, npts, 1, 1, 1) * ^ * | * USER CONFIGURABLE PORTION | * ********************************************************************** RETURN END * * In this subroutine we compute the result * SUBROUTINE tauto_cor_compute(id, arg_1, result, pmean, . pvar, box) INCLUDE 'ferret_cmn/EF_Util.cmn' INCLUDE 'ferret_cmn/EF_mem_subsc.cmn' INTEGER id REAL bad_flag(1:EF_MAX_ARGS), bad_flag_result REAL arg_1(mem1lox:mem1hix, mem1loy:mem1hiy, . mem1loz:mem1hiz, mem1lot:mem1hit) REAL result(memreslox:memreshix, memresloy:memreshiy, . memresloz:memreshiz, memreslot:memreshit) * After initialization, the 'res_' arrays contain indexing information * for the result axes. The 'arg_' arrays will contain the indexing * information for each variable's axes. INTEGER res_lo_ss(4), res_hi_ss(4), res_incr(4) INTEGER arg_lo_ss(4,1:EF_MAX_ARGS), arg_hi_ss(4,1:EF_MAX_ARGS), . arg_incr(4,1:EF_MAX_ARGS) * ********************************************************************** * USER CONFIGURABLE PORTION | * | * V REAL psum, diff, diff2 REAL dsum, bsize INTEGER lr, lm, m * Dimension work arrays REAL pmean(wrk1lox:wrk1hix, wrk1loy:wrk1hiy, . wrk1loz:wrk1hiz, wrk1lot:wrk1hit) REAL pvar(wrk2lox:wrk2hix, wrk2loy:wrk2hiy, . wrk2loz:wrk2hiz, wrk2lot:wrk2hit) REAL box(wrk3lox:wrk3hix, wrk3loy:wrk3hiy, . wrk3loz:wrk3hiz, wrk3lot:wrk3hit) INTEGER nd, arg INTEGER i, j, k, l INTEGER i1, j1, k1, l1 CALL ef_get_res_subscripts(id, res_lo_ss, res_hi_ss, res_incr) CALL ef_get_arg_subscripts(id, arg_lo_ss, arg_hi_ss, arg_incr) CALL ef_get_bad_flags(id, bad_flag, bad_flag_result) arg = 1 CALL ef_get_box_size(id, arg, T_AXIS, arg_lo_ss(T_AXIS,arg), . arg_hi_ss(T_AXIS,arg), box) nd = (arg_hi_ss(T_AXIS,arg) - arg_lo_ss(T_AXIS,arg) + 1) i1 = arg_lo_ss(X_AXIS,ARG1) DO 400 i=res_lo_ss(X_AXIS), res_hi_ss(X_AXIS) j1 = arg_lo_ss(Y_AXIS,ARG1) DO 300 j=res_lo_ss(Y_AXIS), res_hi_ss(Y_AXIS) k1 = arg_lo_ss(Z_AXIS,ARG1) DO 200 k=res_lo_ss(Z_AXIS), res_hi_ss(Z_AXIS) * * Calculate the autocorrelation * First step is to compute the partial means [1/(n-i)]* sum[m=1,n-i]dat(m+i) DO 120 l = 1, nd psum = 0. dsum = 0. lm = l-1 l1 = arg_lo_ss(T_AXIS,ARG1) DO 110 m = 1, nd-lm IF (arg_1(i1,j1,k1,l1+lm) .NE. bad_flag(ARG1)) THEN bsize = box(m+lm,1,1,1) psum = psum + bsize* arg_1(i1,j1,k1,l1+lm) dsum = dsum + bsize ENDIF l1 = l1 + arg_incr(T_AXIS,ARG1) 110 CONTINUE IF (dsum .gt. 0.) pmean(l,1,1,1) = psum/ dsum 120 CONTINUE * Compute the partial variances RMS[dat(m+l) - pmean(l)] * Don't divide by dsum; the denominators cancel when the autocorrelation * is computed below. DO 160 l = 1, nd psum = 0. dsum = 0. lm = l-1 l1 = arg_lo_ss(T_AXIS,ARG1) DO 150 m = 1, nd-lm IF (arg_1(i1,j1,k1,l1+lm) .NE. bad_flag(ARG1)) THEN bsize = box(m+lm,1,1,1) diff = . arg_1(i1,j1,k1,l1+lm) - pmean(l,1,1,1) psum = psum + bsize* diff* diff dsum = dsum + bsize ENDIF l1 = l1 + arg_incr(T_AXIS,ARG1) 150 CONTINUE IF (dsum .gt. 0.) THEN pvar(l,1,1,1) = sqrt(psum) ELSE pvar(l,1,1,1) = 0. ENDIF 160 CONTINUE * Compute the autocorrelation for lag l=0,1,2,...,ND-1 l1 = arg_lo_ss(T_AXIS,ARG1) lr = res_lo_ss(T_AXIS) DO 180 l = 1, nd psum = 0. dsum = 0. lm = l-1 l1 = arg_lo_ss(T_AXIS,ARG1) DO 170 m = 1, nd-lm IF (arg_1(i1,j1,k1,l1+lm) .NE. bad_flag(ARG1)) THEN bsize = (box(m+lm,1,1,1) + box(m,1,1,1))/ 2. diff = . arg_1(i1,j1,k1,l1+lm) - pmean(l,1,1,1) diff2 = . arg_1(i1,j1,k1,l1) - pmean(1,1,1,1) psum = psum + bsize* diff* diff2 dsum = dsum + box(m+lm,1,1,1)* box(m,1,1,1) ENDIF l1 = l1 + arg_incr(T_AXIS,ARG1) 170 CONTINUE IF (pvar(1,1,1,1) .NE. 0. .AND. . pvar(l,1,1,1) .NE. 0. .AND. . psum .NE. 0.) THEN . result(i,j,k,lr) = psum/ . (pvar(1,1,1,1)* pvar(l,1,1,1)) ELSE result(i,j,k,lr) = bad_flag_result ENDIF l1 = l1 + arg_incr(T_AXIS,ARG1) lr = lr + res_incr(T_AXIS) 180 CONTINUE k1 = k1 + arg_incr(Z_AXIS,ARG1) 200 CONTINUE j1 = j1 + arg_incr(Y_AXIS,ARG1) 300 CONTINUE i1 = i1 + arg_incr(X_AXIS,ARG1) 400 CONTINUE * ^ * | * USER CONFIGURABLE PORTION | * ********************************************************************** RETURN END