Plot.xtl

1⍝│ Plot: text charts -- bars, sparklines, histograms, scatter plots on
2⍝│ a character grid -- and line charts as pictures, with axes, labels
3⍝│ and several lines in one chart.
4⍝│ Import it with an alias of your choice: "p:" u_se< "Plot".
5⍝│ Put libs/Plot/src on XETAL_PATH ("just path"); the reference is libs/Plot/docs.
6⍝│ Names with l: are exported; those under h: are private to this file.
7⍝│
8⍝│ A text chart is a character matrix: it prints as lines in a terminal,
9⍝│ a notebook or the live demo. A picture (l_ine!) is an SVG document
10⍝│ shown with []S_HOW: numbered files from the command line, a pane in
11⍝│ the browser.
12
13"t:" u̲se< "Strings"
14"f:" u̲se< "Format"
15"v:" u̲se< "Svg"
16
17blocks ← "▁▂▃▄▅▆▇█"                          ⍝ eight heights, lowest first
18width ← 40                                    ⍝ the longest bar
19
20⍝━━ Text charts
21
22⍝│ v scaled to 0..m, rounded (all 0 when v is all 0).
23ʰs̲cale ← { m v →
24  top ← 'm̲ax r̲/ a̲bs f̲loat v
25  top = 0.0 ? (s̲hape v) r̲eshape 0
26  f̲loor 0.5 + (f̲loat m) × (f̲loat v) ÷ top
27}
28
29⍝│ labels b_ars values: a horizontal bar per value, labeled, the
30⍝│ longest 40 wide, each followed by its value (values >= 0).
31ˡb̲ars ← { labels v →
32  w ← 'm̲ax r̲/ '{ t̲ally d̲isclose ⍵ } e̲ach labels
33  n ← width ʰs̲cale v
34  ᵗm̲ix '{ i →
35    label ← w ᵗp̲adRight d̲isclose i s̲elect labels
36    bar ← (f̲irst i s̲elect n) r̲eshape "#"
37    label c̲at " |" c̲at bar c̲at " " c̲at f̲ormat f̲irst i s̲elect v
38  } m̲ap r̲ange t̲ally v
39}
40
41⍝│ s_park v: v as a sparkline, one block character per value, its
42⍝│ height from the least (lowest) to the greatest (highest).
43ˡs̲park ← { v →
44  lo ← 'm̲in r̲/ f̲loat v
45  hi ← 'm̲ax r̲/ f̲loat v
46  hi = lo ? (t̲ally v) r̲eshape 4 s̲elect blocks
47  (1 + f̲loor 0.5 + 7.0 × ((f̲loat v) − lo) ÷ hi − lo) s̲elect blocks
48}
49
50⍝│ n h_istogram v: v counted into n bins of equal width from its least
51⍝│ to its greatest, drawn as bars labeled by each bin's range.
52ˡh̲istogram ← { n v →
53  lo ← 'm̲in r̲/ f̲loat v
54  hi ← 'm̲ax r̲/ f̲loat v
55  step ← (hi − lo) ÷ f̲loat n
56  bin ← 1 + (n − 1) m̲in f̲loor ((f̲loat v) − lo) ÷ step m̲ax 0.000000000001
57  counts ← '{ t̲ally w̲here bin = ⍵ } e̲ach r̲ange n
58  edges ← lo + step × f̲loat o̲ffsets n + 1
59  labels ← '{ i → (d̲isclose i s̲elect 2 ᶠf̲ixed edges) c̲at "-" c̲at d̲isclose (i + 1) s̲elect 2 ᶠf̲ixed edges } m̲ap r̲ange n
60  labels ˡb̲ars counts
61}
62
63⍝│ (w c_at h) s_catter xy: the points xy (2 rows, x over y, as []P_ATH
64⍝│ takes them) marked * on a character grid w wide and h high, y up.
65ˡs̲catter ← { size xy →
66  w ← f̲irst size
67  h ← f̲irst 1 d̲rop size
68  x ← f̲loat f̲irst xy
69  y ← f̲loat f̲irst 1 d̲rop xy
70  col ← 1 + f̲loor 0.5 + (f̲loat w − 1) × (x − 'm̲in r̲/ x) ÷ 1.0 m̲ax ('m̲ax r̲/ x) − 'm̲in r̲/ x
71  row ← h − f̲loor 0.5 + (f̲loat h − 1) × (y − 'm̲in r̲/ y) ÷ 1.0 m̲ax ('m̲ax r̲/ y) − 'm̲in r̲/ y
72  at ← (col − 1) + w × row − 1                   ⍝ offsets into the grid
73  marks ← (o̲ffsets h × w) m̲ember? at
74  (h c̲at w) r̲eshape (1 + marks) s̲elect " *"
75}
76
77⍝━━ Line charts
78
79⍝│ l_ine! v: v as a line chart with axes, a picture shown with []S_HOW;
80⍝│ gives the picture's SVG text. The vertical axis spans the values
81⍝│ (however small their range), the horizontal one the positions 1 to
82⍝│ t_ally v; a single value is drawn as a point.
83ˡl̲ine! ← { v → ⎕S̲HOW ("" "" "") ʰc̲hart 1 r̲eshape e̲nclose f̲loat r̲avel v }
84
85⍝│ names l_ines! series: several lines in one chart, one per boxed
86⍝│ vector of series (each its own length), colored in turn and named in
87⍝│ a legend by names (a boxed text per series).
88ˡl̲ines! ← { names series → ⎕S̲HOW ("" "" "" c̲at names) ʰc̲hart '{ x → f̲loat r̲avel d̲isclose x } m̲ap series }
89
90⍝│ labels c_hart! series: as l_ines!, with a title and the names of the
91⍝│ axes: labels is the title, the horizontal axis's name, the vertical
92⍝│ axis's name, then a name per series ("" for none).
93ˡc̲hart! ← { labels series → ⎕S̲HOW labels ʰc̲hart '{ x → f̲loat r̲avel d̲isclose x } m̲ap series }
94
95⍝━━ Function plots (a real x-axis, not a position: l_ine! and its
96⍝━━ kin space a series across the plot area by count alone, fine for
97⍝━━ a sequence but not for y = f(x) over a range, where a reader
98⍝━━ expects the axis itself to read x's own values)
99
100⍝│ n l_inspace (lo, hi): n evenly spaced Floats from lo to hi
101⍝│ inclusive (n = 1 gives lo). Sample a function over it with e_ach or
102⍝│ m_ap: ys := 'f e_ach (n l_inspace (lo, hi)).
103ˡl̲inspace ← { n (lo, hi) →
104  1 = n ? (f̲loat lo) + (0.0 × (f̲loat o̲ffsets n))
105  (f̲loat lo) + (((f̲loat hi) − (f̲loat lo)) × ((f̲loat o̲ffsets n) ÷ (f̲loat n − 1)))
106}
107
108⍝│ xy f_unction!: xy (2 rows, x over y, as []P_ATH and s_catter take
109⍝│ them) as a line chart with a real-valued horizontal axis, a picture
110⍝│ shown with []S_HOW; gives the picture's SVG text. The vertical axis
111⍝│ spans y's values; the horizontal one spans x's.
112ˡf̲unction! ← { xy → ⎕S̲HOW ("" "" "") ʰc̲hartXY (ʰx̲box xy, 1 r̲eshape e̲nclose f̲loat xy) }
113
114⍝│ names f_unctions! series: several curves in one chart, one per
115⍝│ boxed (x over y) pair of series (each its own length and its own x
116⍝│ values), colored in turn and named in a legend by names.
117ˡf̲unctions! ← { names series → ⎕S̲HOW ("" "" "" c̲at names) ʰc̲hartXY (ʰx̲boxAll series, '{ xy → f̲loat d̲isclose xy } m̲ap series) }
118
119⍝│ labels f_unctionChart! series: as f_unctions!, with a title and the
120⍝│ names of the axes (as c_hart!'s labels).
121ˡf̲unctionChart! ← { labels series → ⎕S̲HOW labels ʰc̲hartXY (ʰx̲boxAll series, '{ xy → f̲loat d̲isclose xy } m̲ap series) }
122
123⍝━━ Chart drawing (private)
124
125⍝│ The horizontal range of one (x over y) pair, padded as the
126⍝│ vertical axis is.
127ʰx̲box ← { xy →
128  x ← f̲irst xy
129  lo ← 'm̲in r̲/ x
130  hi ← 'm̲ax r̲/ x
131  pad ← lo ʰp̲ad hi
132  (lo − pad) c̲at hi + pad
133}
134
135⍝│ The horizontal range across every boxed (x over y) pair of series,
136⍝│ so curves of different x values still share one axis.
137ʰx̲boxAll ← { series →
138  xs ← ʰj̲oined '{ xy → f̲irst d̲isclose xy } m̲ap series
139  lo ← 'm̲in r̲/ xs
140  hi ← 'm̲ax r̲/ xs
141  pad ← lo ʰp̲ad hi
142  (lo − pad) c̲at hi + pad
143}
144
145⍝│ The chart's frame: the picture's size and the plot area's edges.
146ʰW ← 480.0
147ʰH ← 280.0
148ʰL ← 64.0
149ʰR ← 456.0
150ʰT ← 44.0
151ʰB ← 232.0
152
153⍝│ The line colors, in turn (blue, red, green, amber, violet, teal).
154ʰcolors ← "#2563eb" "#dc2626" "#16a34a" "#d97706" "#7c3aed" "#0d9488"
155
156⍝│ Boxed numbers joined into one vector.
157ʰj̲oined ← { b → d̲isclose '{ x y → e̲nclose (d̲isclose x) c̲at d̲isclose y } r̲/ b }
158
159⍝│ labels c_hart series: the picture's SVG text.
160ʰc̲hart ← { labels series →
161  all ← ʰj̲oined series
162  lo ← 'm̲in r̲/ all
163  hi ← 'm̲ax r̲/ all
164  pad ← lo ʰp̲ad hi
165  box ← (lo − pad) c̲at hi + pad
166  n ← 'm̲ax r̲/ '{ x → t̲ally d̲isclose x } e̲ach series
167  lines ← ʰj̲oinText '{ i → (i ʰc̲olor ʰcolors) ʰs̲eries (e̲nclose f̲loat n) c̲at (e̲nclose box) c̲at i s̲elect series } m̲ap r̲ange t̲ally series
168  body ← (n ʰf̲rame box) c̲at lines c̲at ʰt̲itles labels
169  (ʰW c̲at ʰH) ᵛp̲icture body
170}
171
172⍝│ How far past its least and greatest values the vertical axis goes: 0,
173⍝│ or for a flat series a tenth of its size (1 when it is 0).
174ʰp̲ad ← { lo hi →
175  hi > lo ? 0.0
176  lo = 0.0 ? 1.0
177  0.1 × a̲bs lo
178}
179
180⍝│ Boxed texts joined into one text (none is the empty text).
181ʰj̲oinText ← { b →
182  0 = t̲ally b ? ""
183  d̲isclose '{ x y → e̲nclose (d̲isclose x) c̲at d̲isclose y } r̲/ b
184}
185
186⍝│ The color of series i (1, 2, ...), the colors in turn.
187ʰc̲olor ← { i c → d̲isclose (1 + (i − 1) m̲od t̲ally c) s̲elect c }
188
189⍝│ The x of positions p (0, 1, ...) of n: spread across the plot area,
190⍝│ one position in its middle.
191ʰx̲at ← { n p →
192  n = 1 ? (s̲hape p) r̲eshape (ʰL + ʰR) ÷ 2.0
193  ʰr̲ound ʰL + (ʰR − ʰL) × (f̲loat p) ÷ f̲loat n − 1
194}
195
196⍝│ x rounded to a whole number, still a Float.
197ʰr̲ound ← { x → f̲loat f̲loor 0.5 + x }
198
199⍝│ The y of values v in the vertical range box (least, greatest).
200ʰy̲at ← { box v →
201  lo ← f̲irst box
202  hi ← f̲irst 1 d̲rop box
203  ʰr̲ound ʰB − (ʰB − ʰT) × ((f̲loat v) − lo) ÷ hi − lo
204}
205
206⍝│ The x of values v in the horizontal range box (least, greatest):
207⍝│ h:y_at's mapping, left to right instead of inverted.
208ʰx̲atValue ← { box v →
209  lo ← f̲irst box
210  hi ← f̲irst 1 d̲rop box
211  ʰr̲ound ʰL + (ʰR − ʰL) × ((f̲loat v) − lo) ÷ hi − lo
212}
213
214⍝│ One (x over y) series as a polyline (and a point when it has one
215⍝│ value), in its color: color s_eriesXY (xbox; ybox; xy), boxed.
216ʰs̲eriesXY ← { color rest →
217  xbox ← d̲isclose f̲irst rest
218  ybox ← d̲isclose f̲irst 1 d̲rop rest
219  xy ← d̲isclose f̲irst 2 d̲rop rest
220  x ← f̲irst xy
221  y ← f̲irst 1 d̲rop xy
222  xs ← xbox ʰx̲atValue x
223  ys ← ybox ʰy̲at y
224  line ← ((ᵛf̲ill "none") c̲at color ᵛs̲troke 2) ᵛp̲olyline (2 c̲at t̲ally x) r̲eshape xs c̲at ys
225  1 < t̲ally x ? line
226  line c̲at "<circle" c̲at ("cx" ᵛa̲ttr f̲ormat f̲irst xs) c̲at ("cy" ᵛa̲ttr f̲ormat f̲irst ys) c̲at " r=\"3\"" c̲at (ᵛf̲ill color) c̲at "/>"
227}
228
229⍝│ One series as a polyline (and a point when it has one value), in its
230⍝│ color: color s_eries (n; box; values), boxed (n a Float).
231ʰs̲eries ← { color rest →
232  n ← f̲loor f̲irst d̲isclose f̲irst rest
233  box ← d̲isclose f̲irst 1 d̲rop rest
234  v ← d̲isclose f̲irst 2 d̲rop rest
235  xs ← n ʰx̲at o̲ffsets t̲ally v
236  ys ← box ʰy̲at v
237  line ← ((ᵛf̲ill "none") c̲at color ᵛs̲troke 2) ᵛp̲olyline (2 c̲at t̲ally v) r̲eshape xs c̲at ys
238  1 < t̲ally v ? line
239  line c̲at "<circle" c̲at ("cx" ᵛa̲ttr f̲ormat f̲irst xs) c̲at ("cy" ᵛa̲ttr f̲ormat f̲irst ys) c̲at " r=\"3\"" c̲at (ᵛf̲ill color) c̲at "/>"
240}
241
242⍝│ The text attributes of tick labels and names.
243ʰsmall ← " font-family=\"sans-serif\" font-size=\"11\" fill=\"#475569\""
244
245⍝│ The axes, the grid lines and the tick labels: three values on the
246⍝│ vertical axis (least, middle, greatest), the first and last
247⍝│ positions on the horizontal one.
248ʰf̲rame ← { n box →
249  lo ← f̲irst box
250  hi ← f̲irst 1 d̲rop box
251  ticks ← lo c̲at ((lo + hi) ÷ 2.0) c̲at hi
252  ys ← box ʰy̲at ticks
253  d ← 0 m̲ax 8 m̲in 1 − f̲loor (l̲og (hi − lo) ÷ 2.0) ÷ l̲og 10           ⍝ decimals enough to tell the ticks apart
254  texts ← d ᶠf̲ixed ticks
255  grid ← ʰj̲oinText '{ y → ((ᵛf̲ill "none") c̲at "#e2e8f0" ᵛs̲troke 1) ᵛp̲olyline 2 2 r̲eshape ʰL c̲at ʰR c̲at y c̲at y } m̲ap ys
256  left ← ʰj̲oinText '{ k → ((ᵛa̲t (ʰL − 8.0) c̲at 4.0 + k s̲elect ys) c̲at ʰsmall c̲at "text-anchor" ᵛa̲ttr "end") ᵛt̲ext d̲isclose k s̲elect texts } m̲ap r̲ange 3
257  last ← 1 m̲ax n
258  at ← n ʰx̲at (1 + n > 1) r̲eshape 0 c̲at n − 1
259  marks ← (1 + n > 1) r̲eshape 1 c̲at last
260  bottom ← ʰj̲oinText '{ k → ((ᵛa̲t (k s̲elect at) c̲at ʰB + 18.0) c̲at ʰsmall c̲at "text-anchor" ᵛa̲ttr "middle") ᵛt̲ext f̲ormat k s̲elect marks } m̲ap r̲ange t̲ally at
261  axes ← ((ᵛf̲ill "none") c̲at "#64748b" ᵛs̲troke 1) ᵛp̲olyline 2 3 r̲eshape ʰL c̲at ʰL c̲at ʰR c̲at ʰT c̲at ʰB c̲at ʰB
262  back ← "<rect" c̲at ("width" ᵛa̲ttr f̲ormat ʰW) c̲at ("height" ᵛa̲ttr f̲ormat ʰH) c̲at (ᵛf̲ill "#ffffff") c̲at "/>"
263  back c̲at grid c̲at axes c̲at left c̲at bottom
264}
265
266⍝│ The axes, the grid lines and the tick labels, both real-valued:
267⍝│ three ticks on each axis (least, middle, greatest), as h:f_rame's
268⍝│ vertical axis already reads, but the horizontal one too.
269ʰf̲rameXY ← { xbox ybox →
270  ylo ← f̲irst ybox
271  yhi ← f̲irst 1 d̲rop ybox
272  yticks ← ylo c̲at ((ylo + yhi) ÷ 2.0) c̲at yhi
273  ys ← ybox ʰy̲at yticks
274  yd ← 0 m̲ax 8 m̲in 1 − f̲loor (l̲og (yhi − ylo) ÷ 2.0) ÷ l̲og 10
275  ytexts ← yd ᶠf̲ixed yticks
276  xlo ← f̲irst xbox
277  xhi ← f̲irst 1 d̲rop xbox
278  xticks ← xlo c̲at ((xlo + xhi) ÷ 2.0) c̲at xhi
279  xs ← xbox ʰx̲atValue xticks
280  xd ← 0 m̲ax 8 m̲in 1 − f̲loor (l̲og (xhi − xlo) ÷ 2.0) ÷ l̲og 10
281  xtexts ← xd ᶠf̲ixed xticks
282  grid ← ʰj̲oinText '{ y → ((ᵛf̲ill "none") c̲at "#e2e8f0" ᵛs̲troke 1) ᵛp̲olyline 2 2 r̲eshape ʰL c̲at ʰR c̲at y c̲at y } m̲ap ys
283  left ← ʰj̲oinText '{ k → ((ᵛa̲t (ʰL − 8.0) c̲at 4.0 + k s̲elect ys) c̲at ʰsmall c̲at "text-anchor" ᵛa̲ttr "end") ᵛt̲ext d̲isclose k s̲elect ytexts } m̲ap r̲ange 3
284  bottom ← ʰj̲oinText '{ k → ((ᵛa̲t (k s̲elect xs) c̲at ʰB + 18.0) c̲at ʰsmall c̲at "text-anchor" ᵛa̲ttr "middle") ᵛt̲ext d̲isclose k s̲elect xtexts } m̲ap r̲ange 3
285  axes ← ((ᵛf̲ill "none") c̲at "#64748b" ᵛs̲troke 1) ᵛp̲olyline 2 3 r̲eshape ʰL c̲at ʰL c̲at ʰR c̲at ʰT c̲at ʰB c̲at ʰB
286  back ← "<rect" c̲at ("width" ᵛa̲ttr f̲ormat ʰW) c̲at ("height" ᵛa̲ttr f̲ormat ʰH) c̲at (ᵛf̲ill "#ffffff") c̲at "/>"
287  back c̲at grid c̲at axes c̲at left c̲at bottom
288}
289
290⍝│ labels c_hartXY (xbox, series): as h:c_hart, but series is a boxed
291⍝│ (x over y) pair per curve and the horizontal axis spans xbox (its
292⍝│ own real values, not a count) instead of a position.
293ʰc̲hartXY ← { labels (xbox, series) →
294  allY ← ʰj̲oined '{ xy → f̲irst 1 d̲rop d̲isclose xy } m̲ap series
295  ylo ← 'm̲in r̲/ allY
296  yhi ← 'm̲ax r̲/ allY
297  ypad ← ylo ʰp̲ad yhi
298  ybox ← (ylo − ypad) c̲at yhi + ypad
299  lines ← ʰj̲oinText '{ i → (i ʰc̲olor ʰcolors) ʰs̲eriesXY (e̲nclose xbox) c̲at (e̲nclose ybox) c̲at i s̲elect series } m̲ap r̲ange t̲ally series
300  body ← (xbox ʰf̲rameXY ybox) c̲at lines c̲at ʰt̲itles labels
301  (ʰW c̲at ʰH) ᵛp̲icture body
302}
303
304⍝│ The title, the axes' names and the legend from labels (title,
305⍝│ horizontal axis, vertical axis, then a name per series); empty ones
306⍝│ are left out.
307ʰt̲itles ← { labels →
308  n̲ame ← { k → 0 = t̲ally d̲isclose k s̲elect labels ? ""◆ d̲isclose k s̲elect labels }
309  title ← ((ᵛa̲t ʰL c̲at 24.0) c̲at " font-family=\"sans-serif\" font-size=\"14\" font-weight=\"bold\" fill=\"#0f172a\"") ᵛt̲ext n̲ame 1
310  across ← ((ᵛa̲t ((ʰL + ʰR) ÷ 2.0) c̲at ʰB + 38.0) c̲at ʰsmall c̲at "text-anchor" ᵛa̲ttr "middle") ᵛt̲ext n̲ame 2
311  up ← (ʰsmall c̲at ("text-anchor" ᵛa̲ttr "middle") c̲at "transform" ᵛa̲ttr "translate(18 " c̲at (f̲ormat (ʰT + ʰB) ÷ 2.0) c̲at ") rotate(-90)") ᵛt̲ext n̲ame 3
312  names ← 3 d̲rop labels
313  keys ← ʰj̲oinText '{ i → ((i ʰc̲olor ʰcolors) ᵛs̲pan "■ ") c̲at ("#334155" ᵛs̲pan d̲isclose i s̲elect names) c̲at "   " } m̲ap r̲ange t̲ally names
314  legend ← ((ᵛa̲t ʰR c̲at 24.0) c̲at ʰsmall c̲at "text-anchor" ᵛa̲ttr "end") ᵛm̲arkup keys
315  ((n̲ame 1) ʰk̲ept title) c̲at ((n̲ame 2) ʰk̲ept across) c̲at ((n̲ame 3) ʰk̲ept up) c̲at keys ʰk̲ept legend
316}
317
318⍝│ An element, or nothing when the text it shows is empty.
319ʰk̲ept ← { t element →
320  0 = t̲ally t ? ""
321  element
322}