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1.1 ! root 1: .\" Copyright (c) 1990 Regents of the University of California. ! 2: .\" All rights reserved. The Berkeley software License Agreement ! 3: .\" specifies the terms and conditions for redistribution. ! 4: .\" ! 5: .\" @(#)spline.1 6.2 (Berkeley) 6/24/90 ! 6: .\" ! 7: .TH SPLINE 1 "%Q" ! 8: .AT 3 ! 9: .SH NAME ! 10: spline \- interpolate smooth curve ! 11: .SH SYNOPSIS ! 12: .B spline ! 13: [ option ] ... ! 14: .SH DESCRIPTION ! 15: .I Spline ! 16: takes pairs of numbers from the standard input as abcissas and ordinates ! 17: of a function. ! 18: It produces a similar set, which ! 19: is approximately equally spaced and ! 20: includes the input set, on the standard output. ! 21: The cubic spline output ! 22: (R. W. Hamming, ! 23: .ft I ! 24: Numerical Methods for Scientists and Engineers, ! 25: .ft R ! 26: 2nd ed., 349ff) ! 27: has two continuous derivatives, ! 28: and sufficiently many points to look smooth when plotted, for ! 29: example by ! 30: .IR graph (1G). ! 31: .PP ! 32: The following options are recognized, ! 33: each as a separate argument. ! 34: .TP 5 ! 35: .B \-a ! 36: Supply abscissas automatically (they are missing from ! 37: the input); spacing is given by the next ! 38: argument, or is assumed to be 1 if next argument is not a number. ! 39: .TP 5 ! 40: .B \-k ! 41: The constant ! 42: .IR k "" ! 43: used in the boundary value computation ! 44: .IP ! 45: .if n .ig ! 46: .ti +1.5i ! 47: .ds ' \h'-\w'\(fm\(fm'u' ! 48: .EQ ! 49: .nr 99 \n(.s ! 50: .nr 98 \n(.f ! 51: 'ps 10 ! 52: .ft I ! 53: .ds 11 "y\(fm\(fm ! 54: .nr 11 \w'\*(11' ! 55: .ds 12 "\*' ! 56: .nr 12 \w'\*(12' ! 57: 'ps 8 ! 58: .ds 13 "\fR0\fP ! 59: .nr 13 \w'\*(13' ! 60: .as 12 \v'18u'\s8\*(13\|\s10\v'-18u' ! 61: 'ps 10 ! 62: .nr 12 \n(12+\n(13+\w'\s8\|' ! 63: .as 11 "\*(12 ! 64: .nr 11 \w'\*(11' ! 65: .ds 12 "\|\| ! 66: .nr 12 \w'\*(12' ! 67: .as 11 "\*(12 ! 68: .nr 11 \w'\*(11' ! 69: .ds 12 "\|=\| ! 70: .nr 12 \w'\*(12' ! 71: .as 11 "\*(12 ! 72: .nr 11 \w'\*(11' ! 73: .ds 12 "\|\| ! 74: .nr 12 \w'\*(12' ! 75: .as 11 "\*(12 ! 76: .nr 11 \w'\*(11' ! 77: .ds 12 "ky\(fm\(fm ! 78: .nr 12 \w'\*(12' ! 79: .as 11 "\*(12 ! 80: .nr 11 \w'\*(11' ! 81: .ds 12 "\*' ! 82: .nr 12 \w'\*(12' ! 83: 'ps 8 ! 84: .ds 13 "\fR1\fP ! 85: .nr 13 \w'\*(13' ! 86: .as 12 \v'18u'\s8\*(13\|\s10\v'-18u' ! 87: 'ps 10 ! 88: .nr 12 \n(12+\n(13+\w'\s8\|' ! 89: .as 11 "\*(12 ! 90: .nr 11 \w'\*(11' ! 91: .ds 12 ", ! 92: .nr 12 \w'\*(12' ! 93: .as 11 "\*(12 ! 94: .nr 11 \w'\*(11' ! 95: .ds 12 "\|\| ! 96: .nr 12 \w'\*(12' ! 97: .as 11 "\*(12 ! 98: .nr 11 \w'\*(11' ! 99: .ds 12 "\|\| ! 100: .nr 12 \w'\*(12' ! 101: .as 11 "\*(12 ! 102: .nr 11 \w'\*(11' ! 103: .ds 12 "\|\| ! 104: .nr 12 \w'\*(12' ! 105: .as 11 "\*(12 ! 106: .nr 11 \w'\*(11' ! 107: .ds 12 "y\(fm\(fm ! 108: .nr 12 \w'\*(12' ! 109: .as 11 "\*(12 ! 110: .nr 11 \w'\*(11' ! 111: .ds 12 "\*' ! 112: .nr 12 \w'\*(12' ! 113: 'ps 8 ! 114: .ds 13 "n ! 115: .nr 13 \w'\*(13' ! 116: .as 12 \v'18u'\s8\*(13\|\s10\v'-18u' ! 117: 'ps 10 ! 118: .nr 12 \n(12+\n(13+\w'\s8\|' ! 119: .as 11 "\*(12 ! 120: .nr 11 \w'\*(11' ! 121: .ds 12 "\|\| ! 122: .nr 12 \w'\*(12' ! 123: .as 11 "\*(12 ! 124: .nr 11 \w'\*(11' ! 125: .ds 12 "\|=\| ! 126: .nr 12 \w'\*(12' ! 127: .as 11 "\*(12 ! 128: .nr 11 \w'\*(11' ! 129: .ds 12 "\|\| ! 130: .nr 12 \w'\*(12' ! 131: .as 11 "\*(12 ! 132: .nr 11 \w'\*(11' ! 133: .ds 12 "ky\(fm\(fm ! 134: .nr 12 \w'\*(12' ! 135: .as 11 "\*(12 ! 136: .nr 11 \w'\*(11' ! 137: .ds 12 "\*' ! 138: .nr 12 \w'\*(12' ! 139: 'ps 8 ! 140: .ds 13 "n\|\(mi\|\fR1\fP ! 141: .nr 13 \w'\*(13' ! 142: .as 12 \v'18u'\s8\*(13\|\s10\v'-18u' ! 143: 'ps 10 ! 144: .nr 12 \n(12+\n(13+\w'\s8\|' ! 145: .as 11 "\*(12 ! 146: .nr 11 \w'\*(11' ! 147: .ds 11 \x'0'\fI\*(11\s\n(99\f\n(98 ! 148: .ne 78u ! 149: \*(11 ! 150: 'ps \n(99 ! 151: .ft \n(98 ! 152: .EN ! 153: .. ! 154: .if t .ig ! 155: .ce ! 156: (2nd deriv. at end) = k*(2nd deriv. next to end) ! 157: .. ! 158: .IP ! 159: .br ! 160: is set by the next argument. ! 161: By default ! 162: .IR k "" ! 163: = 0. ! 164: .TP 5 ! 165: .B \-n ! 166: Space output points ! 167: so that approximately ! 168: .I n ! 169: intervals occur between the lower and upper ! 170: .I x ! 171: limits. ! 172: (Default ! 173: .I n ! 174: = 100.) ! 175: .TP 5 ! 176: .B \-p ! 177: Make output periodic, i.e. match ! 178: derivatives at ends. ! 179: First and last input values should normally agree. ! 180: .TP 5 ! 181: .B \-x ! 182: Next ! 183: 1 (or 2) arguments are lower (and upper) ! 184: .I x ! 185: limits. ! 186: Normally these limits are calculated from the data. ! 187: Automatic abcissas start at lower limit ! 188: (default 0). ! 189: .SH "SEE ALSO" ! 190: graph(1), plot(1) ! 191: .SH DIAGNOSTICS ! 192: When data is not strictly monotone in ! 193: .I x, ! 194: .I spline ! 195: reproduces the input without interpolating extra points. ! 196: .SH BUGS ! 197: A limit of 1000 input points is enforced silently.
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