00000000  2f 2a 20 41 72 72 61 79  20 4c 69 62 72 61 72 79  |/* Array Library|
00000010  0a 20 20 20 53 65 65 20  61 72 72 61 79 2e 44 6f  |.   See array.Do|
00000020  63 20 66 6f 72 20 61 20  64 65 74 61 69 6c 65 64  |c for a detailed|
00000030  20 64 65 73 63 72 69 70  74 69 6f 6e 20 6f 66 20  | description of |
00000040  74 68 65 20 66 75 6e 63  74 69 6f 6e 73 2e 2a 2f  |the functions.*/|
00000050  0a 0a 66 6f 72 6d 5f 6d  61 74 72 69 78 28 6d 2c  |..form_matrix(m,|
00000060  6e 2c 76 29 0a 2f 2a 20  2d 2d 2d 2d 2d 2d 2d 2d  |n,v)./* --------|
00000070  2d 2d 2d 2d 2d 2d 2d 2d  2d 2d 2d 2d 2d 2d 2d 2d  |----------------|
*
00000090  2d 2d 2d 2d 2d 2d 2d 2d  2d 2d 2d 2d 0a 20 20 20  |------------.   |
000000a0  52 65 74 75 72 6e 73 20  61 6e 20 6d 20 78 20 6e  |Returns an m x n|
000000b0  20 6d 61 74 72 69 78 20  66 72 6f 6d 20 61 20 56  | matrix from a V|
000000c0  45 43 54 4f 52 20 76 20  6f 66 20 73 69 7a 65 20  |ECTOR v of size |
000000d0  6d 2a 6e 2c 0a 20 20 20  77 68 6f 73 65 20 72 6f  |m*n,.   whose ro|
000000e0  77 73 20 61 72 65 20 73  75 63 63 65 73 73 69 76  |ws are successiv|
000000f0  65 20 73 65 74 73 20 6f  66 20 6e 20 65 6c 65 6d  |e sets of n elem|
00000100  65 6e 74 73 20 6f 66 20  76 2e 0a 20 20 20 2d 2d  |ents of v..   --|
00000110  2d 2d 2d 2d 2d 2d 2d 2d  2d 2d 2d 2d 2d 2d 2d 2d  |----------------|
*
00000140  2d 2d 2a 2f 0a 7b 0a 20  20 6c 6f 63 61 6c 20 69  |--*/.{.  local i|
00000150  2c 6a 2c 73 2c 75 2c 56  3b 0a 20 20 75 20 3d 20  |,j,s,u,V;.  u = |
00000160  6e 65 77 76 65 63 74 6f  72 28 6e 29 3b 0a 20 20  |newvector(n);.  |
00000170  56 20 3d 20 6e 65 77 6d  61 74 72 69 78 28 6d 2c  |V = newmatrix(m,|
00000180  6e 29 3b 0a 20 20 73 20  3d 20 73 69 7a 65 6f 66  |n);.  s = sizeof|
00000190  28 76 29 3b 0a 20 20 69  66 20 28 73 20 21 3d 20  |(v);.  if (s != |
000001a0  6d 2a 6e 29 20 71 75 69  74 28 22 66 6f 72 6d 5f  |m*n) quit("form_|
000001b0  6d 61 74 72 69 78 3a 20  64 61 74 61 20 69 6e 63  |matrix: data inc|
000001c0  6f 6d 70 61 74 69 62 6c  65 20 77 69 74 68 20 6f  |ompatible with o|
000001d0  72 64 65 72 5c 6e 22 29  3b 0a 20 20 66 6f 72 20  |rder\n");.  for |
000001e0  28 69 20 3d 20 30 3b 20  69 20 3c 20 6d 3b 20 69  |(i = 0; i < m; i|
000001f0  2b 2b 29 0a 20 20 20 20  7b 0a 20 20 20 20 20 20  |++).    {.      |
00000200  66 6f 72 20 28 6a 20 3d  20 30 3b 20 6a 20 3c 20  |for (j = 0; j < |
00000210  6e 3b 20 6a 2b 2b 29 0a  20 20 20 20 20 20 20 20  |n; j++).        |
00000220  56 5b 69 5d 5b 6a 5d 20  3d 20 76 5b 69 2a 6e 20  |V[i][j] = v[i*n |
00000230  2b 20 6a 5d 3b 0a 20 20  20 20 7d 0a 20 20 72 65  |+ j];.    }.  re|
00000240  74 75 72 6e 20 56 3b 0a  7d 0a 0a 66 6f 72 6d 5f  |turn V;.}..form_|
00000250  63 6f 6c 75 6d 6e 28 76  29 0a 2f 2a 20 2d 2d 2d  |column(v)./* ---|
00000260  2d 2d 2d 2d 2d 2d 2d 2d  2d 2d 2d 2d 2d 2d 2d 2d  |----------------|
*
00000280  2d 2d 2d 2d 2d 0a 20 20  20 52 65 74 75 72 6e 73  |-----.   Returns|
00000290  20 61 20 63 6f 6c 75 6d  6e 20 76 65 63 74 6f 72  | a column vector|
000002a0  20 66 72 6f 6d 20 61 20  56 45 43 54 4f 52 20 76  | from a VECTOR v|
000002b0  2e 0a 20 20 20 2d 2d 2d  2d 2d 2d 2d 2d 2d 2d 2d  |..   -----------|
000002c0  2d 2d 2d 2d 2d 2d 2d 2d  2d 2d 2d 2d 2d 2d 2d 2d  |----------------|
000002d0  2d 2d 2d 2d 2d 2d 2d 2d  2d 2d 2d 2d 2d 2a 2f 0a  |-------------*/.|
000002e0  7b 0a 20 20 6c 6f 63 61  6c 20 69 2c 6d 2c 56 3b  |{.  local i,m,V;|
000002f0  0a 20 20 6d 20 3d 20 73  69 7a 65 6f 66 28 76 29  |.  m = sizeof(v)|
00000300  3b 0a 20 20 56 20 3d 20  6e 65 77 6d 61 74 72 69  |;.  V = newmatri|
00000310  78 28 6d 2c 31 29 3b 0a  20 20 66 6f 72 20 28 69  |x(m,1);.  for (i|
00000320  20 3d 20 30 3b 20 69 20  3c 20 6d 3b 20 69 2b 2b  | = 0; i < m; i++|
00000330  29 20 56 5b 69 5d 5b 30  5d 20 3d 20 76 5b 69 5d  |) V[i][0] = v[i]|
00000340  2a 31 2e 30 3b 0a 20 20  72 65 74 75 72 6e 20 56  |*1.0;.  return V|
00000350  3b 0a 7d 0a 0a 66 6f 72  6d 5f 72 6f 77 28 76 29  |;.}..form_row(v)|
00000360  0a 2f 2a 20 2d 2d 2d 2d  2d 2d 2d 2d 2d 2d 2d 2d  |./* ------------|
00000370  2d 2d 2d 2d 2d 2d 2d 2d  2d 2d 2d 2d 2d 2d 2d 2d  |----------------|
00000380  2d 2d 2d 2d 2d 2d 2d 2d  2d 0a 20 20 20 52 65 74  |---------.   Ret|
00000390  75 72 6e 73 20 61 20 72  6f 77 20 76 65 63 74 6f  |urns a row vecto|
000003a0  72 20 66 72 6f 6d 20 61  20 56 45 43 54 4f 52 20  |r from a VECTOR |
000003b0  76 2e 0a 20 20 20 2d 2d  2d 2d 2d 2d 2d 2d 2d 2d  |v..   ----------|
000003c0  2d 2d 2d 2d 2d 2d 2d 2d  2d 2d 2d 2d 2d 2d 2d 2d  |----------------|
000003d0  2d 2d 2d 2d 2d 2d 2d 2d  2d 2d 2d 2a 2f 0a 7b 0a  |-----------*/.{.|
000003e0  20 20 6c 6f 63 61 6c 20  6a 2c 6e 2c 56 3b 0a 20  |  local j,n,V;. |
000003f0  20 6e 20 3d 20 73 69 7a  65 6f 66 28 64 29 3b 0a  | n = sizeof(d);.|
00000400  20 20 56 20 3d 20 6e 65  77 6d 61 74 72 69 78 28  |  V = newmatrix(|
00000410  31 2c 6e 29 3b 0a 20 20  66 6f 72 20 28 6a 20 3d  |1,n);.  for (j =|
00000420  20 30 3b 20 6a 20 3c 20  6e 3b 20 6a 2b 2b 29 20  | 0; j < n; j++) |
00000430  56 5b 30 5d 5b 6a 5d 20  3d 20 64 5b 6a 5d 3b 0a  |V[0][j] = d[j];.|
00000440  20 20 72 65 74 75 72 6e  20 56 3b 0a 7d 0a 0a 70  |  return V;.}..p|
00000450  72 69 6e 74 61 72 72 61  79 28 41 2c 6c 2c 70 29  |rintarray(A,l,p)|
00000460  0a 2f 2a 20 2d 2d 2d 2d  2d 2d 2d 2d 2d 2d 2d 2d  |./* ------------|
00000470  2d 2d 2d 2d 2d 2d 2d 2d  2d 2d 2d 2d 2d 2d 2d 2d  |----------------|
*
000004a0  2d 2d 2d 2d 2d 2d 2d 0a  20 20 20 50 72 69 6e 74  |-------.   Print|
000004b0  73 20 74 68 65 20 65 6c  65 6d 65 6e 74 73 20 6f  |s the elements o|
000004c0  66 20 61 6e 20 61 72 72  61 79 20 28 6d 61 74 72  |f an array (matr|
000004d0  69 78 20 6f 72 20 76 65  63 74 6f 72 29 20 41 20  |ix or vector) A |
000004e0  69 6e 20 73 75 63 63 65  73 73 69 76 65 0a 20 20  |in successive.  |
000004f0  20 72 6f 77 73 2c 20 65  61 63 68 20 77 69 74 68  | rows, each with|
00000500  20 66 69 65 6c 64 20 77  69 64 74 68 20 6c 20 61  | field width l a|
00000510  6e 64 20 70 20 64 69 67  69 74 73 20 61 66 74 65  |nd p digits afte|
00000520  72 20 74 68 65 20 64 65  63 69 6d 61 6c 20 70 6f  |r the decimal po|
00000530  69 6e 74 2e 0a 20 20 20  2d 2d 2d 2d 2d 2d 2d 2d  |int..   --------|
00000540  2d 2d 2d 2d 2d 2d 2d 2d  2d 2d 2d 2d 2d 2d 2d 2d  |----------------|
*
00000570  2d 2d 2d 2d 2d 2d 2d 2d  2d 2d 2d 2a 2f 0a 7b 0a  |-----------*/.{.|
00000580  20 20 6c 6f 63 61 6c 20  69 2c 6a 2c 6d 2c 6e 3b  |  local i,j,m,n;|
00000590  0a 20 20 6d 20 3d 20 73  69 7a 65 6f 66 28 41 29  |.  m = sizeof(A)|
000005a0  3b 0a 20 20 6e 20 3d 20  73 69 7a 65 6f 66 28 41  |;.  n = sizeof(A|
000005b0  5b 30 5d 29 3b 0a 20 20  69 66 20 28 74 79 70 65  |[0]);.  if (type|
000005c0  6f 66 28 6e 29 20 3d 3d  20 49 4e 54 45 47 45 52  |of(n) == INTEGER|
000005d0  29 0a 20 20 20 20 7b 66  6f 72 20 28 69 20 3d 20  |).    {for (i = |
000005e0  30 3b 20 69 20 3c 20 6d  3b 20 69 2b 2b 29 0a 20  |0; i < m; i++). |
000005f0  20 20 20 20 20 7b 20 66  6f 72 20 28 6a 20 3d 20  |     { for (j = |
00000600  30 3b 20 6a 20 3c 20 6e  3b 20 6a 2b 2b 29 20 70  |0; j < n; j++) p|
00000610  72 69 6e 74 28 66 6f 72  6d 61 74 28 41 5b 69 5d  |rint(format(A[i]|
00000620  5b 6a 5d 2c 6c 2c 70 29  29 3b 0a 20 20 20 20 20  |[j],l,p));.     |
00000630  20 20 20 70 72 69 6e 74  28 22 5c 6e 22 29 3b 0a  |   print("\n");.|
00000640  20 20 20 20 20 20 7d 0a  20 20 20 20 7d 0a 20 20  |      }.    }.  |
00000650  65 6c 73 65 0a 20 20 20  20 7b 66 6f 72 20 28 69  |else.    {for (i|
00000660  20 3d 20 30 3b 20 69 20  3c 20 6d 3b 20 69 2b 2b  | = 0; i < m; i++|
00000670  29 20 70 72 69 6e 74 28  66 6f 72 6d 61 74 28 41  |) print(format(A|
00000680  5b 69 5d 2c 6c 2c 70 29  29 3b 0a 20 20 20 20 20  |[i],l,p));.     |
00000690  70 72 69 6e 74 28 22 5c  6e 22 29 3b 0a 20 20 20  |print("\n");.   |
000006a0  20 7d 0a 7d 0a 0a 66 6f  72 6d 61 74 28 6e 2c 6c  | }.}..format(n,l|
000006b0  2c 70 29 0a 2f 2a 2d 2d  2d 2d 2d 2d 2d 2d 2d 2d  |,p)./*----------|
000006c0  2d 2d 2d 2d 2d 2d 2d 2d  2d 2d 2d 2d 2d 2d 2d 2d  |----------------|
*
000006f0  2d 2d 2d 2d 2d 2d 2d 2d  2d 2d 2d 2d 2d 2d 0a 20  |--------------. |
00000700  66 6f 72 6d 61 74 28 6e  2c 6c 2c 70 29 20 66 6f  |format(n,l,p) fo|
00000710  72 6d 61 74 73 20 76 61  72 69 61 62 6c 65 73 20  |rmats variables |
00000720  6f 66 20 74 79 70 65 73  20 49 4e 54 45 47 45 52  |of types INTEGER|
00000730  2c 20 52 45 41 4c 20 61  6e 64 20 53 54 52 49 4e  |, REAL and STRIN|
00000740  47 20 66 6f 72 0a 20 6f  75 74 70 75 74 2e 20 20  |G for. output.  |
00000750  49 74 20 63 6f 6e 76 65  72 74 73 20 52 45 41 4c  |It converts REAL|
00000760  20 6f 72 20 49 4e 54 45  47 45 52 20 6e 75 6d 62  | or INTEGER numb|
00000770  65 72 73 20 6e 20 74 6f  20 73 69 67 6e 65 64 20  |ers n to signed |
00000780  64 65 63 69 6d 61 6c 20  73 74 72 69 6e 67 73 2c  |decimal strings,|
00000790  0a 20 77 69 74 68 20 70  20 64 69 67 69 74 73 20  |. with p digits |
000007a0  61 66 74 65 72 20 74 68  65 20 64 65 63 69 6d 61  |after the decima|
000007b0  6c 20 70 6f 69 6e 74 20  66 6f 72 20 72 65 61 6c  |l point for real|
000007c0  73 20 28 70 20 69 73 20  69 72 72 65 6c 65 76 61  |s (p is irreleva|
000007d0  6e 74 20 66 6f 72 0a 20  69 6e 74 65 67 65 72 73  |nt for. integers|
000007e0  20 61 6e 64 20 73 74 72  69 6e 67 73 29 2c 20 61  | and strings), a|
000007f0  6e 64 20 72 65 74 75 72  6e 73 20 74 68 65 6d 2c  |nd returns them,|
00000800  20 6f 72 20 73 74 72 69  6e 67 73 20 6e 2c 20 65  | or strings n, e|
00000810  69 74 68 65 72 20 70 61  64 64 65 64 20 77 69 74  |ither padded wit|
00000820  68 0a 20 6c 65 61 64 69  6e 67 20 73 70 61 63 65  |h. leading space|
00000830  73 20 74 6f 20 6d 61 6b  65 20 74 68 65 69 72 20  |s to make their |
00000840  6c 65 6e 67 74 68 73 20  75 70 20 74 6f 20 6c 20  |lengths up to l |
00000850  6f 72 2c 20 69 66 20 6c  20 69 73 20 74 6f 6f 20  |or, if l is too |
00000860  73 6d 61 6c 6c 20 28 69  6e 0a 20 70 61 72 74 69  |small (in. parti|
00000870  63 75 6c 61 72 20 69 66  20 6c 20 3d 20 30 29 2c  |cular if l = 0),|
00000880  20 61 74 20 66 75 6c 6c  20 6c 65 6e 67 74 68 20  | at full length |
00000890  77 69 74 68 6f 75 74 20  61 6e 79 20 6c 65 61 64  |without any lead|
000008a0  69 6e 67 20 73 70 61 63  65 73 2e 0a 20 2d 2d 2d  |ing spaces.. ---|
000008b0  2d 2d 2d 2d 2d 2d 2d 2d  2d 2d 2d 2d 2d 2d 2d 2d  |----------------|
*
000008f0  2d 2d 2d 2d 2d 2d 2a 2f  0a 7b 0a 20 20 6c 6f 63  |------*/.{.  loc|
00000900  61 6c 20 64 2c 64 65 63  2c 69 2c 69 6e 74 2c 6e  |al d,dec,i,int,n|
00000910  65 67 2c 72 2c 73 3b 0a  20 20 73 20 3d 20 22 22  |eg,r,s;.  s = ""|
00000920  3b 0a 20 20 73 77 69 74  63 68 20 28 74 79 70 65  |;.  switch (type|
00000930  6f 66 28 6e 29 29 0a 20  20 20 20 7b 0a 20 20 20  |of(n)).    {.   |
00000940  20 20 20 63 61 73 65 20  52 45 41 4c 3a 0a 20 20  |   case REAL:.  |
00000950  20 20 20 20 20 20 69 66  20 28 6e 65 67 20 3d 20  |      if (neg = |
00000960  28 6e 20 3c 20 30 2e 30  29 29 20 6e 20 3d 20 2d  |(n < 0.0)) n = -|
00000970  6e 3b 0a 20 20 20 20 20  20 20 20 72 20 3d 20 30  |n;.        r = 0|
00000980  2e 35 3b 0a 20 20 20 20  20 20 20 20 66 6f 72 20  |.5;.        for |
00000990  28 69 20 3d 20 30 3b 20  69 20 3c 20 70 3b 20 69  |(i = 0; i < p; i|
000009a0  2b 2b 29 20 72 20 2f 3d  20 31 30 2e 30 3b 0a 20  |++) r /= 10.0;. |
000009b0  20 20 20 20 20 20 20 69  66 20 28 6e 20 3c 20 72  |       if (n < r|
000009c0  29 20 7b 20 6e 20 3d 20  30 2e 30 3b 20 6e 65 67  |) { n = 0.0; neg|
000009d0  20 3d 20 46 41 4c 53 45  3b 20 7d 20 65 6c 73 65  | = FALSE; } else|
000009e0  20 6e 20 2b 3d 20 72 3b  20 20 20 20 20 20 20 20  | n += r;        |
000009f0  0a 20 20 20 20 20 20 20  20 69 6e 74 20 3d 20 66  |.        int = f|
00000a00  6c 6f 6f 72 28 6e 29 3b  0a 20 20 20 20 20 20 20  |loor(n);.       |
00000a10  20 69 66 20 28 6e 65 67  29 20 73 20 3d 20 22 2d  | if (neg) s = "-|
00000a20  22 3b 0a 20 20 20 20 20  20 20 20 73 20 2b 3d 20  |";.        s += |
00000a30  69 6e 74 5f 31 30 28 69  6e 74 29 3b 0a 20 20 20  |int_10(int);.   |
00000a40  20 20 20 20 20 73 20 2b  3d 20 22 2e 22 3b 0a 20  |     s += ".";. |
00000a50  20 20 20 20 20 20 20 64  65 63 20 3d 20 6e 20 2d  |       dec = n -|
00000a60  20 31 2e 30 2a 69 6e 74  3b 20 0a 20 20 20 20 20  | 1.0*int; .     |
00000a70  20 20 20 66 6f 72 20 28  69 20 3d 20 30 3b 20 69  |   for (i = 0; i|
00000a80  20 3c 20 70 3b 20 69 2b  2b 29 20 64 65 63 20 2a  | < p; i++) dec *|
00000a90  3d 20 31 30 2e 30 3b 0a  20 20 20 20 20 20 20 20  |= 10.0;.        |
00000aa0  64 65 63 20 3d 20 66 6c  6f 6f 72 28 64 65 63 29  |dec = floor(dec)|
00000ab0  3b 0a 20 20 20 20 20 20  20 20 64 20 3d 20 22 22  |;.        d = ""|
00000ac0  3b 0a 20 20 20 20 20 20  20 20 66 6f 72 20 28 69  |;.        for (i|
00000ad0  20 3d 20 30 3b 69 20 3c  20 70 3b 20 69 2b 2b 29  | = 0;i < p; i++)|
00000ae0  0a 20 20 20 20 20 20 20  20 20 20 7b 20 64 20 20  |.          { d  |
00000af0  3d 20 27 30 27 20 2b 20  64 65 63 25 31 30 20 2b  |= '0' + dec%10 +|
00000b00  20 64 3b 20 64 65 63 20  2f 3d 20 31 30 3b 20 7d  | d; dec /= 10; }|
00000b10  0a 20 20 20 20 20 20 20  20 73 20 2b 3d 20 64 3b  |.        s += d;|
00000b20  0a 20 20 20 20 20 20 20  20 62 72 65 61 6b 3b 0a  |.        break;.|
00000b30  20 20 20 20 20 20 63 61  73 65 20 49 4e 54 45 47  |      case INTEG|
00000b40  45 52 3a 0a 20 20 20 20  20 20 20 20 69 66 20 28  |ER:.        if (|
00000b50  6e 65 67 20 3d 20 28 6e  20 3c 20 30 29 29 20 6e  |neg = (n < 0)) n|
00000b60  20 3d 20 2d 6e 3b 0a 20  20 20 20 20 20 20 20 69  | = -n;.        i|
00000b70  66 20 28 6e 65 67 29 20  73 20 3d 20 22 2d 22 3b  |f (neg) s = "-";|
00000b80  0a 20 20 20 20 20 20 20  20 73 20 2b 3d 20 69 6e  |.        s += in|
00000b90  74 5f 31 30 28 6e 29 3b  0a 20 20 20 20 20 20 20  |t_10(n);.       |
00000ba0  20 62 72 65 61 6b 3b 0a  20 20 20 20 20 20 63 61  | break;.      ca|
00000bb0  73 65 20 53 54 52 49 4e  47 3a 0a 20 20 20 20 20  |se STRING:.     |
00000bc0  20 20 20 73 20 3d 20 6e  3b 0a 20 20 20 20 20 20  |   s = n;.      |
00000bd0  20 20 62 72 65 61 6b 3b  0a 20 20 20 20 20 20 64  |  break;.      d|
00000be0  65 66 61 75 6c 74 3a 0a  20 20 20 20 20 20 20 20  |efault:.        |
00000bf0  73 20 3d 20 22 66 6f 72  6d 61 74 3a 20 31 73 74  |s = "format: 1st|
00000c00  20 61 72 67 75 6d 65 6e  74 20 6e 6f 74 20 72 65  | argument not re|
00000c10  61 6c 2c 20 69 6e 74 65  67 65 72 20 6f 72 20 73  |al, integer or s|
00000c20  74 72 69 6e 67 22 3b 20  20 20 20 20 20 20 20 0a  |tring";        .|
00000c30  20 20 20 20 7d 0a 20 20  66 6f 72 20 28 69 20 3d  |    }.  for (i =|
00000c40  20 6c 20 2d 20 73 69 7a  65 6f 66 28 73 29 3b 20  | l - sizeof(s); |
00000c50  69 20 3e 20 30 3b 20 69  20 2d 2d 29 20 73 20 3d  |i > 0; i --) s =|
00000c60  20 22 20 22 20 2b 20 73  3b 0a 20 20 72 65 74 75  | " " + s;.  retu|
00000c70  72 6e 20 73 3b 0a 7d 0a  0a 61 64 64 28 63 2c 41  |rn s;.}..add(c,A|
00000c80  29 0a 2f 2a 20 2d 2d 2d  2d 2d 2d 2d 2d 2d 2d 2d  |)./* -----------|
00000c90  2d 2d 2d 2d 2d 2d 2d 2d  2d 2d 2d 2d 2d 2d 2d 2d  |----------------|
*
00000cb0  2d 2d 2d 2d 2d 2d 2d 2d  2d 0a 20 20 20 41 64 64  |---------.   Add|
00000cc0  73 20 74 68 65 20 63 6f  6e 73 74 61 6e 74 20 63  |s the constant c|
00000cd0  20 74 6f 20 65 76 65 72  79 20 65 6c 65 6d 65 6e  | to every elemen|
00000ce0  74 20 6f 66 20 74 68 65  20 61 72 72 61 79 20 41  |t of the array A|
00000cf0  2e 0a 20 20 20 2d 2d 2d  2d 2d 2d 2d 2d 2d 2d 2d  |..   -----------|
00000d00  2d 2d 2d 2d 2d 2d 2d 2d  2d 2d 2d 2d 2d 2d 2d 2d  |----------------|
*
00000d20  2d 2d 2d 2d 2d 2d 2d 2d  2d 2a 2f 0a 7b 0a 20 20  |---------*/.{.  |
00000d30  6c 6f 63 61 6c 20 61 2c  66 2c 69 2c 6a 2c 6d 2c  |local a,f,i,j,m,|
00000d40  6e 2c 74 2c 74 61 2c 56  3b 0a 20 20 74 20 3d 20  |n,t,ta,V;.  t = |
00000d50  74 79 70 65 6f 66 28 63  29 3b 0a 20 20 69 66 20  |typeof(c);.  if |
00000d60  28 28 74 20 21 3d 20 49  4e 54 45 47 45 52 29 20  |((t != INTEGER) |
00000d70  26 26 20 28 74 20 21 3d  20 52 45 41 4c 29 29 0a  |&& (t != REAL)).|
00000d80  20 20 20 20 71 75 69 74  28 22 61 64 64 3a 20 31  |    quit("add: 1|
00000d90  73 74 20 61 72 67 75 6d  65 6e 74 20 69 73 20 6e  |st argument is n|
00000da0  6f 74 20 61 20 63 6f 6e  73 74 61 6e 74 5c 6e 22  |ot a constant\n"|
00000db0  29 3b 0a 20 20 69 66 20  28 74 79 70 65 6f 66 28  |);.  if (typeof(|
00000dc0  41 29 20 21 3d 20 56 45  43 54 4f 52 29 20 71 75  |A) != VECTOR) qu|
00000dd0  69 74 28 22 61 64 64 3a  20 32 6e 64 20 61 72 67  |it("add: 2nd arg|
00000de0  75 6d 65 6e 74 20 69 73  20 6e 6f 74 20 61 6e 20  |ument is not an |
00000df0  61 72 72 61 79 5c 6e 22  29 3b 0a 20 20 6d 20 3d  |array\n");.  m =|
00000e00  20 73 69 7a 65 6f 66 28  41 29 3b 0a 20 20 6e 20  | sizeof(A);.  n |
00000e10  3d 20 73 69 7a 65 6f 66  28 41 5b 30 5d 29 3b 0a  |= sizeof(A[0]);.|
00000e20  20 20 61 20 3d 20 63 2a  41 5b 30 5d 5b 30 5d 3b  |  a = c*A[0][0];|
00000e30  0a 2f 2f 20 71 75 69 74  28 22 74 65 73 74 20 73  |.// quit("test s|
00000e40  74 6f 70 5c 6e 22 29 3b  0a 20 20 74 61 20 3d 20  |top\n");.  ta = |
00000e50  74 79 70 65 6f 66 28 61  29 3b 0a 20 20 69 66 20  |typeof(a);.  if |
00000e60  28 74 61 20 3d 3d 20 49  4e 54 45 47 45 52 29 20  |(ta == INTEGER) |
00000e70  66 20 3d 20 31 3b 20 65  6c 73 65 20 66 20 3d 20  |f = 1; else f = |
00000e80  31 2e 30 3b 0a 20 20 63  20 3d 20 66 2a 63 3b 0a  |1.0;.  c = f*c;.|
00000e90  20 20 69 66 20 28 74 79  70 65 6f 66 28 6e 29 20  |  if (typeof(n) |
00000ea0  3d 3d 20 49 4e 54 45 47  45 52 29 0a 20 20 20 20  |== INTEGER).    |
00000eb0  7b 0a 20 20 20 20 20 56  20 3d 20 6e 65 77 6d 61  |{.     V = newma|
00000ec0  74 72 69 78 28 6d 2c 6e  29 3b 0a 20 20 20 20 20  |trix(m,n);.     |
00000ed0  66 6f 72 20 28 69 20 3d  20 30 3b 20 69 20 3c 20  |for (i = 0; i < |
00000ee0  6d 3b 20 69 2b 2b 29 0a  20 20 20 20 20 20 20 66  |m; i++).       f|
00000ef0  6f 72 20 28 6a 20 3d 20  30 3b 20 6a 20 3c 20 6e  |or (j = 0; j < n|
00000f00  3b 20 6a 2b 2b 29 20 56  5b 69 5d 5b 6a 5d 20 3d  |; j++) V[i][j] =|
00000f10  20 63 20 2b 20 66 2a 41  5b 69 5d 5b 6a 5d 3b 0a  | c + f*A[i][j];.|
00000f20  20 20 20 20 7d 0a 20 20  65 6c 73 65 0a 20 20 20  |    }.  else.   |
00000f30  20 7b 20 56 20 3d 20 6e  65 77 76 65 63 74 6f 72  | { V = newvector|
00000f40  28 6d 29 3b 0a 20 20 20  20 20 20 66 6f 72 20 28  |(m);.      for (|
00000f50  6a 20 3d 20 30 3b 20 6a  20 3c 20 6d 3b 20 6a 2b  |j = 0; j < m; j+|
00000f60  2b 29 20 56 5b 69 5d 20  3d 20 63 20 2b 20 66 2a  |+) V[i] = c + f*|
00000f70  41 5b 6a 5d 3b 0a 20 20  20 20 7d 0a 20 20 72 65  |A[j];.    }.  re|
00000f80  74 75 72 6e 20 56 3b 0a  7d 0a 0a 73 75 6d 28 41  |turn V;.}..sum(A|
00000f90  2c 42 29 0a 2f 2a 20 2d  2d 2d 2d 2d 2d 2d 2d 2d  |,B)./* ---------|
00000fa0  2d 2d 2d 2d 2d 2d 2d 2d  2d 2d 2d 2d 2d 2d 2d 2d  |----------------|
*
00000fc0  2d 2d 2d 2d 2d 2d 2d 2d  2d 0a 20 20 20 52 65 74  |---------.   Ret|
00000fd0  75 72 6e 73 20 74 68 65  20 61 72 72 61 79 20 73  |urns the array s|
00000fe0  75 6d 20 41 20 2b 20 42  20 6f 66 20 74 68 65 20  |um A + B of the |
00000ff0  61 72 72 61 79 73 20 41  20 61 6e 64 20 42 2e 0a  |arrays A and B..|
00001000  20 20 20 2d 2d 2d 2d 2d  2d 2d 2d 2d 2d 2d 2d 2d  |   -------------|
00001010  2d 2d 2d 2d 2d 2d 2d 2d  2d 2d 2d 2d 2d 2d 2d 2d  |----------------|
*
00001030  2d 2d 2d 2d 2d 2a 2f 0a  7b 0a 20 20 6c 6f 63 61  |-----*/.{.  loca|
00001040  6c 20 69 2c 6a 2c 6b 2c  6d 61 2c 6e 61 2c 6d 62  |l i,j,k,ma,na,mb|
00001050  2c 6e 62 2c 74 2c 74 61  2c 74 62 2c 56 3b 0a 20  |,nb,t,ta,tb,V;. |
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00001070  20 74 62 20 3d 20 74 79  70 65 6f 66 28 42 29 3b  | tb = typeof(B);|
00001080  0a 20 20 69 66 20 28 74  61 20 21 3d 20 56 45 43  |.  if (ta != VEC|
00001090  54 4f 52 29 20 71 75 69  74 28 22 73 75 6d 3a 20  |TOR) quit("sum: |
000010a0  31 73 74 20 61 72 67 75  6d 65 6e 74 20 69 73 20  |1st argument is |
000010b0  6e 6f 74 20 61 6e 20 61  72 72 61 79 5c 6e 22 29  |not an array\n")|
000010c0  3b 0a 20 20 69 66 20 28  74 62 20 21 3d 20 56 45  |;.  if (tb != VE|
000010d0  43 54 4f 52 29 20 71 75  69 74 28 22 73 75 6d 3a  |CTOR) quit("sum:|
000010e0  20 32 6e 64 20 61 72 67  75 6d 65 6e 74 20 69 73  | 2nd argument is|
000010f0  20 6e 6f 74 20 61 6e 20  61 72 72 61 79 5c 6e 22  | not an array\n"|
00001100  29 3b 0a 20 20 6d 61 20  3d 20 73 69 7a 65 6f 66  |);.  ma = sizeof|
00001110  28 41 29 3b 0a 20 20 6d  62 20 3d 20 73 69 7a 65  |(A);.  mb = size|
00001120  6f 66 28 42 29 3b 0a 20  20 6e 61 20 3d 20 73 69  |of(B);.  na = si|
00001130  7a 65 6f 66 28 41 5b 30  5d 29 3b 0a 20 20 6e 62  |zeof(A[0]);.  nb|
00001140  20 3d 20 73 69 7a 65 6f  66 28 42 5b 30 5d 29 3b  | = sizeof(B[0]);|
00001150  0a 20 20 74 61 20 3d 20  74 79 70 65 6f 66 28 6e  |.  ta = typeof(n|
00001160  61 29 3b 20 74 62 20 3d  20 74 79 70 65 6f 66 28  |a); tb = typeof(|
00001170  6e 62 29 3b 0a 20 20 69  66 20 28 74 61 20 21 3d  |nb);.  if (ta !=|
00001180  20 74 62 29 20 71 75 69  74 28 22 73 75 6d 3a 20  | tb) quit("sum: |
00001190  61 72 72 61 79 73 20 61  72 65 20 6e 6f 74 20 6f  |arrays are not o|
000011a0  66 20 73 61 6d 65 20 74  79 70 65 5c 6e 22 29 3b  |f same type\n");|
000011b0  0a 20 20 69 66 20 28 74  61 20 21 3d 20 49 4e 54  |.  if (ta != INT|
000011c0  45 47 45 52 29 0a 20 20  20 20 7b 20 69 66 20 28  |EGER).    { if (|
000011d0  6d 61 20 21 3d 20 6d 62  29 20 71 75 69 74 28 22  |ma != mb) quit("|
000011e0  73 75 6d 3a 20 76 65 63  74 6f 72 73 20 61 72 65  |sum: vectors are|
000011f0  20 69 6e 63 6f 6d 70 61  74 69 62 6c 65 20 66 6f  | incompatible fo|
00001200  72 20 61 64 64 69 74 69  6f 6e 5c 6e 22 29 3b 0a  |r addition\n");.|
00001210  20 20 20 20 20 20 74 20  3d 20 74 79 70 65 6f 66  |      t = typeof|
00001220  28 41 5b 30 5d 2a 42 5b  30 5d 29 3b 0a 20 20 20  |(A[0]*B[0]);.   |
00001230  20 20 20 69 66 20 28 74  20 3d 3d 20 49 4e 54 45  |   if (t == INTE|
00001240  47 45 52 29 20 66 20 3d  20 31 3b 20 65 6c 73 65  |GER) f = 1; else|
00001250  20 66 20 3d 20 31 2e 30  3b 0a 20 20 20 20 20 20  | f = 1.0;.      |
00001260  56 20 3d 20 6e 65 77 76  65 63 74 6f 72 3b 0a 20  |V = newvector;. |
00001270  20 20 20 20 20 66 6f 72  20 28 6a 20 3d 20 30 3b  |     for (j = 0;|
00001280  20 6a 20 3c 6d 62 3b 20  6a 2b 2b 29 20 56 5b 6a  | j <mb; j++) V[j|
00001290  5d 20 3d 20 66 2a 41 5b  6a 5d 20 2b 20 66 2a 42  |] = f*A[j] + f*B|
000012a0  5b 6a 5d 3b 0a 20 20 20  20 7d 0a 20 20 65 6c 73  |[j];.    }.  els|
000012b0  65 20 0a 20 20 20 20 7b  20 69 66 20 28 28 6d 61  |e .    { if ((ma|
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000012d0  3d 20 6e 62 29 29 20 71  75 69 74 28 22 73 75 6d  |= nb)) quit("sum|
000012e0  3a 20 6d 61 74 72 69 63  65 73 20 61 72 65 20 69  |: matrices are i|
000012f0  6e 63 6f 6d 70 61 74 69  62 6c 65 20 66 6f 72 20  |ncompatible for |
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00001310  20 20 20 20 74 20 3d 20  74 79 70 65 6f 66 28 41  |    t = typeof(A|
00001320  5b 30 5d 5b 30 5d 2a 42  5b 30 5d 5b 30 5d 29 3b  |[0][0]*B[0][0]);|
00001330  0a 20 20 20 20 20 20 69  66 20 28 74 20 3d 3d 20  |.      if (t == |
00001340  49 4e 54 45 47 45 52 29  20 66 20 3d 20 31 3b 20  |INTEGER) f = 1; |
00001350  65 6c 73 65 20 66 20 3d  20 31 2e 30 3b 0a 20 20  |else f = 1.0;.  |
00001360  20 20 20 20 56 20 3d 20  6e 65 77 6d 61 74 72 69  |    V = newmatri|
00001370  78 28 6d 61 2c 6e 61 29  3b 0a 20 20 20 20 20 20  |x(ma,na);.      |
00001380  66 6f 72 20 28 69 20 3d  20 30 3b 20 69 20 3c 20  |for (i = 0; i < |
00001390  6d 61 3b 20 69 2b 2b 29  0a 20 20 20 20 20 20 20  |ma; i++).       |
000013a0  20 7b 20 66 6f 72 20 28  6a 20 3d 20 30 3b 20 6a  | { for (j = 0; j|
000013b0  20 3c 20 6e 62 3b 20 6a  2b 2b 29 20 56 5b 69 5d  | < nb; j++) V[i]|
000013c0  5b 6a 5d 20 3d 20 66 2a  41 5b 69 5d 5b 6a 5d 20  |[j] = f*A[i][j] |
000013d0  2b 20 66 2a 42 5b 69 5d  5b 6a 5d 3b 0a 20 20 20  |+ f*B[i][j];.   |
000013e0  20 20 20 20 20 7d 0a 20  20 20 20 7d 0a 20 20 72  |     }.    }.  r|
000013f0  65 74 75 72 6e 20 56 3b  0a 7d 0a 0a 6d 75 6c 74  |eturn V;.}..mult|
00001400  69 70 6c 65 28 63 2c 41  29 0a 2f 2a 20 2d 2d 2d  |iple(c,A)./* ---|
00001410  2d 2d 2d 2d 2d 2d 2d 2d  2d 2d 2d 2d 2d 2d 2d 2d  |----------------|
*
00001430  2d 2d 2d 2d 2d 2d 2d 2d  2d 2d 2d 2d 2d 2d 0a 20  |--------------. |
00001440  20 20 52 65 74 75 72 6e  73 20 74 68 65 20 61 72  |  Returns the ar|
00001450  72 61 79 20 41 20 6d 75  6c 74 69 70 6c 69 65 64  |ray A multiplied|
00001460  20 62 79 20 74 68 65 20  63 6f 6e 73 74 61 6e 74  | by the constant|
00001470  20 63 2e 0a 20 20 20 2d  2d 2d 2d 2d 2d 2d 2d 2d  | c..   ---------|
00001480  2d 2d 2d 2d 2d 2d 2d 2d  2d 2d 2d 2d 2d 2d 2d 2d  |----------------|
*
000014a0  2d 2d 2d 2d 2d 2d 2d 2d  2a 2f 0a 7b 0a 20 20 6c  |--------*/.{.  l|
000014b0  6f 63 61 6c 20 69 2c 6a  2c 6d 2c 6e 2c 74 2c 56  |ocal i,j,m,n,t,V|
000014c0  3b 0a 20 20 74 20 3d 20  74 79 70 65 6f 66 28 63  |;.  t = typeof(c|
000014d0  29 3b 0a 20 20 69 66 20  28 28 74 20 21 3d 20 49  |);.  if ((t != I|
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000014f0  20 52 45 41 4c 29 29 0a  20 20 20 20 71 75 69 74  | REAL)).    quit|
00001500  28 22 70 72 6f 64 75 63  74 3a 20 31 73 74 20 61  |("product: 1st a|
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00001520  20 63 6f 6e 73 74 61 6e  74 5c 6e 22 29 3b 0a 20  | constant\n");. |
00001530  20 69 66 20 28 74 79 70  65 6f 66 28 41 29 20 21  | if (typeof(A) !|
00001540  3d 20 56 45 43 54 4f 52  29 20 71 75 69 74 28 22  |= VECTOR) quit("|
00001550  70 72 6f 64 75 63 74 3a  20 32 6e 64 20 61 72 67  |product: 2nd arg|
00001560  75 6d 65 6e 74 20 69 73  20 6e 6f 74 20 61 6e 20  |ument is not an |
00001570  61 72 72 61 79 5c 6e 22  29 3b 0a 20 20 6d 20 3d  |array\n");.  m =|
00001580  20 73 69 7a 65 6f 66 28  41 29 3b 0a 20 20 6e 20  | sizeof(A);.  n |
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000015a0  20 20 69 66 20 28 74 79  70 65 6f 66 28 6e 29 20  |  if (typeof(n) |
000015b0  3d 3d 20 49 4e 54 45 47  45 52 29 0a 20 20 20 20  |== INTEGER).    |
000015c0  7b 0a 20 20 20 20 20 56  20 3d 20 6e 65 77 6d 61  |{.     V = newma|
000015d0  74 72 69 78 28 6d 2c 6e  29 3b 0a 20 20 20 20 20  |trix(m,n);.     |
000015e0  66 6f 72 20 28 69 20 3d  20 30 3b 20 69 20 3c 20  |for (i = 0; i < |
000015f0  6d 3b 20 69 2b 2b 29 0a  20 20 20 20 20 20 20 7b  |m; i++).       {|
00001600  20 66 6f 72 20 28 6a 20  3d 20 30 3b 20 6a 20 3c  | for (j = 0; j <|
00001610  20 6e 3b 20 6a 2b 2b 29  20 56 5b 69 5d 5b 6a 5d  | n; j++) V[i][j]|
00001620  20 3d 20 63 2a 41 5b 69  5d 5b 6a 5d 3b 0a 20 20  | = c*A[i][j];.  |
00001630  20 20 20 20 20 7d 0a 20  20 20 20 7d 0a 20 20 65  |     }.    }.  e|
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00001670  3c 20 6d 3b 20 69 2b 2b  29 20 56 5b 69 5d 20 3d  |< m; i++) V[i] =|
00001680  20 63 2a 41 5b 69 5d 3b  0a 20 20 20 20 7d 0a 20  | c*A[i];.    }. |
00001690  20 72 65 74 75 72 6e 20  56 3b 0a 7d 0a 0a 70 72  | return V;.}..pr|
000016a0  6f 64 75 63 74 28 41 2c  42 29 0a 2f 2a 20 2d 2d  |oduct(A,B)./* --|
000016b0  2d 2d 2d 2d 2d 2d 2d 2d  2d 2d 2d 2d 2d 2d 2d 2d  |----------------|
*
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00001760  2d 2d 2d 2d 2d 2d 2d 2d  2d 2d 2d 2d 2d 2d 2d 2d  |----------------|
*
00001790  2d 2d 2d 2a 2f 0a 7b 0a  20 20 6c 6f 63 61 6c 20  |---*/.{.  local |
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000017c0  79 70 65 6f 66 28 41 29  20 21 3d 20 56 45 43 54  |ypeof(A) != VECT|
000017d0  4f 52 29 20 71 75 69 74  28 22 70 72 6f 64 75 63  |OR) quit("produc|
000017e0  74 3a 20 31 73 74 20 61  72 67 75 6d 65 6e 74 20  |t: 1st argument |
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00001800  6e 22 29 3b 0a 20 20 69  66 20 28 74 79 70 65 6f  |n");.  if (typeo|
00001810  66 28 42 29 20 21 3d 20  56 45 43 54 4f 52 29 20  |f(B) != VECTOR) |
00001820  71 75 69 74 28 22 70 72  6f 64 75 63 74 3a 20 32  |quit("product: 2|
00001830  6e 64 20 61 72 67 75 6d  65 6e 74 20 69 73 20 6e  |nd argument is n|
00001840  6f 74 20 61 6e 20 61 72  72 61 79 5c 6e 22 29 3b  |ot an array\n");|
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00001890  20 73 69 7a 65 6f 66 28  42 5b 30 5d 29 3b 0a 20  | sizeof(B[0]);. |
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00001940  6f 64 75 63 74 3a 20 61  72 72 61 79 73 20 61 72  |oduct: arrays ar|
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00001980  20 6e 65 77 76 65 63 74  6f 72 28 6d 61 29 3b 0a  | newvector(ma);.|
00001990  20 20 20 20 20 20 69 66  20 28 74 79 70 65 6f 66  |      if (typeof|
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000019b0  3d 20 52 45 41 4c 29 20  76 20 3d 20 30 2e 30 3b  |= REAL) v = 0.0;|
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000019f0  20 20 20 20 7b 20 75 20  3d 20 76 3b 0a 20 20 20  |    { u = v;.   |
00001a00  20 20 20 20 20 20 20 66  6f 72 20 28 6b 20 3d 20  |       for (k = |
00001a10  30 3b 20 6b 20 3c 20 6d  61 3b 20 6b 2b 2b 29 20  |0; k < ma; k++) |
00001a20  75 20 2b 3d 20 41 5b 6b  5d 2a 42 5b 6b 5d 5b 69  |u += A[k]*B[k][i|
00001a30  5d 3b 0a 20 20 20 20 20  20 20 20 20 20 56 5b 69  |];.          V[i|
00001a40  5d 20 3d 20 75 3b 0a 20  20 20 20 20 20 20 20 7d  |] = u;.        }|
00001a50  0a 20 20 20 20 7d 0a 20  20 65 6c 73 65 0a 20 20  |.    }.  else.  |
00001a60  20 20 7b 20 69 66 20 28  6e 61 20 21 3d 20 6d 62  |  { if (na != mb|
00001a70  29 20 71 75 69 74 28 22  70 72 6f 64 75 63 74 3a  |) quit("product:|
00001a80  20 61 72 72 61 79 73 20  61 72 65 20 69 6e 63 6f  | arrays are inco|
00001a90  6d 70 61 74 69 62 6c 65  20 66 6f 72 20 6d 75 6c  |mpatible for mul|
00001aa0  74 69 70 6c 69 63 61 74  69 6f 6e 5c 6e 22 29 3b  |tiplication\n");|
00001ab0  0a 20 20 20 20 20 20 56  20 3d 20 6e 65 77 6d 61  |.      V = newma|
00001ac0  74 72 69 78 28 6d 61 2c  6e 62 29 3b 0a 20 20 20  |trix(ma,nb);.   |
00001ad0  20 20 20 69 66 20 28 74  79 70 65 6f 66 28 41 5b  |   if (typeof(A[|
00001ae0  30 5d 5b 30 5d 2a 42 5b  30 5d 5b 30 5d 29 20 3d  |0][0]*B[0][0]) =|
00001af0  3d 20 52 45 41 4c 29 20  76 20 3d 20 30 2e 30 3b  |= REAL) v = 0.0;|
00001b00  20 65 6c 73 65 20 76 20  3d 20 30 3b 0a 20 20 20  | else v = 0;.   |
00001b10  20 20 20 66 6f 72 20 28  69 20 3d 20 30 3b 20 69  |   for (i = 0; i|
00001b20  20 3c 20 6d 61 3b 20 69  2b 2b 29 0a 20 20 20 20  | < ma; i++).    |
00001b30  20 20 20 20 7b 20 66 6f  72 20 28 6a 20 3d 20 30  |    { for (j = 0|
00001b40  3b 20 6a 20 3c 20 6e 62  3b 20 6a 2b 2b 29 0a 20  |; j < nb; j++). |
00001b50  20 20 20 20 20 20 20 20  20 20 20 7b 20 75 20 3d  |           { u =|
00001b60  20 76 3b 0a 20 20 20 20  20 20 20 20 20 20 20 20  | v;.            |
00001b70  20 20 66 6f 72 20 28 6b  20 3d 20 30 3b 20 6b 20  |  for (k = 0; k |
00001b80  3c 20 6e 61 3b 20 6b 2b  2b 29 20 75 20 2b 3d 20  |< na; k++) u += |
00001b90  41 5b 69 5d 5b 6b 5d 2a  42 5b 6b 5d 5b 6a 5d 3b  |A[i][k]*B[k][j];|
00001ba0  0a 20 20 20 20 20 20 20  20 20 20 20 20 20 20 56  |.              V|
00001bb0  5b 69 5d 5b 6a 5d 20 3d  20 75 3b 0a 20 20 20 20  |[i][j] = u;.    |
00001bc0  20 20 20 20 20 20 20 20  7d 0a 20 20 20 20 20 20  |        }.      |
00001bd0  20 20 7d 0a 20 20 20 20  7d 0a 20 20 72 65 74 75  |  }.    }.  retu|
00001be0  72 6e 20 56 3b 0a 7d 0a  0a 74 72 61 63 65 28 41  |rn V;.}..trace(A|
00001bf0  29 0a 2f 2a 20 2d 2d 2d  2d 2d 2d 2d 2d 2d 2d 2d  |)./* -----------|
00001c00  2d 2d 2d 2d 2d 2d 2d 2d  2d 2d 2d 2d 2d 2d 2d 2d  |----------------|
00001c10  2d 2d 2d 2d 2d 2d 2d 2d  2d 2d 2d 2d 2d 2d 0a 20  |--------------. |
00001c20  20 20 52 65 74 75 72 6e  73 20 74 68 65 20 74 72  |  Returns the tr|
00001c30  61 63 65 20 6f 66 20 74  68 65 20 73 71 75 61 72  |ace of the squar|
00001c40  65 20 6d 61 74 72 69 78  20 41 2e 0a 20 20 20 2d  |e matrix A..   -|
00001c50  2d 2d 2d 2d 2d 2d 2d 2d  2d 2d 2d 2d 2d 2d 2d 2d  |----------------|
*
00001c70  2d 2d 2d 2d 2d 2d 2d 2d  2a 2f 0a 7b 0a 20 20 6c  |--------*/.{.  l|
00001c80  6f 63 61 6c 20 69 2c 6d  2c 6e 2c 74 3b 0a 20 20  |ocal i,m,n,t;.  |
00001c90  69 66 20 28 74 79 70 65  6f 66 28 41 29 20 21 3d  |if (typeof(A) !=|
00001ca0  20 56 45 43 54 4f 52 29  20 71 75 69 74 28 22 74  | VECTOR) quit("t|
00001cb0  72 61 63 65 3a 20 61 72  67 75 6d 65 6e 74 20 69  |race: argument i|
00001cc0  73 20 6e 6f 74 20 61 20  6d 61 74 72 69 78 5c 6e  |s not a matrix\n|
00001cd0  22 29 3b 0a 20 20 6d 20  3d 20 73 69 7a 65 6f 66  |");.  m = sizeof|
00001ce0  28 41 29 3b 0a 20 20 6e  20 3d 20 73 69 7a 65 6f  |(A);.  n = sizeo|
00001cf0  66 28 41 5b 30 5d 29 3b  0a 20 20 69 66 20 28 6d  |f(A[0]);.  if (m|
00001d00  20 21 3d 20 6e 29 20 71  75 69 74 28 22 74 72 61  | != n) quit("tra|
00001d10  63 65 3a 20 6d 61 74 72  69 78 20 69 73 20 6e 6f  |ce: matrix is no|
00001d20  74 20 73 71 75 61 72 65  5c 6e 22 29 3b 0a 20 20  |t square\n");.  |
00001d30  69 66 20 28 74 79 70 65  6f 66 28 41 5b 30 5d 29  |if (typeof(A[0])|
00001d40  20 3d 3d 20 52 45 41 4c  29 20 74 20 3d 20 30 2e  | == REAL) t = 0.|
00001d50  30 3b 20 65 6c 73 65 20  74 20 3d 20 30 3b 0a 20  |0; else t = 0;. |
00001d60  20 66 6f 72 20 28 69 20  3d 20 30 3b 20 69 20 3c  | for (i = 0; i <|
00001d70  20 6d 3b 20 69 2b 2b 29  20 74 20 2b 3d 20 41 5b  | m; i++) t += A[|
00001d80  69 5d 5b 69 5d 3b 0a 20  20 72 65 74 75 72 6e 20  |i][i];.  return |
00001d90  74 3b 0a 7d 0a 0a 74 72  61 6e 73 70 6f 73 65 28  |t;.}..transpose(|
00001da0  41 29 0a 2f 2a 20 2d 2d  2d 2d 2d 2d 2d 2d 2d 2d  |A)./* ----------|
00001db0  2d 2d 2d 2d 2d 2d 2d 2d  2d 2d 2d 2d 2d 2d 2d 2d  |----------------|
00001dc0  2d 2d 2d 2d 2d 2d 2d 2d  2d 2d 2d 2d 0a 20 20 20  |------------.   |
00001dd0  52 65 74 75 72 6e 73 20  74 68 65 20 74 72 61 6e  |Returns the tran|
00001de0  73 70 6f 73 65 20 6f 66  20 74 68 65 20 6d 61 74  |spose of the mat|
00001df0  72 69 78 20 41 2e 0a 20  20 20 2d 2d 2d 2d 2d 2d  |rix A..   ------|
00001e00  2d 2d 2d 2d 2d 2d 2d 2d  2d 2d 2d 2d 2d 2d 2d 2d  |----------------|
*
00001e20  2a 2f 0a 7b 0a 20 20 6c  6f 63 61 6c 20 69 2c 6a  |*/.{.  local i,j|
00001e30  2c 6d 2c 6e 2c 56 3b 0a  20 20 69 66 20 28 74 79  |,m,n,V;.  if (ty|
00001e40  70 65 6f 66 28 41 29 20  21 3d 20 56 45 43 54 4f  |peof(A) != VECTO|
00001e50  52 29 20 71 75 69 74 28  22 74 72 61 6e 73 70 6f  |R) quit("transpo|
00001e60  73 65 3a 20 61 72 67 75  6d 65 6e 74 20 69 73 20  |se: argument is |
00001e70  6e 6f 74 20 61 20 6d 61  74 72 69 78 5c 6e 22 29  |not a matrix\n")|
00001e80  3b 0a 20 20 6d 20 3d 20  73 69 7a 65 6f 66 28 41  |;.  m = sizeof(A|
00001e90  29 3b 0a 20 20 6e 20 3d  20 73 69 7a 65 6f 66 28  |);.  n = sizeof(|
00001ea0  41 5b 30 5d 29 3b 0a 20  20 69 66 20 28 74 79 70  |A[0]);.  if (typ|
00001eb0  65 6f 66 28 6e 29 20 21  3d 20 49 4e 54 45 47 45  |eof(n) != INTEGE|
00001ec0  52 29 20 71 75 69 74 28  22 74 72 61 6e 73 70 6f  |R) quit("transpo|
00001ed0  73 65 3a 20 61 72 67 75  6d 65 6e 74 20 69 73 20  |se: argument is |
00001ee0  6e 6f 74 20 61 20 6d 61  74 72 69 78 5c 6e 22 29  |not a matrix\n")|
00001ef0  3b 0a 20 20 56 20 3d 20  6e 65 77 6d 61 74 72 69  |;.  V = newmatri|
00001f00  78 28 6e 2c 6d 29 3b 0a  20 20 66 6f 72 20 28 69  |x(n,m);.  for (i|
00001f10  20 3d 20 30 3b 20 69 20  3c 20 6d 3b 20 69 2b 2b  | = 0; i < m; i++|
00001f20  29 0a 20 20 20 20 66 6f  72 20 28 6a 20 3d 20 30  |).    for (j = 0|
00001f30  3b 20 6a 20 3c 20 6e 3b  20 6a 2b 2b 29 20 56 5b  |; j < n; j++) V[|
00001f40  6a 5d 5b 69 5d 20 3d 20  41 5b 69 5d 5b 6a 5d 3b  |j][i] = A[i][j];|
00001f50  0a 20 20 72 65 74 75 72  6e 20 56 3b 0a 7d 0a 0a  |.  return V;.}..|
00001f60  69 6e 76 65 72 73 65 28  41 29 0a 2f 2a 20 2d 2d  |inverse(A)./* --|
00001f70  2d 2d 2d 2d 2d 2d 2d 2d  2d 2d 2d 2d 2d 2d 2d 2d  |----------------|
*
00001fa0  2d 2d 2d 2d 0a 20 20 20  52 65 74 75 72 6e 73 20  |----.   Returns |
00001fb0  74 68 65 20 69 6e 76 65  72 73 65 20 6f 66 20 61  |the inverse of a|
00001fc0  20 6e 6f 6e 2d 73 69 6e  67 75 6c 61 72 20 73 71  | non-singular sq|
00001fd0  75 61 72 65 20 6d 61 74  72 69 78 20 41 2e 0a 20  |uare matrix A.. |
00001fe0  20 20 2d 2d 2d 2d 2d 2d  2d 2d 2d 2d 2d 2d 2d 2d  |  --------------|
00001ff0  2d 2d 2d 2d 2d 2d 2d 2d  2d 2d 2d 2d 2d 2d 2d 2d  |----------------|
*
00002010  2d 2d 2d 2d 2d 2d 2d 2d  2a 2f 0a 7b 0a 20 20 6c  |--------*/.{.  l|
00002020  6f 63 61 6c 20 64 2c 69  2c 6a 2c 6b 2c 6c 2c 6d  |ocal d,i,j,k,l,m|
00002030  2c 6e 2c 6e 63 6f 6c 2c  6e 6f 72 6d 2c 70 2c 71  |,n,ncol,norm,p,q|
00002040  2c 73 2c 74 65 6d 70 76  2c 74 6f 6c 2c 56 3b 0a  |,s,tempv,tol,V;.|
00002050  20 20 69 66 20 28 74 79  70 65 6f 66 28 41 29 20  |  if (typeof(A) |
00002060  21 3d 20 56 45 43 54 4f  52 29 20 71 75 69 74 28  |!= VECTOR) quit(|
00002070  22 69 6e 76 65 72 73 65  3a 20 61 72 67 75 6d 65  |"inverse: argume|
00002080  6e 74 20 69 73 20 6e 6f  74 20 61 20 6d 61 74 72  |nt is not a matr|
00002090  69 78 5c 6e 22 29 3b 0a  20 20 6d 20 3d 20 73 69  |ix\n");.  m = si|
000020a0  7a 65 6f 66 28 41 29 3b  0a 20 20 6e 20 3d 20 73  |zeof(A);.  n = s|
000020b0  69 7a 65 6f 66 28 41 5b  30 5d 29 3b 0a 20 20 69  |izeof(A[0]);.  i|
000020c0  66 20 28 74 79 70 65 6f  66 28 6e 29 20 21 3d 20  |f (typeof(n) != |
000020d0  49 4e 54 45 47 45 52 29  20 71 75 69 74 28 22 69  |INTEGER) quit("i|
000020e0  6e 76 65 72 73 65 3a 20  61 72 67 75 6d 65 6e 74  |nverse: argument|
000020f0  20 69 73 20 6e 6f 74 20  61 20 6d 61 74 72 69 78  | is not a matrix|
00002100  5c 6e 22 29 3b 0a 20 20  69 66 20 28 6d 20 21 3d  |\n");.  if (m !=|
00002110  20 6e 29 20 71 75 69 74  28 22 69 6e 76 65 72 73  | n) quit("invers|
00002120  65 3a 20 6d 61 74 72 69  78 20 69 73 20 6e 6f 74  |e: matrix is not|
00002130  20 73 71 75 61 72 65 5c  6e 22 29 3b 0a 20 20 0a  | square\n");.  .|
00002140  20 20 2f 2a 20 2d 2d 2d  20 66 6f 72 6d 20 61 75  |  /* --- form au|
00002150  67 6d 65 6e 74 65 64 20  6d 61 74 72 69 78 20 55  |gmented matrix U|
00002160  20 3d 28 41 2c 49 29 20  2d 2d 2d 20 20 2a 2f 20  | =(A,I) ---  */ |
00002170  0a 20 20 6e 63 6f 6c 20  3d 20 32 2a 6e 3b 0a 20  |.  ncol = 2*n;. |
00002180  20 55 20 3d 20 6e 65 77  6d 61 74 72 69 78 28 6d  | U = newmatrix(m|
00002190  2c 6e 63 6f 6c 29 3b 0a  20 20 66 6f 72 20 28 69  |,ncol);.  for (i|
000021a0  20 3d 20 30 3b 20 69 20  3c 20 6d 3b 20 69 2b 2b  | = 0; i < m; i++|
000021b0  29 0a 20 20 20 20 7b 20  66 6f 72 20 28 6a 20 3d  |).    { for (j =|
000021c0  20 30 3b 20 6a 20 3c 20  6e 3b 20 6a 2b 2b 29 20  | 0; j < n; j++) |
000021d0  55 5b 69 5d 5b 6a 5d 20  3d 20 31 2e 30 2a 41 5b  |U[i][j] = 1.0*A[|
000021e0  69 5d 5b 6a 5d 3b 0a 20  20 20 20 20 20 66 6f 72  |i][j];.      for|
000021f0  20 28 6a 20 3d 20 6e 3b  20 6a 20 3c 20 6e 63 6f  | (j = n; j < nco|
00002200  6c 3b 20 6a 2b 2b 29 20  55 5b 69 5d 5b 6a 5d 20  |l; j++) U[i][j] |
00002210  3d 20 30 2e 30 3b 0a 20  20 20 20 20 20 55 5b 69  |= 0.0;.      U[i|
00002220  5d 5b 69 2b 6e 5d 20 3d  20 31 2e 30 3b 0a 20 20  |][i+n] = 1.0;.  |
00002230  20 20 7d 0a 20 20 2f 2a  20 2d 2d 2d 20 73 65 74  |  }.  /* --- set|
00002240  20 74 6f 6c 65 72 61 6e  63 65 20 2d 2d 2d 20 2a  | tolerance --- *|
00002250  2f 20 0a 20 20 6e 6f 72  6d 20 3d 20 30 2e 30 3b  |/ .  norm = 0.0;|
00002260  0a 20 20 66 6f 72 20 28  69 20 3d 20 30 20 3b 69  |.  for (i = 0 ;i|
00002270  20 3c 20 6d 3b 20 69 2b  2b 29 0a 20 20 20 20 7b  | < m; i++).    {|
00002280  20 66 6f 72 20 28 6a 20  3d 20 30 20 3b 6a 20 3c  | for (j = 0 ;j <|
00002290  20 6e 3b 20 6a 2b 2b 29  20 6e 6f 72 6d 20 2b 3d  | n; j++) norm +=|
000022a0  20 61 62 73 28 55 5b 69  5d 5b 6a 5d 29 3b 0a 20  | abs(U[i][j]);. |
000022b0  20 20 20 7d 0a 20 20 69  66 20 28 6e 6f 72 6d 20  |   }.  if (norm |
000022c0  3d 3d 20 30 2e 30 29 20  6e 6f 72 6d 20 3d 20 31  |== 0.0) norm = 1|
000022d0  2e 30 3b 0a 20 20 74 6f  6c 20 3d 20 6e 6f 72 6d  |.0;.  tol = norm|
000022e0  2f 31 30 30 30 30 30 30  2e 30 3b 0a 0a 20 20 64  |/1000000.0;..  d|
000022f0  20 3d 20 31 2e 30 3b 20  2f 2a 20 2d 2d 2d 20 69  | = 1.0; /* --- i|
00002300  6e 69 74 69 61 6c 69 73  65 20 64 65 74 65 72 6d  |nitialise determ|
00002310  69 6e 61 6e 74 20 2d 2d  2d 20 2a 2f 0a 20 20 74  |inant --- */.  t|
00002320  65 6d 70 76 20 3d 20 6e  65 77 76 65 63 74 6f 72  |empv = newvector|
00002330  28 6e 63 6f 6c 29 3b 20  2f 2a 20 2d 2d 2d 20 66  |(ncol); /* --- f|
00002340  6f 72 20 72 6f 77 20 69  6e 74 65 72 63 68 61 6e  |or row interchan|
00002350  67 65 20 2d 2d 2d 20 2a  2f 0a 0a 20 20 2f 2a 20  |ge --- */..  /* |
00002360  2d 2d 2d 20 72 6f 77 20  6f 70 65 72 61 74 69 6f  |--- row operatio|
00002370  6e 73 20 6f 6e 20 55 20  74 6f 20 72 65 64 75 63  |ns on U to reduc|
00002380  65 20 41 20 74 6f 20 75  70 2e 74 72 20 66 6f 72  |e A to up.tr for|
00002390  6d 20 2d 2d 2d 20 2a 2f  0a 20 20 66 6f 72 20 28  |m --- */.  for (|
000023a0  69 20 3d 20 30 3b 20 69  20 3c 20 6d 3b 20 69 2b  |i = 0; i < m; i+|
000023b0  2b 29 0a 20 20 20 20 7b  20 2f 2a 20 2d 2d 2d 20  |+).    { /* --- |
000023c0  66 69 6e 64 20 70 69 76  6f 74 20 2d 2d 2d 20 2a  |find pivot --- *|
000023d0  2f 0a 20 20 20 20 20 20  73 20 3d 20 30 2e 30 3b  |/.      s = 0.0;|
000023e0  0a 20 20 20 20 20 20 66  6f 72 20 28 6a 20 3d 20  |.      for (j = |
000023f0  69 3b 20 6a 20 3c 20 6d  3b 20 6a 2b 2b 29 0a 20  |i; j < m; j++). |
00002400  20 20 20 20 20 20 20 7b  20 69 66 20 28 61 62 73  |       { if (abs|
00002410  28 55 5b 6a 5d 5b 69 5d  29 20 3e 20 73 29 0a 20  |(U[j][i]) > s). |
00002420  20 20 20 20 20 20 20 20  20 20 20 7b 20 73 20 3d  |           { s =|
00002430  20 61 62 73 28 55 5b 6a  5d 5b 69 5d 29 3b 20 65  | abs(U[j][i]); e|
00002440  3d 6a 3b 20 7d 0a 20 20  20 20 20 20 20 20 7d 0a  |=j; }.        }.|
00002450  20 20 20 20 20 20 69 66  20 28 65 20 21 3d 20 69  |      if (e != i|
00002460  29 0a 20 20 20 20 20 20  20 20 7b 20 2f 2a 20 2d  |).        { /* -|
00002470  2d 2d 20 69 6e 74 65 72  63 68 61 6e 67 65 20 72  |-- interchange r|
00002480  6f 77 73 20 69 20 26 20  65 20 2d 2d 2d 20 2a 2f  |ows i & e --- */|
00002490  0a 20 20 20 20 20 20 20  20 20 20 74 65 6d 70 76  |.          tempv|
000024a0  20 3d 20 55 5b 65 5d 3b  20 55 5b 65 5d 20 3d 20  | = U[e]; U[e] = |
000024b0  55 5b 69 5d 3b 20 55 5b  69 5d 20 3d 20 74 65 6d  |U[i]; U[i] = tem|
000024c0  70 76 3b 0a 20 20 20 20  20 20 20 20 20 20 64 20  |pv;.          d |
000024d0  3d 20 2d 64 3b 0a 20 20  20 20 20 20 20 20 7d 0a  |= -d;.        }.|
000024e0  0a 20 20 20 20 20 20 64  20 3d 20 64 2a 55 5b 69  |.      d = d*U[i|
000024f0  5d 5b 69 5d 3b 20 69 66  20 28 61 62 73 28 64 29  |][i]; if (abs(d)|
00002500  20 3c 20 74 6f 6c 29 20  71 75 69 74 28 22 69 6e  | < tol) quit("in|
00002510  76 65 72 73 65 3a 20 6d  61 74 72 69 78 20 69 73  |verse: matrix is|
00002520  20 73 69 6e 67 75 6c 61  72 5c 6e 22 29 3b 0a 0a  | singular\n");..|
00002530  20 20 20 20 20 20 2f 2a  20 2d 2d 2d 20 6d 61 6b  |      /* --- mak|
00002540  65 20 75 6e 69 74 20 64  69 61 67 6f 6e 61 6c 20  |e unit diagonal |
00002550  2d 2d 2d 20 2a 2f 0a 20  20 20 20 20 20 71 20 3d  |--- */.      q =|
00002560  20 31 2e 30 20 2f 20 55  5b 69 5d 5b 69 5d 3b 0a  | 1.0 / U[i][i];.|
00002570  20 20 20 20 20 20 66 6f  72 20 28 6a 3d 69 20 3b  |      for (j=i ;|
00002580  6a 20 3c 20 6e 63 6f 6c  3b 20 6a 2b 2b 29 20 55  |j < ncol; j++) U|
00002590  5b 69 5d 5b 6a 5d 20 3d  20 71 2a 55 5b 69 5d 5b  |[i][j] = q*U[i][|
000025a0  6a 5d 3b 0a 0a 20 20 20  20 20 20 2f 2a 20 2d 2d  |j];..      /* --|
000025b0  2d 20 66 6f 72 6d 20 75  70 2e 74 72 20 41 20 2d  |- form up.tr A -|
000025c0  2d 2d 20 2a 2f 0a 20 20  20 20 20 20 66 6f 72 20  |-- */.      for |
000025d0  28 6b 20 3d 20 69 2b 31  20 3b 6b 20 3c 20 6d 3b  |(k = i+1 ;k < m;|
000025e0  20 6b 2b 2b 29 0a 20 20  20 20 20 20 20 20 7b 20  | k++).        { |
000025f0  70 20 3d 20 55 5b 6b 5d  5b 69 5d 3b 0a 20 20 20  |p = U[k][i];.   |
00002600  20 20 20 20 20 20 20 66  6f 72 20 28 6c 3d 69 3b  |       for (l=i;|
00002610  20 6c 20 3c 20 6e 63 6f  6c 3b 20 6c 2b 2b 29 0a  | l < ncol; l++).|
00002620  20 20 20 20 20 20 20 20  20 20 20 20 7b 20 74 65  |            { te|
00002630  6d 70 20 3d 20 55 5b 6b  5d 5b 6c 5d 20 2d 20 70  |mp = U[k][l] - p|
00002640  2a 55 5b 69 5d 5b 6c 5d  3b 20 55 5b 6b 5d 5b 6c  |*U[i][l]; U[k][l|
00002650  5d 20 3d 20 74 65 6d 70  3b 0a 20 20 20 20 20 20  |] = temp;.      |
00002660  20 20 20 20 20 20 20 20  69 66 20 28 61 62 73 28  |        if (abs(|
00002670  55 5b 6b 5d 5b 6c 5d 29  20 3c 20 74 6f 6c 29 20  |U[k][l]) < tol) |
00002680  55 5b 6b 5d 5b 6c 5d 3d  30 2e 30 3b 0a 20 20 20  |U[k][l]=0.0;.   |
00002690  20 20 20 20 20 20 20 20  20 7d 0a 20 20 20 20 20  |         }.     |
000026a0  20 20 20 7d 0a 20 20 20  20 7d 0a 0a 20 20 64 3d  |   }.    }..  d=|
000026b0  64 20 2a 20 55 5b 6d 2d  31 5d 5b 6d 2d 31 5d 3b  |d * U[m-1][m-1];|
000026c0  20 2f 2a 20 2d 2d 2d 20  64 20 69 73 20 74 68 65  | /* --- d is the|
000026d0  20 76 61 6c 75 65 20 6f  66 20 64 65 74 20 41 20  | value of det A |
000026e0  2d 2d 2d 20 2a 2f 0a 20  20 69 66 20 28 61 62 73  |--- */.  if (abs|
000026f0  28 64 29 20 3c 20 74 6f  6c 29 20 71 75 69 74 28  |(d) < tol) quit(|
00002700  22 69 6e 76 65 72 73 65  3a 20 6d 61 74 72 69 78  |"inverse: matrix|
00002710  20 69 73 20 73 69 6e 67  75 6c 61 72 5c 6e 22 29  | is singular\n")|
00002720  3b 0a 20 20 0a 20 20 69  66 20 28 6d 20 3e 20 31  |;.  .  if (m > 1|
00002730  29 0a 20 20 20 20 2f 2a  20 2d 2d 2d 20 72 65 64  |).    /* --- red|
00002740  75 63 65 20 55 20 74 6f  20 28 49 2c 69 6e 76 28  |uce U to (I,inv(|
00002750  41 29 29 20 2d 2d 2d 20  2a 2f 0a 20 20 20 20 7b  |A)) --- */.    {|
00002760  20 66 6f 72 20 28 6c 20  3d 20 6d 3b 20 6c 3c 20  | for (l = m; l< |
00002770  6e 63 6f 6c 3b 20 6c 2b  2b 29 0a 20 20 20 20 20  |ncol; l++).     |
00002780  20 20 7b 0a 20 20 20 20  20 20 20 20 20 66 6f 72  |  {.         for|
00002790  20 28 69 3d 6d 2d 31 20  3b 20 69 20 3e 3d 20 30  | (i=m-1 ; i >= 0|
000027a0  3b 20 69 2d 2d 29 0a 20  20 20 20 20 20 20 20 20  |; i--).         |
000027b0  20 20 7b 73 20 3d 20 55  5b 69 5d 5b 6c 5d 3b 0a  |  {s = U[i][l];.|
000027c0  20 20 20 20 20 20 20 20  20 20 20 20 20 66 6f 72  |             for|
000027d0  20 28 6a 3d 69 2b 31 20  3b 20 6a 20 3c 20 6e 3b  | (j=i+1 ; j < n;|
000027e0  20 6a 2b 2b 29 20 73 3d  73 2d 55 5b 69 5d 5b 6a  | j++) s=s-U[i][j|
000027f0  5d 2a 55 5b 6a 5d 5b 6c  5d 3b 0a 20 20 20 20 20  |]*U[j][l];.     |
00002800  20 20 20 20 20 20 20 20  55 5b 69 5d 5b 6c 5d 20  |        U[i][l] |
00002810  3d 20 73 3b 0a 20 20 20  20 20 20 20 20 20 20 20  |= s;.           |
00002820  7d 0a 20 20 20 20 20 20  20 7d 20 20 20 20 0a 20  |}.       }    . |
00002830  20 20 20 7d 0a 20 20 20  20 0a 20 20 56 20 3d 20  |   }.    .  V = |
00002840  6e 65 77 6d 61 74 72 69  78 28 6d 2c 6e 29 3b 0a  |newmatrix(m,n);.|
00002850  20 20 2f 2a 20 2d 2d 2d  20 74 72 61 6e 73 66 65  |  /* --- transfe|
00002860  72 20 69 6e 76 65 72 73  65 20 74 6f 20 56 20 2d  |r inverse to V -|
00002870  2d 2d 20 2a 2f 0a 20 20  66 6f 72 20 28 69 20 3d  |-- */.  for (i =|
00002880  20 30 3b 20 69 20 3c 20  6d 3b 20 69 2b 2b 29 0a  | 0; i < m; i++).|
00002890  20 20 20 20 7b 20 66 6f  72 20 28 6a 20 3d 20 30  |    { for (j = 0|
000028a0  3b 20 6a 20 3c 20 6e 3b  20 6a 2b 2b 29 20 56 5b  |; j < n; j++) V[|
000028b0  69 5d 5b 6a 5d 20 3d 20  55 5b 69 5d 5b 6a 2b 6e  |i][j] = U[i][j+n|
000028c0  5d 3b 0a 20 20 20 20 7d  0a 20 20 20 20 0a 20 20  |];.    }.    .  |
000028d0  72 65 74 75 72 6e 20 56  3b 0a 7d 0a 0a 63 6f 6e  |return V;.}..con|
000028e0  63 61 74 28 41 2c 42 29  0a 2f 2a 20 2d 2d 2d 2d  |cat(A,B)./* ----|
000028f0  2d 2d 2d 2d 2d 2d 2d 2d  2d 2d 2d 2d 2d 2d 2d 2d  |----------------|
*
00002920  2d 2d 2d 2d 2d 2d 2d 2d  2d 2d 2d 2d 2d 2d 2d 0a  |---------------.|
00002930  20 20 20 52 65 74 75 72  6e 73 20 74 68 65 20 61  |   Returns the a|
00002940  72 72 61 79 20 63 6f 6e  63 61 74 65 6e 61 74 69  |rray concatenati|
00002950  6f 6e 20 41 20 2b 20 42  20 6f 66 20 74 68 65 20  |on A + B of the |
00002960  53 54 52 49 4e 47 20 61  72 72 61 79 73 20 41 20  |STRING arrays A |
00002970  61 6e 64 20 42 2e 0a 20  20 20 2d 2d 2d 2d 2d 2d  |and B..   ------|
00002980  2d 2d 2d 2d 2d 2d 2d 2d  2d 2d 2d 2d 2d 2d 2d 2d  |----------------|
*
000029b0  2d 2d 2d 2d 2d 2d 2d 2d  2d 2d 2d 2d 2d 2a 2f 0a  |-------------*/.|
000029c0  7b 0a 20 20 6c 6f 63 61  6c 20 69 2c 6a 2c 6b 2c  |{.  local i,j,k,|
000029d0  6d 61 2c 6e 61 2c 6d 62  2c 6e 62 2c 74 2c 74 61  |ma,na,mb,nb,t,ta|
000029e0  2c 74 62 2c 56 3b 0a 20  20 74 61 20 3d 20 74 79  |,tb,V;.  ta = ty|
000029f0  70 65 6f 66 28 41 29 3b  20 74 62 20 3d 20 74 79  |peof(A); tb = ty|
00002a00  70 65 6f 66 28 42 29 3b  0a 20 20 69 66 20 28 74  |peof(B);.  if (t|
00002a10  61 20 21 3d 20 56 45 43  54 4f 52 29 20 71 75 69  |a != VECTOR) qui|
00002a20  74 28 22 63 6f 6e 63 61  74 3a 20 31 73 74 20 61  |t("concat: 1st a|
00002a30  72 67 75 6d 65 6e 74 20  69 73 20 6e 6f 74 20 61  |rgument is not a|
00002a40  6e 20 61 72 72 61 79 5c  6e 22 29 3b 0a 20 20 69  |n array\n");.  i|
00002a50  66 20 28 74 62 20 21 3d  20 56 45 43 54 4f 52 29  |f (tb != VECTOR)|
00002a60  20 71 75 69 74 28 22 63  6f 6e 63 61 74 3a 20 32  | quit("concat: 2|
00002a70  6e 64 20 61 72 67 75 6d  65 6e 74 20 69 73 20 6e  |nd argument is n|
00002a80  6f 74 20 61 6e 20 61 72  72 61 79 5c 6e 22 29 3b  |ot an array\n");|
00002a90  0a 20 20 6d 61 20 3d 20  73 69 7a 65 6f 66 28 41  |.  ma = sizeof(A|
00002aa0  29 3b 0a 20 20 6d 62 20  3d 20 73 69 7a 65 6f 66  |);.  mb = sizeof|
00002ab0  28 42 29 3b 0a 20 20 6e  61 20 3d 20 73 69 7a 65  |(B);.  na = size|
00002ac0  6f 66 28 41 5b 30 5d 29  3b 0a 20 20 6e 62 20 3d  |of(A[0]);.  nb =|
00002ad0  20 73 69 7a 65 6f 66 28  42 5b 30 5d 29 3b 0a 20  | sizeof(B[0]);. |
00002ae0  20 74 61 20 3d 20 74 79  70 65 6f 66 28 6e 61 29  | ta = typeof(na)|
00002af0  3b 20 74 62 20 3d 20 74  79 70 65 6f 66 28 6e 62  |; tb = typeof(nb|
00002b00  29 3b 0a 20 20 69 66 20  28 74 61 20 21 3d 20 74  |);.  if (ta != t|
00002b10  62 29 20 71 75 69 74 28  22 63 6f 6e 63 61 74 3a  |b) quit("concat:|
00002b20  20 61 72 72 61 79 73 20  61 72 65 20 6e 6f 74 20  | arrays are not |
00002b30  6f 66 20 73 61 6d 65 20  74 79 70 65 5c 6e 22 29  |of same type\n")|
00002b40  3b 0a 20 20 69 66 20 28  74 61 20 21 3d 20 49 4e  |;.  if (ta != IN|
00002b50  54 45 47 45 52 29 0a 20  20 20 20 7b 20 69 66 20  |TEGER).    { if |
00002b60  28 6d 61 20 21 3d 20 6d  62 29 20 71 75 69 74 28  |(ma != mb) quit(|
00002b70  22 63 6f 6e 63 61 74 3a  20 76 65 63 74 6f 72 73  |"concat: vectors|
00002b80  20 61 72 65 20 69 6e 63  6f 6d 70 61 74 69 62 6c  | are incompatibl|
00002b90  65 20 66 6f 72 20 63 6f  6e 63 61 74 69 6e 61 74  |e for concatinat|
00002ba0  69 6f 6e 5c 6e 22 29 3b  0a 20 20 20 20 20 20 74  |ion\n");.      t|
00002bb0  20 3d 20 74 79 70 65 6f  66 28 41 5b 30 5d 29 3b  | = typeof(A[0]);|
00002bc0  0a 20 20 20 20 20 20 69  66 20 28 74 20 21 3d 20  |.      if (t != |
00002bd0  53 54 52 49 4e 47 29 20  20 71 75 69 74 28 22 63  |STRING)  quit("c|
00002be0  6f 6e 63 61 74 3a 20 31  73 74 20 61 72 67 75 6d  |oncat: 1st argum|
00002bf0  65 6e 74 20 69 73 20 6e  6f 74 20 6f 66 20 74 79  |ent is not of ty|
00002c00  70 65 20 53 54 52 49 4e  47 5c 6e 22 29 3b 0a 20  |pe STRING\n");. |
00002c10  20 20 20 20 20 74 20 3d  20 74 79 70 65 6f 66 28  |     t = typeof(|
00002c20  42 5b 30 5d 29 3b 0a 20  20 20 20 20 20 69 66 20  |B[0]);.      if |
00002c30  28 74 20 21 3d 20 53 54  52 49 4e 47 29 20 20 71  |(t != STRING)  q|
00002c40  75 69 74 28 22 63 6f 6e  63 61 74 3a 20 32 6e 64  |uit("concat: 2nd|
00002c50  20 61 72 67 75 6d 65 6e  74 20 69 73 20 6e 6f 74  | argument is not|
00002c60  20 6f 66 20 74 79 70 65  20 53 54 52 49 4e 47 5c  | of type STRING\|
00002c70  6e 22 29 3b 0a 20 20 20  20 20 20 56 20 3d 20 6e  |n");.      V = n|
00002c80  65 77 76 65 63 74 6f 72  3b 0a 20 20 20 20 20 20  |ewvector;.      |
00002c90  66 6f 72 20 28 6a 20 3d  20 30 3b 20 6a 20 3c 6d  |for (j = 0; j <m|
00002ca0  62 3b 20 6a 2b 2b 29 20  56 5b 6a 5d 20 3d 20 41  |b; j++) V[j] = A|
00002cb0  5b 6a 5d 20 2b 20 42 5b  6a 5d 3b 0a 20 20 20 20  |[j] + B[j];.    |
00002cc0  7d 0a 20 20 65 6c 73 65  20 0a 20 20 20 20 7b 20  |}.  else .    { |
00002cd0  69 66 20 28 28 6d 61 20  21 3d 20 6d 62 29 20 7c  |if ((ma != mb) ||
00002ce0  7c 20 28 6e 61 20 21 3d  20 6e 62 29 29 20 71 75  || (na != nb)) qu|
00002cf0  69 74 28 22 63 6f 6e 63  61 74 3a 20 6d 61 74 72  |it("concat: matr|
00002d00  69 63 65 73 20 61 72 65  20 69 6e 63 6f 6d 70 61  |ices are incompa|
00002d10  74 69 62 6c 65 20 66 6f  72 20 63 6f 6e 63 61 74  |tible for concat|
00002d20  69 6e 61 74 69 6f 6e 5c  6e 22 29 3b 0a 20 20 20  |ination\n");.   |
00002d30  20 20 20 74 20 3d 20 74  79 70 65 6f 66 28 41 5b  |   t = typeof(A[|
00002d40  30 5d 5b 30 5d 29 3b 0a  20 20 20 20 20 20 69 66  |0][0]);.      if|
00002d50  20 28 74 20 21 3d 20 53  54 52 49 4e 47 29 20 20  | (t != STRING)  |
00002d60  71 75 69 74 28 22 63 6f  6e 63 61 74 3a 20 31 73  |quit("concat: 1s|
00002d70  74 20 61 72 67 75 6d 65  6e 74 20 69 73 20 6e 6f  |t argument is no|
00002d80  74 20 6f 66 20 74 79 70  65 20 53 54 52 49 4e 47  |t of type STRING|
00002d90  5c 6e 22 29 3b 0a 20 20  20 20 20 20 74 20 3d 20  |\n");.      t = |
00002da0  74 79 70 65 6f 66 28 42  5b 30 5d 5b 30 5d 29 3b  |typeof(B[0][0]);|
00002db0  0a 20 20 20 20 20 20 69  66 20 28 74 20 21 3d 20  |.      if (t != |
00002dc0  53 54 52 49 4e 47 29 20  20 71 75 69 74 28 22 63  |STRING)  quit("c|
00002dd0  6f 6e 63 61 74 3a 20 32  6e 64 20 61 72 67 75 6d  |oncat: 2nd argum|
00002de0  65 6e 74 20 69 73 20 6e  6f 74 20 6f 66 20 74 79  |ent is not of ty|
00002df0  70 65 20 53 54 52 49 4e  47 5c 6e 22 29 3b 0a 20  |pe STRING\n");. |
00002e00  20 20 20 20 20 56 20 3d  20 6e 65 77 6d 61 74 72  |     V = newmatr|
00002e10  69 78 28 6d 61 2c 6e 61  29 3b 0a 20 20 20 20 20  |ix(ma,na);.     |
00002e20  20 66 6f 72 20 28 69 20  3d 20 30 3b 20 69 20 3c  | for (i = 0; i <|
00002e30  20 6d 61 3b 20 69 2b 2b  29 0a 20 20 20 20 20 20  | ma; i++).      |
00002e40  20 20 7b 20 66 6f 72 20  28 6a 20 3d 20 30 3b 20  |  { for (j = 0; |
00002e50  6a 20 3c 20 6e 62 3b 20  6a 2b 2b 29 20 56 5b 69  |j < nb; j++) V[i|
00002e60  5d 5b 6a 5d 20 3d 20 41  5b 69 5d 5b 6a 5d 20 2b  |][j] = A[i][j] +|
00002e70  20 42 5b 69 5d 5b 6a 5d  3b 0a 20 20 20 20 20 20  | B[i][j];.      |
00002e80  20 20 7d 0a 20 20 20 20  7d 0a 20 20 72 65 74 75  |  }.    }.  retu|
00002e90  72 6e 20 56 3b 0a 7d 0a  0a 0a 6e 65 77 6d 61 74  |rn V;.}...newmat|
00002ea0  72 69 78 28 6d 2c 6e 29  0a 2f 2a 20 2d 2d 2d 2d  |rix(m,n)./* ----|
00002eb0  2d 2d 2d 2d 2d 2d 2d 2d  2d 2d 2d 2d 2d 2d 2d 2d  |----------------|
*
00002ee0  2d 0a 20 20 20 52 65 74  75 72 6e 73 20 61 20 6e  |-.   Returns a n|
00002ef0  65 77 20 6d 20 78 20 6e  20 6d 61 74 72 69 78 20  |ew m x n matrix |
00002f00  77 69 74 68 20 65 6c 65  6d 65 6e 74 73 20 6f 66  |with elements of|
00002f10  20 74 79 70 65 20 4e 49  4c 2e 0a 20 20 20 2d 2d  | type NIL..   --|
00002f20  2d 2d 2d 2d 2d 2d 2d 2d  2d 2d 2d 2d 2d 2d 2d 2d  |----------------|
*
00002f50  2d 2d 2d 2a 2f 0a 7b 0a  20 20 6c 6f 63 61 6c 20  |---*/.{.  local |
00002f60  69 2c 56 3b 0a 20 20 56  20 3d 20 6e 65 77 76 65  |i,V;.  V = newve|
00002f70  63 74 6f 72 28 6d 29 3b  0a 20 20 66 6f 72 28 69  |ctor(m);.  for(i|
00002f80  20 3d 20 30 3b 20 69 20  3c 20 6d 3b 20 69 2b 2b  | = 0; i < m; i++|
00002f90  29 0a 20 20 20 20 56 5b  69 5d 20 3d 20 6e 65 77  |).    V[i] = new|
00002fa0  76 65 63 74 6f 72 28 6e  29 3b 0a 20 20 72 65 74  |vector(n);.  ret|
00002fb0  75 72 6e 20 56 3b 0a 7d  0a 0a 61 62 73 28 6e 29  |urn V;.}..abs(n)|
00002fc0  0a 7b 20 6c 6f 63 61 6c  20 6d 3b 0a 20 20 69 66  |.{ local m;.  if|
00002fd0  20 28 6e 20 3c 20 30 2e  30 29 20 6d 20 3d 20 2d  | (n < 0.0) m = -|
00002fe0  6e 3b 20 65 6c 73 65 20  6d 20 3d 20 6e 3b 0a 20  |n; else m = n;. |
00002ff0  20 72 65 74 75 72 6e 20  6d 3b 0a 7d 0a 0a 20 0a  | return m;.}.. .|
00003000  69 6e 74 5f 31 30 28 6e  29 0a 2f 2a 20 2d 2d 2d  |int_10(n)./* ---|
00003010  2d 2d 2d 2d 2d 2d 2d 2d  2d 2d 2d 2d 2d 2d 2d 2d  |----------------|
*
00003030  2d 2d 0a 20 20 20 52 65  74 75 72 6e 73 20 64 65  |--.   Returns de|
00003040  63 69 6d 61 6c 20 73 74  72 69 6e 67 20 66 6f 72  |cimal string for|
00003050  20 69 6e 74 65 67 65 72  20 6e 2e 0a 20 20 20 2d  | integer n..   -|
00003060  2d 2d 2d 2d 2d 2d 2d 2d  2d 2d 2d 2d 2d 2d 2d 2d  |----------------|
*
00003080  2d 2d 2d 2d 2a 2f 0a 7b  0a 20 20 6c 6f 63 61 6c  |----*/.{.  local|
00003090  20 73 3b 0a 20 20 73 20  3d 20 22 22 3b 0a 20 20  | s;.  s = "";.  |
000030a0  69 66 20 28 6e 20 3d 3d  20 30 29 20 73 20 3d 20  |if (n == 0) s = |
000030b0  22 30 22 3b 0a 20 20 65  6c 73 65 20 77 68 69 6c  |"0";.  else whil|
000030c0  65 28 6e 29 20 7b 20 73  20 3d 20 27 30 27 20 2b  |e(n) { s = '0' +|
000030d0  20 6e 25 31 30 20 2b 20  73 3b 20 6e 20 2f 3d 20  | n%10 + s; n /= |
000030e0  31 30 3b 20 7d 0a 20 20  72 65 74 75 72 6e 20 73  |10; }.  return s|
000030f0  3b 0a 7d 0a 0a                                    |;.}..|
000030f5