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Unknown  |  1994-01-13  |  6.4 KB

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+--------+-------------------------+-------------------------+--------+--------+
|00000000| 72 6f 28 59 29 3b 0a 20 | 20 20 6d 5f 7a 65 72 6f |ro(Y);. | m_zero|
|00000010| 28 6f 75 74 29 3b 0a 20 | 20 20 0a 23 64 65 66 69 |(out);. | .#defi|
|00000020| 6e 65 20 5a 28 6b 29 20 | 20 20 20 20 28 28 6b 29 |ne Z(k) | ((k)|
|00000030| 20 26 20 31 20 3f 20 74 | 6d 70 20 3a 20 26 79 30 | & 1 ? t|mp : &y0|
|00000040| 29 0a 23 64 65 66 69 6e | 65 20 5a 5a 28 6b 29 20 |).#defin|e ZZ(k) |
|00000050| 20 20 20 28 28 6b 29 20 | 26 20 31 20 3f 20 74 6d | ((k) |& 1 ? tm|
|00000060| 70 2d 3e 76 65 20 3a 20 | 79 30 2e 76 65 29 0a 0a |p->ve : |y0.ve)..|
|00000070| 20 20 20 66 6f 72 28 20 | 6a 20 3d 20 30 3b 20 6a | for( |j = 0; j|
|00000080| 20 3c 20 41 2d 3e 6e 3b | 20 6a 2b 2b 29 0a 20 20 | < A->n;| j++). |
|00000090| 20 7b 0a 20 20 20 20 20 | 20 69 66 28 20 6a 20 3e | {. | if( j >|
|000000a0| 20 30 20 29 0a 09 59 2d | 3e 6d 65 5b 30 5d 5b 6a | 0 )..Y-|>me[0][j|
|000000b0| 2d 31 5d 20 3d 20 30 2e | 30 3b 0a 20 20 20 20 20 |-1] = 0.|0;. |
|000000c0| 20 59 2d 3e 6d 65 5b 30 | 5d 5b 6a 5d 20 3d 20 31 | Y->me[0|][j] = 1|
|000000d0| 2e 30 3b 0a 0a 20 20 20 | 20 20 20 79 30 2e 76 65 |.0;.. | y0.ve|
|000000e0| 20 3d 20 59 2d 3e 6d 65 | 5b 30 5d 3b 0a 20 20 20 | = Y->me|[0];. |
|000000f0| 20 20 20 66 6f 72 20 28 | 6b 20 3d 20 30 3b 20 6b | for (|k = 0; k|
|00000100| 20 3c 20 73 2d 31 3b 20 | 6b 2b 2b 29 0a 20 20 20 | < s-1; |k++). |
|00000110| 20 20 20 7b 0a 09 20 79 | 31 2e 76 65 20 3d 20 59 | {.. y|1.ve = Y|
|00000120| 2d 3e 6d 65 5b 6b 2b 31 | 5d 3b 0a 09 20 6d 76 5f |->me[k+1|];.. mv_|
|00000130| 6d 6c 74 28 41 2c 26 79 | 30 2c 26 79 31 29 3b 0a |mlt(A,&y|0,&y1);.|
|00000140| 09 20 79 30 2e 76 65 20 | 3d 20 79 31 2e 76 65 3b |. y0.ve |= y1.ve;|
|00000150| 0a 20 20 20 20 20 20 7d | 0a 20 20 20 20 20 20 0a |. }|. .|
|00000160| 20 20 20 20 20 20 79 30 | 2e 76 65 20 3d 20 6f 75 | y0|.ve = ou|
|00000170| 74 2d 3e 6d 65 5b 6a 5d | 3b 0a 0a 20 20 20 20 20 |t->me[j]|;.. |
|00000180| 20 74 20 3d 20 73 2a 72 | 3b 0a 20 20 20 20 20 20 | t = s*r|;. |
|00000190| 66 6f 72 20 28 20 6c 20 | 3d 20 30 3b 20 6c 20 3c |for ( l |= 0; l <|
|000001a0| 3d 20 71 2d 74 3b 20 6c | 2b 2b 20 29 0a 09 5f 5f |= q-t; l|++ )..__|
|000001b0| 6d 6c 74 61 64 64 5f 5f | 28 79 30 2e 76 65 2c 59 |mltadd__|(y0.ve,Y|
|000001c0| 2d 3e 6d 65 5b 6c 5d 2c | 61 2d 3e 76 65 5b 74 2b |->me[l],|a->ve[t+|
|000001d0| 6c 5d 2c 59 2d 3e 6e 29 | 3b 0a 20 20 20 20 20 20 |l],Y->n)|;. |
|000001e0| 0a 20 20 20 20 20 20 66 | 6f 72 20 28 6b 3d 31 3b |. f|or (k=1;|
|000001f0| 20 6b 20 3c 3d 20 72 3b | 20 6b 2b 2b 29 0a 20 20 | k <= r;| k++). |
|00000200| 20 20 20 20 7b 0a 09 20 | 6d 76 5f 6d 6c 74 28 41 | {.. |mv_mlt(A|
|00000210| 70 6f 77 2c 5a 28 6b 2d | 31 29 2c 5a 28 6b 29 29 |pow,Z(k-|1),Z(k))|
|00000220| 3b 20 0a 09 20 74 20 3d | 20 73 2a 28 72 2d 6b 29 |; .. t =| s*(r-k)|
|00000230| 3b 0a 09 20 66 6f 72 20 | 28 6c 3d 30 3b 20 6c 20 |;.. for |(l=0; l |
|00000240| 3c 20 73 3b 20 6c 2b 2b | 29 0a 09 20 20 20 5f 5f |< s; l++|).. __|
|00000250| 6d 6c 74 61 64 64 5f 5f | 28 5a 5a 28 6b 29 2c 59 |mltadd__|(ZZ(k),Y|
|00000260| 2d 3e 6d 65 5b 6c 5d 2c | 61 2d 3e 76 65 5b 74 2b |->me[l],|a->ve[t+|
|00000270| 6c 5d 2c 59 2d 3e 6e 29 | 3b 0a 20 20 20 20 20 20 |l],Y->n)|;. |
|00000280| 7d 0a 20 20 20 20 20 20 | 69 66 20 28 5a 28 6b 29 |}. |if (Z(k)|
|00000290| 20 3d 3d 20 26 79 30 29 | 20 76 5f 63 6f 70 79 28 | == &y0)| v_copy(|
|000002a0| 74 6d 70 2c 26 79 30 29 | 3b 0a 20 20 20 7d 0a 0a |tmp,&y0)|;. }..|
|000002b0| 20 20 20 6d 5f 74 72 61 | 6e 73 70 28 6f 75 74 2c | m_tra|nsp(out,|
|000002c0| 6f 75 74 29 3b 0a 20 20 | 20 0a 20 20 20 72 65 74 |out);. | . ret|
|000002d0| 75 72 6e 20 6f 75 74 3b | 0a 7d 0a 0a 0a 46 69 6c |urn out;|.}...Fil|
|000002e0| 65 44 61 74 61 82 6d 66 | 75 6e 74 6f 72 74 00 00 |eData.mf|untort..|
|000002f0| 00 b5 11 00 00 45 ff ff | ff b0 60 ab 17 03 00 15 |.....E..|..`.....|
|00000300| f8 0a 2f 2a 2a 2a 2a 2a | 2a 2a 2a 2a 2a 2a 2a 2a |../*****|********|
|00000310| 2a 2a 2a 2a 2a 2a 2a 2a | 2a 2a 2a 2a 2a 2a 2a 2a |********|********|
|00000320| 2a 2a 2a 2a 2a 2a 2a 2a | 2a 2a 2a 2a 2a 2a 2a 2a |********|********|
|00000330| 2a 2a 2a 2a 2a 2a 2a 2a | 2a 2a 2a 2a 2a 2a 2a 2a |********|********|
|00000340| 2a 2a 2a 2a 2a 2a 2a 2a | 2a 2a 2a 2a 2a 0a 2a 2a |********|*****.**|
|00000350| 0a 2a 2a 20 43 6f 70 79 | 72 69 67 68 74 20 28 43 |.** Copy|right (C|
|00000360| 29 20 31 39 39 33 20 44 | 61 76 69 64 20 45 2e 20 |) 1993 D|avid E. |
|00000370| 53 74 65 77 61 72 64 20 | 26 20 5a 62 69 67 6e 69 |Steward |& Zbigni|
|00000380| 65 77 20 4c 65 79 6b 2c | 20 61 6c 6c 20 72 69 67 |ew Leyk,| all rig|
|00000390| 68 74 73 20 72 65 73 65 | 72 76 65 64 2e 0a 2a 2a |hts rese|rved..**|
|000003a0| 0a 2a 2a 09 09 09 20 20 | 20 20 20 4d 65 73 63 68 |.**... | Mesch|
|000003b0| 61 63 68 20 4c 69 62 72 | 61 72 79 0a 2a 2a 20 0a |ach Libr|ary.** .|
|000003c0| 2a 2a 20 54 68 69 73 20 | 4d 65 73 63 68 61 63 68 |** This |Meschach|
|000003d0| 20 4c 69 62 72 61 72 79 | 20 69 73 20 70 72 6f 76 | Library| is prov|
|000003e0| 69 64 65 64 20 22 61 73 | 20 69 73 22 20 77 69 74 |ided "as| is" wit|
|000003f0| 68 6f 75 74 20 61 6e 79 | 20 65 78 70 72 65 73 73 |hout any| express|
|00000400| 20 0a 2a 2a 20 6f 72 20 | 69 6d 70 6c 69 65 64 20 | .** or |implied |
|00000410| 77 61 72 72 61 6e 74 79 | 20 6f 66 20 61 6e 79 20 |warranty| of any |
|00000420| 6b 69 6e 64 20 77 69 74 | 68 20 72 65 73 70 65 63 |kind wit|h respec|
|00000430| 74 20 74 6f 20 74 68 69 | 73 20 73 6f 66 74 77 61 |t to thi|s softwa|
|00000440| 72 65 2e 20 0a 2a 2a 20 | 49 6e 20 70 61 72 74 69 |re. .** |In parti|
|00000450| 63 75 6c 61 72 20 74 68 | 65 20 61 75 74 68 6f 72 |cular th|e author|
|00000460| 73 20 73 68 61 6c 6c 20 | 6e 6f 74 20 62 65 20 6c |s shall |not be l|
|00000470| 69 61 62 6c 65 20 66 6f | 72 20 61 6e 79 20 64 69 |iable fo|r any di|
|00000480| 72 65 63 74 2c 20 0a 2a | 2a 20 69 6e 64 69 72 65 |rect, .*|* indire|
|00000490| 63 74 2c 20 73 70 65 63 | 69 61 6c 2c 20 69 6e 63 |ct, spec|ial, inc|
|000004a0| 69 64 65 6e 74 61 6c 20 | 6f 72 20 63 6f 6e 73 65 |idental |or conse|
|000004b0| 71 75 65 6e 74 69 61 6c | 20 64 61 6d 61 67 65 73 |quential| damages|
|000004c0| 20 61 72 69 73 69 6e 67 | 20 0a 2a 2a 20 69 6e 20 | arising| .** in |
|000004d0| 61 6e 79 20 77 61 79 20 | 66 72 6f 6d 20 75 73 65 |any way |from use|
|000004e0| 20 6f 66 20 74 68 65 20 | 73 6f 66 74 77 61 72 65 | of the |software|
|000004f0| 2e 0a 2a 2a 20 0a 2a 2a | 20 45 76 65 72 79 6f 6e |..** .**| Everyon|
|00000500| 65 20 69 73 20 67 72 61 | 6e 74 65 64 20 70 65 72 |e is gra|nted per|
|00000510| 6d 69 73 73 69 6f 6e 20 | 74 6f 20 63 6f 70 79 2c |mission |to copy,|
|00000520| 20 6d 6f 64 69 66 79 20 | 61 6e 64 20 72 65 64 69 | modify |and redi|
|00000530| 73 74 72 69 62 75 74 65 | 20 74 68 69 73 0a 2a 2a |stribute| this.**|
|00000540| 20 4d 65 73 63 68 61 63 | 68 20 4c 69 62 72 61 72 | Meschac|h Librar|
|00000550| 79 2c 20 70 72 6f 76 69 | 64 65 64 3a 0a 2a 2a 20 |y, provi|ded:.** |
|00000560| 20 31 2e 20 20 41 6c 6c | 20 63 6f 70 69 65 73 20 | 1. All| copies |
|00000570| 63 6f 6e 74 61 69 6e 20 | 74 68 69 73 20 63 6f 70 |contain |this cop|
|00000580| 79 72 69 67 68 74 20 6e | 6f 74 69 63 65 2e 0a 2a |yright n|otice..*|
|00000590| 2a 20 20 32 2e 20 20 41 | 6c 6c 20 6d 6f 64 69 66 |* 2. A|ll modif|
|000005a0| 69 65 64 20 63 6f 70 69 | 65 73 20 73 68 61 6c 6c |ied copi|es shall|
|000005b0| 20 63 61 72 72 79 20 61 | 20 6e 6f 74 69 63 65 20 | carry a| notice |
|000005c0| 73 74 61 74 69 6e 67 20 | 77 68 6f 0a 2a 2a 20 20 |stating |who.** |
|000005d0| 20 20 20 20 6d 61 64 65 | 20 74 68 65 20 6c 61 73 | made| the las|
|000005e0| 74 20 6d 6f 64 69 66 69 | 63 61 74 69 6f 6e 20 61 |t modifi|cation a|
|000005f0| 6e 64 20 74 68 65 20 64 | 61 74 65 20 6f 66 20 73 |nd the d|ate of s|
|00000600| 75 63 68 20 6d 6f 64 69 | 66 69 63 61 74 69 6f 6e |uch modi|fication|
|00000610| 2e 0a 2a 2a 20 20 33 2e | 20 20 4e 6f 20 63 68 61 |..** 3.| No cha|
|00000620| 72 67 65 20 69 73 20 6d | 61 64 65 20 66 6f 72 20 |rge is m|ade for |
|00000630| 74 68 69 73 20 73 6f 66 | 74 77 61 72 65 20 6f 72 |this sof|tware or|
|00000640| 20 77 6f 72 6b 73 20 64 | 65 72 69 76 65 64 20 66 | works d|erived f|
|00000650| 72 6f 6d 20 69 74 2e 20 | 20 0a 2a 2a 20 20 20 20 |rom it. | .** |
|00000660| 20 20 54 68 69 73 20 63 | 6c 61 75 73 65 20 73 68 | This c|lause sh|
|00000670| 61 6c 6c 20 6e 6f 74 20 | 62 65 20 63 6f 6e 73 74 |all not |be const|
|00000680| 72 75 65 64 20 61 73 20 | 63 6f 6e 73 74 72 61 69 |rued as |constrai|
|00000690| 6e 69 6e 67 20 6f 74 68 | 65 72 20 73 6f 66 74 77 |ning oth|er softw|
|000006a0| 61 72 65 0a 2a 2a 20 20 | 20 20 20 20 64 69 73 74 |are.** | dist|
|000006b0| 72 69 62 75 74 65 64 20 | 6f 6e 20 74 68 65 20 73 |ributed |on the s|
|000006c0| 61 6d 65 20 6d 65 64 69 | 75 6d 20 61 73 20 74 68 |ame medi|um as th|
|000006d0| 69 73 20 73 6f 66 74 77 | 61 72 65 2c 20 6e 6f 72 |is softw|are, nor|
|000006e0| 20 69 73 20 61 0a 2a 2a | 20 20 20 20 20 20 64 69 | is a.**| di|
|000006f0| 73 74 72 69 62 75 74 69 | 6f 6e 20 66 65 65 20 63 |stributi|on fee c|
|00000700| 6f 6e 73 69 64 65 72 65 | 64 20 61 20 63 68 61 72 |onsidere|d a char|
|00000710| 67 65 2e 0a 2a 2a 0a 2a | 2a 2a 2a 2a 2a 2a 2a 2a |ge..**.*|********|
|00000720| 2a 2a 2a 2a 2a 2a 2a 2a | 2a 2a 2a 2a 2a 2a 2a 2a |********|********|
|00000730| 2a 2a 2a 2a 2a 2a 2a 2a | 2a 2a 2a 2a 2a 2a 2a 2a |********|********|
|00000740| 2a 2a 2a 2a 2a 2a 2a 2a | 2a 2a 2a 2a 2a 2a 2a 2a |********|********|
|00000750| 2a 2a 2a 2a 2a 2a 2a 2a | 2a 2a 2a 2a 2a 2a 2a 2a |********|********|
|00000760| 2a 2a 2f 0a 0a 0a 2f 2a | 20 6d 66 75 6e 74 6f 72 |**/.../*| mfuntor|
|00000770| 74 2e 63 2c 20 20 31 30 | 2f 31 31 2f 39 33 20 2a |t.c, 10|/11/93 *|
|00000780| 2f 0a 0a 73 74 61 74 69 | 63 20 63 68 61 72 20 72 |/..stati|c char r|
|00000790| 63 73 69 64 5b 5d 20 3d | 20 22 24 49 64 3a 20 6d |csid[] =| "$Id: m|
|000007a0| 66 75 6e 74 6f 72 74 2e | 63 2c 76 20 31 2e 32 20 |funtort.|c,v 1.2 |
|000007b0| 31 39 39 34 2f 30 31 2f | 31 34 20 30 31 3a 30 38 |1994/01/|14 01:08|
|000007c0| 3a 30 36 20 64 65 73 20 | 45 78 70 20 24 22 3b 0a |:06 des |Exp $";.|
|000007d0| 0a 23 69 6e 63 6c 75 64 | 65 20 20 20 20 20 20 20 |.#includ|e |
|000007e0| 20 3c 73 74 64 69 6f 2e | 68 3e 0a 23 69 6e 63 6c | <stdio.|h>.#incl|
|000007f0| 75 64 65 20 20 20 20 20 | 20 20 20 3c 6d 61 74 68 |ude | <math|
|00000800| 2e 68 3e 0a 23 69 6e 63 | 6c 75 64 65 20 20 20 20 |.h>.#inc|lude |
|00000810| 20 20 20 20 22 6d 61 74 | 72 69 78 2e 68 22 0a 23 | "mat|rix.h".#|
|00000820| 69 6e 63 6c 75 64 65 20 | 20 20 20 20 20 20 20 22 |include | "|
|00000830| 6d 61 74 72 69 78 32 2e | 68 22 0a 0a 0a 23 64 65 |matrix2.|h"...#de|
|00000840| 66 69 6e 65 20 65 72 72 | 6d 65 73 67 28 6d 65 73 |fine err|mesg(mes|
|00000850| 67 29 20 20 20 70 72 69 | 6e 74 66 28 22 45 72 72 |g) pri|ntf("Err|
|00000860| 6f 72 3a 20 25 73 20 65 | 72 72 6f 72 3a 20 6c 69 |or: %s e|rror: li|
|00000870| 6e 65 20 25 64 5c 6e 22 | 2c 6d 65 73 67 2c 5f 5f |ne %d\n"|,mesg,__|
|00000880| 4c 49 4e 45 5f 5f 29 0a | 23 64 65 66 69 6e 65 20 |LINE__).|#define |
|00000890| 6e 6f 74 69 63 65 28 6d | 65 73 67 29 20 20 20 20 |notice(m|esg) |
|000008a0| 70 72 69 6e 74 66 28 22 | 23 20 54 65 73 74 69 6e |printf("|# Testin|
|000008b0| 67 20 25 73 2e 2e 2e 5c | 6e 22 2c 6d 65 73 67 29 |g %s...\|n",mesg)|
|000008c0| 3b 0a 0a 23 64 65 66 69 | 6e 65 20 44 49 4d 20 20 |;..#defi|ne DIM |
|000008d0| 31 30 0a 0a 76 6f 69 64 | 20 6d 61 69 6e 28 29 0a |10..void| main().|
|000008e0| 7b 0a 0a 20 20 20 4d 41 | 54 20 2a 41 2c 20 2a 42 |{.. MA|T *A, *B|
|000008f0| 2c 20 2a 43 2c 20 2a 4f | 55 54 41 2c 20 2a 4f 55 |, *C, *O|UTA, *OU|
|00000900| 54 42 2c 20 2a 54 4d 50 | 3b 0a 20 20 20 4d 41 54 |TB, *TMP|;. MAT|
|00000910| 20 2a 65 78 70 5f 41 5f | 65 78 70 65 63 74 65 64 | *exp_A_|expected|
|00000920| 2c 20 2a 65 78 70 5f 41 | 3b 0a 20 20 20 56 45 43 |, *exp_A|;. VEC|
|00000930| 20 2a 78 2c 20 2a 62 3b | 0a 20 20 20 64 6f 75 62 | *x, *b;|. doub|
|00000940| 6c 65 20 63 2c 20 65 70 | 73 20 3d 20 31 65 2d 31 |le c, ep|s = 1e-1|
|00000950| 30 3b 0a 20 20 20 69 6e | 74 20 69 2c 20 6a 2c 20 |0;. in|t i, j, |
|00000960| 71 5f 6f 75 74 2c 20 6a | 5f 6f 75 74 3b 0a 0a 20 |q_out, j|_out;.. |
|00000970| 20 20 6d 65 6d 5f 69 6e | 66 6f 5f 6f 6e 28 54 52 | mem_in|fo_on(TR|
|00000980| 55 45 29 3b 0a 0a 20 20 | 20 41 20 3d 20 6d 5f 67 |UE);.. | A = m_g|
|00000990| 65 74 28 44 49 4d 2c 44 | 49 4d 29 3b 0a 20 20 20 |et(DIM,D|IM);. |
|000009a0| 42 20 3d 20 6d 5f 67 65 | 74 28 44 49 4d 2c 44 49 |B = m_ge|t(DIM,DI|
|000009b0| 4d 29 3b 0a 20 20 20 43 | 20 3d 20 6d 5f 67 65 74 |M);. C| = m_get|
|000009c0| 28 44 49 4d 2c 44 49 4d | 29 3b 0a 20 20 20 4f 55 |(DIM,DIM|);. OU|
|000009d0| 54 41 20 3d 20 6d 5f 67 | 65 74 28 44 49 4d 2c 44 |TA = m_g|et(DIM,D|
|000009e0| 49 4d 29 3b 0a 20 20 20 | 4f 55 54 42 20 3d 20 6d |IM);. |OUTB = m|
|000009f0| 5f 67 65 74 28 44 49 4d | 2c 44 49 4d 29 3b 0a 20 |_get(DIM|,DIM);. |
|00000a00| 20 20 54 4d 50 20 3d 20 | 6d 5f 67 65 74 28 44 49 | TMP = |m_get(DI|
|00000a10| 4d 2c 44 49 4d 29 3b 0a | 20 20 20 78 20 3d 20 76 |M,DIM);.| x = v|
|00000a20| 5f 67 65 74 28 44 49 4d | 29 3b 0a 20 20 20 62 20 |_get(DIM|);. b |
|00000a30| 3d 20 76 5f 67 65 74 28 | 36 29 3b 0a 0a 20 20 20 |= v_get(|6);.. |
|00000a40| 6e 6f 74 69 63 65 28 22 | 65 78 70 6f 6e 65 6e 74 |notice("|exponent|
|00000a50| 20 6f 66 20 61 20 6d 61 | 74 72 69 78 22 29 3b 0a | of a ma|trix");.|
|00000a60| 0a 20 20 20 6d 5f 69 64 | 65 6e 74 28 41 29 3b 0a |. m_id|ent(A);.|
|00000a70| 20 20 20 6d 65 6d 5f 73 | 74 61 74 5f 6d 61 72 6b | mem_s|tat_mark|
|00000a80| 28 31 29 3b 0a 20 20 20 | 5f 6d 5f 65 78 70 28 41 |(1);. |_m_exp(A|
|00000a90| 2c 65 70 73 2c 4f 55 54 | 41 2c 26 71 5f 6f 75 74 |,eps,OUT|A,&q_out|
|00000aa0| 2c 26 6a 5f 6f 75 74 29 | 3b 0a 20 20 20 70 72 69 |,&j_out)|;. pri|
|00000ab0| 6e 74 66 28 22 23 20 71 | 5f 6f 75 74 20 3d 20 25 |ntf("# q|_out = %|
|00000ac0| 64 2c 20 6a 5f 6f 75 74 | 20 3d 20 25 64 5c 6e 22 |d, j_out| = %d\n"|
|00000ad0| 2c 71 5f 6f 75 74 2c 6a | 5f 6f 75 74 29 3b 0a 0a |,q_out,j|_out);..|
|00000ae0| 20 20 20 6d 5f 65 78 70 | 28 41 2c 65 70 73 2c 4f | m_exp|(A,eps,O|
|00000af0| 55 54 41 29 3b 0a 20 20 | 20 73 6d 5f 6d 6c 74 28 |UTA);. | sm_mlt(|
|00000b00| 65 78 70 28 31 2e 30 29 | 2c 41 2c 41 29 3b 0a 20 |exp(1.0)|,A,A);. |
|00000b10| 20 20 6d 5f 73 75 62 28 | 4f 55 54 41 2c 41 2c 54 | m_sub(|OUTA,A,T|
|00000b20| 4d 50 29 3b 0a 20 20 20 | 70 72 69 6e 74 66 28 22 |MP);. |printf("|
|00000b30| 23 20 7c 7c 65 78 70 28 | 49 29 20 2d 20 65 2a 49 |# ||exp(|I) - e*I|
|00000b40| 7c 7c 20 3d 20 25 67 5c | 6e 22 2c 6d 5f 6e 6f 72 ||| = %g\|n",m_nor|
|00000b50| 6d 5f 69 6e 66 28 54 4d | 50 29 29 3b 0a 0a 20 20 |m_inf(TM|P));.. |
|00000b60| 20 6d 5f 72 61 6e 64 28 | 41 29 3b 0a 20 20 20 6d | m_rand(|A);. m|
|00000b70| 5f 74 72 61 6e 73 70 28 | 41 2c 54 4d 50 29 3b 0a |_transp(|A,TMP);.|
|00000b80| 20 20 20 6d 5f 61 64 64 | 28 41 2c 54 4d 50 2c 41 | m_add|(A,TMP,A|
|00000b90| 29 3b 0a 20 20 20 42 20 | 3d 20 6d 5f 63 6f 70 79 |);. B |= m_copy|
|00000ba0| 28 41 2c 42 29 3b 0a 0a | 20 20 20 6d 5f 65 78 70 |(A,B);..| m_exp|
|00000bb0| 28 41 2c 65 70 73 2c 4f | 55 54 41 29 3b 0a 0a 20 |(A,eps,O|UTA);.. |
|00000bc0| 20 20 73 79 6d 6d 65 69 | 67 28 42 2c 4f 55 54 42 | symmei|g(B,OUTB|
|00000bd0| 2c 78 29 3b 0a 20 20 20 | 6d 5f 7a 65 72 6f 28 54 |,x);. |m_zero(T|
|00000be0| 4d 50 29 3b 0a 20 20 20 | 66 6f 72 20 28 69 3d 30 |MP);. |for (i=0|
|00000bf0| 3b 20 69 20 3c 20 78 2d | 3e 64 69 6d 3b 20 69 2b |; i < x-|>dim; i+|
|00000c00| 2b 29 0a 20 20 20 20 20 | 54 4d 50 2d 3e 6d 65 5b |+). |TMP->me[|
|00000c10| 69 5d 5b 69 5d 20 3d 20 | 65 78 70 28 78 2d 3e 76 |i][i] = |exp(x->v|
|00000c20| 65 5b 69 5d 29 3b 0a 20 | 20 20 6d 5f 6d 6c 74 28 |e[i]);. | m_mlt(|
|00000c30| 4f 55 54 42 2c 54 4d 50 | 2c 43 29 3b 0a 20 20 20 |OUTB,TMP|,C);. |
|00000c40| 6d 6d 74 72 5f 6d 6c 74 | 28 43 2c 4f 55 54 42 2c |mmtr_mlt|(C,OUTB,|
|00000c50| 54 4d 50 29 3b 0a 20 20 | 20 6d 5f 73 75 62 28 54 |TMP);. | m_sub(T|
|00000c60| 4d 50 2c 4f 55 54 41 2c | 54 4d 50 29 3b 0a 20 20 |MP,OUTA,|TMP);. |
|00000c70| 20 70 72 69 6e 74 66 28 | 22 23 20 7c 7c 65 78 70 | printf(|"# ||exp|
|00000c80| 28 41 29 20 2d 20 51 2a | 65 78 70 28 6c 61 6d 62 |(A) - Q*|exp(lamb|
|00000c90| 64 61 29 2a 51 5e 54 7c | 7c 20 3d 20 25 67 5c 6e |da)*Q^T||| = %g\n|
|00000ca0| 22 2c 6d 5f 6e 6f 72 6d | 5f 69 6e 66 28 54 4d 50 |",m_norm|_inf(TMP|
|00000cb0| 29 29 3b 0a 0a 20 20 20 | 6e 6f 74 69 63 65 28 22 |));.. |notice("|
|00000cc0| 70 6f 6c 79 6e 6f 6d 69 | 61 6c 20 6f 66 20 61 20 |polynomi|al of a |
|00000cd0| 6d 61 74 72 69 78 22 29 | 3b 0a 20 20 20 6d 5f 72 |matrix")|;. m_r|
|00000ce0| 61 6e 64 28 41 29 3b 0a | 20 20 20 6d 5f 74 72 61 |and(A);.| m_tra|
|00000cf0| 6e 73 70 28 41 2c 54 4d | 50 29 3b 0a 20 20 20 6d |nsp(A,TM|P);. m|
|00000d00| 5f 61 64 64 28 41 2c 54 | 4d 50 2c 41 29 3b 0a 20 |_add(A,T|MP,A);. |
|00000d10| 20 20 42 20 3d 20 6d 5f | 63 6f 70 79 28 41 2c 42 | B = m_|copy(A,B|
|00000d20| 29 3b 0a 20 20 20 76 5f | 72 61 6e 64 28 62 29 3b |);. v_|rand(b);|
|00000d30| 0a 0a 20 20 20 6d 5f 70 | 6f 6c 79 28 41 2c 62 2c |.. m_p|oly(A,b,|
|00000d40| 4f 55 54 41 29 3b 0a 0a | 20 20 20 73 79 6d 6d 65 |OUTA);..| symme|
|00000d50| 69 67 28 42 2c 4f 55 54 | 42 2c 78 29 3b 0a 20 20 |ig(B,OUT|B,x);. |
|00000d60| 20 6d 5f 7a 65 72 6f 28 | 54 4d 50 29 3b 0a 20 20 | m_zero(|TMP);. |
|00000d70| 20 66 6f 72 20 28 69 3d | 30 3b 20 69 20 3c 20 78 | for (i=|0; i < x|
|00000d80| 2d 3e 64 69 6d 3b 20 69 | 2b 2b 29 20 7b 0a 20 20 |->dim; i|++) {. |
|00000d90| 20 20 20 20 63 20 3d 20 | 62 2d 3e 76 65 5b 62 2d | c = |b->ve[b-|
|00000da0| 3e 64 69 6d 2d 31 5d 3b | 0a 20 20 20 20 20 20 66 |>dim-1];|. f|
|00000db0| 6f 72 20 28 6a 3d 62 2d | 3e 64 69 6d 2d 32 3b 20 |or (j=b-|>dim-2; |
|00000dc0| 6a 20 3e 3d 20 30 3b 20 | 6a 2d 2d 29 20 0a 09 63 |j >= 0; |j--) ..c|
|00000dd0| 20 3d 20 63 2a 78 2d 3e | 76 65 5b 69 5d 20 2b 20 | = c*x->|ve[i] + |
|00000de0| 62 2d 3e 76 65 5b 6a 5d | 3b 0a 20 20 20 20 20 20 |b->ve[j]|;. |
|00000df0| 54 4d 50 2d 3e 6d 65 5b | 69 5d 5b 69 5d 20 3d 20 |TMP->me[|i][i] = |
|00000e00| 63 3b 0a 20 20 20 7d 0a | 20 20 20 6d 5f 6d 6c 74 |c;. }.| m_mlt|
|00000e10| 28 4f 55 54 42 2c 54 4d | 50 2c 43 29 3b 0a 20 20 |(OUTB,TM|P,C);. |
|00000e20| 20 6d 6d 74 72 5f 6d 6c | 74 28 43 2c 4f 55 54 42 | mmtr_ml|t(C,OUTB|
|00000e30| 2c 54 4d 50 29 3b 0a 20 | 20 20 6d 5f 73 75 62 28 |,TMP);. | m_sub(|
|00000e40| 54 4d 50 2c 4f 55 54 41 | 2c 54 4d 50 29 3b 0a 20 |TMP,OUTA|,TMP);. |
|00000e50| 20 20 70 72 69 6e 74 66 | 28 22 23 20 7c 7c 70 6f | printf|("# ||po|
|00000e60| 6c 79 28 41 29 20 2d 20 | 51 2a 70 6f 6c 79 28 6c |ly(A) - |Q*poly(l|
|00000e70| 61 6d 62 64 61 29 2a 51 | 5e 54 7c 7c 20 3d 20 25 |ambda)*Q|^T|| = %|
|00000e80| 67 5c 6e 22 2c 6d 5f 6e | 6f 72 6d 5f 69 6e 66 28 |g\n",m_n|orm_inf(|
|00000e90| 54 4d 50 29 29 3b 0a 20 | 20 20 6d 65 6d 5f 73 74 |TMP));. | mem_st|
|00000ea0| 61 74 5f 66 72 65 65 28 | 31 29 3b 0a 0a 0a 20 20 |at_free(|1);... |
|00000eb0| 20 2f 2a 20 42 72 6f 6f | 6b 20 4d 69 6c 6c 69 67 | /* Broo|k Millig|
|00000ec0| 61 6e 27 73 20 74 65 73 | 74 20 2a 2f 0a 0a 20 20 |an's tes|t */.. |
|00000ed0| 20 4d 5f 46 52 45 45 28 | 41 29 3b 0a 20 20 20 4d | M_FREE(|A);. M|
|00000ee0| 5f 46 52 45 45 28 42 29 | 3b 0a 20 20 20 4d 5f 46 |_FREE(B)|;. M_F|
|00000ef0| 52 45 45 28 43 29 3b 0a | 0a 20 20 20 6e 6f 74 69 |REE(C);.|. noti|
|00000f00| 63 65 28 22 65 78 70 6f | 6e 65 6e 74 20 6f 66 20 |ce("expo|nent of |
|00000f10| 61 20 6e 6f 6e 73 79 6d | 6d 65 74 72 69 63 20 6d |a nonsym|metric m|
|00000f20| 61 74 72 69 78 22 29 3b | 0a 20 20 20 41 20 3d 20 |atrix");|. A = |
|00000f30| 6d 5f 67 65 74 20 28 32 | 2c 20 32 29 3b 0a 20 20 |m_get (2|, 2);. |
|00000f40| 20 41 20 2d 3e 20 6d 65 | 20 5b 30 5d 5b 30 5d 20 | A -> me| [0][0] |
|00000f50| 3d 20 31 2e 30 3b 0a 20 | 20 20 41 20 2d 3e 20 6d |= 1.0;. | A -> m|
|00000f60| 65 20 5b 30 5d 5b 31 5d | 20 3d 20 31 2e 30 3b 0a |e [0][1]| = 1.0;.|
|00000f70| 20 20 20 41 20 2d 3e 20 | 6d 65 20 5b 31 5d 5b 30 | A -> |me [1][0|
|00000f80| 5d 20 3d 20 34 2e 30 3b | 0a 20 20 20 41 20 2d 3e |] = 4.0;|. A ->|
|00000f90| 20 6d 65 20 5b 31 5d 5b | 31 5d 20 3d 20 31 2e 30 | me [1][|1] = 1.0|
|00000fa0| 3b 0a 20 20 20 0a 20 20 | 20 65 78 70 5f 41 5f 65 |;. . | exp_A_e|
|00000fb0| 78 70 65 63 74 65 64 20 | 3d 20 6d 5f 67 65 74 28 |xpected |= m_get(|
|00000fc0| 32 2c 20 32 29 3b 0a 20 | 20 20 65 78 70 5f 41 5f |2, 2);. | exp_A_|
|00000fd0| 65 78 70 65 63 74 65 64 | 20 2d 3e 20 6d 65 20 5b |expected| -> me [|
|00000fe0| 30 5d 5b 30 5d 20 3d 20 | 65 78 70 20 28 33 2e 30 |0][0] = |exp (3.0|
|00000ff0| 29 20 2f 20 32 2e 30 20 | 2b 20 65 78 70 20 28 2d |) / 2.0 |+ exp (-|
|00001000| 31 2e 30 29 20 2f 20 32 | 2e 30 3b 0a 20 20 20 65 |1.0) / 2|.0;. e|
|00001010| 78 70 5f 41 5f 65 78 70 | 65 63 74 65 64 20 2d 3e |xp_A_exp|ected ->|
|00001020| 20 6d 65 20 5b 30 5d 5b | 31 5d 20 3d 20 65 78 70 | me [0][|1] = exp|
|00001030| 20 28 33 2e 30 29 20 2f | 20 34 2e 30 20 2d 20 65 | (3.0) /| 4.0 - e|
|00001040| 78 70 20 28 2d 31 2e 30 | 29 20 2f 20 34 2e 30 3b |xp (-1.0|) / 4.0;|
|00001050| 0a 20 20 20 65 78 70 5f | 41 5f 65 78 70 65 63 74 |. exp_|A_expect|
|00001060| 65 64 20 2d 3e 20 6d 65 | 20 5b 31 5d 5b 30 5d 20 |ed -> me| [1][0] |
|00001070| 3d 20 65 78 70 20 28 33 | 2e 30 29 20 20 20 20 20 |= exp (3|.0) |
|00001080| 20 20 2d 20 65 78 70 20 | 28 2d 31 2e 30 29 3b 0a | - exp |(-1.0);.|
|00001090| 20 20 20 65 78 70 5f 41 | 5f 65 78 70 65 63 74 65 | exp_A|_expecte|
|000010a0| 64 20 2d 3e 20 6d 65 20 | 5b 31 5d 5b 31 5d 20 3d |d -> me |[1][1] =|
|000010b0| 20 65 78 70 20 28 33 2e | 30 29 20 2f 20 32 2e 30 | exp (3.|0) / 2.0|
|000010c0| 20 2b 20 65 78 70 20 28 | 2d 31 2e 30 29 20 2f 20 | + exp (|-1.0) / |
|000010d0| 32 2e 30 3b 0a 20 20 20 | 0a 20 20 20 70 72 69 6e |2.0;. |. prin|
|000010e0| 74 66 20 28 22 41 3a 5c | 6e 22 29 3b 0a 20 20 20 |tf ("A:\|n");. |
|000010f0| 66 6f 72 20 28 69 20 3d | 20 30 3b 20 69 20 3c 20 |for (i =| 0; i < |
|00001100| 32 3b 20 69 2b 2b 29 0a | 20 20 20 7b 0a 20 20 20 |2; i++).| {. |
|00001110| 20 20 20 66 6f 72 20 28 | 6a 20 3d 20 30 3b 20 6a | for (|j = 0; j|
|00001120| 20 3c 20 32 3b 20 6a 2b | 2b 29 0a 20 20 20 20 20 | < 2; j+|+). |
|00001130| 20 20 20 70 72 69 6e 74 | 66 20 28 22 20 20 20 25 | print|f (" %|
|00001140| 31 35 2e 38 65 22 2c 20 | 41 20 2d 3e 20 6d 65 20 |15.8e", |A -> me |
|00001150| 5b 69 5d 5b 6a 5d 29 3b | 0a 20 20 20 20 20 20 70 |[i][j]);|. p|
|00001160| 72 69 6e 74 66 20 28 22 | 5c 6e 22 29 3b 0a 20 20 |rintf ("|\n");. |
|00001170| 20 7d 0a 20 20 20 0a 20 | 20 20 70 72 69 6e 74 66 | }. . | printf|
|00001180| 20 28 22 5c 6e 65 78 70 | 28 41 29 20 28 65 78 70 | ("\nexp|(A) (exp|
|00001190| 65 63 74 65 64 29 3a 5c | 6e 22 29 3b 0a 20 20 20 |ected):\|n");. |
|000011a0| 66 6f 72 20 28 69 20 3d | 20 30 3b 20 69 20 3c 20 |for (i =| 0; i < |
|000011b0| 32 3b 20 69 2b 2b 29 0a | 20 20 20 7b 0a 20 20 20 |2; i++).| {. |
|000011c0| 20 20 20 66 6f 72 20 28 | 6a 20 3d 20 30 3b 20 6a | for (|j = 0; j|
|000011d0| 20 3c 20 32 3b 20 6a 2b | 2b 29 0a 20 20 20 20 20 | < 2; j+|+). |
|000011e0| 20 20 20 70 72 69 6e 74 | 66 20 28 22 20 20 20 25 | print|f (" %|
|000011f0| 31 35 2e 38 65 22 2c 20 | 65 78 70 5f 41 5f 65 78 |15.8e", |exp_A_ex|
|00001200| 70 65 63 74 65 64 20 2d | 3e 20 6d 65 20 5b 69 5d |pected -|> me [i]|
|00001210| 5b 6a 5d 29 3b 0a 20 20 | 20 20 20 20 70 72 69 6e |[j]);. | prin|
|00001220| 74 66 20 28 22 5c 6e 22 | 29 3b 0a 20 20 20 7d 0a |tf ("\n"|);. }.|
|00001230| 20 20 20 0a 20 20 20 6d | 65 6d 5f 73 74 61 74 5f | . m|em_stat_|
|00001240| 6d 61 72 6b 28 33 29 3b | 0a 20 20 20 65 78 70 5f |mark(3);|. exp_|
|00001250| 41 20 3d 20 6d 5f 65 78 | 70 20 28 41 2c 20 31 65 |A = m_ex|p (A, 1e|
|00001260| 2d 31 36 2c 4e 55 4c 4c | 29 3b 0a 20 20 20 6d 65 |-16,NULL|);. me|
|00001270| 6d 5f 73 74 61 74 5f 66 | 72 65 65 28 33 29 3b 0a |m_stat_f|ree(3);.|
|00001280| 0a 20 20 20 70 72 69 6e | 74 66 20 28 22 5c 6e 65 |. prin|tf ("\ne|
|00001290| 78 70 28 41 29 3a 5c 6e | 22 29 3b 0a 20 20 20 66 |xp(A):\n|");. f|
|000012a0| 6f 72 20 28 69 20 3d 20 | 30 3b 20 69 20 3c 20 32 |or (i = |0; i < 2|
|000012b0| 3b 20 69 2b 2b 29 0a 20 | 20 20 7b 0a 20 20 20 20 |; i++). | {. |
|000012c0| 20 20 66 6f 72 20 28 6a | 20 3d 20 30 3b 20 6a 20 | for (j| = 0; j |
|000012d0| 3c 20 32 3b 20 6a 2b 2b | 29 0a 20 20 20 20 20 20 |< 2; j++|). |
|000012e0| 20 20 70 72 69 6e 74 66 | 20 28 22 20 20 20 25 31 | printf| (" %1|
|000012f0| 35 2e 38 65 22 2c 20 65 | 78 70 5f 41 20 2d 3e 20 |5.8e", e|xp_A -> |
|00001300| 6d 65 20 5b 69 5d 5b 6a | 5d 29 3b 0a 20 20 20 20 |me [i][j|]);. |
|00001310| 20 20 70 72 69 6e 74 66 | 20 28 22 5c 6e 22 29 3b | printf| ("\n");|
|00001320| 0a 20 20 20 7d 0a 20 20 | 20 70 72 69 6e 74 66 20 |. }. | printf |
|00001330| 28 22 5c 6e 65 78 70 28 | 41 29 20 2d 20 65 78 70 |("\nexp(|A) - exp|
|00001340| 28 41 29 20 28 65 78 70 | 65 63 74 65 64 29 3a 5c |(A) (exp|ected):\|
|00001350| 6e 22 29 3b 0a 20 20 20 | 66 6f 72 20 28 69 20 3d |n");. |for (i =|
|00001360| 20 30 3b 20 69 20 3c 20 | 32 3b 20 69 2b 2b 29 0a | 0; i < |2; i++).|
|00001370| 20 20 20 7b 0a 20 20 20 | 20 20 20 66 6f 72 20 28 | {. | for (|
|00001380| 6a 20 3d 20 30 3b 20 6a | 20 3c 20 32 3b 20 6a 2b |j = 0; j| < 2; j+|
|00001390| 2b 29 0a 20 20 20 20 20 | 20 20 20 70 72 69 6e 74 |+). | print|
|000013a0| 66 20 28 22 20 20 20 25 | 31 35 2e 38 65 22 2c 20 |f (" %|15.8e", |
|000013b0| 65 78 70 5f 41 20 2d 3e | 20 6d 65 20 5b 69 5d 5b |exp_A ->| me [i][|
|000013c0| 6a 5d 20 2d 20 65 78 70 | 5f 41 5f 65 78 70 65 63 |j] - exp|_A_expec|
|000013d0| 74 65 64 20 2d 3e 20 6d | 65 20 5b 69 5d 5b 6a 5d |ted -> m|e [i][j]|
|000013e0| 29 3b 0a 20 20 20 20 20 | 20 70 72 69 6e 74 66 20 |);. | printf |
|000013f0| 28 22 5c 6e 22 29 3b 0a | 20 20 20 7d 0a 0a 20 20 |("\n");.| }.. |
|00001400| 20 4d 5f 46 52 45 45 28 | 41 29 3b 0a 20 20 20 4d | M_FREE(|A);. M|
|00001410| 5f 46 52 45 45 28 42 29 | 3b 0a 20 20 20 4d 5f 46 |_FREE(B)|;. M_F|
|00001420| 52 45 45 28 43 29 3b 0a | 20 20 20 4d 5f 46 52 45 |REE(C);.| M_FRE|
|00001430| 45 28 65 78 70 5f 41 29 | 3b 0a 20 20 20 4d 5f 46 |E(exp_A)|;. M_F|
|00001440| 52 45 45 28 65 78 70 5f | 41 5f 65 78 70 65 63 74 |REE(exp_|A_expect|
|00001450| 65 64 29 3b 0a 20 20 20 | 4d 5f 46 52 45 45 28 4f |ed);. |M_FREE(O|
|00001460| 55 54 41 29 3b 0a 20 20 | 20 4d 5f 46 52 45 45 28 |UTA);. | M_FREE(|
|00001470| 4f 55 54 42 29 3b 0a 20 | 20 20 4d 5f 46 52 45 45 |OUTB);. | M_FREE|
|00001480| 28 54 4d 50 29 3b 0a 20 | 20 20 56 5f 46 52 45 45 |(TMP);. | V_FREE|
|00001490| 28 62 29 3b 0a 20 20 20 | 56 5f 46 52 45 45 28 78 |(b);. |V_FREE(x|
|000014a0| 29 3b 0a 0a 20 20 20 6d | 65 6d 5f 69 6e 66 6f 28 |);.. m|em_info(|
|000014b0| 29 3b 0a 7d 0a 0a 46 69 | 6c 65 44 61 74 61 82 6e |);.}..Fi|leData.n|
|000014c0| 6f 72 6d 00 00 00 00 00 | 00 00 5b 10 00 00 45 ff |orm.....|..[...E.|
|000014d0| ff ff c0 e9 3f 17 03 00 | 10 e9 0a 2f 2a 2a 2a 2a |....?...|.../****|
|000014e0| 2a 2a 2a 2a 2a 2a 2a 2a | 2a 2a 2a 2a 2a 2a 2a 2a |********|********|
|000014f0| 2a 2a 2a 2a 2a 2a 2a 2a | 2a 2a 2a 2a 2a 2a 2a 2a |********|********|
|00001500| 2a 2a 2a 2a 2a 2a 2a 2a | 2a 2a 2a 2a 2a 2a 2a 2a |********|********|
|00001510| 2a 2a 2a 2a 2a 2a 2a 2a | 2a 2a 2a 2a 2a 2a 2a 2a |********|********|
|00001520| 2a 2a 2a 2a 2a 2a 0a 2a | 2a 0a 2a 2a 20 43 6f 70 |******.*|*.** Cop|
|00001530| 79 72 69 67 68 74 20 28 | 43 29 20 31 39 39 33 20 |yright (|C) 1993 |
|00001540| 44 61 76 69 64 20 45 2e | 20 53 74 65 77 61 72 64 |David E.| Steward|
|00001550| 20 26 20 5a 62 69 67 6e | 69 65 77 20 4c 65 79 6b | & Zbign|iew Leyk|
|00001560| 2c 20 61 6c 6c 20 72 69 | 67 68 74 73 20 72 65 73 |, all ri|ghts res|
|00001570| 65 72 76 65 64 2e 0a 2a | 2a 0a 2a 2a 09 09 09 20 |erved..*|*.**... |
|00001580| 20 20 20 20 4d 65 73 63 | 68 61 63 68 20 4c 69 62 | Mesc|hach Lib|
|00001590| 72 61 72 79 0a 2a 2a 20 | 0a 2a 2a 20 54 68 69 73 |rary.** |.** This|
|000015a0| 20 4d 65 73 63 68 61 63 | 68 20 4c 69 62 72 61 72 | Meschac|h Librar|
|000015b0| 79 20 69 73 20 70 72 6f | 76 69 64 65 64 20 22 61 |y is pro|vided "a|
|000015c0| 73 20 69 73 22 20 77 69 | 74 68 6f 75 74 20 61 6e |s is" wi|thout an|
|000015d0| 79 20 65 78 70 72 65 73 | 73 20 0a 2a 2a 20 6f 72 |y expres|s .** or|
|000015e0| 20 69 6d 70 6c 69 65 64 | 20 77 61 72 72 61 6e 74 | implied| warrant|
|000015f0| 79 20 6f 66 20 61 6e 79 | 20 6b 69 6e 64 20 77 69 |y of any| kind wi|
|00001600| 74 68 20 72 65 73 70 65 | 63 74 20 74 6f 20 74 68 |th respe|ct to th|
|00001610| 69 73 20 73 6f 66 74 77 | 61 72 65 2e 20 0a 2a 2a |is softw|are. .**|
|00001620| 20 49 6e 20 70 61 72 74 | 69 63 75 6c 61 72 20 74 | In part|icular t|
|00001630| 68 65 20 61 75 74 68 6f | 72 73 20 73 68 61 6c 6c |he autho|rs shall|
|00001640| 20 6e 6f 74 20 62 65 20 | 6c 69 61 62 6c 65 20 66 | not be |liable f|
|00001650| 6f 72 20 61 6e 79 20 64 | 69 72 65 63 74 2c 20 0a |or any d|irect, .|
|00001660| 2a 2a 20 69 6e 64 69 72 | 65 63 74 2c 20 73 70 65 |** indir|ect, spe|
|00001670| 63 69 61 6c 2c 20 69 6e | 63 69 64 65 6e 74 61 6c |cial, in|cidental|
|00001680| 20 6f 72 20 63 6f 6e 73 | 65 71 75 65 6e 74 69 61 | or cons|equentia|
|00001690| 6c 20 64 61 6d 61 67 65 | 73 20 61 72 69 73 69 6e |l damage|s arisin|
|000016a0| 67 20 0a 2a 2a 20 69 6e | 20 61 6e 79 20 77 61 79 |g .** in| any way|
|000016b0| 20 66 72 6f 6d 20 75 73 | 65 20 6f 66 20 74 68 65 | from us|e of the|
|000016c0| 20 73 6f 66 74 77 61 72 | 65 2e 0a 2a 2a 20 0a 2a | softwar|e..** .*|
|000016d0| 2a 20 45 76 65 72 79 6f | 6e 65 20 69 73 20 67 72 |* Everyo|ne is gr|
|000016e0| 61 6e 74 65 64 20 70 65 | 72 6d 69 73 73 69 6f 6e |anted pe|rmission|
|000016f0| 20 74 6f 20 63 6f 70 79 | 2c 20 6d 6f 64 69 66 79 | to copy|, modify|
|00001700| 20 61 6e 64 20 72 65 64 | 69 73 74 72 69 62 75 74 | and red|istribut|
|00001710| 65 20 74 68 69 73 0a 2a | 2a 20 4d 65 73 63 68 61 |e this.*|* Mescha|
|00001720| 63 68 20 4c 69 62 72 61 | 72 79 2c 20 70 72 6f 76 |ch Libra|ry, prov|
|00001730| 69 64 65 64 3a 0a 2a 2a | 20 20 31 2e 20 20 41 6c |ided:.**| 1. Al|
|00001740| 6c 20 63 6f 70 69 65 73 | 20 63 6f 6e 74 61 69 6e |l copies| contain|
|00001750| 20 74 68 69 73 20 63 6f | 70 79 72 69 67 68 74 20 | this co|pyright |
|00001760| 6e 6f 74 69 63 65 2e 0a | 2a 2a 20 20 32 2e 20 20 |notice..|** 2. |
|00001770| 41 6c 6c 20 6d 6f 64 69 | 66 69 65 64 20 63 6f 70 |All modi|fied cop|
|00001780| 69 65 73 20 73 68 61 6c | 6c 20 63 61 72 72 79 20 |ies shal|l carry |
|00001790| 61 20 6e 6f 74 69 63 65 | 20 73 74 61 74 69 6e 67 |a notice| stating|
|000017a0| 20 77 68 6f 0a 2a 2a 20 | 20 20 20 20 20 6d 61 64 | who.** | mad|
|000017b0| 65 20 74 68 65 20 6c 61 | 73 74 20 6d 6f 64 69 66 |e the la|st modif|
|000017c0| 69 63 61 74 69 6f 6e 20 | 61 6e 64 20 74 68 65 20 |ication |and the |
|000017d0| 64 61 74 65 20 6f 66 20 | 73 75 63 68 20 6d 6f 64 |date of |such mod|
|000017e0| 69 66 69 63 61 74 69 6f | 6e 2e 0a 2a 2a 20 20 33 |ificatio|n..** 3|
|000017f0| 2e 20 20 4e 6f 20 63 68 | 61 72 67 65 20 69 73 20 |. No ch|arge is |
|00001800| 6d 61 64 65 20 66 6f 72 | 20 74 68 69 73 20 73 6f |made for| this so|
|00001810| 66 74 77 61 72 65 20 6f | 72 20 77 6f 72 6b 73 20 |ftware o|r works |
|00001820| 64 65 72 69 76 65 64 20 | 66 72 6f 6d 20 69 74 2e |derived |from it.|
|00001830| 20 20 0a 2a 2a 20 20 20 | 20 20 20 54 68 69 73 20 | .** | This |
|00001840| 63 6c 61 75 73 65 20 73 | 68 61 6c 6c 20 6e 6f 74 |clause s|hall not|
|00001850| 20 62 65 20 63 6f 6e 73 | 74 72 75 65 64 20 61 73 | be cons|trued as|
|00001860| 20 63 6f 6e 73 74 72 61 | 69 6e 69 6e 67 20 6f 74 | constra|ining ot|
|00001870| 68 65 72 20 73 6f 66 74 | 77 61 72 65 0a 2a 2a 20 |her soft|ware.** |
|00001880| 20 20 20 20 20 64 69 73 | 74 72 69 62 75 74 65 64 | dis|tributed|
|00001890| 20 6f 6e 20 74 68 65 20 | 73 61 6d 65 20 6d 65 64 | on the |same med|
|000018a0| 69 75 6d 20 61 73 20 74 | 68 69 73 20 73 6f 66 74 |ium as t|his soft|
|000018b0| 77 61 72 65 2c 20 6e 6f | 72 20 69 73 20 61 0a 2a |ware, no|r is a.*|
|000018c0| 2a 20 20 20 20 20 20 64 | 69 73 74 72 69 62 75 74 |* d|istribut|
|000018d0| 69 6f 6e 20 66 65 65 20 | 63 6f 6e 73 69 64 65 72 |ion fee |consider|
|000018e0| 65 64 20 61 20 63 68 61 | 72 67 65 2e 0a 2a 2a 0a |ed a cha|rge..**.|
|000018f0| 2a 2a 2a 2a 2a 2a 2a 2a | 2a 2a 2a 2a 2a 2a 2a 2a |********|********|
|00001900| 2a 2a 2a 2a 2a 2a 2a 2a | 2a 2a 2a 2a 2a 2a 2a 2a |********|********|
|00001910| 2a 2a 2a 2a 2a 2a 2a 2a | 2a 2a 2a 2a 2a 2a 2a 2a |********|********|
|00001920| 2a 2a 2a 2a 2a 2a 2a 2a | 2a 2a 2a 2a 2a 2a 2a 2a |********|********|
|00001930| 2a 2a 2a 2a 2a 2a 2a 2a | 2a 2a 2a 2f 0a 0a 0a 2f |********|***/.../|
|00001940| 2a 0a 09 41 20 63 6f 6c | 6c 65 63 74 69 6f 6e 20 |*..A col|lection |
|00001950| 6f 66 20 66 75 6e 63 74 | 69 6f 6e 73 20 66 6f 72 |of funct|ions for|
|00001960| 20 63 6f 6d 70 75 74 69 | 6e 67 20 6e 6f 72 6d 73 | computi|ng norms|
|00001970| 3a 20 73 63 61 6c 65 64 | 20 61 6e 64 20 75 6e 73 |: scaled| and uns|
|00001980| 63 61 6c 65 64 0a 2a 2f | 0a 73 74 61 74 69 63 09 |caled.*/|.static.|
|00001990| 63 68 61 72 09 72 63 73 | 69 |char.rcs|i |
+--------+-------------------------+-------------------------+--------+--------+