* * fftp.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 * Dec 1998 * * * This function computes fft phase spectrum for each time series. Result * time axis is a custom axis in period 1./time The input variable must have * the time axis specified explicitly in the function call e.g. * LET sstp = fftp(ssttim[l=1:492]) * and the time axis must be regular. * Note current limitations as of 1-Jan-2000 * - Will have a utility to get the length of the input time axis at the * point when the custom freq axis is set up, to use in computing the * length of the frequency axis. Currently need to specify explicitly, * in the function call e.g. fftp(sst[l=1:400]). * NOTE: * IT IS GENERALLY ADVISABLE TO INCLUDE EXPLICIT LIMITS WHEN WORKING WITH * FUNCTIONS THAT REPLACE AXES. FOR EXAMPLE, THE CONSIDER THE FUNCTION * SORTL(v). THE EXPRESSION * LIST/L=6:10 SORTL(v) * IS NOT EQUIVALENT TO * LIST SORTL(v[L=6:10]) * THE FORMER WILL LIST THE 6TH THROUGH 10TH SORTED INDICES FROM THE ENTIRE * L RANGE OF VARIABLE V. THE LATTER WILL LIST ALL OF THE INDICES THAT * RESULT FROM SORTING v[L=6:10]. * * * 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 fftp_init(id) INCLUDE 'ferret_cmn/EF_Util.cmn' INTEGER id, arg CHARACTER*110 arg_desc c CALL ef_version_test(ef_version) * ********************************************************************** * USER CONFIGURABLE PORTION | * | * V * V CALL ef_set_desc(id, 'Computes fft phase' ) CALL ef_set_num_args(id, 1) CALL ef_set_axis_inheritance(id, IMPLIED_BY_ARGS, . IMPLIED_BY_ARGS, IMPLIED_BY_ARGS, CUSTOM) CALL ef_set_piecemeal_ok(id, NO, NO, NO, NO) CALL ef_set_num_work_arrays(id, 4) arg = 1 CALL ef_set_arg_name(id, arg, 'A') CALL ef_set_arg_unit(id, arg, ' ') WRITE (arg_desc, 10) 10 FORMAT ('Variable with regular time axis. Specify time ', . 'explicitly e.g. fftp(var[l=1,120])') CALL ef_set_arg_desc(id, arg, arg_desc) CALL ef_set_axis_influence(id, arg, YES, YES, YES, NO) * ^ * | * USER CONFIGURABLE PORTION | *********************************************************************** RETURN END SUBROUTINE fftp_custom_axes(id) INCLUDE 'ferret_cmn/EF_Util.cmn' INTEGER id * ********************************************************************** * USER CONFIGURABLE PORTION | * | * * * Use utility functions to get grid information about the * argument; use this info to determine the custom axis lo/hi/del INTEGER nfreq_lo_l, nfreq_hi_l INTEGER arg_lo_ss(4,EF_MAX_ARGS), arg_hi_ss(4,EF_MAX_ARGS), . arg_incr(4,EF_MAX_ARGS) INTEGER arg INTEGER nfreq, nd REAL yquist, freq1, freqn CHARACTER outunits*32 REAL boxsize(1) CHARACTER ax_name(4)*16, ax_units(4)*16 LOGICAL backward(4), modulo(4), regular(4) arg = 1 CALL ef_get_arg_subscripts(id, arg_lo_ss, arg_hi_ss, arg_incr) CALL ef_get_axis_info(id, arg, ax_name, ax_units, backward, . modulo, regular) CALL ef_get_box_size(id, arg, T_AXIS, arg_lo_ss(T_AXIS,arg), . arg_lo_ss(T_AXIS,arg), boxsize) IF ( arg_hi_ss(T_AXIS,arg) - arg_lo_ss(T_AXIS,arg) .EQ. 0 ) THEN nfreq_lo_l = 1 nfreq_hi_l = 2 ELSE nfreq_lo_l = arg_lo_ss(T_AXIS,arg) nfreq_hi_l = arg_hi_ss(T_AXIS,arg) ENDIF nd = abs(nfreq_hi_l - nfreq_lo_l) + 1 C The FFT code returns frequencies W(k) for k=1 to N/2, with N/2 rounded down nfreq = nd/2 yquist = 1./(2.*boxsize(1)) ! Nyquist frequency freq1 = 1.* yquist/ float(nfreq) freqn = 1.001*yquist C Set label for the frequency axis CYC/units. outunits = 'CYC/' // ax_units(T_AXIS) CALL ef_set_custom_axis (id, T_AXIS, freq1, freqn, freq1, . outunits, 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 fftp_result_limits(id) INCLUDE 'ferret_cmn/EF_Util.cmn' INCLUDE 'ferret_cmn/EF_mem_subsc.cmn' INTEGER id * ********************************************************************** * USER CONFIGURABLE PORTION | * | * V INTEGER ntime, nfreq INTEGER arg 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) nfreq = 1 arg = 1 ntime = arg_hi_ss(T_AXIS,arg) - arg_lo_ss(T_AXIS,arg) + 1 C The FFT code returns frequencies W(k) for k=1 to N/2, with N/2 rounded down nfreq = ntime/ 2 if (ntime .ne. nfreq*2) nfreq = (ntime+1)/2 ! see FFTPACK comments in rfftf CALL ef_set_axis_limits(id, T_AXIS, 1, nfreq) * ^ * | * 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 fftp_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 mtdat, mtwork 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) mtdat = 1 + arg_hi_ss(T_AXIS,ARG1) - arg_lo_ss(T_AXIS,ARG1) mtwork = 2.5* mtdat + 15 * a CALL ef_set_work_array_dims (id, 1, 1, 1, 1, 1, mtdat, 1, 1, 1) * b CALL ef_set_work_array_dims (id, 2, 1, 1, 1, 1, mtdat, 1, 1, 1) * wft CALL ef_set_work_array_dims (id, 3, 1, 1, 1, 1, mtwork, 1, 1, 1) * ts CALL ef_set_work_array_dims (id, 4, 1, 1, 1, 1, mtdat, 1, 1, 1) * ^ * | * USER CONFIGURABLE PORTION | * ********************************************************************** RETURN END * * In this subroutine we compute the result * SUBROUTINE fftp_compute(id, arg_1, result, a, b, wft, ts) INCLUDE 'ferret_cmn/EF_Util.cmn' INCLUDE 'ferret_cmn/EF_mem_subsc.cmn' INTEGER id, arg 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 CHARACTER ax_name(4)*16, ax_units(4)*16 LOGICAL backward(4), modulo(4), regular(4) * Dimension work arrays REAL a(wrk1lox:wrk1hix, wrk1loy:wrk1hiy, . wrk1loz:wrk1hiz, wrk1lot:wrk1hit) REAL b(wrk2lox:wrk2hix, wrk2loy:wrk2hiy, . wrk2loz:wrk2hiz, wrk2lot:wrk2hit) REAL wft(wrk3lox:wrk3hix, wrk3loy:wrk3hiy, . wrk3loz:wrk3hiz, wrk3lot:wrk3hit) REAL ts(wrk4lox:wrk4hix, wrk4loy:wrk4hiy, . wrk4loz:wrk4hiz, wrk4lot:wrk4hit) REAL aa, bb, rad INTEGER nd, nf INTEGER i,j,k,l INTEGER i1, j1, k1, l1 CHARACTER*80 err_msg 40 FORMAT ('FFTP encountered missing data at (i,j,k,l)', 4I5) rad = 180.0/ 3.141592654 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) * number of time points. arg = 1 nd = (arg_hi_ss(T_AXIS,arg) - arg_lo_ss(T_AXIS,arg) + 1) nf = nd/ 2 * Check that the time axis is regular. CALL ef_get_axis_info (id, 1, ax_name, ax_units, backward, . modulo, regular) IF (.NOT. regular(T_AXIS)) THEN WRITE (err_msg, *) 'Time axis must be a regular axis' GO TO 999 ENDIF * Set WFT for fft; prime factorization of ND and trig functions. CALL rffti (nd, wft) 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 FFT for each time series which have no missing data. * l1 =arg_lo_ss(T_AXIS,ARG1) DO 100 l = 1, nd IF (arg_1(i1,j1,k1,l1) .EQ. bad_flag(ARG1)) THEN WRITE (err_msg, 40) i1,j1,k1,l GO TO 999 ENDIF ts(l,1,1,1) = arg_1(i1,j1,k1,l1) l1 = l1 + arg_incr(T_AXIS,ARG1) 100 CONTINUE l1 = arg_lo_ss(T_AXIS,ARG1) l = res_lo_ss(T_AXIS) CALL four_re (nd, ts, a, b, wft) DO 110 l = res_lo_ss(T_AXIS), res_hi_ss(T_AXIS) aa = a(l,1,1,1) bb = b(l,1,1,1) result(i,j,k,l) = rad* ATAN2(-1.*bb, aa) 110 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 RETURN 999 CALL ef_bail_out (id, err_msg) * ^ * | * USER CONFIGURABLE PORTION | * ********************************************************************** RETURN END