3 // PSPP - a program for statistical analysis.
4 // Copyright (C) 2005, 2006, 2009, 2010, 2011, 2012, 2015, 2016 Free Software Foundation, Inc.
6 // This program is free software: you can redistribute it and/or modify
7 // it under the terms of the GNU General Public License as published by
8 // the Free Software Foundation, either version 3 of the License, or
9 // (at your option) any later version.
11 // This program is distributed in the hope that it will be useful,
12 // but WITHOUT ANY WARRANTY; without even the implied warranty of
13 // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
14 // GNU General Public License for more details.
16 // You should have received a copy of the GNU General Public License
17 // along with this program. If not, see <http://www.gnu.org/licenses/>.
19 operator NEG (x) = -x;
21 operator ADD (a, b) = a + b;
22 operator SUB (a, b) = a - b;
24 absorb_miss operator MUL (a, b)
25 = (a == 0. || b == 0. ? 0.
26 : a == SYSMIS || b == SYSMIS ? SYSMIS
29 absorb_miss operator DIV (a, b)
31 : a == SYSMIS || b == SYSMIS ? SYSMIS
34 absorb_miss operator POW (a, b)
35 = (a == SYSMIS ? (b == 0. ? 1. : a)
36 : b == SYSMIS ? (a == 0. ? 0. : SYSMIS)
37 : a == 0. && b <= 0. ? SYSMIS
40 absorb_miss boolean operator AND (boolean a, boolean b)
43 : b == SYSMIS ? SYSMIS
46 absorb_miss boolean operator OR (boolean a, boolean b)
49 : b == SYSMIS ? SYSMIS
52 boolean operator NOT (boolean a)
57 // Numeric relational operators.
58 boolean operator EQ (a, b) = a == b;
59 boolean operator GE (a, b) = a >= b;
60 boolean operator GT (a, b) = a > b;
61 boolean operator LE (a, b) = a <= b;
62 boolean operator LT (a, b) = a < b;
63 boolean operator NE (a, b) = a != b;
65 // String relational operators.
66 boolean operator EQ_STRING (string a, string b) = compare_string_3way (&a, &b) == 0;
67 boolean operator GE_STRING (string a, string b) = compare_string_3way (&a, &b) >= 0;
68 boolean operator GT_STRING (string a, string b) = compare_string_3way (&a, &b) > 0;
69 boolean operator LE_STRING (string a, string b) = compare_string_3way (&a, &b) <= 0;
70 boolean operator LT_STRING (string a, string b) = compare_string_3way (&a, &b) < 0;
71 boolean operator NE_STRING (string a, string b) = compare_string_3way (&a, &b) != 0;
74 function ABS (x) = fabs (x);
75 extension function ACOS (x >= -1 && x <= 1) = acos (x);
76 function ASIN (x >= -1 && x <= 1) = asin (x);
77 function ATAN (x) = atan (x);
78 extension function ARCOS (x >= -1 && x <= 1) = acos (x);
79 function ARSIN (x >= -1 && x <= 1) = asin (x);
80 function ARTAN (x) = atan (x);
81 function COS (x) = cos (x);
82 function EXP (x) = check_errno (exp (x));
83 function LG10(x) = check_errno (log10 (x));
84 function LN (x) = check_errno (log (x));
85 function LNGAMMA (x >= 0) = gsl_sf_lngamma (x);
86 function MOD10 (x) = fmod (x, 10);
87 function RND (x) = round_nearest (x, 1, 0);
88 function RND (x, mult != 0) = round_nearest (x, mult, 0);
89 function RND (x, mult != 0, fuzzbits >= 0) = round_nearest (x, mult, fuzzbits);
90 function SIN (x) = sin (x);
91 function SQRT (x >= 0) = sqrt (x);
92 function TAN (x) = check_errno (tan (x));
93 function TRUNC (x) = round_zero (x, 1, 0);
94 function TRUNC (x, mult != 0) = round_zero (x, mult, 0);
95 function TRUNC (x, mult != 0, fuzzbits >= 0) = round_zero (x, mult, fuzzbits);
97 absorb_miss function MOD (n, d)
100 return n != SYSMIS ? fmod (n, d) : SYSMIS;
102 return n != 0. ? SYSMIS : 0.;
105 // N-ary numeric functions.
106 absorb_miss boolean function ANY (x != SYSMIS, a[n])
111 for (i = 0; i < n; i++)
114 else if (a[i] == SYSMIS)
117 return sysmis ? SYSMIS : 0.;
120 boolean function ANY (string x, string a[n])
124 for (i = 0; i < n; i++)
125 if (!compare_string_3way (&x, &a[i]))
130 function CFVAR.2 (a[n])
132 double mean, variance;
134 moments_of_doubles (a, n, NULL, &mean, &variance, NULL, NULL);
136 if (mean == SYSMIS || mean == 0 || variance == SYSMIS)
139 return sqrt (variance) / mean;
142 function MAX.1 (a[n])
148 for (i = 0; i < n; i++)
149 if (a[i] != SYSMIS && a[i] > max)
154 string function MAX (string a[n])
156 struct substring *max;
160 for (i = 1; i < n; i++)
161 if (compare_string_3way (&a[i], max) > 0)
166 function MEAN.1 (a[n])
169 moments_of_doubles (a, n, NULL, &mean, NULL, NULL, NULL);
173 function MEDIAN.1 (a[n])
175 return median (a, n);
178 function MIN.1 (a[n])
184 for (i = 0; i < n; i++)
185 if (a[i] != SYSMIS && a[i] < min)
190 string function MIN (string a[n])
192 struct substring *min;
196 for (i = 1; i < n; i++)
197 if (compare_string_3way (&a[i], min) < 0)
202 absorb_miss function NMISS (a[n])
204 size_t n_missings = 0;
205 for (size_t i = 0; i < n; i++)
206 n_missings += a[i] == SYSMIS;
210 absorb_miss function NVALID (a[n])
213 for (size_t i = 0; i < n; i++)
214 n_valids += a[i] != SYSMIS;
218 absorb_miss boolean function RANGE (x != SYSMIS, a[n*2])
222 for (size_t i = 0; i < n; i++)
225 double y = a[2 * i + 1];
226 if (w != SYSMIS && y != SYSMIS)
228 if (w <= x && x <= y)
236 return found ? true : valid ? false : SYSMIS;
239 boolean function RANGE (string x, string a[n*2])
242 for (size_t i = 0; i < n; i++)
244 struct substring *w = &a[2 * i];
245 struct substring *y = &a[2 * i + 1];
246 if (compare_string_3way (w, &x) <= 0 && compare_string_3way (&x, y) <= 0)
248 else if (compare_string_3way (w, y) > 0)
257 moments_of_doubles (a, n, NULL, NULL, &variance, NULL, NULL);
258 return sqrt (variance);
261 function SUM.1 (a[n])
267 for (i = 0; i < n; i++)
273 function VARIANCE.2 (a[n])
276 moments_of_doubles (a, n, NULL, NULL, &variance, NULL, NULL);
280 // Time construction & extraction functions.
281 function TIME.HMS (h, m, s)
285 if ((h > 0. || m > 0. || s > 0.) && (h < 0. || m < 0. || s < 0.))
287 msg_at (SW, expr_location (e, n),
288 _("TIME.HMS cannot accept a mix of positive and negative "
290 double args[] = { h, m, s };
291 for (size_t i = 0; i < 3; i++)
293 msg_at (SN, expr_location (e, n->args[i]),
294 _("This argument has positive value %g."), args[i]);
295 else if (args[i] < 0)
296 msg_at (SN, expr_location (e, n->args[i]),
297 _("This argument has negative value %g."), args[i]);
301 return H_S * h + MIN_S * m + s;
303 function TIME.DAYS (days) = days * DAY_S;
304 function CTIME.DAYS (time) = time / DAY_S;
305 function CTIME.HOURS (time) = time / H_S;
306 function CTIME.MINUTES (time) = time / MIN_S;
307 function CTIME.SECONDS (time) = time;
309 // Date construction functions.
310 function DATE.DMY (integer d, integer m, integer y)
313 = expr_ymd_to_date (y, m, d, e, n, 3, 2, 1);
315 function DATE.MDY (integer m, integer d, integer y)
318 = expr_ymd_to_date (y, m, d, e, n, 3, 1, 2);
320 function DATE.MOYR (integer m, integer y)
323 = expr_ymd_to_date (y, m, 1, e, n, 2, 1, 0);
325 function DATE.QYR (integer q, integer y)
331 msg_at (SW, expr_location (e, n->args[0]),
332 _("Argument 1 to DATE.QYR must be 1, 2, 3, or 4 (not %d)."), q);
335 return expr_ymd_to_date (y, q * 3 - 2, 1, e, n, 2, 0, 0);
338 function DATE.WKYR (integer w, integer y)
344 msg_at (SE, expr_location (e, n->args[0]),
345 _("The week argument to DATE.WKYR is outside the acceptable "
346 "range of 1 to 53. The result will be system-missing."));
351 double yr_1_1 = expr_ymd_to_ofs (y, 1, 1, e, n, 2, 0, 0);
352 if (yr_1_1 != SYSMIS)
353 return DAY_S * (yr_1_1 + WEEK_DAY * (w - 1));
359 function DATE.YRDAY (integer y, integer yd)
363 if (yd < 1 || yd > 366)
365 msg_at (SE, expr_location (e, n->args[1]),
366 _("DATE.YRDAY day argument %d is outside the acceptable "
367 "range of 1 to 366. The result will be system-missing."), yd);
372 double yr_1_1 = expr_ymd_to_ofs (y, 1, 1, e, n, 1, 0, 0);
373 if (yr_1_1 != SYSMIS)
374 return DAY_S * (yr_1_1 + yd - 1.);
380 function YRMODA (integer y, integer m, integer d)
384 if (y >= 0 && y <= 99)
388 msg_at (SE, expr_location (e, n->args[0]),
389 _("The year argument to YRMODA is greater than 47516. "
390 "The result will be system-missing."));
394 return expr_ymd_to_ofs (y, m, d, e, n, 1, 2, 3);
397 // Date extraction functions.
398 function XDATE.TDAY (date) = floor (date / DAY_S);
399 function XDATE.HOUR (date) = fmod (floor (date / H_S), DAY_H);
400 function XDATE.MINUTE (date) = fmod (floor (date / H_MIN), H_MIN);
401 function XDATE.SECOND (date) = fmod (date, MIN_S);
402 function XDATE.DATE (date) = floor (date / DAY_S) * DAY_S;
403 function XDATE.TIME (date) = fmod (date, DAY_S);
405 function XDATE.JDAY (date >= DAY_S) = calendar_offset_to_yday (date / DAY_S);
406 function XDATE.MDAY (date >= DAY_S) = calendar_offset_to_mday (date / DAY_S);
407 function XDATE.MONTH (date >= DAY_S)
408 = calendar_offset_to_month (date / DAY_S);
409 function XDATE.QUARTER (date >= DAY_S)
410 = (calendar_offset_to_month (date / DAY_S) - 1) / 3 + 1;
411 function XDATE.WEEK (date >= DAY_S)
412 = (calendar_offset_to_yday (date / DAY_S) - 1) / 7 + 1;
413 function XDATE.WKDAY (date >= DAY_S) = calendar_offset_to_wday (date / DAY_S);
414 function XDATE.YEAR (date >= DAY_S) = calendar_offset_to_year (date / DAY_S);
416 // Date arithmetic functions.
417 no_abbrev function DATEDIFF (date2 >= DAY_S, date1 >= DAY_S, string unit)
420 = expr_date_difference (date1, date2, unit, e, n);
422 no_abbrev function DATESUM (date, quantity, string unit)
425 = expr_date_sum_closest (date, quantity, unit, e, n);
426 no_abbrev function DATESUM (date, quantity, string unit, string method)
429 = expr_date_sum (date, quantity, unit, method, e, n);
433 string function CONCAT (string a[n])
436 struct substring dst;
439 dst = alloc_string (e, MAX_STRING);
441 for (i = 0; i < n; i++)
443 struct substring *src = &a[i];
446 copy_len = src->length;
447 if (dst.length + copy_len > MAX_STRING)
448 copy_len = MAX_STRING - dst.length;
449 memcpy (&dst.string[dst.length], src->string, copy_len);
450 dst.length += copy_len;
456 function INDEX (string haystack, string needle)
458 if (haystack.length >= needle.length)
460 size_t limit = haystack.length - needle.length + 1;
461 for (size_t i = 1; i <= limit; i++)
462 if (!memcmp (&haystack.string[i - 1], needle.string, needle.length))
468 function INDEX (string haystack, string needles, integer needle_len)
472 if (needle_len <= 0 || needles.length % needle_len != 0)
474 msg_at (SE, expr_location (e, n),
475 _("INDEX needle length argument must evenly divide the "
476 "length of the needles argument."));
477 msg_at (SN, expr_location (e, n->args[1]),
478 _("The needles argument has length %zu."), needles.length);
479 msg_at (SN, expr_location (e, n->args[2]),
480 _("The needle length argument has value %d."), needle_len);
484 if (haystack.length >= needle_len)
486 size_t limit = haystack.length - needle_len + 1;
487 for (size_t i = 1; i <= limit; i++)
488 for (size_t j = 0; j < needles.length; j += needle_len)
489 if (!memcmp (&haystack.string[i - 1], &needles.string[j], needle_len))
496 function RINDEX (string haystack, string needle)
498 if (haystack.length >= needle.length)
500 size_t limit = haystack.length - needle.length + 1;
501 for (size_t i = limit; i >= 1; i--)
502 if (!memcmp (&haystack.string[i - 1], needle.string, needle.length))
509 function RINDEX (string haystack, string needles, integer needle_len)
513 if (needle_len <= 0 || needles.length % needle_len != 0)
515 msg_at (SE, expr_location (e, n),
516 _("RINDEX needle length argument must evenly divide the "
517 "length of the needles argument."));
518 msg_at (SN, expr_location (e, n->args[1]),
519 _("The needles argument has length %zu."), needles.length);
520 msg_at (SN, expr_location (e, n->args[2]),
521 _("The needle length argument has value %d."), needle_len);
525 if (haystack.length >= needle_len)
527 size_t limit = haystack.length - needle_len + 1;
528 for (size_t i = limit; i >= 1; i--)
529 for (size_t j = 0; j < needles.length; j += needle_len)
530 if (!memcmp (&haystack.string[i - 1], &needles.string[j], needle_len))
537 function LENGTH (string s)
542 string function LOWER (string s)
546 for (i = 0; i < s.length; i++)
547 s.string[i] = tolower ((unsigned char) s.string[i]);
551 function MBLEN.BYTE (string s, idx)
553 if (idx < 0 || idx >= s.length || (int) idx != idx)
559 string function UPCASE (string s)
563 for (i = 0; i < s.length; i++)
564 s.string[i] = toupper ((unsigned char) s.string[i]);
568 absorb_miss string function LPAD (string s, integer n)
572 if (n < 0 || n > MAX_STRING)
576 msg_at (SE, expr_location (e, node),
577 _("The length argument to LPAD must be between 0 and %d."),
579 msg_at (SN, expr_location (e, node->args[1]),
580 _("The length argument is %d."), n);
585 else if (s.length >= n)
589 struct substring t = alloc_string (e, n);
590 size_t pad = n - s.length;
591 memset (t.string, ' ', pad);
592 memcpy (&t.string[pad], s.string, s.length);
597 absorb_miss string function LPAD (string s, integer n, string c)
601 if (n < 0 || n > MAX_STRING)
605 msg_at (SE, expr_location (e, node),
606 _("The length argument to LPAD must be between 0 and %d."),
608 msg_at (SN, expr_location (e, node->args[1]),
609 _("The length argument is %d."), n);
614 else if (s.length >= n)
616 else if (c.length == 0)
618 msg_at (SE, expr_location (e, node),
619 _("The padding argument to LPAD must not be an empty string."));
624 size_t n_pad = (n - s.length) / c.length;
628 struct substring t = alloc_string (e, n);
630 for (size_t i = 0; i < n_pad; i++)
632 memcpy (t.string + t.length, c.string, c.length);
633 t.length += c.length;
635 memcpy (t.string + t.length, s.string, s.length);
636 t.length += s.length;
641 string function REPLACE (string haystack, string needle, string replacement)
643 = replace_string (e, haystack, needle, replacement, INT_MAX);
645 absorb_miss string function REPLACE (string haystack, string needle,
646 string replacement, integer n)
648 = replace_string (e, haystack, needle, replacement, n);
650 absorb_miss string function RPAD (string s, integer n)
654 if (n < 0 || n > MAX_STRING)
658 msg_at (SE, expr_location (e, node),
659 _("The length argument to RPAD must be between 0 and %d."),
661 msg_at (SN, expr_location (e, node->args[1]),
662 _("The length argument is %d."), n);
667 else if (s.length >= n)
671 struct substring t = alloc_string (e, n);
672 size_t pad = n - s.length;
673 memcpy (t.string, s.string, s.length);
674 memset (t.string + s.length, ' ', pad);
679 absorb_miss string function RPAD (string s, integer n, string c)
683 if (n < 0 || n > MAX_STRING)
687 msg_at (SE, expr_location (e, node),
688 _("The length argument to RPAD must be between 0 and %d."),
690 msg_at (SN, expr_location (e, node->args[1]),
691 _("The length argument is %d."), n);
696 else if (s.length >= n)
698 else if (c.length == 0)
700 msg_at (SE, expr_location (e, node),
701 _("The padding argument to RPAD must not be an empty string."));
706 size_t n_pad = (n - s.length) / c.length;
710 struct substring t = alloc_string (e, n);
711 memcpy (t.string, s.string, s.length);
713 for (size_t i = 0; i < n_pad; i++)
715 memcpy (t.string + t.length, c.string, c.length);
716 t.length += c.length;
722 string function LTRIM (string s)
724 while (s.length > 0 && s.string[0] == ' ')
732 string function LTRIM (string s, string c)
735 while (s.length >= c.length && !memcmp (s.string, c.string, c.length))
737 s.length -= c.length;
738 s.string += c.length;
743 string function RTRIM (string s)
745 while (s.length > 0 && s.string[s.length - 1] == ' ')
750 string function RTRIM (string s, string c)
753 while (s.length >= c.length
754 && !memcmp (&s.string[s.length - c.length], c.string, c.length))
755 s.length -= c.length;
759 function NUMBER (string s, ni_format f)
767 char *error = data_in (s, C_ENCODING, f->type, settings_get_fmt_settings (),
770 data_in_imply_decimals (s, C_ENCODING, f->type, f->d,
771 settings_get_fmt_settings (), &out);
774 msg_at (SE, expr_location (e, n->args[0]),
775 _("Cannot parse \"%.*s\" as format %s: %s"),
776 (int) s.length, s.string, fmt_name (f->type), error);
782 absorb_miss string function STRING (x, no_format f)
786 struct substring dst;
791 assert (!fmt_is_string (f->type));
792 s = data_out (&v, C_ENCODING, f, settings_get_fmt_settings ());
793 dst = alloc_string (e, strlen (s));
794 strcpy (dst.string, s);
799 absorb_miss string function STRUNC (string s, integer n)
802 return n == INT_MIN ? s : empty_string;
806 while (s.length > 0 && s.string[s.length - 1] == ' ')
811 absorb_miss string function SUBSTR (string s, ofs)
814 if (ofs >= 1 && ofs <= s.length && (int) ofs == ofs)
815 return copy_string (e, &s.string[(int) ofs - 1], s.length - ofs + 1);
820 absorb_miss string function SUBSTR (string s, ofs, cnt)
823 if (ofs >= 1 && ofs <= s.length && (int) ofs == ofs
824 && cnt >= 1 && cnt <= INT_MAX && (int) cnt == cnt)
826 int cnt_max = s.length - (int) ofs + 1;
827 return copy_string (e, &s.string[(int) ofs - 1],
828 cnt <= cnt_max ? cnt : cnt_max);
834 absorb_miss no_opt no_abbrev string function VALUELABEL (var v)
838 const char *label = var_lookup_value_label (v, case_data (c, v));
840 return copy_string (e, label, strlen (label));
846 operator SQUARE (x) = x * x;
848 absorb_miss boolean operator OPERAND_TO_BOOLEAN (x, expr_node parent)
852 if (x == 0. || x == 1. || x == SYSMIS)
855 switch (parent->n_args)
858 msg_at (SE, expr_location (e, parent),
859 /* TRANSLATORS: There are exactly two operands. */
860 _("The operands of %s must have value 0 or 1."),
861 operations[parent->type].name);
865 msg_at (SE, expr_location (e, parent),
866 _("The operand of %s must have value 0 or 1."),
867 operations[parent->type].name);
874 msg_at (SN, expr_location (e, n),
875 _("This operand with unexpected value %g will be treated as 0."), x);
879 absorb_miss boolean operator EXPR_TO_BOOLEAN (x)
883 if (x == 0. || x == 1. || x == SYSMIS)
886 msg_at (SE, expr_location (e, n),
887 _("This expression, which must be 0 or 1, evaluated to %g. "
888 "It will be treated as 0."), x);
892 operator NUM_TO_INTEGER (x)
896 if (x == floor (x) && x > INT_MIN && x <= INT_MAX)
899 msg_at (SE, expr_location (e, n),
900 _("Treating unexpected non-integer value %g as missing."), x);
904 operator BOOLEAN_TO_NUM (boolean x) = x;
906 // Beta distribution.
907 function PDF.BETA (x >= 0 && x <= 1, a > 0, b > 0)
908 = gsl_ran_beta_pdf (x, a, b);
909 function CDF.BETA (x >= 0 && x <= 1, a > 0, b > 0) = gsl_cdf_beta_P (x, a, b);
910 function IDF.BETA (P >= 0 && P <= 1, a > 0, b > 0)
911 = gsl_cdf_beta_Pinv (P, a, b);
912 no_opt function RV.BETA (a > 0, b > 0) = gsl_ran_beta (get_rng (), a, b);
913 function NCDF.BETA (x >= 0, a > 0, b > 0, lambda > 0)
914 = ncdf_beta (x, a, b, lambda);
915 function NPDF.BETA (x >= 0, a > 0, b > 0, lambda > 0)
916 = npdf_beta (x, a, b, lambda);
918 // Bivariate normal distribution.
919 function CDF.BVNOR (x0, x1, r >= -1 && r <= 1) = cdf_bvnor (x0, x1, r);
920 function PDF.BVNOR (x0, x1, r >= -1 && r <= 1)
921 = gsl_ran_bivariate_gaussian_pdf (x0, x1, 1, 1, r);
923 // Cauchy distribution.
924 function CDF.CAUCHY (x, a, b > 0) = gsl_cdf_cauchy_P ((x - a) / b, 1);
925 function IDF.CAUCHY (P > 0 && P < 1, a, b > 0)
926 = a + b * gsl_cdf_cauchy_Pinv (P, 1);
927 function PDF.CAUCHY (x, a, b > 0) = gsl_ran_cauchy_pdf ((x - a) / b, 1) / b;
928 no_opt function RV.CAUCHY (a, b > 0) = a + b * gsl_ran_cauchy (get_rng (), 1);
930 // Chi-square distribution.
931 function CDF.CHISQ (x >= 0, df > 0) = gsl_cdf_chisq_P (x, df);
932 function IDF.CHISQ (P >= 0 && P < 1, df > 0) = gsl_cdf_chisq_Pinv (P, df);
933 function PDF.CHISQ (x >= 0, df > 0) = gsl_ran_chisq_pdf (x, df);
934 no_opt function RV.CHISQ (df > 0) = gsl_ran_chisq (get_rng (), df);
935 function NCDF.CHISQ (x >= 0, df > 0, c) = unimplemented;
936 function NPDF.CHISQ (x >= 0, df > 0, c) = unimplemented;
937 function SIG.CHISQ (x >= 0, df > 0) = gsl_cdf_chisq_Q (x, df);
939 // Exponential distribution.
940 function CDF.EXP (x >= 0, a > 0) = gsl_cdf_exponential_P (x, 1. / a);
941 function IDF.EXP (P >= 0 && P < 1, a > 0)
942 = gsl_cdf_exponential_Pinv (P, 1. / a);
943 function PDF.EXP (x >= 0, a > 0) = gsl_ran_exponential_pdf (x, 1. / a);
944 no_opt function RV.EXP (a > 0) = gsl_ran_exponential (get_rng (), 1. / a);
946 // Exponential power distribution.
947 extension function PDF.XPOWER (x, a > 0, b >= 0)
948 = gsl_ran_exppow_pdf (x, a, b);
949 no_opt extension function RV.XPOWER (a > 0, b >= 0)
950 = gsl_ran_exppow (get_rng (), a, b);
953 function CDF.F (x >= 0, df1 > 0, df2 > 0) = gsl_cdf_fdist_P (x, df1, df2);
954 function IDF.F (P >= 0 && P < 1, df1 > 0, df2 > 0) = idf_fdist (P, df1, df2);
955 function PDF.F (x >= 0, df1 > 0, df2 > 0) = gsl_ran_fdist_pdf (x, df1, df2);
956 no_opt function RV.F (df1 > 0, df2 > 0) = gsl_ran_fdist (get_rng (), df1, df2);
957 function NCDF.F (x >= 0, df1 > 0, df2 > 0, lambda >= 0) = unimplemented;
958 function NPDF.F (x >= 0, df1 > 0, df2 > 0, lmabda >= 0) = unimplemented;
959 function SIG.F (x >= 0, df1 > 0, df2 > 0) = gsl_cdf_fdist_Q (x, df1, df2);
961 // Gamma distribution.
962 function CDF.GAMMA (x >= 0, a > 0, b > 0) = gsl_cdf_gamma_P (x, a, 1. / b);
963 function IDF.GAMMA (P >= 0 && P <= 1, a > 0, b > 0)
964 = gsl_cdf_gamma_Pinv (P, a, 1. / b);
965 function PDF.GAMMA (x >= 0, a > 0, b > 0) = gsl_ran_gamma_pdf (x, a, 1. / b);
966 no_opt function RV.GAMMA (a > 0, b > 0)
967 = gsl_ran_gamma (get_rng (), a, 1. / b);
969 // Half-normal distribution.
970 function CDF.HALFNRM (x, a, b > 0) = unimplemented;
971 function IDF.HALFNRM (P > 0 && P < 1, a, b > 0) = unimplemented;
972 function PDF.HALFNRM (x, a, b > 0) = unimplemented;
973 no_opt function RV.HALFNRM (a, b > 0) = unimplemented;
975 // Inverse Gaussian distribution.
976 function CDF.IGAUSS (x > 0, a > 0, b > 0) = unimplemented;
977 function IDF.IGAUSS (P >= 0 && P < 1, a > 0, b > 0) = unimplemented;
978 function PDF.IGAUSS (x > 0, a > 0, b > 0) = unimplemented;
979 no_opt function RV.IGAUSS (a > 0, b > 0) = unimplemented;
981 // Landau distribution.
982 extension function PDF.LANDAU (x) = gsl_ran_landau_pdf (x);
983 no_opt extension function RV.LANDAU () = gsl_ran_landau (get_rng ());
985 // Laplace distribution.
986 function CDF.LAPLACE (x, a, b > 0) = gsl_cdf_laplace_P ((x - a) / b, 1);
987 function IDF.LAPLACE (P > 0 && P < 1, a, b > 0)
988 = a + b * gsl_cdf_laplace_Pinv (P, 1);
989 function PDF.LAPLACE (x, a, b > 0) = gsl_ran_laplace_pdf ((x - a) / b, 1) / b;
990 no_opt function RV.LAPLACE (a, b > 0)
991 = a + b * gsl_ran_laplace (get_rng (), 1);
993 // Levy alpha-stable distribution.
994 no_opt extension function RV.LEVY (c, alpha > 0 && alpha <= 2)
995 = gsl_ran_levy (get_rng (), c, alpha);
997 // Levy skew alpha-stable distribution.
998 no_opt extension function RV.LVSKEW (c, alpha > 0 && alpha <= 2,
999 beta >= -1 && beta <= 1)
1000 = gsl_ran_levy_skew (get_rng (), c, alpha, beta);
1002 // Logistic distribution.
1003 function CDF.LOGISTIC (x, a, b > 0) = gsl_cdf_logistic_P ((x - a) / b, 1);
1004 function IDF.LOGISTIC (P > 0 && P < 1, a, b > 0)
1005 = a + b * gsl_cdf_logistic_Pinv (P, 1);
1006 function PDF.LOGISTIC (x, a, b > 0)
1007 = gsl_ran_logistic_pdf ((x - a) / b, 1) / b;
1008 no_opt function RV.LOGISTIC (a, b > 0)
1009 = a + b * gsl_ran_logistic (get_rng (), 1);
1011 // Lognormal distribution.
1012 function CDF.LNORMAL (x >= 0, m > 0, s > 0)
1013 = gsl_cdf_lognormal_P (x, log (m), s);
1014 function IDF.LNORMAL (P >= 0 && P < 1, m > 0, s > 0)
1015 = gsl_cdf_lognormal_Pinv (P, log (m), s);
1016 function PDF.LNORMAL (x >= 0, m > 0, s > 0)
1017 = gsl_ran_lognormal_pdf (x, log (m), s);
1018 no_opt function RV.LNORMAL (m > 0, s > 0)
1019 = gsl_ran_lognormal (get_rng (), log (m), s);
1021 // Normal distribution.
1022 function CDF.NORMAL (x, u, s > 0) = gsl_cdf_gaussian_P (x - u, s);
1023 function IDF.NORMAL (P > 0 && P < 1, u, s > 0)
1024 = u + gsl_cdf_gaussian_Pinv (P, s);
1025 function PDF.NORMAL (x, u, s > 0) = gsl_ran_gaussian_pdf ((x - u) / s, 1) / s;
1026 no_opt function RV.NORMAL (u, s > 0) = u + gsl_ran_gaussian (get_rng (), s);
1027 function CDFNORM (x) = gsl_cdf_ugaussian_P (x);
1028 function PROBIT (P > 0 && P < 1) = gsl_cdf_ugaussian_Pinv (P);
1029 no_opt function NORMAL (s > 0) = gsl_ran_gaussian (get_rng (), s);
1031 // Normal tail distribution.
1032 function PDF.NTAIL (x, a > 0, sigma > 0)
1033 = gsl_ran_gaussian_tail_pdf (x, a, sigma);
1034 no_opt function RV.NTAIL (a > 0, sigma > 0)
1035 = gsl_ran_gaussian_tail (get_rng (), a, sigma);
1037 // Pareto distribution.
1038 function CDF.PARETO (x >= a, a > 0, b > 0) = gsl_cdf_pareto_P (x, b, a);
1039 function IDF.PARETO (P >= 0 && P < 1, a > 0, b > 0)
1040 = gsl_cdf_pareto_Pinv (P, b, a);
1041 function PDF.PARETO (x >= a, a > 0, b > 0) = gsl_ran_pareto_pdf (x, b, a);
1042 no_opt function RV.PARETO (a > 0, b > 0) = gsl_ran_pareto (get_rng (), b, a);
1044 // Rayleigh distribution.
1045 extension function CDF.RAYLEIGH (x, sigma > 0) = gsl_cdf_rayleigh_P (x, sigma);
1046 extension function IDF.RAYLEIGH (P >= 0 && P <= 1, sigma > 0)
1047 = gsl_cdf_rayleigh_Pinv (P, sigma);
1048 extension function PDF.RAYLEIGH (x, sigma > 0)
1049 = gsl_ran_rayleigh_pdf (x, sigma);
1050 no_opt extension function RV.RAYLEIGH (sigma > 0)
1051 = gsl_ran_rayleigh (get_rng (), sigma);
1053 // Rayleigh tail distribution.
1054 extension function PDF.RTAIL (x, a, sigma)
1055 = gsl_ran_rayleigh_tail_pdf (x, a, sigma);
1056 no_opt extension function RV.RTAIL (a, sigma)
1057 = gsl_ran_rayleigh_tail (get_rng (), a, sigma);
1059 // Studentized maximum modulus distribution.
1060 function CDF.SMOD (x > 0, a >= 1, b >= 1) = unimplemented;
1061 function IDF.SMOD (P >= 0 && P < 1, a >= 1, b >= 1) = unimplemented;
1063 // Studentized range distribution.
1064 function CDF.SRANGE (x > 0, a >= 1, b >= 1) = unimplemented;
1065 function IDF.SRANGE (P >= 0 && P < 1, a >= 1, b >= 1) = unimplemented;
1067 // Student t distribution.
1068 function CDF.T (x, df > 0) = gsl_cdf_tdist_P (x, df);
1069 function IDF.T (P > 0 && P < 1, df > 0) = gsl_cdf_tdist_Pinv (P, df);
1070 function PDF.T (x, df > 0) = gsl_ran_tdist_pdf (x, df);
1071 no_opt function RV.T (df > 0) = gsl_ran_tdist (get_rng (), df);
1072 function NCDF.T (x, df > 0, nc) = unimplemented;
1073 function NPDF.T (x, df > 0, nc) = unimplemented;
1075 // Type-1 Gumbel distribution.
1076 extension function CDF.T1G (x, a, b) = gsl_cdf_gumbel1_P (x, a, b);
1077 extension function IDF.T1G (P >= 0 && P <= 1, a, b)
1078 = gsl_cdf_gumbel1_Pinv (P, a, b);
1079 extension function PDF.T1G (x, a, b) = gsl_ran_gumbel1_pdf (x, a, b);
1080 no_opt extension function RV.T1G (a, b) = gsl_ran_gumbel1 (get_rng (), a, b);
1082 // Type-2 Gumbel distribution.
1083 extension function CDF.T2G (x, a, b) = gsl_cdf_gumbel2_P (x, a, b);
1084 extension function IDF.T2G (P >= 0 && P <= 1, a, b)
1085 = gsl_cdf_gumbel2_Pinv (P, a, b);
1086 extension function PDF.T2G (x, a, b) = gsl_ran_gumbel2_pdf (x, a, b);
1087 no_opt extension function RV.T2G (a, b) = gsl_ran_gumbel2 (get_rng (), a, b);
1089 // Uniform distribution.
1090 function CDF.UNIFORM (x <= b, a <= x, b) = gsl_cdf_flat_P (x, a, b);
1091 function IDF.UNIFORM (P >= 0 && P <= 1, a <= b, b)
1092 = gsl_cdf_flat_Pinv (P, a, b);
1093 function PDF.UNIFORM (x <= b, a <= x, b) = gsl_ran_flat_pdf (x, a, b);
1094 no_opt function RV.UNIFORM (a <= b, b) = gsl_ran_flat (get_rng (), a, b);
1095 no_opt function UNIFORM (b >= 0) = gsl_ran_flat (get_rng (), 0, b);
1097 // Weibull distribution.
1098 function CDF.WEIBULL (x >= 0, a > 0, b > 0) = gsl_cdf_weibull_P (x, a, b);
1099 function IDF.WEIBULL (P >= 0 && P < 1, a > 0, b > 0)
1100 = gsl_cdf_weibull_Pinv (P, a, b);
1101 function PDF.WEIBULL (x >= 0, a > 0, b > 0) = gsl_ran_weibull_pdf (x, a, b);
1102 no_opt function RV.WEIBULL (a > 0, b > 0) = gsl_ran_weibull (get_rng (), a, b);
1104 // Bernoulli distribution.
1105 function CDF.BERNOULLI (k == 0 || k == 1, p >= 0 && p <= 1)
1107 function PDF.BERNOULLI (k == 0 || k == 1, p >= 0 && p <= 1)
1108 = gsl_ran_bernoulli_pdf (k, p);
1109 no_opt function RV.BERNOULLI (p >= 0 && p <= 1)
1110 = gsl_ran_bernoulli (get_rng (), p);
1112 // Binomial distribution.
1113 function CDF.BINOM (k, n > 0 && n == floor (n), p >= 0 && p <= 1)
1114 = gsl_cdf_binomial_P (k, p, n);
1115 function PDF.BINOM (k >= 0 && k == floor (k) && k <= n,
1116 n > 0 && n == floor (n),
1118 = gsl_ran_binomial_pdf (k, p, n);
1119 no_opt function RV.BINOM (p > 0 && p == floor (p), n >= 0 && n <= 1)
1120 = gsl_ran_binomial (get_rng (), p, n);
1122 // Geometric distribution.
1123 function CDF.GEOM (k >= 1 && k == floor (k), p >= 0 && p <= 1)
1124 = gsl_cdf_geometric_P (k, p);
1125 function PDF.GEOM (k >= 1 && k == floor (k),
1127 = gsl_ran_geometric_pdf (k, p);
1128 no_opt function RV.GEOM (p >= 0 && p <= 1) = gsl_ran_geometric (get_rng (), p);
1130 // Hypergeometric distribution.
1131 function CDF.HYPER (k >= 0 && k == floor (k) && k <= c,
1132 a > 0 && a == floor (a),
1133 b > 0 && b == floor (b) && b <= a,
1134 c > 0 && c == floor (c) && c <= a)
1135 = gsl_cdf_hypergeometric_P (k, c, a - c, b);
1136 function PDF.HYPER (k >= 0 && k == floor (k) && k <= c,
1137 a > 0 && a == floor (a),
1138 b > 0 && b == floor (b) && b <= a,
1139 c > 0 && c == floor (c) && c <= a)
1140 = gsl_ran_hypergeometric_pdf (k, c, a - c, b);
1141 no_opt function RV.HYPER (a > 0 && a == floor (a),
1142 b > 0 && b == floor (b) && b <= a,
1143 c > 0 && c == floor (c) && c <= a)
1144 = gsl_ran_hypergeometric (get_rng (), c, a - c, b);
1146 // Logarithmic distribution.
1147 extension function PDF.LOG (k >= 1, p > 0 && p <= 1)
1148 = gsl_ran_logarithmic_pdf (k, p);
1149 no_opt extension function RV.LOG (p > 0 && p <= 1)
1150 = gsl_ran_logarithmic (get_rng (), p);
1152 // Negative binomial distribution.
1153 function CDF.NEGBIN (k >= 1, n == floor (n), p > 0 && p <= 1)
1154 = gsl_cdf_negative_binomial_P (k, p, n);
1155 function PDF.NEGBIN (k >= 1, n == floor (n), p > 0 && p <= 1)
1156 = gsl_ran_negative_binomial_pdf (k, p, n);
1157 no_opt function RV.NEGBIN (n == floor (n), p > 0 && p <= 1)
1158 = gsl_ran_negative_binomial (get_rng (), p, n);
1160 // Poisson distribution.
1161 function CDF.POISSON (k >= 0 && k == floor (k), mu > 0)
1162 = gsl_cdf_poisson_P (k, mu);
1163 function PDF.POISSON (k >= 0 && k == floor (k), mu > 0)
1164 = gsl_ran_poisson_pdf (k, mu);
1165 no_opt function RV.POISSON (mu > 0) = gsl_ran_poisson (get_rng (), mu);
1168 absorb_miss boolean function MISSING (x) = x == SYSMIS || !isfinite (x);
1169 absorb_miss boolean function SYSMIS (x) = x == SYSMIS || !isfinite (x);
1170 no_opt boolean function SYSMIS (num_var v)
1173 return case_num (c, v) == SYSMIS;
1175 no_opt function VALUE (num_var v)
1178 return case_num (c, v);
1180 no_opt function VALUE (num_vec_elem v)
1185 // A numeric vector element used in a "normal" context, in which a user-missing
1186 // value becomes system-missing.
1187 absorb_miss no_opt operator VEC_ELEM_NUM (idx)
1193 const struct variable *var = expr_index_vector (e, n, v, idx);
1196 double d = case_num (c, var);
1197 if (!var_is_num_missing (var, d, MV_USER))
1203 // A numeric vector element used as the argument to the VALUE() function, in
1204 // which a user-missing value retains its value.
1206 // All numeric vector elements are initially parsed this way. In most contexts
1207 // they then get coerced into numbers.
1208 absorb_miss no_opt num_vec_elem operator VEC_ELEM_NUM_RAW (idx)
1214 const struct variable *var = expr_index_vector (e, n, v, idx);
1215 return var ? case_num (c, var) : SYSMIS;
1218 absorb_miss no_opt string operator VEC_ELEM_STR (idx)
1224 const struct variable *var = expr_index_vector (e, n, v, idx);
1226 ? copy_string (e, CHAR_CAST_BUG (char *, case_str (c, var)),
1227 var_get_width (var))
1233 no_opt operator NUM_VAR ()
1237 double d = case_num (c, v);
1238 return !var_is_num_missing (v, d, MV_USER) ? d : SYSMIS;
1241 no_opt string operator STR_VAR ()
1246 struct substring s = alloc_string (e, var_get_width (v));
1247 memcpy (s.string, case_str (c, v), var_get_width (v));
1251 no_opt perm_only function LAG (num_var v, pos_int n_before)
1254 const struct ccase *c = lagged_case (ds, n_before);
1257 double x = case_num (c, v);
1258 return !var_is_num_missing (v, x, MV_USER) ? x : SYSMIS;
1264 no_opt perm_only function LAG (num_var v)
1267 const struct ccase *c = lagged_case (ds, 1);
1270 double x = case_num (c, v);
1271 return !var_is_num_missing (v, x, MV_USER) ? x : SYSMIS;
1277 no_opt perm_only string function LAG (str_var v, pos_int n_before)
1281 const struct ccase *c = lagged_case (ds, n_before);
1283 return copy_string (e, CHAR_CAST_BUG (char *, case_str (c, v)),
1286 return empty_string;
1289 no_opt perm_only string function LAG (str_var v)
1293 const struct ccase *c = lagged_case (ds, 1);
1295 return copy_string (e, CHAR_CAST_BUG (char *, case_str (c, v)),
1298 return empty_string;
1301 no_opt operator NUM_SYS ()
1305 return case_num (c, v) == SYSMIS;
1308 no_opt operator NUM_VAL ()
1312 return case_num (c, v);
1315 no_opt operator CASENUM ()