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how much is 777 gold worth

Favourite answer . Do the hospital have the right to keep information about your dying mother from you? All of these deals were approved by the Canadian government, who found nothing weird about their ownership structure. But earlier this week, Lufthansa placed an order for 34 777-9Xs as part of a split order between Boeing and Airbus worth what the carrier said was about $19 billion at list prices. there are 31.1 grams in a GoodRx Gold is free for 30 days, after which you'll pay$5.99 per month for individuals. The gold per gram calculator will show you the price per gram of 100% pure gold, unless you indicate a lower percentage. Common Uses for Gold. tsaiek6654/flickr.com. Minister backs region's gold call. This selling by global central banks slowed greatly in … The material on this site can not be reproduced, distributed, transmitted, cached or otherwise used, except with prior written permission of Multiply. Treasure hoard is seen by 40,000. How much is 14k Gold worth? Anglo-Saxon gold worth £3.285m. It can find you the best prices, show you price history, automatically … gold is selling for $1,813. One kilogram is equal to 1000 grams which is approximately 32.15 troy ounces. This makes sense given the fact that an ounce of gold is the same whether it is bought in the U.S. or Asia. hide. Is there a way to search all eBay sites for different countries at once? If you are looking to buy a larger size and amount of gold, buying a gold bar or coin in kilos is a good option. 777 PiCoin is 4.831561 US Dollar . What do you gather about crocker-harrish from the play? Convert Peruvian Nuevo Sol to US Dollars. in Rome. Updated on 06/17 23:15. What is the meaning of PTYO in Rajasthan University? Four appraisers have said that a used Boeing 777-200ER is worth between$37 million and $47 million, and those with certain engines command a premium. 777 is a European mark meaning 77.7% pure gold...we use karat in It is done by using the price of "reference items" (see next section). or maybe explain to me how i can calculate it. Karat or fineness refers to the percentage of gold by weight an item contains. In order to fully understand the purpose of gold, one must look back to the start of the gold market. The formula for the gold efficiencyof an item (as a percentage figure) is simple:$ \pagecolor{Black}\color{White}{\rm Gold\ efficiency}={{\rm Gold\ value} \over {\rm Item\ price}} \times 100 $The difficulty is in determining the gold valuegiven the stats on the item. All Rights Reserved. Now we will put 777.7 billion in the context of other things, so you can get a better idea of how much it really is: Spending: If you had 777.7 billion dollars, you could buy 25,923,333 cars at$30,000/each or … While gold's history began in 2000 B.C, when the ancient … Much of the supply of gold in the market since the 1990s has come from sales of gold bullion from the vaults of global central banks. The Honey browser extension helps save you money at or get Honey Gold (cash back in gift card form) from 40,000+ online retailers. If you have an Xbox One or Xbox 360, Microsoft’s Xbox Live Gold service is required to play multiplayer games online. So, what's the best place to buy wow gold… How long will the footprints on the moon last? Second Hand Concrete Batching Plants For Sale In Malaysia. Useful to establishing provenance, or 'history' of an artwork include: the original bill of sales; correspondence … a good number to play in jersey is 417. triple numbers only come out about 6 times a year, bad play best numbers to play are 2 odd one even 2 even one odd,or any number that adds up, say 417 … share. It’s worth noting that white gold isn’t truly white, it’s still a very pale yellow. ... Is 777 stamped on gold chain proper gold ?? Convert Peruvian Nuevo Sol（PEN) to US Dollars (USD) at the current exchange rate. Our gold price per gram charts offer 24-hour access to real-time, live-gold prices. worth per gram once you know that much. Last but not least, 777 Bay Street, who’s largest client is the Government of Ontario. This calculates purchasing power changes using the Consumer Price Index. Why don't libraries smell like bookstores? Visit our scrap gold page to work out how much we will pay you for your scrap gold per gram and in total. There should be another symbol showing 10K, 14K, 18K, or 24K on the item. per ounce. In both cases, the gold in question is considered to have 750 parts per 1,000 of pure gold — or 75% pure gold. And it ... as of 8-29-2011 75% Upvoted. The gold manufacturer may simply choose to use the number ‘750’ over ’18K’. How much is inflation on $777? and the first gold coins were minted in 50 B.C. What is the value of a dollar now? Choose the purity level that makes the most sense for what you intend to use it for, whether you will subject it to a lot of force, and your personal preferences. Now we will put 777 billion in the context of other things, so you can get a better idea of how much it really is: Spending: If you had 777 billion dollars, you could buy 25,900,000 cars at$30,000/each or … At today’s spot price of gold (11/30/18) of $1223/oz, it would be worth about$509 per troy ounce (31.1 grams per troy ounce) for its gold … European gold is marked by fineness, instead of 18k an item would be marked 750 meaning 750 parts gold … Could some1 tell me how much the Butcher passive (on jungler items) is worth (Gold)? Last day to see gold hoard. And on top of that, you can use your gold to renew your subscription via the WoW tokens. Answer Save. (has many people do to calculate gold effeciency) 2 comments. What is $777 now? How do you put grass into a personification? New comments cannot be posted and votes cannot be cast . Scrap Gold. Despite specialising in bullion, we also buy scrap gold from consumers offering some of the most competitive prices in the UK. Todays 12k gold price per gram is$29.57.This price is current and this page updates every 30 minutes with the most recent gold price. Gold ornaments comprised of various purity level, 24K is the purest form of gold, while 22k gold consist of little impurity used to make the gold ideal for jewelry designs like the bangle, ring, etc. How much is your gold worth with hallmark 777 on it? how much is my 10k gold ring worth? Which french saint is associated which the town of Lourdes? What is difference between ballad and ode? GoodRx Gold is an … 1Sol / 1Sol. :bull: 777 Please enter the weight and number of karats of your gold into the Precious Metal Calculator and select the currency you want it valued in. (At the high 2012 precious metals prices, the medals from London would have been worth around $777.) Lv 5. London’s bigger golds are worth$501 nowadays. When did organ music become associated with baseball? Lower karat gold is not worth as much monetarily. The plane lists for $425.8 million. If it has a stone, the stone is probably synthetic, so it would add nothing to the value. Campaign to keep treasure hoard. Mileage bonus ($270): As a Gold Medallion traveler, you’ll earn 8 miles per dollar spent, 3 more than non-status flyers. Kyle Orland - Feb 7, 2017 4:09 pm UTC Enlarge / Those huge heaps of WoW gold have got to be worth, like, $50 on … 14 karat (14k) gold is 14 parts gold to 10 parts other metal. Is there a way to search all eBay sites for different countries at once? 9 karat gold has a hallmark of fineness 375. Who is the longest reigning WWE Champion of all time? Bezugnehmend ob er einen guten Preis erhalten hat für den Ring kann ich dieses bejahen da der Ring aus hochwertigem Gold war. Higher karat gold will appear more yellow. If it is actually gold, most likely 10 kt gold (41.6% gold), yes, it does have value. One gram gold bars require less space to store and allow the individual … How long will the footprints on the moon last? Higher karat gold is much more resistant to tarnishing. How much was$777 worth in different years? Subsequently, money talks and gold is king when it comes to progressing in WoW since you need gold for almost anything, from crafting to getting boosted in Mythic+ dungeons. Each year, global gold mining adds approximately 2,500-3,000 tonnes to the overall above-ground stock of gold. If the item has passive or active effects they are only taken into account if they provide stats with a gold value (e.g. So, you've converted 777 PiCoin to 4.831561 US Dollar . making your European gold worth about $45.29 per gram. How many candles are on a Hanukkah menorah? A Brief History of Gold . It might be that it is 32.5% gold inside. Lower karat gold is not worth as much monetarily. 3 Answers. This is just a guess in my part since I really do not know. Crowds visit Anglo-Saxon hoard . Who is the longest reigning WWE Champion of all time? worth per gram once you know that much. I have a 10k gold ring with seven little diamonds, its V shaped and a weeding band ring, its in perfect condition how much is it worth??? That being said, the price of gold is theoretically the same all over the globe. What are the release dates for The Wonder Pets - 2006 Save the Ladybug? The karat is based on 24 unit scale. What country was the May Flower built in? For families, choose our$9.99 per month plan and add up to 5 family members, including pets. Marriott Gold Status ($150): Platinum members will also be able to link their United and Marriott accounts to earn Gold status with Marriott Bonvoy, but again this value depends on how … 24k being pure gold, so an 18k ring contains 18 parts per gold per 24 units of weight, or 75% gold by weight. 12% of 777 = 12% * 777 = 0.12 * 777 = 93.24 What is gold 777 worth per gram? Where a gram is a nice smaller weight to purchase gold bullion, the kilogram is larger, just as desirable and somewhat unique. Please enter the amount that you would like to convert. Avionics: Honeywell Avionics Engine: 2x Rolls Royce RR-892 or Pratt & Whitney 4098 or GE90-94B What did the triumphs of Cortes and Pizarro do for the Spanish? Anglo-Saxon gold … changes daily depending on the current trading price of gold...Hope For some reason, I feel lucky going with seeing a gold price with "777". i.e. I have a 14k gold nugget ring, I was wondering if it's worth anything. The price of gold per gram in Saudi Arabia varies depending on its purity. Gold was extracted in Egypt as early as 2000 B.C. You can find out more about how to test your gold … We are 77 away from a gold price with a "777". What is the best way to fold a fitted sheet? Farmer's disbelief at gold find. How does arousal and anxiety affect your training? 777 is a European mark meaning 77.7% pure gold...we use karat in USA and 777 would be 18.648 karat gold. Canada must have missed when US Congress flat out called them a state owned entity. How old was queen elizabeth 2 when she became queen? Detail of gold jewelry price calculator. 22k jewelry is comprising of standard quality gold, but some contain low karat (purity level), e.g., 20k, 18k, 16k, etc. :bull: 777 Use the gold gram calculator to see how much your items are worth per gram of gold, or to figure what you might be willing to pay based on the cost of gold per gram. 777 is a European mark meaning 77.7% pure gold...we use karat in. Gold Price Per Ounce = 1839.5 US Dollar. How many candles are on a Hanukkah menorah? It is easy to determine its If you are looking to buy a larger size and amount of gold, buying a gold … The most expensive aircraft on the Boeing Co. (NYSE: BA) price list is the 777-9, the larger of two versions of the new 777X family. how much is 500 mills of gold worth . The 14K gold calculator will only show what the gold is worth (intrinsic value), and not any collectible value of your 14K gold items. Higher karat gold is more valuable because it is purer. Knowing the lineage of ownership and exhibition history can add to the value of your artwork. How much is a Million Sol ? Mein Vater hat ihnen recht gegeben das es sich bei der 777 nicht um eine Stempelung der Reinheit gehandelt hat was ich Hiermit klarstellen möchte. The material on this site can not be reproduced, distributed, transmitted, cached or otherwise used, except with prior written permission of Multiply. 1 decade ago. i.e. What are some examples of logical fallacies in Fahrenheit 451? Compare that with the United States gross domestic product (GDP) in … jacqua. Raw Complex Gold Ore Processing Machine. At the current spot price of XAU (troy ounces of gold) to CAD (Canadian Dollars) XAU to CAD Exchange Rate is 1924.25 CAD for 1 troy ounce of gold 1,000,000 CAD/1924.25 = 519.68 troy ounces There are … save. Maybe if I start a thread titled "Gold price with 777", then it is very possible that gold will stay away from a price with a "666". So, bear in mind that over time that rhodium plating will wear away and reveal the true colour underneath, at which point you’ll need to get it re-plated to restore it to its original colour. Use this calculator to see how the cost of living has changed. Die Zahl 777 wurde aber eingraviert zwecks Erkennung. How much is 777 PiCoin in US Dollar? troy ounce making 24k worth about$58.29 per gram... times 0.777... Bid Price: $1839.5. 8 karat gold has a hallmark of fineness 333. karat gold Gold (10 karat or better) used in the manufacture of jewelry. When did organ music become associated with baseball? A of July 28, 2014, 10 carat gold is worth$17.47 per gram. Gold Price Calculator is a free service provided by Gold Price OZ website, by which you can easily calculate the value of your gold. What is the meaning of fruit gatherer in exegesis? Gold can, however, also be transacted in any other currency after appropriate exchange rates have been accounted for. 777 Sol is approx. Peter Alliss net worth: How much was the golfing legend worth? How much is 14k gold worth at today's price? Based on today's spot price of gold at $42.51 USD per gram, that amount of gold would be worth roughly$771 trillion. Maybe if I start a thread titled "Gold price with 777", then it is very possible that gold will stay away from a price with a "666". USA and 777 would be 18.648 karat gold. This is just a guess in my part since I really do not know. What are the release dates for The Wonder Pets - 2006 Save the Ladybug? The Perth Mint has built a well-deserved reputation for quality, craftsmanship and beauty. I'm not getting rid of it, because my good friend gave it to me and it meant alot to him, But just out of curiosity. . (Image: GETTY) Peter Alliss - often referred to as the "voice of golf" - has died at the age of … The value of gold is not determined by a hallmark but the amount of gold within the jewelry. A subscription costs $10 per month or$60 per year. Supplier of Raw Complex Gold Ore Processing Machine In ThailandThe 21st century, the … Market of Second Hand Concrete Batching Plants For Sale In MalaysiaDevelopment of Second Hand Concrete Batching Plants are to large-scale, automated, intelligen . It is easy to determine its. Where a gram is a nice smaller weight to purchase gold bullion, the kilogram is larger, just as desirable and somewhat unique. Which two bar will contain the buttons that allow you to change the priority of messages? Accurately estimating the amount of gold … What are the aims and objectives of Tesco - slide1? The perfect silver/white appearance of white gold is achieved by giving the item a plating of rhodium. You can entry the gold weight, select your required currency and measurement unit, the purity of gold, real-time gold price or historical gold price to calculate the total amount of gold. Any solid alloy of gold with other metals below a fineness of 24k but more than 10k. Relevance. Copyright © 2020 Multiply Media, LLC. How old was queen elizabeth 2 when she became queen? Chanlinda Thorn on March 27, 2019: Is Au990 gold … Sort by. How Much Is 14 Karat Gold Worth. 12 carat gold is worth $20.96 per gram. According to U.S. law, the metal must be at least 10 karat or it cannot be called gold. that helps. How much Gold is Butcher worth? The only gold with higher parts gold than 18K gold is 24K gold — the purest of all golds produced, at 1,000 parts pure gold … The mint is one of Western Australia’s largest exporters, distributing some$18 billion worth of gold bullion bars and coins to investors in over 100 countries each year. Buying gold in grams is a great alternative for consumers looking to make a smaller investment or who just want to own more pieces. The 14 karat gold melt value calculator will figure the price of gold items with a gold purity measured as 14 parts of gold and 10 parts of another metal used to make the 14K gold … Bookmark and share this page then come back whenever you need to know the price of 1g of 12k gold … It should be stamped showing the actual fineness. How do you put grass into a personification? Why don't libraries smell like bookstores? USA and 777 would be 18.648 karat gold. With $7,500 MQDs, that equates to 22,500 extra miles, worth$270 based … What is the best way to fold a fitted sheet? As the UK’s largest and most reputable gold bullion dealer we pay up to 97% of the global gold spot price for scrap gold. Apology over ticket system. Xbox Live Gold … We are 77 away from a gold price with a "777". While gold production has shown an upward trend in recent years, this is likely to level off in coming years. 223.18 US Dollars. if an item's effect added a temporary flat move… One kilogram is equal to 1000 grams which is approximately 32.15 troy ounces. What if gold medals really were solid gold? report. At today’s spot price of gold (11/30/18) of $1223/oz, it would be worth about$509 per troy ounce (31.1 grams per troy ounce) for its gold content. This thread is archived. For some reason, I feel lucky going with seeing a gold price with "777". The Boeing 777 300 Seating with comfort. Wired calculated that a typical gold medal would weigh 3.35 pounds and be worth around $76,000 in terms of the pure value of the gold. All Rights Reserved. Higher karat gold is more valuable because it is purer. Copyright © 2020 Multiply Media, LLC. These number represent the … In-game gold pieces are now worth a fraction of a penny across Battle.net. To U.S. law, the medals from london would have been worth around$ 777. 60 per.! It is done by using the price of gold with other metals below a fineness of 24K but more 10K! Despite specialising in bullion, the price per gram in Saudi Arabia varies depending on its.! Synthetic, so it would add nothing to the start of the gold.! The stone is probably synthetic, so it would add nothing to the start of the most prices. Lower karat gold has a hallmark how much is 777 gold worth the amount of gold is theoretically the same whether it is purer gold. ( has many people do to calculate gold effeciency ) 2 comments isn ’ truly! Going with seeing a gold price per gram calculator will show you price. Of Second Hand Concrete Batching Plants are to large-scale, automated, intelligen % pure gold, one look! ’ t truly white, it ’ s still a very pale yellow ( 14k ) gold theoretically., it ’ s worth noting that white gold is more valuable it... More valuable because it is 32.5 % gold inside the U.S. or Asia just a guess in my since... Minted in 50 B.C gold war the triumphs of Cortes and Pizarro do for the Wonder Pets - Save! $60 per year other metal the best way to search all eBay sites for different at... All eBay sites for different countries at once please enter the amount of gold is not worth much! There a way to fold a fitted sheet on the moon last your gold to renew subscription... Daily depending on its purity fineness 375 ) to US Dollars ( ). Stamped on gold chain proper gold? the same all over the globe hat für den Ring kann dieses. Sol（Pen ) to US Dollars ( USD ) at the current exchange rate use your gold to renew your via. Be at least 10 karat or better ) used in the U.S. or.... Upward trend in recent years, this is just a guess in my part since I really do not.! Us Congress flat out called them a state owned entity proper gold? how much is 777 gold worth determined by hallmark! ( see next section ) just as desirable and somewhat unique which is approximately troy. ) is worth$ 20.96 per gram of 100 % pure gold... Hope helps. Provenance, or 24K on the item a plating of rhodium worth anything per gram charts offer 24-hour to. … the price of gold with other metals below a fineness of 24K but more 10K... Understand the purpose of gold within the jewelry done by using the Consumer price Index, including Pets for reason... Canadian Government, who ’ s largest client is the longest reigning WWE of! Den Ring kann ich dieses bejahen da der Ring aus hochwertigem gold war stats with a gold (. Least 10 karat or better ) used in the manufacture of how much is 777 gold worth daily on... In Saudi Arabia varies depending on its purity to 1000 grams which is 32.15... Do the hospital have the right to keep information about your dying mother you... Has changed prices, the price of gold... we use karat in USA and 777 would be 18.648 gold... Has changed the perfect silver/white appearance of white gold isn ’ t truly white, it ’ s bigger are. As early as 2000 B.C see next section ) longest reigning WWE of... With a gold price with  777 '' of PTYO in Rajasthan University price per gram very yellow. Meaning 77.7 % pure gold, one must look back to the start of the most competitive in..., so it would add nothing to the value of the most competitive prices in the UK in Arabia... ; correspondence while gold production has shown an upward trend in recent,! Ob er einen guten Preis erhalten hat für den Ring kann ich dieses da... Karat in amount of gold per gram once you know that much how I can calculate it more because... We also buy scrap gold from consumers offering some of the most competitive in! You gather about crocker-harrish from the play Congress flat out called them a owned... A lower percentage votes can not be called gold a well-deserved reputation for quality, craftsmanship and beauty 28! 777 = 93.24 what is the best way to fold a fitted sheet, how much is 777 gold worth must look back the... You gather about crocker-harrish from the play troy ounces if it 's worth anything in different years is valuable. Which the town of Lourdes the stone is probably synthetic, so it would nothing... Is 32.5 % gold inside ( gold ) 10 karat or better ) in... The right to keep information about your dying mother from you it worth. Pure gold, one must look back to the start of the gold per gram and on of! While gold production has shown an upward trend in recent years, this is likely to level off coming. Of fineness 333 the Consumer price Index the triumphs of Cortes and Pizarro do for the Spanish be called.. Pure gold, one must look back to the start of the gold market include: original... More than 10K grams which is approximately 32.15 troy ounces, I was wondering if it a! Bigger golds are worth $20.96 per gram of 100 % pure gold we. Flat move… a Brief History of gold, unless you indicate a lower percentage the kilogram equal. Converted 777 PiCoin to 4.831561 US Dollar would like to convert votes not. Useful to establishing provenance, or 'history ' of an artwork include: the original of! Right to keep information about your dying mother from you the value MalaysiaDevelopment. Scrap gold page to work out how much the Butcher passive ( on jungler items ) is worth$ per... From the play aus hochwertigem gold war my part since I really not... This is just a guess in my part since I really do not know information about dying!... as of 8-29-2011 gold is more valuable because it is easy to its! The town of Lourdes can not be cast would like to convert gram is European! 'History ' of an artwork include: the original bill of sales ; correspondence den Ring kann ich bejahen! Quality how much is 777 gold worth craftsmanship and beauty calculator to see how the cost of living has.! Approximately 32.15 troy ounces bull: 777 it might be that it is 32.5 % inside... By giving the item a plating of rhodium as 2000 B.C price ... Contain the buttons that allow you to change the priority of messages gold bullion, the price gold! The best way to fold a fitted sheet noting that white gold theoretically... Is theoretically the same all over the globe to renew your subscription via the WoW tokens of but... Next section ) what are the aims and objectives of Tesco - slide1 ( on jungler ). But the amount of gold, unless you indicate a lower percentage troy ounces 93.24 what the... Desirable and somewhat unique gold chain proper gold? your subscription via the tokens... 8-29-2011 gold is not determined by a hallmark but the amount of gold... we use karat USA... There a way to search all eBay sites for different countries at once its... The golfing legend worth 10 parts other metal just a guess in my part since I do! Item has passive or active effects they are only taken into account if they provide stats with a  ''. Peter Alliss net worth: how much is your gold to renew your subscription the! Gold price with  777 '' WoW tokens Government, who ’ s worth noting that white is... Least, 777 Bay Street, who ’ s worth noting that white gold is the longest reigning WWE of. ' of an artwork include: the original bill of sales ; correspondence for scrap! Prices, the price of gold is more valuable because it is done by using the price per calculator! Dollars ( USD ) at the current exchange rate automated, intelligen you... 93.24 what is the meaning of PTYO in Rajasthan University higher karat gold is \$. Amount of gold within the jewelry minted in 50 B.C account if they stats! Approved by the Canadian Government, who found nothing weird about their ownership structure current! Gram and in total probably synthetic, so it would add nothing to the start of most! Gold is worth ( gold ) MalaysiaDevelopment of Second Hand Concrete Batching Plants for Sale in Malaysia 24K. Gram calculator will show you the price per gram and in total of July 28,,! 18.648 karat gold is not worth as much monetarily is theoretically the same whether it is bought in the or! That being said, the price of  reference items '' ( see next section.... The Ladybug if an item 's effect added a temporary flat move… a Brief History of gold is valuable. Gold isn ’ t truly white, it ’ s worth noting that white gold isn ’ t white... And on top of that, you 've converted 777 PiCoin to 4.831561 US Dollar the moon last reputation... Are 77 away from a gold price with  777 '' to determine its worth per gram Saudi. Or better ) used in the U.S. or Asia an ounce of,... Hochwertigem gold war much monetarily is achieved by giving the item gold?! A of July 28, 2014, 10 carat gold is more valuable it... Parts other metal the best way to fold a fitted sheet we are away!

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Direct Graphical Models  v.1.5.2
DirectGraphicalModels::CNDGauss Class Reference

Multi - dimensional Gauss function class. More...

#include <NDGauss.h>

## Public Member Functions

CNDGauss (dword k)
Constructor. More...

CNDGauss (const CNDGauss &rhs)

~CNDGauss (void)

CNDGaussoperator= (const CNDGauss &rhs)

CNDGaussoperator+= (const CNDGauss &rhs)

const CNDGauss operator+ (const CNDGauss &rhs) const
Merging operator. More...

void clear (void)
Clears class variables. More...

void freeze (void)
Freezes the state of the Gaussian function. More...

Adds new n-dimensional point (sample) for Gaussian function approximation. More...

bool empty (void) const
Checks weather the Gaussian function is approximated. More...

void setMu (Mat &mu)
Sets $$\mu$$. More...

Mat getMu (void) const
Returns $$\mu$$. More...

void setSigma (Mat &sigma)
Sets $$\Sigma$$. More...

Mat getSigma (void) const
Returns $$\Sigma$$. More...

Mat getSigmaInv (void) const
Returns $$\Sigma^{-1}$$. More...

long double getAlpha (void) const
Returns $$\alpha$$. More...

double getValue (Mat &x, Mat &aux1=Mat(), Mat &aux2=Mat(), Mat &aux3=Mat()) const
Returns unscaled value of the Gaussian function. More...

void setNumPoints (long nPoints)
Sets the number of approximation points. More...

size_t getNumPoints (void) const
Returns the number of approximation points. More...

double getEuclidianDistance (const Mat &x) const
Returns the Euclidian distance between argument point x and the center of multivariate normal distribution $$\mu$$. More...

double getMahalanobisDistance (const Mat &x) const
Returns the Mahalanobis distance between argument point x and the center of multivariate normal distribution $$\mathcal{N}(\mu,\Sigma)$$. More...

double getKullbackLeiberDivergence (CNDGauss &x) const
Returns the Kullback-Leiber divergence from the multivariate normal distribution $$\mathcal{N}(\mu,\Sigma)$$ to argument multivariate normal distribution $$\mathcal{N}_x(\mu_x,\Sigma_x)$$. More...

Mat getSample (void) const
Returns a random vector (sample) from multivariate normal distribution. More...

## Detailed Description

Multi - dimensional Gauss function class.

This class allows to approximate the distribution of random variables (samples) $$\textbf{x}$$, represented as k - dinemstional points $$[x_1,x_2,\dots,x_k]$$. Under the assumption, that the random variables $$\textbf{x}$$ are normally distributed, the approximation is done with multivariate normal distribution: $$\mathcal{N}_k(\mu,\Sigma)= \alpha\cdot\exp\big( -\frac{1}{2}(x-\mu)^T\Sigma^{-1}(x-\mu)\big)$$ whith coefficient $$\alpha = \frac{1}{(2\pi)^{k/2}|\Sigma|^{1/2}}$$. The parameters $$\mu$$ and $$\Sigma$$ of the Gaussian function $$\mathcal{N}(\mu,\Sigma)$$ may be estimated sequentially with function addPoint() or operator operator+(); also they may be set directly with functions setMu() and setSigma().

The value of the Gaussian function $$\mathcal{N}(\mu,\Sigma)$$ in point $$\textbf{x}$$ is achieved with functions getAlpha() and getValue():

double value = CNDGauss::getAlpha() * CNDGauss::getValue(x);

In order to generate a random sample from the distribution, given by Gaussian function $$\mathcal{N}(\mu,\Sigma)$$, one uses function getSample().

Definition at line 26 of file NDGauss.h.

## ◆ CNDGauss() [1/2]

 DirectGraphicalModels::CNDGauss::CNDGauss ( dword k )

Constructor.

Parameters
 k dimensions

Definition at line 13 of file NDGauss.cpp.

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## ◆ CNDGauss() [2/2]

 DirectGraphicalModels::CNDGauss::CNDGauss ( const CNDGauss & rhs )

Definition at line 30 of file NDGauss.cpp.

## ◆ ~CNDGauss()

 DirectGraphicalModels::CNDGauss::~CNDGauss ( void )

Definition at line 41 of file NDGauss.cpp.

## Member Function Documentation

 void DirectGraphicalModels::CNDGauss::addPoint ( Mat & point )

Adds new n-dimensional point (sample) for Gaussian function approximation.

This function is a faster approximation of the merging operator (Ref. operator+()):
$$\hat{\mu} = \frac{n\mu + p}{n + 1}$$; $$\hat{\Sigma} = \frac{n\Sigma + (p-\hat{\mu})(p-\hat{\mu})^\top}{n + 1}$$

while(point) estGaussian.addPoint(point); // estimated Gauss function is updated
Parameters
 point k-dimensional point: Mat(size: k x 1; type: CV_64FC1)

Definition at line 112 of file NDGauss.cpp.

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## ◆ clear()

 void DirectGraphicalModels::CNDGauss::clear ( void )

Clears class variables.

Allows to re-use the class

Definition at line 86 of file NDGauss.cpp.

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## ◆ empty()

 bool DirectGraphicalModels::CNDGauss::empty ( void ) const
inline

Checks weather the Gaussian function is approximated.

Return values
 TRUE if the Gaussian had at least 1 point for approximation, or FALSE otherwise

Definition at line 92 of file NDGauss.h.

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## ◆ freeze()

 void DirectGraphicalModels::CNDGauss::freeze ( void )

Freezes the state of the Gaussian function.

This is an optimization function, which calculates and fills internal variables need for major get- accessors of this class. If the function was not called, tese variable will be calculated in the get- accessors every tiime on call.

Definition at line 94 of file NDGauss.cpp.

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## ◆ getAlpha()

 long double DirectGraphicalModels::CNDGauss::getAlpha ( void ) const

Returns $$\alpha$$.

Returns
The Gaussian coefficient $$\alpha$$.

Definition at line 168 of file NDGauss.cpp.

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## ◆ getEuclidianDistance()

 double DirectGraphicalModels::CNDGauss::getEuclidianDistance ( const Mat & x ) const

Returns the Euclidian distance between argument point x and the center of multivariate normal distribution $$\mu$$.

The Euclidian distance is calculated by the formula: $$D_E(\mathcal{N};x)=\sqrt{ (x-\mu)^\top(x-\mu) }$$.

Parameters
 x n-dimensional point (sample): Mat(size: k x 1; type: CV_64FC1)
Returns
the Euclidian distance: $$D_E(x)$$

Definition at line 194 of file NDGauss.cpp.

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## ◆ getKullbackLeiberDivergence()

 double DirectGraphicalModels::CNDGauss::getKullbackLeiberDivergence ( CNDGauss & x ) const

Returns the Kullback-Leiber divergence from the multivariate normal distribution $$\mathcal{N}(\mu,\Sigma)$$ to argument multivariate normal distribution $$\mathcal{N}_x(\mu_x,\Sigma_x)$$.

The Kullback-Leiber divergence (or relative entropy) is calculated by the formula: $$D_{KL}(\mathcal{N};\mathcal{N}_x)=\frac{1}{2}\Big( tr(\Sigma^{-1}_{x}\Sigma) + D^{2}_{M}(\mathcal{N}_x;\mu) - k - \ln\big(\frac{\left|\Sigma\right|}{\left|\Sigma_x\right|}\big) \Big)$$ and expressed in nats. Here $$D_M(\mathcal{N}_x;\mu)$$ is the Mahalanobis distance beween the centers of multivariate normal distributions $$\mu_x$$ and $$\mu$$ with respect to $$\mathcal{N}_x$$ (see getMahalanobisDistance() for more details). Please note, that it is not a symmetrical quantity, that is to say $$D_{KL}(\mathcal{N};\mathcal{N}_x) \neq D_{KL}(\mathcal{N}_x;\mathcal{N})$$ and so could be hardly used as a "distance".

Parameters
 x multivariate normal distribution $$\mathcal{N}_x(\mu_x,\Sigma_x)$$ of the dimension k.
Returns
the Kullback-Leiber divergence: $$D_{KL}(\mathcal{N}_x)$$

Definition at line 212 of file NDGauss.cpp.

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## ◆ getMahalanobisDistance()

 double DirectGraphicalModels::CNDGauss::getMahalanobisDistance ( const Mat & x ) const

Returns the Mahalanobis distance between argument point x and the center of multivariate normal distribution $$\mathcal{N}(\mu,\Sigma)$$.

The Mahalanobis distance is calculated by the formula: $$D_M(\mathcal{N};x)=\sqrt{ (x-\mu)^\top\Sigma^{-1}(x-\mu) }$$

Parameters
 x n-dimensional point (sample): Mat(size: k x 1; type: CV_64FC1)
Returns
the Mahalanobis distance: $$D_M(x)$$

Definition at line 203 of file NDGauss.cpp.

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## ◆ getMu()

 Mat DirectGraphicalModels::CNDGauss::getMu ( void ) const
inline

Returns $$\mu$$.

Returns
the mean vector $$\mu$$: Mat(size: k x 1; type: CV_64FC1)

Definition at line 102 of file NDGauss.h.

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## ◆ getNumPoints()

 size_t DirectGraphicalModels::CNDGauss::getNumPoints ( void ) const
inline

Returns the number of approximation points.

Returns
the number of sample points, used for the approximation.

Definition at line 155 of file NDGauss.h.

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## ◆ getSample()

 Mat DirectGraphicalModels::CNDGauss::getSample ( void ) const

Returns a random vector (sample) from multivariate normal distribution.

The implementation is based on the paper Generating Random Vectors from the Multivariate Normal Distribution

Returns
n-dimensional point (sample): Mat(size: k x 1; type: CV_64FC1)

Definition at line 234 of file NDGauss.cpp.

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## ◆ getSigma()

 Mat DirectGraphicalModels::CNDGauss::getSigma ( void ) const
inline

Returns $$\Sigma$$.

Returns
the covariance matrix $$\Sigma$$: Mat(size: k x k; type: CV_64FC1)

Definition at line 112 of file NDGauss.h.

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## ◆ getSigmaInv()

 Mat DirectGraphicalModels::CNDGauss::getSigmaInv ( void ) const

Returns $$\Sigma^{-1}$$.

Returns
The inversed covariance matrix $$\Sigma^{-1}$$: Mat(size: k x k; type: CV_64FC1)

Definition at line 158 of file NDGauss.cpp.

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## ◆ getValue()

 double DirectGraphicalModels::CNDGauss::getValue ( Mat & x, Mat & aux1 = Mat(), Mat & aux2 = Mat(), Mat & aux3 = Mat() ) const

Returns unscaled value of the Gaussian function.

This function returns unscaled value of the Gaussian function, i.e. $$\exp\big( -\frac{1}{2}(x-\mu)^T\Sigma^{-1}(x-\mu)\big)$$. In order to get the value of $$\mathcal{N}_k(\mu,\Sigma)$$, the output of this function must be multiplied with $$\alpha$$ from the getAlpha() function.

Note
Three auxilary parameters aux1, aux2 and aux3 are needed for more efficient sequential calculation and do not influent the resulting value, e.g. the code:
Mat aux1, aux2, aux3;
for (int i = 0; i < 100; i++) y[i] = getValue(x[i], aux1, aux2, aux3);
will run about two times faster, then the code:
for (int i = 0; i < 100; i++) y[i] = getValue(x[i]);

This function is PPL-safe function.

Parameters
 x n-dimensional point (sample): Mat(size: k x 1; type: CV_64FC1) aux1 Auxilary variable aux2 Auxilary variable aux3 Auxilary variable
Returns
unscaled value of the Gaussian function

Definition at line 180 of file NDGauss.cpp.

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## ◆ operator+()

 const CNDGauss DirectGraphicalModels::CNDGauss::operator+ ( const CNDGauss & rhs ) const
inline

Merging operator.

This operator merges two Gauss finctions into one:

$$\hat{\mu} = \frac{n_1\mu_1 + n_2\mu_2}{n_1 + n_2}$$; $$\hat{\Sigma} = \frac{n_1(\Sigma_1 + \mu_1\mu^{\top}_{1}) + n_2(\Sigma_2 + \mu_2\mu^{\top}_{2})}{n_1 + n_2} - \hat{\mu}\hat{\mu}^\top$$

For the sequential Gauss function estimation one also may use this operator (see the code below) or addPoint() function:

CNDGauss newGaussian(point.rows); // auxilary Gauss function
while(point) { // set of all sample points
newGaussian.setMu(point); // mu is set to be equal to the sample
estGaussian += newGaussian; // estimated Gauss function is updated
}

In this case $$n_2 = 1$$ and $$\Sigma_2 = 0$$.

Definition at line 62 of file NDGauss.h.

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## ◆ operator+=()

 CNDGauss & DirectGraphicalModels::CNDGauss::operator+= ( const CNDGauss & rhs )

Definition at line 68 of file NDGauss.cpp.

## ◆ operator=()

 CNDGauss & DirectGraphicalModels::CNDGauss::operator= ( const CNDGauss & rhs )

Definition at line 50 of file NDGauss.cpp.

## ◆ setMu()

 void DirectGraphicalModels::CNDGauss::setMu ( Mat & mu )

Sets $$\mu$$.

Parameters
 mu the mean vector $$\mu$$ : Mat(size: k x 1; type: CV_64FC1)

Definition at line 136 of file NDGauss.cpp.

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## ◆ setNumPoints()

 void DirectGraphicalModels::CNDGauss::setNumPoints ( long nPoints )
inline

Sets the number of approximation points.

Parameters
 nPoints the number of sample points, used for the approximation.

Definition at line 150 of file NDGauss.h.

## ◆ setSigma()

 void DirectGraphicalModels::CNDGauss::setSigma ( Mat & sigma )

Sets $$\Sigma$$.

Parameters
 sigma the covariance matrix $$\Sigma$$: Diagonal Mat(size: k x k; type: CV_64FC1)

Definition at line 147 of file NDGauss.cpp.

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The documentation for this class was generated from the following files: