frinZ 4.4.0

fringe search for Yamaguchi Interferometer and Japanese VLBI Network
Documentation
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
use chrono::{DateTime, Utc};
use ndarray::prelude::*;
use num_complex::Complex;

use crate::args::Args;
use crate::fitting;
use crate::header::CorHeader;
use crate::utils::{
    delay_rate_mask_bounds, in_delay_rate_mask, in_window, mjd_cal, noise_level,
    positive_or_epsilon, radec2azalt, rate_cal, rate_delay_to_lm, safe_arg, uvw_cal, window_bounds,
};

type C32 = Complex<f32>;

fn norm_at(data: &Array2<C32>, row: usize, col: usize) -> f32 {
    data[[row, col]].norm()
}

fn norm_sqr_at(data: &Array2<C32>, row: usize, col: usize) -> f32 {
    data[[row, col]].norm_sqr()
}

fn refine_peak_3x3_quadratic(
    surface: &Array2<C32>,
    center_rate_idx: usize,
    center_delay_idx: usize,
    rate_range: &[f32],
    delay_range: &Array1<f32>,
    rrange: &[f32],
    drange: &[f32],
    mask: Option<(f32, f32, f32, f32)>,
) -> Option<(f32, f32)> {
    let (rows, cols) = surface.dim();
    if rows < 3 || cols < 3 {
        return None;
    }
    if center_rate_idx == 0
        || center_delay_idx == 0
        || center_rate_idx + 1 >= rows
        || center_delay_idx + 1 >= cols
    {
        return None;
    }
    if rate_range.len() != rows || delay_range.len() != cols {
        return None;
    }

    let rate_bounds = window_bounds(rrange);
    let delay_bounds = window_bounds(drange);
    for dy in -1isize..=1 {
        for dx in -1isize..=1 {
            let r_idx = (center_rate_idx as isize + dy) as usize;
            let d_idx = (center_delay_idx as isize + dx) as usize;
            if !in_window(rate_range[r_idx], rate_bounds)
                || !in_window(delay_range[d_idx], delay_bounds)
                || in_delay_rate_mask(delay_range[d_idx], rate_range[r_idx], mask)
            {
                return None;
            }
        }
    }

    let f00 = norm_at(surface, center_rate_idx, center_delay_idx) as f64;
    let f_xm = norm_at(surface, center_rate_idx, center_delay_idx - 1) as f64;
    let f_xp = norm_at(surface, center_rate_idx, center_delay_idx + 1) as f64;
    let f_ym = norm_at(surface, center_rate_idx - 1, center_delay_idx) as f64;
    let f_yp = norm_at(surface, center_rate_idx + 1, center_delay_idx) as f64;
    let f_pp = norm_at(surface, center_rate_idx + 1, center_delay_idx + 1) as f64;
    let f_pm = norm_at(surface, center_rate_idx + 1, center_delay_idx - 1) as f64;
    let f_mp = norm_at(surface, center_rate_idx - 1, center_delay_idx + 1) as f64;
    let f_mm = norm_at(surface, center_rate_idx - 1, center_delay_idx - 1) as f64;

    let fx = 0.5 * (f_xp - f_xm);
    let fy = 0.5 * (f_yp - f_ym);
    let fxx = f_xp - 2.0 * f00 + f_xm;
    let fyy = f_yp - 2.0 * f00 + f_ym;
    let fxy = 0.25 * (f_pp - f_pm - f_mp + f_mm);

    let det = fxx * fyy - fxy * fxy;
    if !det.is_finite() || det.abs() < 1e-12 {
        return None;
    }
    // Negative definite Hessian is required for a local maximum.
    if !(fxx < 0.0 && fyy < 0.0 && det > 0.0) {
        return None;
    }

    let delta_delay_bin = -((fyy * fx) - (fxy * fy)) / det;
    let delta_rate_bin = ((fxy * fx) - (fxx * fy)) / det;
    if !delta_delay_bin.is_finite() || !delta_rate_bin.is_finite() {
        return None;
    }
    if delta_delay_bin.abs() > 1.0 || delta_rate_bin.abs() > 1.0 {
        return None;
    }

    let delay_step =
        (delay_range[center_delay_idx + 1] as f64 - delay_range[center_delay_idx - 1] as f64) * 0.5;
    let rate_step =
        (rate_range[center_rate_idx + 1] as f64 - rate_range[center_rate_idx - 1] as f64) * 0.5;
    if delay_step.abs() < 1e-12 || rate_step.abs() < 1e-12 {
        return None;
    }

    let refined_delay = delay_range[center_delay_idx] as f64 + delta_delay_bin * delay_step;
    let refined_rate = rate_range[center_rate_idx] as f64 + delta_rate_bin * rate_step;
    let refined_delay = refined_delay as f32;
    let refined_rate = refined_rate as f32;

    if !in_window(refined_delay, delay_bounds) || !in_window(refined_rate, rate_bounds) {
        return None;
    }

    Some((refined_delay, refined_rate))
}

#[derive(Debug, Clone)]
pub struct AnalysisResults {
    // Common
    pub yyyydddhhmmss1: String,
    pub source_name: String,
    pub length_f32: f32,
    pub ant1_az: f32,
    pub ant1_el: f32,
    pub ant1_hgt: f32,
    pub ant2_az: f32,
    pub ant2_el: f32,
    pub ant2_hgt: f32,
    pub mjd: f64,
    // Delay
    pub delay_range: Array1<f32>,
    pub visibility: Array1<f32>,
    pub delay_rate: Array1<f32>,
    pub delay_max_amp: f32,
    pub delay_phase: f32,
    pub delay_snr: f32,
    pub delay_noise: f32,
    pub residual_delay: f32,
    pub corrected_delay: f32,
    pub delay_offset: f32,
    // Frequency
    pub freq_max_amp: f32,
    pub freq_phase: f32,
    pub freq_freq: f32,
    pub freq_snr: f32,
    pub freq_noise: f32,
    pub freq_rate: Array1<f32>,
    pub freq_rate_spectrum: Array1<C32>,
    pub freq_range: Array1<f32>,
    pub freq_max_freq: f32,
    pub residual_rate: f32,
    pub corrected_rate: f32,
    pub rate_offset: f32,
    // Add new fields here
    // pub residual_acel: f32,
    pub corrected_acel: f32,
    // Ranges
    pub rate_range: Vec<f32>,
    // Sky Coordinates
    #[allow(dead_code)]
    pub l_coord: f64,
    #[allow(dead_code)]
    pub m_coord: f64,
}

pub fn analyze_results(
    freq_rate_array: &Array2<C32>,
    delay_rate_array: &Array2<C32>,
    header: &CorHeader,
    length: i32,
    effective_integ_time: f32,
    obs_time: &DateTime<Utc>,
    padding_length: usize,
    args: &Args,
    search_mode: Option<&str>,
) -> AnalysisResults {
    let fft_point_half = freq_rate_array.dim().0;
    let fft_point_usize = fft_point_half * 2;
    let fft_point_f32 = fft_point_usize as f32;
    let length_f32 = length as f32;
    let padding_length_half = padding_length / 2;

    // --- Ranges ---
    let delay_range = Array::linspace(
        -(fft_point_f32 / 2.0) + 1.0,
        fft_point_f32 / 2.0,
        fft_point_usize,
    );

    let freq_step_mhz = (header.sampling_speed as f32 / header.fft_point as f32) / 1_000_000.0;
    let freq_range = Array1::from_iter((0..fft_point_half).map(|i| i as f32 * freq_step_mhz));
    let rate_range = rate_cal(padding_length as f32, effective_integ_time);
    let keep_delay_profiles = args.plot && !args.frequency;
    let keep_freq_profiles = args.plot && args.frequency;
    let keep_freq_spectrum =
        args.frequency || args.spectrum || args.bandpass_table || !args.multi_sideband.is_empty();
    let skip_delay_plane_analysis =
        args.frequency && search_mode.is_none() && args.drange.is_empty();
    let rate_padding_noise_scale = (args.rate_padding.max(1) as f32).sqrt();

    // --- Delay Analysis ---
    let delay_array_mean = if skip_delay_plane_analysis {
        C32::new(0.0, 0.0)
    } else {
        delay_rate_array
            .mean()
            .unwrap_or_else(|| C32::new(0.0, 0.0))
    };
    let mut delay_noise_raw_from_peak_scan = None;
    let delay_rate_mask = if args.frequency {
        None
    } else {
        delay_rate_mask_bounds(&args.mask)
    };

    let (peak_rate_idx, peak_delay_idx) = if skip_delay_plane_analysis {
        (padding_length_half, fft_point_half - 1)
    } else if !args.drange.is_empty() || !args.rrange.is_empty() {
        // Case 3: Window options are specified (either/both), search within them.
        let (delay_win_low, delay_win_high) = if !args.drange.is_empty() {
            (args.drange[0], args.drange[1])
        } else {
            (
                delay_range[0],
                *delay_range.last().unwrap_or(&delay_range[0]),
            )
        };
        let (rate_win_low, rate_win_high) = if !args.rrange.is_empty() {
            (args.rrange[0], args.rrange[1])
        } else {
            (rate_range[0], *rate_range.last().unwrap_or(&rate_range[0]))
        };

        let mut max_power_in_window = 0.0f32;
        let mut temp_peak_rate_idx = padding_length_half;
        let mut temp_peak_delay_idx = fft_point_half;

        for r_idx in 0..rate_range.len() {
            if rate_range[r_idx] >= rate_win_low && rate_range[r_idx] <= rate_win_high {
                for d_idx in 0..delay_range.len() {
                    if delay_range[d_idx] >= delay_win_low && delay_range[d_idx] <= delay_win_high {
                        if in_delay_rate_mask(
                            delay_range[d_idx],
                            rate_range[r_idx],
                            delay_rate_mask,
                        ) {
                            continue;
                        }
                        let current_power = norm_sqr_at(delay_rate_array, r_idx, d_idx);
                        if current_power > max_power_in_window {
                            max_power_in_window = current_power;
                            temp_peak_rate_idx = r_idx;
                            temp_peak_delay_idx = d_idx;
                        }
                    }
                }
            }
        }
        (temp_peak_rate_idx, temp_peak_delay_idx)
    } else if matches!(search_mode, Some("peak") | Some("deep") | Some("deep2")) {
        // Case 2: --search or --search_deep is specified, no window. Find the global maximum.
        let (mut max_power, mut max_r_idx, mut max_d_idx) = (0.0f32, 0, 0);
        let mut noise_abs_dev_sum = 0.0f32;
        let mut noise_count = 0usize;
        for r_idx in 0..delay_rate_array.shape()[0] {
            for d_idx in 0..delay_rate_array.shape()[1] {
                let value = delay_rate_array[[r_idx, d_idx]];
                noise_abs_dev_sum += (value - delay_array_mean).norm();
                noise_count += 1;
                if in_delay_rate_mask(delay_range[d_idx], rate_range[r_idx], delay_rate_mask) {
                    continue;
                }
                let current_power = value.norm_sqr();
                if current_power > max_power {
                    max_power = current_power;
                    max_r_idx = r_idx;
                    max_d_idx = d_idx;
                }
            }
        }
        if noise_count > 0 {
            delay_noise_raw_from_peak_scan = Some(noise_abs_dev_sum / noise_count as f32);
        }
        (max_r_idx, max_d_idx)
    } else if delay_rate_mask.is_some() {
        let (mut max_power, mut max_r_idx, mut max_d_idx) =
            (0.0f32, padding_length_half, fft_point_half - 1);
        for r_idx in 0..delay_rate_array.shape()[0] {
            for d_idx in 0..delay_rate_array.shape()[1] {
                if in_delay_rate_mask(delay_range[d_idx], rate_range[r_idx], delay_rate_mask) {
                    continue;
                }
                let current_power = norm_sqr_at(delay_rate_array, r_idx, d_idx);
                if current_power > max_power {
                    max_power = current_power;
                    max_r_idx = r_idx;
                    max_d_idx = d_idx;
                }
            }
        }
        (max_r_idx, max_d_idx)
    } else {
        // Case 1: No window and no --search. Use the center point (delay=0, rate=0).
        (padding_length_half, fft_point_half - 1)
    };

    let delay_noise = if skip_delay_plane_analysis {
        f32::EPSILON
    } else {
        let delay_noise_raw = delay_noise_raw_from_peak_scan
            .unwrap_or_else(|| noise_level(delay_rate_array.view(), delay_array_mean));
        positive_or_epsilon(delay_noise_raw * rate_padding_noise_scale)
    };

    let delay_max_amp = if skip_delay_plane_analysis {
        0.0
    } else {
        norm_at(delay_rate_array, peak_rate_idx, peak_delay_idx)
    };
    let delay_phase = if skip_delay_plane_analysis {
        0.0
    } else {
        safe_arg(&delay_rate_array[[peak_rate_idx, peak_delay_idx]]).to_degrees()
    };
    let delay_rate_slice = if keep_delay_profiles {
        Array1::from_iter(
            (0..delay_rate_array.shape()[0])
                .map(|r_idx| norm_at(delay_rate_array, r_idx, peak_delay_idx)),
        )
    } else {
        Array1::zeros(0)
    };
    let refined_peak_3x3 = if search_mode == Some("peak") && !args.frequency {
        refine_peak_3x3_quadratic(
            delay_rate_array,
            peak_rate_idx,
            peak_delay_idx,
            &rate_range,
            &delay_range,
            &args.rrange,
            &args.drange,
            delay_rate_mask,
        )
    } else {
        None
    };

    let mut residual_delay_val: f32 = delay_range[peak_delay_idx];
    let mut delay_offset = 0.0;
    if search_mode == Some("peak") {
        if let Some((refined_delay, _)) = refined_peak_3x3 {
            delay_offset = refined_delay;
            residual_delay_val = refined_delay;
        } else {
            // Fallback: 1D quadratic fitting on delay axis using center +/- 1 bins.
            let mut x_coords: Vec<f64> = Vec::new();
            let mut y_values: Vec<f64> = Vec::new();
            let delay_bounds = window_bounds(&args.drange);

            for i in -1isize..=1 {
                let current_idx = peak_delay_idx as isize + i;
                if current_idx >= 0 && current_idx < delay_range.len() as isize {
                    let d_idx = current_idx as usize;
                    let delay_val = delay_range[d_idx];
                    if in_window(delay_val, delay_bounds)
                        && !in_delay_rate_mask(
                            delay_val,
                            rate_range[peak_rate_idx],
                            delay_rate_mask,
                        )
                    {
                        x_coords.push(delay_val as f64);
                        y_values.push(norm_at(delay_rate_array, peak_rate_idx, d_idx) as f64);
                    }
                }
            }

            if x_coords.len() >= 3 {
                if let Ok(fit_result) = fitting::fit_quadratic_least_squares(&x_coords, &y_values) {
                    delay_offset = fit_result.peak_x as f32;
                    residual_delay_val = delay_offset;
                } else {
                    eprintln!("Warning: Quadratic fitting for delay failed. Using original peak.");
                }
            }
        }
    }

    let delay_snr = if skip_delay_plane_analysis {
        0.0
    } else {
        delay_max_amp / delay_noise
    };
    let visibility = if keep_delay_profiles {
        Array1::from_iter(
            (0..delay_rate_array.shape()[1])
                .map(|d_idx| norm_at(delay_rate_array, peak_rate_idx, d_idx)),
        )
    } else {
        Array1::zeros(0)
    };

    let mut residual_rate_val: f32;
    let mut rate_offset = 0.0;

    // --- Frequency Analysis ---

    let (peak_freq_row_idx, peak_rate_col_idx) = if !args.frequency {
        let peak_rate_col_idx = peak_rate_idx.min(freq_rate_array.shape()[1].saturating_sub(1));
        (0, peak_rate_col_idx)
    } else if !args.rrange.is_empty() || !args.frange.is_empty() {
        // Case 3: Window option is specified.
        let (rate_win_low, rate_win_high) = if !args.rrange.is_empty() {
            (args.rrange[0], args.rrange[1])
        } else {
            (rate_range[0], *rate_range.last().unwrap_or(&rate_range[0]))
        };
        let (freq_win_low, freq_win_high) = if args.frange.len() == 2 {
            (args.frange[0], args.frange[1])
        } else {
            (freq_range[0], *freq_range.last().unwrap_or(&freq_range[0]))
        };

        let mut max_power_in_window = 0.0f32;
        let mut temp_peak_freq_row_idx = 0;
        let mut temp_peak_rate_col_idx = padding_length_half;

        for r_idx in 0..rate_range.len() {
            if rate_range[r_idx] >= rate_win_low && rate_range[r_idx] <= rate_win_high {
                for f_idx in 0..freq_range.len() {
                    let freq_mhz = freq_range[f_idx];
                    if freq_mhz < freq_win_low || freq_mhz > freq_win_high {
                        continue;
                    }
                    let current_power = norm_sqr_at(freq_rate_array, f_idx, r_idx);
                    if current_power > max_power_in_window {
                        max_power_in_window = current_power;
                        temp_peak_freq_row_idx = f_idx;
                        temp_peak_rate_col_idx = r_idx;
                    }
                }
            }
        }
        (temp_peak_freq_row_idx, temp_peak_rate_col_idx)
    } else if matches!(search_mode, Some("peak") | Some("deep") | Some("deep2")) {
        // Case 2: --search or --search_deep is specified, no window. Find the global maximum.
        let (mut max_power, mut max_f_idx, mut max_r_idx) = (0.0f32, 0, 0);
        let (freq_win_low, freq_win_high) = if args.frange.len() == 2 {
            (args.frange[0], args.frange[1])
        } else {
            (freq_range[0], *freq_range.last().unwrap_or(&freq_range[0]))
        };
        for f_idx in 0..freq_rate_array.shape()[0] {
            let freq_mhz = freq_range[f_idx];
            if freq_mhz < freq_win_low || freq_mhz > freq_win_high {
                continue;
            }
            for r_idx in 0..freq_rate_array.shape()[1] {
                let current_power = norm_sqr_at(freq_rate_array, f_idx, r_idx);
                if current_power > max_power {
                    max_power = current_power;
                    max_f_idx = f_idx;
                    max_r_idx = r_idx;
                }
            }
        }
        (max_f_idx, max_r_idx)
    } else {
        // Case 1: No window and no --search. Use the center point (rate=0) and find max frequency.
        let (max_f_idx, _) =
            (0..freq_rate_array.shape()[0]).fold((0, 0.0f32), |(i_max, v_max), i| {
                let v = norm_sqr_at(freq_rate_array, i, padding_length_half);
                if v > v_max {
                    (i, v)
                } else {
                    (i_max, v_max)
                }
            });
        (max_f_idx, padding_length_half)
    };

    let freq_max_amp = if args.frequency {
        norm_at(freq_rate_array, peak_freq_row_idx, peak_rate_col_idx)
    } else {
        0.0
    };
    let freq_phase = if args.frequency {
        safe_arg(&freq_rate_array[[peak_freq_row_idx, peak_rate_col_idx]]).to_degrees()
    } else {
        0.0
    };
    let mut freq_freq = freq_range[peak_freq_row_idx];

    // Calculate noise from regions away from the peak rate
    let freq_noise_raw = if args.frequency {
        let peak_rate_hz = rate_range[peak_rate_col_idx];
        let noise_rate_threshold = 0.1; // Hz

        let mut noise_sum = C32::new(0.0, 0.0);
        let mut noise_count = 0usize;
        for (r_idx, &rate_val) in rate_range.iter().enumerate() {
            if (rate_val - peak_rate_hz).abs() > noise_rate_threshold {
                for f_idx in 0..freq_rate_array.shape()[0] {
                    noise_sum += freq_rate_array[[f_idx, r_idx]];
                    noise_count += 1;
                }
            }
        }

        if noise_count > 0 {
            let noise_mean = noise_sum / noise_count as f32;
            let mut noise_abs_dev_sum = 0.0f32;
            for (r_idx, &rate_val) in rate_range.iter().enumerate() {
                if (rate_val - peak_rate_hz).abs() > noise_rate_threshold {
                    for f_idx in 0..freq_rate_array.shape()[0] {
                        noise_abs_dev_sum += (freq_rate_array[[f_idx, r_idx]] - noise_mean).norm();
                    }
                }
            }
            noise_abs_dev_sum / noise_count as f32
        } else {
            // Fallback to old method if no noise region is found
            eprintln!("Warning: Could not find noise region for frequency SNR calculation. Falling back to old method.");
            noise_level(freq_rate_array.view(), freq_rate_array.mean().unwrap())
        }
    } else {
        f32::EPSILON
    };

    if args.frequency && search_mode == Some("peak") {
        let center_idx = peak_freq_row_idx as isize;
        if center_idx > 0 && center_idx + 1 < freq_range.len() as isize {
            let left_idx = (center_idx - 1) as usize;
            let mid_idx = center_idx as usize;
            let right_idx = (center_idx + 1) as usize;

            let y_left = norm_at(freq_rate_array, left_idx, peak_rate_col_idx) as f64;
            let y_mid = norm_at(freq_rate_array, mid_idx, peak_rate_col_idx) as f64;
            let y_right = norm_at(freq_rate_array, right_idx, peak_rate_col_idx) as f64;

            let is_local_max = y_mid.is_finite()
                && y_left.is_finite()
                && y_right.is_finite()
                && y_mid >= y_left
                && y_mid >= y_right;
            let side_max = y_left.max(y_right);
            // For near-delta peaks at very high frequency resolution, 3-point quadratic fitting
            // becomes numerically unstable and adds little value. Skip fitting in that regime.
            let is_delta_like = y_mid > 0.0 && (side_max / y_mid) < 0.02;

            if is_local_max && !is_delta_like {
                let x_coords = vec![
                    freq_range[left_idx] as f64,
                    freq_range[mid_idx] as f64,
                    freq_range[right_idx] as f64,
                ];
                let y_values = vec![y_left, y_mid, y_right];
                if let Ok(fit_result) = fitting::fit_quadratic_least_squares(&x_coords, &y_values) {
                    let x_min = x_coords[0].min(x_coords[2]);
                    let x_max = x_coords[0].max(x_coords[2]);
                    if fit_result.peak_x >= x_min && fit_result.peak_x <= x_max {
                        freq_freq = fit_result.peak_x as f32;
                    }
                }
            }
        }
    }

    let freq_noise = positive_or_epsilon(freq_noise_raw * rate_padding_noise_scale);
    let freq_snr = freq_max_amp / freq_noise;
    let freq_rate = if keep_freq_profiles {
        Array1::from_iter(
            (0..freq_rate_array.shape()[1])
                .map(|r_idx| norm_at(freq_rate_array, peak_freq_row_idx, r_idx)),
        )
    } else {
        Array1::zeros(0)
    };
    let freq_rate_spectrum = if keep_freq_spectrum {
        freq_rate_array.column(peak_rate_col_idx).to_owned()
    } else {
        Array1::zeros(0)
    };

    // Set the final residual_rate_val based on the mode
    if args.frequency {
        residual_rate_val = rate_range[peak_rate_col_idx];
    } else {
        residual_rate_val = rate_range[peak_rate_idx];
    };

    if search_mode == Some("peak") {
        if args.length == 1 {
            // When length is 1, rate fitting is unstable, so force residual_rate to 0.
            //eprintln!("Warning: Rate fitting is skipped because --length is 1. Residual rate is set to 0.");
            residual_rate_val = 0.0;
            rate_offset = 0.0;
        } else if args.frequency {
            let mut x_coords: Vec<f64> = Vec::new();
            let mut y_values: Vec<f64> = Vec::new();
            let rate_bounds = window_bounds(&args.rrange);
            for i in -1isize..=1 {
                let current_idx = peak_rate_col_idx as isize + i;
                if current_idx >= 0 && current_idx < rate_range.len() as isize {
                    let r_idx = current_idx as usize;
                    let rate_val = rate_range[r_idx];
                    if in_window(rate_val, rate_bounds) {
                        x_coords.push(rate_val as f64);
                        y_values.push(norm_at(freq_rate_array, peak_freq_row_idx, r_idx) as f64);
                    }
                }
            }

            let rate_scale_factor = (10.0 * padding_length as f64) * effective_integ_time as f64;
            let scaled_x_coords: Vec<f64> =
                x_coords.iter().map(|&x| x * rate_scale_factor).collect();

            if scaled_x_coords.len() >= 3 {
                if let Ok(fit_result) =
                    fitting::fit_quadratic_least_squares(&scaled_x_coords, &y_values)
                {
                    rate_offset = (fit_result.peak_x / rate_scale_factor) as f32;
                    residual_rate_val = rate_offset;
                }
            }
        } else if let Some((_, refined_rate)) = refined_peak_3x3 {
            rate_offset = refined_rate;
            residual_rate_val = refined_rate;
        } else {
            let mut x_coords: Vec<f64> = Vec::new();
            let mut y_values: Vec<f64> = Vec::new();
            let rate_bounds = window_bounds(&args.rrange);
            for i in -1isize..=1 {
                let current_idx = peak_rate_idx as isize + i;
                if current_idx >= 0 && current_idx < rate_range.len() as isize {
                    let r_idx = current_idx as usize;
                    let rate_val = rate_range[r_idx];
                    if in_window(rate_val, rate_bounds)
                        && !in_delay_rate_mask(
                            delay_range[peak_delay_idx],
                            rate_val,
                            delay_rate_mask,
                        )
                    {
                        x_coords.push(rate_val as f64);
                        y_values.push(delay_rate_array[[r_idx, peak_delay_idx]].norm() as f64);
                    }
                }
            }

            let rate_scale_factor = (10.0 * padding_length as f64) * effective_integ_time as f64;
            let scaled_x_coords: Vec<f64> =
                x_coords.iter().map(|&x| x * rate_scale_factor).collect();

            if scaled_x_coords.len() >= 3 {
                if let Ok(fit_result) =
                    fitting::fit_quadratic_least_squares(&scaled_x_coords, &y_values)
                {
                    rate_offset = (fit_result.peak_x / rate_scale_factor) as f32;
                    residual_rate_val = rate_offset;
                }
            }
        }
    }

    // --- Sky Coordinate Calculation ---
    let (u, v, _w, du_dt, dv_dt) = uvw_cal(
        header.station1_position,
        header.station2_position,
        *obs_time,
        header.source_position_ra,
        header.source_position_dec,
        true,
    );

    let (l_coord, m_coord) = rate_delay_to_lm(
        residual_rate_val as f64,
        residual_delay_val as f64,
        header,
        u,
        v,
        du_dt,
        dv_dt,
    );

    // --- Antenna Az/El Calculation ---
    let (ant1_az, ant1_el, ant1_hgt) = radec2azalt(
        [
            header.station1_position[0] as f32,
            header.station1_position[1] as f32,
            header.station1_position[2] as f32,
        ],
        *obs_time,
        header.source_position_ra as f32,
        header.source_position_dec as f32,
    );
    let (ant2_az, ant2_el, ant2_hgt) = radec2azalt(
        [
            header.station2_position[0] as f32,
            header.station2_position[1] as f32,
            header.station2_position[2] as f32,
        ],
        *obs_time,
        header.source_position_ra as f32,
        header.source_position_dec as f32,
    );

    AnalysisResults {
        yyyydddhhmmss1: obs_time.format("%Y/%j %H:%M:%S").to_string(),
        source_name: header.source_name.clone(),
        length_f32,
        ant1_az: ant1_az as f32,
        ant1_el: ant1_el as f32,
        ant1_hgt: ant1_hgt as f32,
        ant2_az: ant2_az as f32,
        ant2_el: ant2_el as f32,
        ant2_hgt: ant2_hgt as f32,
        mjd: mjd_cal(*obs_time),
        delay_range,
        visibility,
        delay_rate: delay_rate_slice,
        delay_max_amp,
        delay_phase,
        delay_snr,
        delay_noise,
        residual_delay: residual_delay_val,
        corrected_delay: args.delay_correct,
        delay_offset,
        freq_max_amp,
        freq_phase,
        freq_freq,
        freq_snr,
        freq_noise,
        freq_rate,
        freq_rate_spectrum,
        freq_range,
        freq_max_freq: freq_freq,
        residual_rate: residual_rate_val,
        corrected_rate: args.rate_correct,
        rate_offset,
        // Initialize new fields
        // residual_acel: 0.0, // Placeholder
        corrected_acel: args.acel_correct,
        rate_range,
        l_coord,
        m_coord,
    }
}