;+ ; NAME: ; DLASOLVE ; PURPOSE: ; Given the DELAY CENTER offsets for each baseline, solve for the best ; values of DELAY CENTERs. ; CATEGORY: ; OVRO APC CALIBRATION ; CALLING SEQUENCE: ; dlasolve,d,ss,r ; INPUTS: ; d the delay centers for each antenna, as given in the CONFIG ; segment, corresponding to the value in force at the time ; of the observations. ; ss the delay shifts determined by DLAFIT routine. ; OPTIONAL (KEYWORD) INPUT PARAMETERS: ; ROUTINES CALLED: ; openarc, getdata, lasthrec, tl_decode, decode, get_cycle, congrid ; OUTPUTS: ; r the updated delay values, which are to replace the current ; values in D. ; COMMENTS: ; This routine is very specific to the MUX sequence. Currently two ; MUX sequences are defined, one for 5-element and one for 6-element. ; The channel assignments are: ; ; 5-element MUX sequence, 124, 125, 126, 456 yields: ; abchan = [ 5,19] ; Baselines 12 and 45 ; bcchan = [13,15,17,23] ; Baselines 24, 25, 26, 56 ; cachan = [ 7, 9,11,21] ; Baselines 14, 15, 16, 46 ; ; 6-element MUX sequence, 457, 456, 124, 125, 167, 267 yields: ; abchan = [ 6,12,20,24] ; Baselines 12, 16, 26, 45 ; bcchan = [16,18,30,32,34] ; Baselines 24, 25, 56, 57, 67 ; cachan = [ 8,10,14,22,26,28] ; Baselines 14, 15, 17, 27, 46, 47 ; ; SIDE EFFECTS: ; RESTRICTIONS: ; MODIFICATION HISTORY: ; Written 22-May-2000 by Dale Gary ; Adapted from DLAFITSYS routine ; 10-Jan-2001 DG ; Added A and B channel delays as d[6] and d[7], for 6-element data ; 10-Jul-2004 DG ; Added a case for 7-element data. This also needs to be able to handle ; missing values. ;- pro dlasolve, d,ss,r,new=new s = indgen(120)/2 - 30 nant = n_elements(d)-2 ; if (nant gt 6) then nant = 6 ; The following patterns apply. ; ; The equations to be solved are: ; For AB baselines ; D_B - D_A + B_AB - A_AB = T_B - T_A ; e.g. D_5 - D_4 + B_45 - A_45 = T_5 - T_4 for 45 baseline ; For BC baselines ; D_B - D_C + B_BC = T_B - T_C ; e.g. D_2 - D_4 + B_24 = T_2 - T_4 for 24 baseline ; For CA baselines ; D_B - D_C + A_AC = T_A - T_C ; e.g. D_1 - D_4 + A_14 = T_1 - T_4 for 14 baseline ; ; Here, the D's are the current delays from the CONFIG segment, the A's and B's are derived ; from the delay center shifts (SS) in a rather complicated way (see DELAY SCAN documentation), ; and the T's are the new delays to be solved for. ; The following code is very specific to the MUX sequence case nant of 5: begin ; Set up column vector C and matrix M for 5-element data, representing the ; existing MUX sequence described in the header ; Derive the A's and B's from the delay center shifts a12 = ( s[ss[0] + 60.0]) ; AB baseline (12) b12 = (-s[ss[0] + 61.0]) ; AB baseline (12) a14 = ss[1] ; CA baseline (14) a15 = ss[2] ; CA baseline (15) a16 = ss[3] ; CA baseline (16) b24 = ss[4] ; BC baseline (24) b25 = ss[5] ; BC baseline (25) b26 = ss[6] ; BC baseline (26) a45 = ( s[ss[7] + 60.0]) ; AB baseline (45) b45 = (-s[ss[7] + 61.0]) ; AB baseline (45) a46 = ss[8] ; CA baseline (46) b56 = ss[9] ; BC baseline (56) ; Set up the column vector C, representing the left-hand-side of the above equations. ; The order is arbitrary, but MUST agree with order of matrix entries below. c = fltarr(10) c[0] = d[0] - d[2] + a14 c[1] = d[0] - d[3] + a15 c[2] = d[0] - d[4] + a16 c[3] = d[1] - d[2] + b24 c[4] = d[1] - d[3] + b25 c[5] = d[1] - d[4] + b26 c[6] = d[1] - d[0] + b12 - a12 c[7] = d[2] - d[4] + a46 c[8] = d[3] - d[4] + b56 c[9] = d[3] - d[2] + b45 - a45 ; Set up the matrix M, representing the right-hand-side of the above equations. ; These are simply the coefficients of the T's, either +/- 1. This is an ; NANT x NBL matrix M = [[ 1, 0,-1, 0, 0], $ [ 1, 0, 0,-1, 0], $ [ 1, 0, 0, 0,-1], $ [ 0, 1,-1, 0, 0], $ [ 0, 1, 0,-1, 0], $ [ 0, 1, 0, 0,-1], $ [-1, 1, 0, 0, 0], $ [ 0, 0, 1, 0,-1], $ [ 0, 0, 0, 1,-1], $ [ 0, 0,-1, 1, 0]] end 6: begin if (new eq 0) then begin ; The equations to be solved are: ; For AB baselines ; D_B - D_A + D_b - D_a + B_AB - A_AB = T_B - T_A + T_b - T_a ; e.g. D_5 - D_4 + D_b - D_a + B_45 - A_45 = T_5 - T_4 + T_b - T_a for 45 baseline ; For BC baselines ; D_B - D_C + D_b + B_BC = T_B - T_C + T_b ; e.g. D_2 - D_4 + D_b + B_24 = T_2 - T_4 + T_b for 24 baseline ; For CA baselines ; D_A - D_C + D_a + A_AC = T_A - T_C + T_a ; e.g. D_1 - D_4 + D_a + A_14 = T_1 - T_4 + T_a for 14 baseline ; ; This is the same as above, except the original channel offsets D_a and D_b and the ; new channel offsets T_a and T_b have been included. ; Set up column vector C and matrix M for 6-element data, representing the ; existing MUX sequence described in the header ; Derive the A's and B's from the delay center shifts a12 = ( s[ss[0] + 60.0]) ; AB baseline (12) b12 = (-s[ss[0] + 61.0]) ; AB baseline (12) a14 = ss[1] ; CA baseline (14) a15 = ss[2] ; CA baseline (15) a16 = ( s[ss[3] + 60.0]) ; AB baseline (16) b16 = (-s[ss[3] + 61.0]) ; AB baseline (16) a17 = ss[4] ; CA baseline (17) b24 = ss[5] ; BC baseline (24) b25 = ss[6] ; BC baseline (25) a26 = ( s[ss[7] + 60.0]) ; AB baseline (26) b26 = (-s[ss[7] + 61.0]) ; AB baseline (26) a27 = ss[8] ; CA baseline (27) a45 = ( s[ss[9] + 60.0]) ; AB baseline (45) b45 = (-s[ss[9] + 61.0]) ; AB baseline (45) a46 = ss[10] ; CA baseline (46) a47 = ss[11] ; CA baseline (47) b56 = ss[12] ; BC baseline (56) b57 = ss[13] ; BC baseline (57) b67 = ss[14] ; BC baseline (67) ; Set up the column vector C, representing the left-hand-side of the above equations. ; The order is arbitrary, but MUST agree with order of matrix entries below. c = fltarr(15) c[0] = d[0] - d[2] + d[6] + a14 c[1] = d[0] - d[3] + d[6] + a15 c[2] = d[4] - d[0] + d[7] - d[6] + b16 - a16 c[3] = d[1] - d[2] + d[7] + b24 c[4] = d[1] - d[3] + d[7] + b25 c[5] = d[4] - d[1] + d[7] - d[6] + b26 - a26 c[6] = d[1] - d[0] + d[7] - d[6] + b12 - a12 c[7] = d[2] - d[4] + d[6] + a46 c[8] = d[3] - d[4] + d[7] + b56 c[9] = d[3] - d[2] + d[7] - d[6] + b45 - a45 c[10] = d[0] - d[5] + d[6] + a17 c[11] = d[1] - d[5] + d[6] + a27 c[12] = d[2] - d[5] + d[6] + a47 c[13] = d[3] - d[5] + d[7] + b57 c[14] = d[4] - d[5] + d[7] + b67 ; Set up the matrix M, representing the right-hand-side of the above equations. ; These are simply the coefficients of the T's, either +/- 1. This is an ; NANT x NBL matrix M = [[ 1, 0,-1, 0, 0, 0, 1, 0], $ [ 1, 0, 0,-1, 0, 0, 1, 0], $ [-1, 0, 0, 0, 1, 0,-1, 1], $ [ 0, 1,-1, 0, 0, 0, 0, 1], $ [ 0, 1, 0,-1, 0, 0, 0, 1], $ [ 0,-1, 0, 0, 1, 0,-1, 1], $ [-1, 1, 0, 0, 0, 0,-1, 1], $ [ 0, 0, 1, 0,-1, 0, 1, 0], $ [ 0, 0, 0, 1,-1, 0, 0, 1], $ [ 0, 0,-1, 1, 0, 0,-1, 1], $ [ 1, 0, 0, 0, 0,-1, 1, 0], $ [ 0, 1, 0, 0, 0,-1, 1, 0], $ [ 0, 0, 1, 0, 0,-1, 1, 0], $ [ 0, 0, 0, 1, 0,-1, 0, 1], $ [ 0, 0, 0, 0, 1,-1, 0, 1]] endif else begin ; Set up column vector C and matrix M for 6-element data, representing the ; existing MUX sequence described in the header ; Derive the A's and B's from the delay center shifts b12 = ss[0] ; BC baseline (12) a14 = ss[1] ; CA baseline (14) a15 = ( s[ss[2] + 60.0]) ; AB baseline (15) b15 = (-s[ss[2] + 61.0]) ; AB baseline (15) a16 = ss[3] ; CA baseline (16) a17 = ss[4] ; CA baseline (17) a24 = ( s[ss[5] + 60.0]) ; AB baseline (24) b24 = (-s[ss[5] + 61.0]) ; AB baseline (24) a25 = ( s[ss[6] + 60.0]) ; AB baseline (25) b25 = (-s[ss[6] + 61.0]) ; AB baseline (25) a26 = ss[7] ; CA baseline (26) a27 = ( s[ss[8] + 60.0]) ; AB baseline (27) b27 = (-s[ss[8] + 61.0]) ; AB baseline (27) b45 = ss[9] ; BC baseline (45) b46 = ss[10] ; BC baseline (46) a47 = ( s[ss[11] + 60.0]) ; AB baseline (47) b47 = (-s[ss[11] + 61.0]) ; AB baseline (47) b56 = ss[12] ; BC baseline (56) a57 = ss[13] ; CA baseline (57) a67 = ss[14] ; CA baseline (67) ; Set up the column vector C, representing the left-hand-side of the above equations. ; The order is arbitrary, but MUST agree with order of matrix entries below. c = fltarr(15) c[0] = d[1] - d[0] + d[7] + b12 c[1] = d[2] - d[0] + d[6] + a14 c[2] = d[3] - d[0] + d[7] - d[6] + b15 - a15 c[3] = d[0] - d[4] + d[6] + a16 c[4] = d[5] - d[0] + d[6] + a17 c[5] = d[1] - d[2] + d[7] - d[6] + b24 - a24 c[6] = d[3] - d[1] + d[7] - d[6] + b25 - a25 c[7] = d[1] - d[4] + d[6] + a26 c[8] = d[1] - d[5] + d[7] - d[6] + b27 - a27 c[9] = d[2] - d[3] + d[7] + b45 c[10] = d[2] - d[4] + d[7] + b46 c[11] = d[2] - d[5] + d[7] - d[6] + b47 - a47 c[12] = d[3] - d[4] + d[7] + b56 c[13] = d[5] - d[3] + d[6] + a57 c[14] = d[5] - d[4] + d[6] + a67 ; Set up the matrix M, representing the right-hand-side of the above equations. ; These are simply the coefficients of the T's, either +/- 1. This is an ; NANT x NBL matrix M = [[-1, 1, 0, 0, 0, 0, 0, 1], $ [-1, 0, 1, 0, 0, 0, 1, 0], $ [-1, 0, 0, 1, 0, 0,-1, 1], $ [ 1, 0, 0, 0,-1, 0, 1, 0], $ [-1, 0, 0, 0, 0, 1, 1, 0], $ [ 0, 1,-1, 0, 0, 0,-1, 1], $ [ 0,-1, 0, 1, 0, 0,-1, 1], $ [ 0, 1, 0, 0,-1, 0, 1, 0], $ [ 0, 1, 0, 0, 0,-1,-1, 1], $ [ 0, 0, 1,-1, 0, 0, 0, 1], $ [ 0, 0, 1, 0,-1, 0, 0, 1], $ [ 0, 0, 1, 0, 0,-1,-1, 1], $ [ 0, 0, 0, 1,-1, 0, 0, 1], $ [ 0, 0, 0,-1, 0, 1, 1, 0], $ [ 0, 0, 0, 0,-1, 1, 1, 0]] endelse end 7: begin ; Set up column vector C and matrix M for 6-element data, representing the ; existing MUX sequence described in the header ; Derive the A's and B's from the delay center shifts b12 = ss[0] ; BC baseline (12) a14 = ( s[ss[1] + 60.0]) ; AB baseline (14) b14 = (-s[ss[1] + 61.0]) ; AB baseline (14) a15 = ( s[ss[2] + 60.0]) ; AB baseline (15) b15 = (-s[ss[2] + 61.0]) ; AB baseline (15) a16 = ss[3] ; CA baseline (16) a17 = ss[4] ; CA baseline (17) a18 = ss[5] ; CA baseline (18) a24 = ( s[ss[6] + 60.0]) ; AB baseline (24) b24 = (-s[ss[6] + 61.0]) ; AB baseline (24) a25 = ( s[ss[7] + 60.0]) ; AB baseline (25) b25 = (-s[ss[7] + 61.0]) ; AB baseline (25) a26 = ss[8] ; CA baseline (26) a27 = ( s[ss[9] + 60.0]) ; AB baseline (27) b27 = (-s[ss[9] + 61.0]) ; AB baseline (27) a28 = ss[10] ; CA baseline (28) b45 = ss[11] ; BC baseline (45) b46 = ss[12] ; BC baseline (46) a47 = ( s[ss[13] + 60.0]) ; AB baseline (47) b47 = (-s[ss[13] + 61.0]) ; AB baseline (47) b48 = ss[14] ; BC baseline (48) b56 = ss[15] ; BC baseline (56) a57 = ss[16] ; CA baseline (57) b58 = ss[17] ; BC baseline (58) a67 = ( s[ss[18] + 60.0]) ; AB baseline (67) b67 = (-s[ss[18] + 61.0]) ; AB baseline (67) b68 = ss[19] ; BC baseline (68) a78 = ss[20] ; CA baseline (78) ; Set up the column vector C, representing the left-hand-side of the above equations. ; The order is arbitrary, but MUST agree with order of matrix entries below. c = fltarr(21) c[0] = d[1] - d[0] + d[8] + b12 c[1] = d[2] - d[0] + d[8] - d[7] + b14 - a14 c[2] = d[3] - d[0] + d[8] - d[7] + b15 - a15 c[3] = d[0] - d[4] + d[7] + a16 c[4] = d[5] - d[0] + d[7] + a17 c[5] = d[0] - d[6] + d[7] + a18 c[6] = d[2] - d[1] + d[8] - d[7] + b24 - a24 c[7] = d[3] - d[1] + d[8] - d[7] + b25 - a25 c[8] = d[1] - d[4] + d[7] + a26 c[9] = d[1] - d[5] + d[8] - d[7] + b27 - a27 c[10] = d[1] - d[6] + d[7] + a28 c[11] = d[2] - d[3] + d[8] + b45 c[12] = d[2] - d[4] + d[8] + b46 c[13] = d[2] - d[5] + d[8] - d[7] + b47 - a47 c[14] = d[2] - d[6] + d[8] + b48 c[15] = d[3] - d[4] + d[8] + b56 c[16] = d[5] - d[3] + d[7] + a57 c[17] = d[3] - d[6] + d[8] + b58 c[18] = d[4] - d[5] + d[8] - d[7] + b67 - a67 c[19] = d[4] - d[6] + d[8] + b68 c[20] = d[5] - d[6] + d[7] + a78 ; Set up the matrix M, representing the right-hand-side of the above equations. ; These are simply the coefficients of the T's, either +/- 1. This is an ; NANT x NBL matrix M = [[-1, 1, 0, 0, 0, 0, 0, 0, 1], $ [-1, 0, 1, 0, 0, 0, 0,-1, 1], $ [-1, 0, 0, 1, 0, 0, 0,-1, 1], $ [ 1, 0, 0, 0,-1, 0, 0, 1, 0], $ [-1, 0, 0, 0, 0, 1, 0, 1, 0], $ [ 1, 0, 0, 0, 0, 0,-1, 1, 0], $ [ 0,-1, 1, 0, 0, 0, 0,-1, 1], $ [ 0,-1, 0, 1, 0, 0, 0,-1, 1], $ [ 0, 1, 0, 0,-1, 0, 0, 1, 0], $ [ 0, 1, 0, 0, 0,-1, 0,-1, 1], $ [ 0, 1, 0, 0, 0, 0,-1, 1, 0], $ [ 0, 0, 1,-1, 0, 0, 0, 0, 1], $ [ 0, 0, 1, 0,-1, 0, 0, 0, 1], $ [ 0, 0, 1, 0, 0,-1, 0,-1, 1], $ [ 0, 0, 1, 0, 0, 0,-1, 0, 1], $ [ 0, 0, 0, 1,-1, 0, 0, 0, 1], $ [ 0, 0, 0,-1, 0, 1, 0, 1, 0], $ [ 0, 0, 0, 1, 0, 0,-1, 0, 1], $ [ 0, 0, 0, 0, 1,-1, 0,-1, 1], $ [ 0, 0, 0, 0, 1, 0,-1, 0, 1], $ [ 0, 0, 0, 0, 0, 1,-1, 1, 0]] end else: begin print,'DLASOLVE: Unexpected number of antennas: ',n_elements(d) return end endcase ; Solve the equations by means of Singular-Value-Decomposition. svdc, m, w, u, v,/double n = n_elements(w) wp = fltarr(n,n) for k = 0, n-1 do $ if abs(w(k)) ge 1.0e-5 then wp(k,k) = 1.0/w(k) ; This matrix equation actually provides the solution to the T's. Note that ; only differences in the values of T are relevant, so the results will be ; shifted relative to the reference antenna 6, whose delay is always zero by ; definition. t = reform(v ## wp ## TRANSPOSE(U) ## C) ; Shift the results (except for the channel offsets) by the refant (Ant 6) delay (t[4]) r = t r[0:nant-1] = t[0:nant-1] - t[4] end