# xCorr_max   xtlang

##### Implementation

```;This closure returns the lag for maximum cross correlation between 2 vectors.
;A result of 0 means that the initial samples of each vector are aligned.
;Negative numbers place vector 1 before vector 2
;Positive numbers place vector 1 after alignment of vector1(0) and vector2(0)
(bind-func xCorr_max:[i64,float*,i64,float*,i64]*
(lambda (vector1:float* len1:i64 vector2:float* len2:i64)
(let ((m:i64 0)
(n:i64 0)
(shift:i64 0)
(lag_max_xCorr:i64 0)
(max_pos:i64 0)
(sum_vec1_2:float 0.0)
(sum_vec2_2:float 0.0)
(denom:float 0.0)
(correlations:float* (salloc (- (+ len1 len2) 1)))
(lags:i64* (salloc (- (+ len1 len2) 1))))
(dotimes (n (- (+ len1 len2) 1))  ;initialise correlations to 0
(pset! correlations n 0.0))
(dotimes (shift (- (+ len1 len2) 1))
(pset! lags shift (- shift (- len1 1)))  ;store the shift value into lags
(cond ((< shift len2)
(dotimes (m (+ shift 1))
(pset! correlations shift (+ (pref correlations shift) (* (pref vector2 m) (pref vector1 (+ (- len1 1 shift) m)))))
(set! sum_vec1_2 (+ sum_vec1_2 (* (pref vector1 (+ (- len1 1 shift) m)) (pref vector1 (+ (- len1 1 shift) m)))))
(set! sum_vec2_2 (+ sum_vec2_2 (* (pref vector2 m) (pref vector2 m))))))
(else
(dotimes (m (- (+ len1 len2) (+ 1 shift)))
(pset! correlations shift (+ (pref correlations shift) (* (pref vector1 m) (pref vector2 (- (+ m shift 1) len1)))))
(set! sum_vec1_2 (+ sum_vec1_2 (* (pref vector1 m) (pref vector1 m))))
(set! sum_vec2_2 (+ sum_vec2_2 (* (pref vector2 (- (+ m shift 1) len1)) (pref vector2 (- (+ m shift 1) len1)))))
)))
(set! denom (sqrt (* sum_vec1_2 sum_vec2_2)))
(cond ((= denom 0.0) (pset! correlations shift 0.0))
(else (pset! correlations shift (/ (pref correlations shift) denom))))
(println (pref correlations shift))
(set! sum_vec1_2 0.0)
(set! sum_vec2_2 0.0))
;return the lag for maximum cross correlation
(set! max_pos (vmax_pos correlations (- (+ len1 len2) 1)))
(set! lag_max_xCorr (pref lags max_pos))
lag_max_xCorr)))
```