_images/toyplot.png

Matrix VisualizationΒΆ

It is often useful to render a two-dimensional matrix as a regular grid, colored by the matrix values, as a way to look for patterns in data. To facilitate this, Toyplot provides toyplot.canvas.Canvas.matrix() and toyplot.matrix() functions. To demonstrate, let’s begin with a visualization of a matrix containing values from a normal distribution centered around 1.0:

import numpy
numpy.random.seed(1234)
matrix = numpy.random.normal(loc=1.0, size=(20, 20))
import toyplot
toyplot.matrix(matrix, label="A matrix");
A matrix01234567891011121314151617181901.47143516373-0.1909756947062.432706968430.6873481039080.2794112666351.887162940311.859588413720.3634764955831.01569637211-1.242684954192.150035724721.991946022341.95332412811-1.021254820190.6659226341921.002118364681.405453411571.289091940982.32115819213-0.54690555322910.7973536753710.3440306558611.193421376471.553438910962.318151554180.5306947152941.67555408512-0.817027226590.8168914598212.058969187570.60215977181.337437653612.047578572892.045938255631.863717291680.8779084251521.124712953770.6772051943921.8416747133.3909605154621.076199587840.4335540695351.03614193668-1.074977600691.247792199750.102843215560.8632051667391.018289191351.75541398241.215268580971.84100879493-0.445810077044-0.4019732815010.8990818000510.4517575508130.8553804916311.35402033220.9644869747221.565738306062.5456588046330.02576366623270.9296551228961.307968855220.7915012368942.03380073256-1.400453633813.03060362084-0.1426312890231.211883386781.704720624320.2145647882371.462059737161.704228225461.523507967890.07374568646983.007842950781.22696254187-0.1526591092511.631979445811.0395126866941.46439232505-2.563516660622.321105615471.15263055221.164529542930.5699043091241.767368735751.984919841911.270835848832.391986193451.079842313010.600035419303-0.02785055868190.4152817887391.816593926550.9180529481730.6552339857451.5282881453-0.06898878348010.48811869087351.291205359741.566533696351.503591759111.285295684781.484288112752.363481512430.2188947163750.5319823336632.22457435513-0.2811082751441.87547550427-0.710715324030.5492348968641.749163805920.7960671338990.8178245883341.68065600438-0.8184989903921.047071635331.3948442093360.7515679456190.3822933520030.3171160035511.43625760434-0.7030127741131.393710599140.5206759964250.7009837070341.694103287681.678629673711.2395559951.151226629291.816127233362.89353446761.639632763190.0379711680948-1.085265642122.93024676747-0.735348874472.210383704971.797435419430.6201892159531.7025622240.1496537283452.17681245010.4756638973681.700907730921.984188070720.8782715913333.365768628841.496142926251.796594866660.5259791098740.9433042835092.357797258110.195166275833-1.123620249090.6664975595670.1132806475151.334197930981.53678382490.2561696320640.6797961177590.08380113873350.1403317000181.225985486731.628775826541.186494348771.952478345111.988137582590.9273916860370.4493970764370.0618473859069-0.2390715625951.139683274030.7769810181183.123691888591.12227343426-0.4094317399232.422985952779-1.14785503764-0.3475325134581.363564556810.9852478881952.27239507855-0.449566608863-0.1955237416670.4081370268530.585495156468-0.4257947334381.209394787540.407113996161-0.4731164134660.1034193846982.104351569860.5684504844840.8388630917561.889157494071.28837684772-0.05153893757100.680438600160.3800069122791.156998376450.428544648922.05763318320.2085111905220.4753726540721.071878039372.910759427281.787964683141.513082144470.4535837197262.04394465553.107785152792.459927481592.015405457811.749184600920.3244785215631.440266391671.68897185633110.7233538727232.924533320021.411204020711.890764956171.22636322725-1.07861789370.6121137680330.9128930300362.126385822141.247111716161.121171805331.298983935540.8429008631530.259530977219-0.2476529230511.249455215151.581073320623.763844079851.399325436981.66848816921120.7242262713441.500482900151.86306486059-0.0516278594652-0.3920540774932.153922240612.1819441061.391371448420.1189529077981.295079959792.86380106213-0.712273924471-0.4070845457431.126781186331.0037598478-0.2689942560730.161157078581.553921251440.4959572819180.211559815482132.529400674481.205454853931.313013128981.866520712171.299070529592.076540643851.363177347542.893679825550.5142472557171.387674455781.023557610390.3397704979560.6813150704220.2773378063261.177386719381.983512729341.023504585891.553776977861.3537692940.724406366232140.5095164085210.625563399807-1.397503976142.541029983281.063084538960.715559316074-0.2656005376012.787979632460.6454912919310.8952388769331.386253689191.822775373770.3162101775692.057203331211.031879973572.343182457530.9494603104510.635990043693-0.5533423394310.68070219818151.527046450951.711112399360.782454519513.6377912107-0.7421376305950.9055651922592.431183752251.592758446551.17029689533-0.7517059477921.288581322340.4574204830931.171602381991.982817829240.9746510979370.7124475507161.924442867340.9387537001340.268966657415-0.0227737046951161.995992970251.955557932631.71384077121.133370962190.1929616915270.6579892181212.908779658091.155923261451.759652532090.5769937715811.181672745321.274492570751.067912357380.9630171851240.8291989693021.266973231542.382997248850.9775391264891.131395367231.4344371851171.264534068321.565658344271.58508427950.825701847248-0.07136867145510.9515394974480.1547096104341.415100558381.42553059140.01927564249940.5721738900282.498569955140.6398434291310.541759610663-0.3379684019510.9586134603851.821047956113.097800780772.282933246871.27033792574182.003140362042.078673551321.340752685130.8019250403763.481458422882.38525487619-0.15460096539-0.2680690503771.60786218621-0.08009648315760.3887183252041.10203511229-0.4365739367721.210717052510.103095829302-0.7243930789922.79233919665-0.3127127065921.555877426390.318118694509192.572742745760.8953484251522.850397801610.6666495732511.193464233820.5032550621352.03272321574-0.7398037975230.2441378243770.1188882673521.393892262910.04997446520371.332506622161.52894440886-0.1205209939931.048264206931.06198845052-0.02751567321790.7616646345332.93217816958

By default, the matrix is rendered using a Color Brewer diverging “BlueRed” linear map, mapped to the minimum and maximum values in the matrix. Thus, dark blue represents the minimum value and dark red is the maximum value. If you hover the mouse over the cells in the matrix you can see their values with a popup.

You can also display an optional color scale that shows the mapping from matrix values to colors:

toyplot.matrix(matrix, label="A matrix", colorshow=True);
A matrix01234567891011121314151617181901.47143516373-0.1909756947062.432706968430.6873481039080.2794112666351.887162940311.859588413720.3634764955831.01569637211-1.242684954192.150035724721.991946022341.95332412811-1.021254820190.6659226341921.002118364681.405453411571.289091940982.32115819213-0.54690555322910.7973536753710.3440306558611.193421376471.553438910962.318151554180.5306947152941.67555408512-0.817027226590.8168914598212.058969187570.60215977181.337437653612.047578572892.045938255631.863717291680.8779084251521.124712953770.6772051943921.8416747133.3909605154621.076199587840.4335540695351.03614193668-1.074977600691.247792199750.102843215560.8632051667391.018289191351.75541398241.215268580971.84100879493-0.445810077044-0.4019732815010.8990818000510.4517575508130.8553804916311.35402033220.9644869747221.565738306062.5456588046330.02576366623270.9296551228961.307968855220.7915012368942.03380073256-1.400453633813.03060362084-0.1426312890231.211883386781.704720624320.2145647882371.462059737161.704228225461.523507967890.07374568646983.007842950781.22696254187-0.1526591092511.631979445811.0395126866941.46439232505-2.563516660622.321105615471.15263055221.164529542930.5699043091241.767368735751.984919841911.270835848832.391986193451.079842313010.600035419303-0.02785055868190.4152817887391.816593926550.9180529481730.6552339857451.5282881453-0.06898878348010.48811869087351.291205359741.566533696351.503591759111.285295684781.484288112752.363481512430.2188947163750.5319823336632.22457435513-0.2811082751441.87547550427-0.710715324030.5492348968641.749163805920.7960671338990.8178245883341.68065600438-0.8184989903921.047071635331.3948442093360.7515679456190.3822933520030.3171160035511.43625760434-0.7030127741131.393710599140.5206759964250.7009837070341.694103287681.678629673711.2395559951.151226629291.816127233362.89353446761.639632763190.0379711680948-1.085265642122.93024676747-0.735348874472.210383704971.797435419430.6201892159531.7025622240.1496537283452.17681245010.4756638973681.700907730921.984188070720.8782715913333.365768628841.496142926251.796594866660.5259791098740.9433042835092.357797258110.195166275833-1.123620249090.6664975595670.1132806475151.334197930981.53678382490.2561696320640.6797961177590.08380113873350.1403317000181.225985486731.628775826541.186494348771.952478345111.988137582590.9273916860370.4493970764370.0618473859069-0.2390715625951.139683274030.7769810181183.123691888591.12227343426-0.4094317399232.422985952779-1.14785503764-0.3475325134581.363564556810.9852478881952.27239507855-0.449566608863-0.1955237416670.4081370268530.585495156468-0.4257947334381.209394787540.407113996161-0.4731164134660.1034193846982.104351569860.5684504844840.8388630917561.889157494071.28837684772-0.05153893757100.680438600160.3800069122791.156998376450.428544648922.05763318320.2085111905220.4753726540721.071878039372.910759427281.787964683141.513082144470.4535837197262.04394465553.107785152792.459927481592.015405457811.749184600920.3244785215631.440266391671.68897185633110.7233538727232.924533320021.411204020711.890764956171.22636322725-1.07861789370.6121137680330.9128930300362.126385822141.247111716161.121171805331.298983935540.8429008631530.259530977219-0.2476529230511.249455215151.581073320623.763844079851.399325436981.66848816921120.7242262713441.500482900151.86306486059-0.0516278594652-0.3920540774932.153922240612.1819441061.391371448420.1189529077981.295079959792.86380106213-0.712273924471-0.4070845457431.126781186331.0037598478-0.2689942560730.161157078581.553921251440.4959572819180.211559815482132.529400674481.205454853931.313013128981.866520712171.299070529592.076540643851.363177347542.893679825550.5142472557171.387674455781.023557610390.3397704979560.6813150704220.2773378063261.177386719381.983512729341.023504585891.553776977861.3537692940.724406366232140.5095164085210.625563399807-1.397503976142.541029983281.063084538960.715559316074-0.2656005376012.787979632460.6454912919310.8952388769331.386253689191.822775373770.3162101775692.057203331211.031879973572.343182457530.9494603104510.635990043693-0.5533423394310.68070219818151.527046450951.711112399360.782454519513.6377912107-0.7421376305950.9055651922592.431183752251.592758446551.17029689533-0.7517059477921.288581322340.4574204830931.171602381991.982817829240.9746510979370.7124475507161.924442867340.9387537001340.268966657415-0.0227737046951161.995992970251.955557932631.71384077121.133370962190.1929616915270.6579892181212.908779658091.155923261451.759652532090.5769937715811.181672745321.274492570751.067912357380.9630171851240.8291989693021.266973231542.382997248850.9775391264891.131395367231.4344371851171.264534068321.565658344271.58508427950.825701847248-0.07136867145510.9515394974480.1547096104341.415100558381.42553059140.01927564249940.5721738900282.498569955140.6398434291310.541759610663-0.3379684019510.9586134603851.821047956113.097800780772.282933246871.27033792574182.003140362042.078673551321.340752685130.8019250403763.481458422882.38525487619-0.15460096539-0.2680690503771.60786218621-0.08009648315760.3887183252041.10203511229-0.4365739367721.210717052510.103095829302-0.7243930789922.79233919665-0.3127127065921.555877426390.318118694509192.572742745760.8953484251522.850397801610.6666495732511.193464233820.5032550621352.03272321574-0.7398037975230.2441378243770.1188882673521.393892262910.04997446520371.332506622161.52894440886-0.1205209939931.048264206931.06198845052-0.02751567321790.7616646345332.93217816958-2024

Note that, because our minimum and maximum data values aren’t symmetric around the origin, the white section of the color map doesn’t map to zero, and some values greater than zero are mapped to the cool blue portion of the spectrum. Let’s fix this and force our our colormap to be symmetric around zero so all blue colors are negative and all red colors are positive. To do so, we simply create a custom toyplot.color.LinearMap, specifying explicit minimum and maximum domain values and using it in the call to create the matrix visualization:

colormap = toyplot.color.brewer.map("BlueRed", domain_min=-4, domain_max=4)
toyplot.matrix((matrix, colormap), label="A matrix", colorshow=True);
A matrix01234567891011121314151617181901.47143516373-0.1909756947062.432706968430.6873481039080.2794112666351.887162940311.859588413720.3634764955831.01569637211-1.242684954192.150035724721.991946022341.95332412811-1.021254820190.6659226341921.002118364681.405453411571.289091940982.32115819213-0.54690555322910.7973536753710.3440306558611.193421376471.553438910962.318151554180.5306947152941.67555408512-0.817027226590.8168914598212.058969187570.60215977181.337437653612.047578572892.045938255631.863717291680.8779084251521.124712953770.6772051943921.8416747133.3909605154621.076199587840.4335540695351.03614193668-1.074977600691.247792199750.102843215560.8632051667391.018289191351.75541398241.215268580971.84100879493-0.445810077044-0.4019732815010.8990818000510.4517575508130.8553804916311.35402033220.9644869747221.565738306062.5456588046330.02576366623270.9296551228961.307968855220.7915012368942.03380073256-1.400453633813.03060362084-0.1426312890231.211883386781.704720624320.2145647882371.462059737161.704228225461.523507967890.07374568646983.007842950781.22696254187-0.1526591092511.631979445811.0395126866941.46439232505-2.563516660622.321105615471.15263055221.164529542930.5699043091241.767368735751.984919841911.270835848832.391986193451.079842313010.600035419303-0.02785055868190.4152817887391.816593926550.9180529481730.6552339857451.5282881453-0.06898878348010.48811869087351.291205359741.566533696351.503591759111.285295684781.484288112752.363481512430.2188947163750.5319823336632.22457435513-0.2811082751441.87547550427-0.710715324030.5492348968641.749163805920.7960671338990.8178245883341.68065600438-0.8184989903921.047071635331.3948442093360.7515679456190.3822933520030.3171160035511.43625760434-0.7030127741131.393710599140.5206759964250.7009837070341.694103287681.678629673711.2395559951.151226629291.816127233362.89353446761.639632763190.0379711680948-1.085265642122.93024676747-0.735348874472.210383704971.797435419430.6201892159531.7025622240.1496537283452.17681245010.4756638973681.700907730921.984188070720.8782715913333.365768628841.496142926251.796594866660.5259791098740.9433042835092.357797258110.195166275833-1.123620249090.6664975595670.1132806475151.334197930981.53678382490.2561696320640.6797961177590.08380113873350.1403317000181.225985486731.628775826541.186494348771.952478345111.988137582590.9273916860370.4493970764370.0618473859069-0.2390715625951.139683274030.7769810181183.123691888591.12227343426-0.4094317399232.422985952779-1.14785503764-0.3475325134581.363564556810.9852478881952.27239507855-0.449566608863-0.1955237416670.4081370268530.585495156468-0.4257947334381.209394787540.407113996161-0.4731164134660.1034193846982.104351569860.5684504844840.8388630917561.889157494071.28837684772-0.05153893757100.680438600160.3800069122791.156998376450.428544648922.05763318320.2085111905220.4753726540721.071878039372.910759427281.787964683141.513082144470.4535837197262.04394465553.107785152792.459927481592.015405457811.749184600920.3244785215631.440266391671.68897185633110.7233538727232.924533320021.411204020711.890764956171.22636322725-1.07861789370.6121137680330.9128930300362.126385822141.247111716161.121171805331.298983935540.8429008631530.259530977219-0.2476529230511.249455215151.581073320623.763844079851.399325436981.66848816921120.7242262713441.500482900151.86306486059-0.0516278594652-0.3920540774932.153922240612.1819441061.391371448420.1189529077981.295079959792.86380106213-0.712273924471-0.4070845457431.126781186331.0037598478-0.2689942560730.161157078581.553921251440.4959572819180.211559815482132.529400674481.205454853931.313013128981.866520712171.299070529592.076540643851.363177347542.893679825550.5142472557171.387674455781.023557610390.3397704979560.6813150704220.2773378063261.177386719381.983512729341.023504585891.553776977861.3537692940.724406366232140.5095164085210.625563399807-1.397503976142.541029983281.063084538960.715559316074-0.2656005376012.787979632460.6454912919310.8952388769331.386253689191.822775373770.3162101775692.057203331211.031879973572.343182457530.9494603104510.635990043693-0.5533423394310.68070219818151.527046450951.711112399360.782454519513.6377912107-0.7421376305950.9055651922592.431183752251.592758446551.17029689533-0.7517059477921.288581322340.4574204830931.171602381991.982817829240.9746510979370.7124475507161.924442867340.9387537001340.268966657415-0.0227737046951161.995992970251.955557932631.71384077121.133370962190.1929616915270.6579892181212.908779658091.155923261451.759652532090.5769937715811.181672745321.274492570751.067912357380.9630171851240.8291989693021.266973231542.382997248850.9775391264891.131395367231.4344371851171.264534068321.565658344271.58508427950.825701847248-0.07136867145510.9515394974480.1547096104341.415100558381.42553059140.01927564249940.5721738900282.498569955140.6398434291310.541759610663-0.3379684019510.9586134603851.821047956113.097800780772.282933246871.27033792574182.003140362042.078673551321.340752685130.8019250403763.481458422882.38525487619-0.15460096539-0.2680690503771.60786218621-0.08009648315760.3887183252041.10203511229-0.4365739367721.210717052510.103095829302-0.7243930789922.79233919665-0.3127127065921.555877426390.318118694509192.572742745760.8953484251522.850397801610.6666495732511.193464233820.5032550621352.03272321574-0.7398037975230.2441378243770.1188882673521.393892262910.04997446520371.332506622161.52894440886-0.1205209939931.048264206931.06198845052-0.02751567321790.7616646345332.93217816958-4-2024

Now we see that the color map is nicely symmetric around the origin, making it clear which values are positive and which are negative.

In addition to the top-level label, you can specify labels on any side of the matrix. Note the convention in the parameter names: t for “top”, l for “left”, r for “right”, and b for “bottom”:

toyplot.matrix((matrix, colormap), label="A matrix", tlabel="Top", llabel="Left", rlabel="Right", blabel="Bottom");
A matrix01234567891011121314151617181901.47143516373-0.1909756947062.432706968430.6873481039080.2794112666351.887162940311.859588413720.3634764955831.01569637211-1.242684954192.150035724721.991946022341.95332412811-1.021254820190.6659226341921.002118364681.405453411571.289091940982.32115819213-0.54690555322910.7973536753710.3440306558611.193421376471.553438910962.318151554180.5306947152941.67555408512-0.817027226590.8168914598212.058969187570.60215977181.337437653612.047578572892.045938255631.863717291680.8779084251521.124712953770.6772051943921.8416747133.3909605154621.076199587840.4335540695351.03614193668-1.074977600691.247792199750.102843215560.8632051667391.018289191351.75541398241.215268580971.84100879493-0.445810077044-0.4019732815010.8990818000510.4517575508130.8553804916311.35402033220.9644869747221.565738306062.5456588046330.02576366623270.9296551228961.307968855220.7915012368942.03380073256-1.400453633813.03060362084-0.1426312890231.211883386781.704720624320.2145647882371.462059737161.704228225461.523507967890.07374568646983.007842950781.22696254187-0.1526591092511.631979445811.0395126866941.46439232505-2.563516660622.321105615471.15263055221.164529542930.5699043091241.767368735751.984919841911.270835848832.391986193451.079842313010.600035419303-0.02785055868190.4152817887391.816593926550.9180529481730.6552339857451.5282881453-0.06898878348010.48811869087351.291205359741.566533696351.503591759111.285295684781.484288112752.363481512430.2188947163750.5319823336632.22457435513-0.2811082751441.87547550427-0.710715324030.5492348968641.749163805920.7960671338990.8178245883341.68065600438-0.8184989903921.047071635331.3948442093360.7515679456190.3822933520030.3171160035511.43625760434-0.7030127741131.393710599140.5206759964250.7009837070341.694103287681.678629673711.2395559951.151226629291.816127233362.89353446761.639632763190.0379711680948-1.085265642122.93024676747-0.735348874472.210383704971.797435419430.6201892159531.7025622240.1496537283452.17681245010.4756638973681.700907730921.984188070720.8782715913333.365768628841.496142926251.796594866660.5259791098740.9433042835092.357797258110.195166275833-1.123620249090.6664975595670.1132806475151.334197930981.53678382490.2561696320640.6797961177590.08380113873350.1403317000181.225985486731.628775826541.186494348771.952478345111.988137582590.9273916860370.4493970764370.0618473859069-0.2390715625951.139683274030.7769810181183.123691888591.12227343426-0.4094317399232.422985952779-1.14785503764-0.3475325134581.363564556810.9852478881952.27239507855-0.449566608863-0.1955237416670.4081370268530.585495156468-0.4257947334381.209394787540.407113996161-0.4731164134660.1034193846982.104351569860.5684504844840.8388630917561.889157494071.28837684772-0.05153893757100.680438600160.3800069122791.156998376450.428544648922.05763318320.2085111905220.4753726540721.071878039372.910759427281.787964683141.513082144470.4535837197262.04394465553.107785152792.459927481592.015405457811.749184600920.3244785215631.440266391671.68897185633110.7233538727232.924533320021.411204020711.890764956171.22636322725-1.07861789370.6121137680330.9128930300362.126385822141.247111716161.121171805331.298983935540.8429008631530.259530977219-0.2476529230511.249455215151.581073320623.763844079851.399325436981.66848816921120.7242262713441.500482900151.86306486059-0.0516278594652-0.3920540774932.153922240612.1819441061.391371448420.1189529077981.295079959792.86380106213-0.712273924471-0.4070845457431.126781186331.0037598478-0.2689942560730.161157078581.553921251440.4959572819180.211559815482132.529400674481.205454853931.313013128981.866520712171.299070529592.076540643851.363177347542.893679825550.5142472557171.387674455781.023557610390.3397704979560.6813150704220.2773378063261.177386719381.983512729341.023504585891.553776977861.3537692940.724406366232140.5095164085210.625563399807-1.397503976142.541029983281.063084538960.715559316074-0.2656005376012.787979632460.6454912919310.8952388769331.386253689191.822775373770.3162101775692.057203331211.031879973572.343182457530.9494603104510.635990043693-0.5533423394310.68070219818151.527046450951.711112399360.782454519513.6377912107-0.7421376305950.9055651922592.431183752251.592758446551.17029689533-0.7517059477921.288581322340.4574204830931.171602381991.982817829240.9746510979370.7124475507161.924442867340.9387537001340.268966657415-0.0227737046951161.995992970251.955557932631.71384077121.133370962190.1929616915270.6579892181212.908779658091.155923261451.759652532090.5769937715811.181672745321.274492570751.067912357380.9630171851240.8291989693021.266973231542.382997248850.9775391264891.131395367231.4344371851171.264534068321.565658344271.58508427950.825701847248-0.07136867145510.9515394974480.1547096104341.415100558381.42553059140.01927564249940.5721738900282.498569955140.6398434291310.541759610663-0.3379684019510.9586134603851.821047956113.097800780772.282933246871.27033792574182.003140362042.078673551321.340752685130.8019250403763.481458422882.38525487619-0.15460096539-0.2680690503771.60786218621-0.08009648315760.3887183252041.10203511229-0.4365739367721.210717052510.103095829302-0.7243930789922.79233919665-0.3127127065921.555877426390.318118694509192.572742745760.8953484251522.850397801610.6666495732511.193464233820.5032550621352.03272321574-0.7398037975230.2441378243770.1188882673521.393892262910.04997446520371.332506622161.52894440886-0.1205209939931.048264206931.06198845052-0.02751567321790.7616646345332.93217816958TopLeftRightBottom

Note that by default, Toyplot provides row and column indices for the matrix, along the top and left sides. As your matrix sizes grow, you may need to thin-out the indices to avoid overlap:

big_matrix = numpy.random.normal(loc=1, size=(50, 50))
toyplot.matrix((big_matrix, colormap), step=5, label="A matrix");
A 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Or, you may wish to leave off the indices altogether:

toyplot.matrix((big_matrix, colormap), tshow=False, lshow=False, label="A matrix");
A 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