class we have discussed that what a derivation of infinite time linear quadratic regulator problems and then corresponding optimal controller if you use to the system then its stability analysis is also studied. So, let us explain or illustrate that LQR problem with a numerical example. So, let us consider our dynamic system which is given is a second order dynamic system x dot is equal to x 2 of t and x 2 dot of t is equal to minus twice x 1 of t plus 2 x 2 of t plus u of t and we have some initial condition is given this is given. So, our problem is to determine a control law if you recollect that our infinite time regulator problem our problem is to determine the control law u such that this performing index quadratic performing index is minimized. The first problem first is you determine the optimal control law u of t small u of t because it is scalar input small u of t is equal to minus k into x of t where x of t is equal to we have a two states are there x 1 of t x 2 of t and this is the controller gain LQR controller gain LQR controller gain and is nothing but a state feedback. What is the information of the state you know from the system that we are being some linear combination of the states will give you the control law u this is the control law. So, we determine the optimal control law key u of t such that such that such that the performing index j is equal to 0 to infinity because it is infinite time regulator problem of horizon infinite horizon control problem is a x 1 square of t plus x 2 square of t plus twice u square of t whole d t is minimized you design a control law u of t such that this performing index is minimized. And this interpretation we have already discussed suppose this is the input free system this equilibrium position is the linear system the equilibrium position is origin is the equilibrium position and due to this initial disturbance or initial condition of the state the state x 1 x 2 will deviate from the equilibrium position and our this interpreted system in interpreters that deviation from the equilibrium point means on the origin x 1 state over the interval 0 to infinity that quantity you have to minimize not only that in addition to that control effort u square u transpose q u transpose r u t which is e re is in this case is twice u square t of this also you have to minimize. So, this is the first problem you have to solve first part of the problem first part is that one second part of this problem is check after designing the controller check the stability of the of the closed loop this is the closed loop closed loop system this is thing. Then third part of this problem is simulate the systems or get the response of the system simulate the system with and without controller with u t is equal to 0 means without controller without when u t is equal to 0 without controller with and with that controller without controller using the designed l q r controller l q r controller with initial state x of 0 is equal to 2 4 2 this one. So, let us solve this problem and if you recollect the basic steps of solving the l q r problem is first step is to solve the algebraic rickety equation first we have to solve the algebraic rickety equation what is the algebraic rickety equation solution we are adding solution. So, first we write the algebraic rickety equation the algebraic rickety equation is before that you see you have to identify which one is a matrix b matrix q matrix r matrix these are the four matrices information is required to solve the infinite time regulator problems. So, we have to identify from the system model what is system matrix a input matrix b and state waiting matrix q and control waiting matrix r that we have to identify it is easily can be seen from the system equation we can write it that x dot is equal to x dot t is equal to 0 1 if you write matrix in vector form is a minus 2 2 into x of t plus 0 1 u of t. So, from this one immediately you can write a is equal to our 0 1 minus 2 2 and this is b is equal to b is equal to 0 1 and if you see this one if you just if you see this our q and r matrix if you see here our q and r matrix this matrix we can easily write it this performance index we have to convert into a standard form that means here itself we can write if you like if you permit me I can write it half because that what is called the performance index that one we should be half into 0 to infinity since I divided by half multiplied by twice x 1 square plus twice x 2 square plus 4 u square of t whole dt why I have made it half our standard formulation you will say half is there this half is we have created there in the derivation because when you will do the partial derivation derivation of this square problem throughout the derivation derivation process the two will come two and this two will be cancelled for this one and based on this one we have derived all our expression. So, that is why I have just in order to make it into standard form I divided by half multiplied by 2. So, this is the standard form from this equation you see that q is what r is what from this. So, our q is if you see this is nothing but a 2 0 0 2 and our r is equal to 4 this is 2 cos 2 matrix this is this. So, once you know a b q r this is the first step identify a b q r from the statement of the problem once you identify this one then you can write it next step is to check that what is the what is stability condition check the controllability condition you check the controllability condition whether you will be able to drive all the states into the what is called desired location or if the open loop poles are unstable whether you will be able to drive this that unstable poles to the stable poles mean the from the right up poles to the left up poles whether you will be able to do it or not that you have to check it and that is done suppose you have a system before that I am just telling you how to check this one if you have a system described by x dot is equal to a x plus b u of t then how to check the controllability of the system means controllability of the system means you will be able to drive the state from initial state to a desired state with a finite time within a finite time by using appropriate control law whether it is possible or not before that we can check it whether the system is controllable or not we can check it that you find out the rank of this matrix rank of let us call the matrix is w is how will you form the rank of the matrix b a b and dot dot a n minus 1 b this you form it this is a n cross 1 n cross n matrix then state of the system is n states so you form a matrix up to a n minus into b so find out the rank r small r is indicates rank of this matrix if the rank of the matrix is n the system is this implies the system is completely controllable the system is completely controllable that may all the states will be able to drive from any position to the n i what is called any other desired position that is so we will check whether system is controllable or not at least it should be stabilizable so if you check this one then we will find out that our rank of rank of b a b in our case rank of b matrix is what 0 1 is a vector in this case or you can matrix of dimension 2 cross 1 this b then a b if you multiply a into b that will be coming say this a into b a into b this will reflect the last column of that one so that will reflect the last column of that one so it will be coming that 1 2 so that ring that rank of this matrix clearly is equal to 2 and which is equal to n in our case n is equal to 2 if you see number of order of the system is 2 so the system is controllable so these are then we can proceed if the system is not controllable or at least is not stabilizable then you have to check whether system is stabilizable or not means stabilizable means if you have a open loop system is a unstable mode that unstable mode should be stabilizable in the sense you will be able to drive the unstable poles or the Eigen values to the from the left half from the right half of the s plane to the left half of the s plane you will be able to drive it by using a control effort if you satisfy that condition then it will be told the system is stabilizable but uncontrollable mode is not controllable then it is not stabilizable hence it indicates that we cannot apply the LQR control problems so unstable in other sense you can unstable modes means Eigen values unstable modes of open loop system must be must be stabilizable so this is the important thing so first if you check the controllability test if it is completely controllable we can proceed first then our step is if you recollect one by one step we have to solve the algebraic equation since it is infinite time regulator the time is 0 to infinity in the performance index integral part 0 to infinity so it is infinite time regulator problems so our equation is h transpose p plus p a minus p b are inverse b transpose p plus q is equal to 0 null matrix of dimension n cross n we know a b r q so only unknown is p you have to solve it by some means we will discuss in details what is the different methods are there to solve the algebraic equation for the time being we just use since it is a smaller dimension 2 by 2 or 3 by 2 we can do algebraic solution of this one because we will get a set of non-linear equations set of algebraic non-linear equation then how to solve this one with a smaller dimension we can do it with a hand calculation let us see I will put the value of that one a transpose a is what this is the a a transpose you write it so this will be a 0 1 minus 2 2 a transpose and then p p is a symmetric matrix and positive definite solution you should get positive definite p 11 p 12 since it is a symmetric matrix p 12 is equal to p 12 p 12 plus again this one p p 11 p 12 p 12 p 22 then multiplied by a 0 minus 2 1 2 this is that one p a all this thing then then minus p p I am writing p p 11 p 12 p 12 p 22 p b b is what 0 p b 0 1 then r inverse r is 4 1 by 4 then b transpose b transpose is 0 1 then multiplied by p so this cross I am writing here next page cross multiplied by that is our p p is p 11 p 12 p 12 p 22 then plus q q is a diagonal matrix is 2 if you see so this and right hand side is equal to 0 0 0 0 again so now you see you multiplied by this into this a a transpose p unknowns are 3 unknowns are there 3 equation at least we are getting 3 equations so we can we will be able to solve but when you will equate left hand side is right hand side you will get in general is non-linear algebraic edicati equation that we have to solve it so that you multiplied by this into this this into this is a minus 2 p 12 so I will write it left hand side minus p 12 is equal to so first we will write it minus this this into this into this so it will be a minus 2 p 12 then it will be next is this row multiplied by this minus 2 p 22 minus 2 p 22 then this row multiplied by this column p 11 twice p 12 p 11 plus twice p 12 then this row p 12 then this row multiplied by this p 12 p 12 plus twice p 22 agree so this and this part this is a transpose p this one and this we have shown this value now look at this one one one cannot solve one not necessary to solve p a so p a is nothing but a transpose of this one once you got the product of this one take the transpose to get p a to take the results of that one a transpose a transpose p take its results transpose then you will get p a so I will take the transpose of that one so this will be a one minus twice p 12 minus 2 p 22 p 11 plus twice p 12 then p 12 plus twice p 22 so this quantity is nothing but a transpose p transpose of this one is nothing but a p a transpose of that quantity is nothing but this one so you can ever this so next is if you see you multiplied by p b are inverse b transpose p agree if you do this one this second part of this one that p b if you multiplied by this you will get the last column of p because you see this 0 1 so it will come last column of this so this into this so ultimately it will come from this one last column of this one that will be p 11 p 1 that will be p 22 that multiplied by r inverse r inverse is what 1 by 4 that means 0.25 now you see this one b p b are inverse and p b if you know it if you take the transpose of that one b transpose p so this you need not to compute from the knowledge of this results I can take the transpose of p b then if you take the transpose of p b I will get it p b transpose p so this is p 11 p 22 then multiplied by what is this p b transpose then p p b transpose we have done it so this part is over p b we have calculated r inverse is 1 by 4 means 0.5 and transpose of this one we have calculated this plus q q is 2 0 0 2 is equal to 2 0 0 0 now now you element wise left hand side right hand side you equate this element means a 11 position so you add this one plus this one plus after multiplying by this you add it so if you see that quantity this quantity after multiplying by this it will be a 1 4th this is 1 4th means point minus 0.25 and this is nothing but a p 11 square p 11 p 22 this then this will be a p 11 p 22 then p 22 square I am writing this quantity only so just like now adding this quantity a 11 element a 11 element this one is this one a 11 element then a 11 element is equal to that one so element wise if you equate now you will get it element wise so I am getting 11 element left hand side and right hand side if you equate I am getting minus 0.25 p 12 minus 4 p 12 plus 2 is equal to 0 you see this and this 4 this is 2 4 2 and this is coming 0.25 p 12 0.25 p 12 what is this this or this is I did mistakes here you just see here if you multiply it by this and this that this and this it is p 12 this row multiplied by this it is p 12 this this row multiplied by the p 22 so it is not a p 11 p 12 so this is also p 12 so this will be coming p 12 multiplied by this this is p 12 again so now I am getting 0.5 p 12 square plus 4 p 1 0 1 element then I write it 2 2 element 2 2 element 2 2 element is that one you see this plus this this is the 2 2 element this is the 2 2 element and here 2 2 element is this one plus 2 2 element is 0 here is right hand side 0 so if you see the 2 2 element minus minus 0.25 minus 2 225 p 22 p 22 square then you will get it twice twice see this one p 22 element p 22 then this so it will come now I am telling sorry that p 22 element that that that means forget about not this one p 2 element is that that one so this one this one and your case is that that one this is the p 2 element I am writing so this is 0.25 p 22 square 0.25 p 22 square what I have written it then this twice here is this one p 12 2 p 22 then p 12 2 p 22 the twice of this one plus 2 so I am writing this one twice of p 12 plus 2 p 22 plus 2 is equal to 0 this is another now I am writing either p 12 element element is same as p 21 element because it is a symmetric matrix so now in this case you see what is that quantity p 12 element is this one agree this one then this one and this is this one and this is 0 this one and this is this one so if you write it that one I can write it p 12 elements are that minus this 0.25 point minus 0.25 p 12 whole square then your minus minus 2 p 22 2 p 22 then your plus p 11 plus twice p 12 is equal to .   So, you have a three equation p 1 2 and three equation and the three equation if you solve it you will get the solution of p 1 1 p 1 2 p 2 2. So, let us solve this three equation then what will get it let us solve from equation one from equation one what we can write it this is a quadratic equation we can write p 1 2 is equal to that is minus b plus minus root over. So, if you just divided by multiplied by what is 4 both side then it will come this if you multiplied by both side by 4 minus 4 then p 1 2 square minus 16 p 1 2 this is minus minus plus minus 8 is equal to 0 that quantity is that one this if you multiplied by minus 4 then this will plus plus minus. So, it will be minus b plus minus root over b square means 16 square minus 4 a c divided by 2 into a. So, we will get this if you solve it you will get 2 values of p 1 2 that is value is 0.485 or I will get minus 16.485. So, out of this two whether we have to accept both the values or one of them we have to accept that will see let us stage. So, let us say once I know p 1 2 from equation 2. So, from equation 2 I know p 1 2 p 1 2 value here if you put up p 1 2 value here you will get a quadratic equation in p 2 2 form and a quadratic equation p 2 form. So, if you just put the values of that one p that expression once again I multiplied by minus 4 both sides both sides minus 4. So, it will be coming if you multiplied by minus 4 both sides it will be coming p 2 2 square minus 16 again 16. Then it will be p 2 2 this is 2 16 how it is coming 2 2 4 multiplied by 4 means it is 16 minus 16 p 2 2 minus 8 I am multiplied by 4 minus 4 minus 2 is there. So, minus 8 p 1 2 minus 8 p 1 2 p 1 2 value is what if I consider 485 first this is the p 1 2 value and minus next is minus 8 is equal to 0. This is minus 4 both side this is minus 4 is equal to 0. So, ultimately our equation is that one p 2 2 square minus 16 p 2 2 minus 11.88 is equal to 0. So, the solution of this is equal to 16 plus minus 256 16 square minus 4 into a into 11.88. So, there divided by twice a and that value will get 2 values of this one 16.7111 value and another value will come what is this is plus minus. So, it will be what is called minus sign minus sign will precede with a that minus more than 16 will get. So, this next quantity will be negative term agree one can easily find out that negative term is what. So, this negative term cannot be considered because our if is a silvestre inequality test if you see a matrix should be positive definite first condition is all diagonal elements must be positive. But here the other values of p roots are negative. So, we cannot discard the negative values of p 2 2 discard the negative value of p 2 2. So, we will consider this one and this is a positive definite. This is the one value of p 1 2 which is 0.485 suppose if you consider the value of p 1 2 is that one. Then you will get solution of p 2 2 is complex. So, we will not consider that values. So, this will give you the we will accept that value accept and this will give you this will give the solution of p what you got p 2 2 this will give the solution of p 2 2 complex value. So, we will consider our this is the we will accept it p value is this one p 2 2 value once I know p 1 2 value and p 2 2 value once I know p 2 2 value and p 1 2 value immediately I can find out from equation 3 the p 1 1 this is known this is known p 1 2 is known and which value we have accepted that we know and we can get the solution of p 1 1. So, from 3 using p 1 2 is equal to 0.485 and p 2 2 is equal to 16.711.  So, this equation once again I multiplied by 4 that will be a minus 4. So, this will 4 p 1 2 this or as it is keep it does not matter for this one.   So, minus twice p 1 2 this is twice p 1 2. So, if you use this values of this then p 1 1 value you are getting 3 4 34.48 p 1 2 from this equation I just find out this is the only unknown thing this is the unknown.   So, if you put this values of p 1 2 34.48 then p 1 2 is minus 0.485 then 0.485 then 16.71. So, and that matrix is positive definite matrix you can check it either finding out the Eigen values of this matrix or Eigen values will be a positive or you can use the silvestre test for testing the what is the matrix is similar whether matrix is positive definite matrix or negative definite matrix or positive definite matrix or negative definite matrix that can be checked by using the silvestre inequality conditions. So, this so our case is p is greater than 0. So, positive definite matrix so this implies that our the controller the way we will design the controller controller will stabilize the systems. So, let us find out the controller gain controller gain. So, controller gain so you know k is equal to R inverse B transpose P you just use the values R inverse means 0.25 B is 0 1 and P is just now we got it is a 34.48 0.4085 0.485 0.485 and that we got 16.71 if you multiply it by this last row will be reflected. So, 0.25 into last row 0.25 into 0.85 16.71. So, multiplied by 0.4 divided by this each element by 4 then you will get it this is 0.121 then 4.178. So, this is the controller gain so this is the controller gain we got it. So, once you know the controller gain immediately I can find out the control law and which is nothing but u of t is equal to minus x of t we assume that these are all accessible measurable by the users this one. So, you know k immediately you can implement u of t. So, u of t is nothing but a minus 0.1210 not 0.4 point just now we got it 4.178 this into that our x is x 1 of t x 2 of t. So, this is our control law and if this control law you apply to the system then it will stabilize the system not only stabilize it will drive the state to a what is called equilibrium position from the initial state x to 0 to the equilibrium position agree in a optimum manner by minimizing the that performance index. So, our check the closed loop system stability so our x dot is equal to a is equal to a of x t plus b u of t u of t and if you put the value of u of t is equal to minus k x of t and our closed loop system will become we take the x of t common then b of k is x of t and this is nothing but a suffix c x of t and this is the our closed loop system matrix. Now, system is stable or not you just find out the Eigen values of this matrix if Eigen values of this matrix with a negative real parts then system is stable. So, find out the what is called Eigen values of this matrix the closed loop system the part 2 is the if you see the part 2 of the problem our the check the stability of the closed loop system part 2 of the problem is check the stability of the closed loop system. So, you find out the Eigen values of Eigen values of a c matrix a c means a minus b k matrix if all the Eigen values of this one with negative real parts the system is stable. So, find out it is just we know how to find out the Eigen values the determinant of a c minus lambda i of this equal to 0 and you will get because a c is known lambda is unknown. So, you will get a polynomial of order in general n where n is the dimension of the system matrix or dimension of the state variables agree. So, this will be the order polynomial you will get in terms of lambda which order will be n same as n is the order of the system matrix. So, you just find out first is a c a c is our a n a is our 0 1 minus 2 2 and b is your 0 1 and your k k we got it 0.1 2 1 4.1 7 8. So, now if you simplify this one ultimately you will get this matrix is 0 1 minus 2.1 minus 2.1 7 8 this is the closed loop system. So, the Eigen values of this one how you find out. So, determinant of what is called matrix a c minus lambda i is equal to 0. So, if you do this one so, I will leave it exercise to this one is nothing but a a c symbol is lambda i of this is equal to 0. If you do this one you will get it the determinant of lambda square is equal to plus twice 0.1 7 8 lambda plus 2.1 2 1 is equal to 0 that Eigen values of this 2 will be this is quadratic equation minus b plus minus root over b square minus 4 a c if you do it you will get it minus 1.01 plus minus 0.967 i. So, this is the real part of this one is negative. So, system is stable that means with the application of this controller the system response will be stable means it will bring back to the state from initial state to an equilibrium state. So, our conclusion this implies that our the closed loop system design with LQR approach stabilize the systems with LQR approach stabilizes the closed loop system design with LQR approach stabilizes. So, this is our conclusion now third part of the third part of the problem is if you see it is nothing but a that is what you call find the system response with the application of that what is called LQR optimal control law and optimal control law is designed based on the LQR. So, you are asked to simulate the system get the response T versus you find out x 1 of T then x 2 of T this is. So, our initial state if you see it is a x 2 if it is a this is 4 0 and it is a 2 4 6 8 10 12 and 16 something like this then our initial state is starting from that our x 1 0 is this one this is the initial state for x 1 of 0 is equal to 4 this is the initial state x 2 of 0 is equal to state by using this what is called control law you find out the response of the systems. Let us call the response of the system just say you have to solve it how it would solve it x dot is equal to x dot is equal to a x plus a x of t plus b u of t or you can write a x minus b k of x t. So, it is a solution of autonomous that autonomous system is a closed loop system you know the value of given x dot x t 0 is equal to x 0 is given. So, you can solve this one say let us call the solution may be like this way ultimately to come g 0 and this is the solution of other state solution may be like this way it is coming to g 2 like this. So, you find out the response of this system and you know the this matrix and you can solve it. So, this will leave it I leave this in an exercise to solve this one. Now, let us say with closed loop control system how it looks like in a block diagram form. So, if you see our system is this is our f integration this is the integration and this is our x dot 2 x dot of t output of this is the integration output of this one is x 2 of t which is nothing but a x 1 dot of t as per the description of the system dynamics and that goes to the integrator. Let us go to the integrator and the output of the integrator this is the integrator. So, output of this one is x 1 of t and this output is going to the minus and this is the summer and x 2 is multiplied by 2 gain 2 you can say x 1 is gain 2 amplifier you can realize this one is in a prepare this is the your plus and this is state information is minus 2 and then it is. So, this is our this portion we x dot is equal to x. So, you have a b u. So, you have a this so x and x 2 information must be available to the controller. So, our controller this is one. So, this is our x 1 x 1 of t and this value is what point 1 2 1 1 2 1 and this value is your this value is 4.178 this is our x 2 of t. So, these 2 signals multiplied and then it is a minus k x negative and this multiplied by your b u and what is our b u and this is u is coming only the you see that in dynamics of that one u is coming only in the second state that makes 2 dot expression. So, this directly I can write it this is nothing but our u u of t. So, if you see this portion from here to here this is our plant or system plant or system and our controller is that part this is the controller that is the controller and this controller is what type of controller that controller is l q r controller. So, one can look at this expression one can change the controller gain by selecting the state weighting matrix q and r this is only the tuning parameter designer have that I can tune the controller parameters that k values by tuning the q and r. So, if so long our response is not satisfied we can always tune q and r to get the desired response of this one. So, this is our the this scheme is the infinite time l q r problem solution this is the thing. Let us now go back to what is we call the how to solve the what is called the algebraic equation how to solve the algebraic equation by different techniques or different methods solution of algebraic equation solution algebraic equation. So, first method is the simplest method, but it takes much time to get the converse value of p. So, method one is the iterative method iterative. So, a re solution so what is our a re equation a transpose p plus p a minus p b r inverse b transpose p plus q is equal to null matrix of dimension n cross n where n is the order of the system matrix or the number of states in the systems this is n.  Now would see this manipulation we have done also earlier when you have discussed the finite time regulator problem what I did it here this term is this and this term I have written a transpose if you see a transpose p this term is there then this will be a transpose then multiply by p. So, it will be a p then it will come b r inverse b transpose into p. So, I am getting that one you know the this a b c whole transpose is equal to c transpose b transpose a transpose that properties I have used it here.  So, this is a one term I have taken more. So, I have added p b r inverse b transpose p. So, this can say that ultimately this remains same. So, this I am writing into this form a minus b r inverse b transpose let us call this is I am writing p suffix k the value of p transpose p k plus one then p a minus b r inverse b transpose this is I am writing k plus one is iteration this is k is equal to if I take this is my that side is equal to q then p k b r inverse b transpose p k what is the k indicates the k iteration what is the value of p let us call starting iteration is zero iteration p of zero and this is means next iteration what is the value of p that is k plus one in this way I have just inside the bracket is a kth iteration outside the bracket is p value is k plus one iteration in this way. So, now you see this matrix q is positive definite matrix positive definite matrix r is positive definite matrix. So, this product will be because it is multiplied by some matrix then positive definite matrix and transpose of that maybe post multiplied by transpose of pre multiplied matrix again. So, this matrix in turn the whole matrix is becoming a positive definite matrix. So, positive definite matrix and positive semi-definite matrix, the result will be positive definite matrix. So, it is something like a standard leaponna function method function, if you consider then you have to find the stability of the autonomous system we know our condition is A transpose p plus p A is equal to minus q, you assign some positive definite matrix. If A is stable that solution of P must be positively defined so that we are using here so our expression now it is coming if you see if I consider a k this is the whole thing is a k a k transpose p k plus 1 plus p k plus 1 a k is equal to minus that one q plus p k plus b or inverse b transpose p k so this please note down what I am written here suppose if I have a x dot is equal to a x is there you want to study the stability of this system by using leoponov function method then our condition is that this solution if you do the solution of this one and with a assigned value of q is equal to positive definite if you get the solution of a is a is if you know a p if you get the solution of p is positive definite it indicates the matrix a is a stable matrix means all eigen values of a matrix is negative real parts so here also how to solve this iteration this one k is equal to 0 1 2 dot dot when is equal to k is equal to 0 means p of 0 so you assign p of 0 value positive definite matrix in such a way so that this matrix is stable so you choose initial value of our required equation solution p in such a way p 0 so that a minus b r inverse b transpose is stable then then this is I just mentioned this this is a positive definite matrix so this is this is a stable matrix this is a positive definite matrix then the solution of this one I will get positive definite matrix whatever the you got it this positive definite use it here once again then you solve this equation and repeatedly you do and you will see finally that you will get the solution of p at k tends to infinity p is converse to a constant value that will discuss in detail next class that convergence of solution of recursive manner if you solve it the convergence of this one solution exist and it tends to a some constant value so here I will stop it


We saw earlier that when you pass an array to a function, that passes the array's address. No ampersand is needed here, because arrays are handled specially. It's possible to use a pointer as the parameter of the function. This will store the address of the array in a pointer. And it can then be used exactly as if it were an array. However, C programmers prefer to use pointers as pointers. Let's get the function out of the way, and use a simplified version with the array and the pointer. Right now, p is a pointer to integer, and it points to element 0 of the array. If you add 1 to the pointer, that will point it to the next element in the array, and adding 2 to the pointer points to the third element in the array. Remember, these are pointers, and in order to access the array elements, you need to dereference them. Here's a table of the correspondences between the array notation and the pointer notation. When you use pointers, you have to add to the pointer to make the pointer refer to the element you want, and then you dereference it. Now let's generalize this table by adding 0 to the pointer to access the first element in the array. And we can now rewrite the sum of array elements function by adding to the pointer, because pointers and arrays are so closely related. There are many ways to rewrite this function that sums the elements of the array. Here's an approach similar to the one that the book uses. They use an array as the parameter and start with the results set to 0. Then, create a pointer to integer called pLimit that points 1 past the end of the array. This will be used to limit our iteration. It will be the array plus the number of items. Now we're going to run a for loop. We'll have a pointer to integer. We'll start it at the beginning of the array, continue as long as the pointer is less than that limit that we established in the preceding line, and increment the iteration pointer by 1 as the end of loop action. The body of the loop sets the new value of result to the preceding value of the result plus the value that we get by dereferencing the pointer. Once the loop is complete, we return the result. Let's build and run, and there's our answer. The book notes the pointers are a more efficient way to do this calculation, which involves iterating through array elements one after another. I wrote a program with four different approaches to summing the array, and called each function a million times with an array of 1,000 random integers. Here are the results, and indeed pointer notation is significantly faster than array notation. And that's why you should use pointers when iterating through an array.


and is outing overall.  Seems like your curve ball and your change up were especially sharp today. Could you tell that early on that it was something special? I wish that in this outing today, the combination of the curve, the change, very effective, very good breaking, very good command of those pitches, did you feel that during the game? Yes, it was something that they had in the attack plan, commanding the change against the right and the left, just like the curve, always joining me in the first pitch of the try, ensuring that I countered the try and was under the zone and it was something very specific today and I was 100% focused and I was able to execute every throw. Yeah, that was part of the plan, the attack plan, you know, make sure that I had good command of the curve and the change up, especially the change up facing the righties and lefties, you know, so it was priority, priority to get strike one and expand whenever I needed to, you know, and I think tonight we were able to do that.


Hi everyone, I went live on the wrong channel But I had to go ahead and keep going because everyone was starting to watch so I kind of flipped the script But I'm on this channel now the correct channel and I want to talk to you guys because a lot of a Lot of y'all have been asking me How do I get my husband or my boyfriend to want more in life to do better to strive and you know get paid more and you know Better himself financially. How do I as a woman? Do this for him, you know Um as a woman if you're married to someone You cannot okay, if you married someone just as they are And you are great to something totally different When you got married you can't go changing things Now if you never said anything like oh, I'll love you and if you're poor for ever blah, blah, blah, blah I don't care. We can be poor and live in poverty and I'll still love you if you've said all that And he mirrored you under those pre tenses then it's kind of like You can't go back and say well now I want you to have money, you know You can't do that. So if that's what you agreed to if you agree to that lifestyle then you're not gonna be able to Have a good Argument as to why you need him to better himself because You agree before you guys got married that this was okay, but if you never agreed to anything and You're able to you know think that you can improve your man You're gonna want to be inspirational to him not negative Okay, you catch more flies with honey than you do vinegar. Okay, you don't want to be the nagging wife Because that's just gonna push him away, you know What you need to do I said to some other video you need to get him around the type of lifestyle that you want You need to get him interested in the type of lifestyle that you want You need to take him to car dealerships to test drive nice cars. You need to take him to model homes to You know walk around and get into the vibration of a better lifestyle You need to take him to the nice areas of town You know when you guys want to go grab something to eat Don't just stay in your little circle go out and venture out get him into the atmosphere That you want him to upgrade to okay, cuz then once he feels like He belongs there or he should have more then he's gonna be right on board with Getting better. Okay And you don't Put him down. You don't put him down. You say, you know what honey?  Oh, you know, you don't want her that in life You're just mediocre You don't say those things to the person you married or that the person you're with if you want them to improve You got to make them feel like they're in charge of their own life That you believe in them that you see them in the position that you know It's successful and that you're waiting on them to get there because You know, that's where they belong. Okay, and by you feeling that thinking that and you bringing them around You know certain environments nice cars nice houses nice places to eat nice areas of town They're gonna start vibrating on that frequency to and wanting those things too and they're gonna figure out how to get them, you know So that's how you get your man to the next level you take him there You take him to visit that level you take him to test drive that level you take him around the people on that level you take him to eat on that level and You know, even if it's just appetizers, you know, you might not afford can afford to eat It's a fancy restaurant except for a drink and an appetizer go for drinks and appetizers You know, so take him to these nice areas of visit your future lifestyle In that moment when you guys are out start talking about this is where we're gonna be in a couple years This is the sound of town. We're gonna be living on don't say Can we move over here or you know, do you think you're gonna afford this? Speak it into existence. This is where we're going to be living not I hope you can get a raise or not a Wish we could live here, but this is where we're gonna be living. Okay, so you speak it into existence.  You can't be like go back and feel good.  My wife would be happier I would be well respected my parents would be proud of me all those starts are gonna start going through his mind My wife thinks I can do this You know, I feel like I deserve it So you're gonna be putting those thoughts in his subconscious mind and eventually he's gonna want To upgrade and he's gonna figure out how to do it, you know, so Don't do it in a negative way because it never works a lot of women lose their men by nagging them and comparing them to other people Yeah, it's fun to talk a trash about them online, but you don't talk trash to them You know, that's just gonna destroy their self-esteem.  He can't feel good about it.  Aren't you proud of me, baby?  I'll pay my phone bill this month, you know Don't go anything above a hundred or two hundred dollars. Okay, if you're in that type of relationship if you're building together Remember ladies When you help someone build up You can't see them as someone who did this great thing You don't see them as successful as the next woman who did not help them build up So you're not gonna look at them the same and they're not gonna feel like the man with you because you help them get there You know, so that's when a lot of men will start cheating on their wives or their longtime girlfriends who have helped them build With someone that didn't help at all, but recognizes the man did it all by himself. That's what he wants he's gonna steal all the The recognition and pretend like he did it all by himself and get, you know All the recognition from another person. So very important not to help anyone build up their You know dream so they can take all the credit and leave and go somewhere else, you know Um Very important to let him make it on his own with just maybe this much help that you really can't even take too much credit For because if you do it the other way He'll never get all the praise and glory he feels he deserves from you since you helped him so Think about it That's why I like right right now If if your husband or a boyfriend is trying to save up money and he's asking you to pay this and pay that and pay this and pay that say no Say but I will You know, I'll give you some gas money this week or Just if you're gonna contribute just do it a little bit not too much because if you Push him too far and you become his crutch. He's not really doing it on his own. You're actually doing Doing it but letting him have the credit Okay, and soon he's gonna want to claim all the credit with someone else. So do not Help him build up his you know empire assist him a little bit You know help him by running errands for I'm doing him a little bit of favor here and there But don't assist him monetarily. Okay, that will be the biggest mistake you will ever make. Okay, that way He can truly take all the credit and if you're married you still get half anyway if he leaves you so You might as well save your time and energy Okay I'm just saying you didn't got to work to get paid in this day and age unless you're So yeah, y'all a funny story if y'all I went live on the wrong channel and people were mad They're like I said, oops, let me let me flip the script. They weren't ready. They weren't ready Okay, so If a man doesn't want to move out of his current Financial status and he's perfectly okay with living mediocre or the lifestyle that you guys are in But you want him to upgrade and he's perfectly fine. I'm happy. I have everything I want. I don't need a bigger house I don't need nicer cars. I don't need this. I don't need that if he's in that mindset And you're like what I do Start doing things on your own Like maybe start an online business start getting paid on the side of your regular job If you work or if you don't work start getting paid by doing something that you started yourself lead by example Okay, if he sees that you're making money, he's gonna like hop on like, you know what I can do this too I can make some extra money on the side. I don't have to work as hard Maybe I can even make more money than I do at my job. Let me see what I can do So there are some guys who have to be led by example.  So that's another way to do it. Okay, take them around nice Neighborhoods make friends with people that have what you want and when you do that, you know When like a successful guy and another guy get together He's gonna want to talk about business not holes and you know sports and stuff He's talking about business stock market, you know, how we gonna next idea next big make money making idea, you know online businesses, you know Stock options and stuff like that. He's not talking about the the remedial things that a lot of other people talk about He's talking about money how to make money how to get money how to maintain money And when you get your man around people like that, then his thinking will change so You want to Get your man in a better environment when you guys hang out of you if you're used to hanging out at, you know places that Are not upscale start switching to upscale places slowly, you know, you want to build him up to it You don't want to just throw him in there So upgrade upgrade him in his taste in his in his desires because That's what's gonna get him to that next level like Even sexually you can do this by like looking online at lingerie, you know expensive lingerie They're like, oh my god, I love this. It's so pretty. It's so expensive though.   Oh my god I would look so good in that but look at the price. It's just so expensive Okay, well, that's maybe I'll find something at Target that's similar or Walmart I could I'll shop at Walmart, you know, make him feel bad Like you deserve those things and he knows you deserve those things and when you when you are get, you know Getting all excited about it and then you realize bang my man broke. He can't afford it So let me just go to Walmart and get the cheap version of it made in China, you know, so That's gonna make him feel bad.  What can I do to push him? Okay? Men who are trying to start their own business who keep having setbacks and then quit it's because they're probably not ready to start their own business They're not financially able to start their own business already or they're not starting the right type of business Maybe they're starting too large or too big instead of little baby steps So try to get him to start baby steps that he will get be guaranteed success, you know Like if he's trying to start a business, why doesn't he start a business online? Why doesn't he raise awareness about his upcoming business through social media? You know You can't just put a business out there and say hey, I'm here come shop or hey I'm here come give me business or hey I'm here you gotta build it step by step if he's starting at step 10 and and skipped You know steps one through nine.  They never saw you before they don't know you You know blah blah blah blah build yourself up first and then You know instruct him to do that because that will help him a lot of people will already have ideas That's been done a thousand times and nobody wants You know to give them business because they can get it somewhere cheaper, you know what I'm saying Just like, you know, a lot of people are trying to open up businesses where they sell candles and soaps and stuff like that But you can get the same type of stuff For like ten times cheaper somewhere. No one is going to you know, buy your stuff unless you create a buzz around it Like why they need to buy this particular item, you know, so Help him be creative help him understand this Okay and Okay, so another thing is a Lot of you guys are starting the same types of business that's been started over and over and it has failed repeatedly Try something new try something different that has not been done or put a spin on it, you know Everybody and their mama wants to be an entertainment a rapper a record label Everybody and their mama wants to do that everybody want and their mama wants to sell soaps and candles Everybody and their mama wants to do the same thing Change it up, you know, if you're gonna sell soaps and candles do something different if you're gonna be a Recording artist if you're gonna have a studio if you're gonna be an entertainment in the entertainment business a producer change it up You know, don't just offer the same thing everyone else does What's different about you, you know So let's see, okay, so she says it's building kitchens and bathrooms, okay Well, that's that's a good business But you know the the type of companies you want to target are builders, you know home builders not People that want their bathrooms redone, but you need to get in with the home builders, you know Like when they're building new neighborhoods, you get you get contract with those neighborhoods to come and install The bathrooms in the kitchen, you know Stuff like that you don't You aim For what, you know, you can do if you don't have the manpower behind it start off small, you know Things like that but that is a very that it's a that's a business that required a lot of hard work and You know, perhaps maybe It's easy to get discouraged because that is a lot of physical labor Maybe you maybe he needs an idea that can make him money without working so hard you know, maybe like an online business of selling the products to Remodel your own house or your own bathroom a drop ship company a supply company, you know Something that's easy that brings them any quick without, you know, lots of labor and time put into it A lot of people don't think they just say oh, I know how to do bathrooms. Let me do that They don't think on the higher level. They don't think as a boss. They think as an employee Why not just sell the products, you know, why not just profit off of selling Why not get a wholesale license and sell bathroom products cheap to to builders? Why not do that? Why why not, you know hire contractors to put in the bathrooms and pay them While you, you know, have a wholesale company want to do something like that, you know, think bigger People think too small. They just think labor labor mind, you know, think management think owner Okay Think about how you can make the most money by doing the least that's how you get places most millionaires Think think like this. How can I make the most money by doing the least work? When you start thinking on that level it's gonna come easy.  Whatever you're gonna sit and think about this besides something illegal How can I make the most money by doing the least work?  Basically, how do I get paid in my sleep? Basically start thinking about that and the answers and the ideas will come I promise you Okay A lot of guys a lot of people think I don't like men. I love men. I don't like boys Okay, man will come up with some money-making ideas men will come up with how to move from Level one to level ten in two years. Okay. These are men. These are people who are invested in their career And their Families that want to do better and build things for their future generation. That's men Boys just want to date and have sex for free and ask the woman to pay half the bill and live in an apartment and make four figure Five figure salaries. That's boys men want to have an empire a kingdom and to leave something to their Children and have their wives bragging about them. That's men. Okay. I don't hate men I don't hate boys, but I don't deal with boys, you know and women grown women shouldn't deal with boys either and You know, I made a video about that but I didn't put it out because I didn't want people to get the wrong idea because I really went in I was like I Was like giving tough love that would have came off as hate, but You know, you can't hate someone unless you love them first That's just true. You can't hate someone unless you love them. You can dislike someone you can disagree with someone you cannot You know of be happy with somebody, but you can't hate somebody unless you love them So tough love is what I called it. I'm not gonna put that out because it was a bit harsh So instead I decided to give some you know Some information on how to get to that next level stop thinking as an employee and think as an owner Okay How can I make the most money? Doing the least that's how you think and the ideas will come if you're smart if you have a high IQ you will figure it out Right Even my daughter's figured out, you know, I'll test them. I was like Layla, you know How could you make money without leaving your house? Give me five ideas. You know do this with your kids Okay, how can you make money while you're asleep? Give me some ideas, you know And people will come up with the ideas, but then they'll talk themselves right out of it because they are afraid of success Why are they afraid of success because they don't feel like they deserve it? Why don't they feel like dessert? They don't deserve it because they've been conditioned With poverty mind so you have to reprogram yourself in these situations, you know what I'm saying How about accepting for your man for who he is and that what he's worth. Well, you know You can do that You can accept your man for who he is instead of what he's worth, right? You can do that, but Are you gonna be happy doing that? Are your kids gonna have the things they need in life by doing that?  I don't know you decide, you know Are you selfish or do you want to push your family into the next just you know into the into the next decade with something?   They'll just work eat drink and then die Be like, okay, I lived a good life But women want their children to thrive and their grandchildren to thrive and their family name to thrive Men don't care about that kind of stuff Women do that's why women pick their men up based upon The level that they can you know elevate their family to So if y'all don't care about y'all's future generations and your children and your grandchildren, you know That's fine, but a lot of women do and that's why they base who they choose their partner on You know what they can provide and that's just that's just good looking out, you know and You know if you if like some guy just said in the comments If you can't afford children don't have them and don't have sex unprotected because that's one of the ways to have it Duh, you know have two forms of contraception not just one They have male birth control pills now.  What else what's not out there? What services can you provide?  You only need Three hours extra and you're making what how much how much does a handyman make per visit?   You can do people's resumes online There's programs. You just stick their information in that they they might not know about, you know And all you got to do is input their information and bam here comes a professional resume You just made 50 to 75 dollars, you know think I Could make money I can make money in my sleep right now if I if I just wrote down every idea I had I could make Ten times as much money as I'm making right now, you know, just from ideas like The easiest way to make money Is the most profitable way so think about it the hardest way to make money?  What are you good at? What is your expertise? Offer consultations on what you're skilled in, you know Things like that learn how to speak correctly so that people take you seriously Speak in a professional tone Improve upon yourself and provide a service and people who need that service will seek you out, you know Think okay, so So this is your homework men I'm gonna give you all some homework because our boys Take take 20 minutes tonight and figure out five ways to make money With what you know and what you have right now not what you need to get in the future not what you need To have in order to start this but what you have right now in your possession How you can make money five different ways and Whittle it down to one or two ways and go and do it. Okay, you'll thank me later. You're welcome Figure it out, you know, it doesn't take it doesn't take a genius to figure out how to make money Some of the richest people in the world don't have a college degree. They just had an idea. Okay? They put down the distractions They put down the excuses and they put their mind to work on Something that they believed in and that they knew they could do With what they had at the moment. Okay, so just go for it.  She's nine years old, you know She's already thinking like that and that's good.  It's not that expensive So if you whatever you can do just go do it, you know I remember There's this guy And he had started off with a food truck And he sold like these tacos or whatever and now he has like a giant I think a giant restaurant From having a food truck for like five years. He saved all his money And then he opened a big restaurant now. He makes probably millions. So start off small. Don't try to get here quick That's the problem with most men. They don't they feel like if they can't get successful quick They want to quit.  It's a process. It's something that You build up to you can't just get there overnight And that's what a lot of people don't understand and sometimes women are a distraction, you know Sometimes chasing women is not going to help you get paid Okay, because they they want your money. Okay, we want your money That's why we rather chase people that already have it instead of people that don't have it So once once you get it, then you have time to enjoy your life. Enjoy the women Pick a woman that you want instead of settling for a woman.  You won't have to worry, you know You won't have to deal with women like me calling you names Because you won't be those things You know, you'll be someone I can brag on or tell a story about a successful story about and compare to other people and say this is who you need to be like You then become a role model You know All men should want to be role models to other men All men should want to be an example of success instead of mediocrity All men should want to be great You know All men should want to hold their head up high and walk with pride and have their women bragging on them and their Daughters proud of them and their kids having stuff that they never had all men should want that You know When they don't that's a problem Okay, when they don't That says something about themselves so as a man Your priorities Should be in order You know Your lower self that chases women that want sex and things like that That energy needs to be channeled into creative energy into money-making energy Okay, men who have sex with a lot of women and chase women who are broke All that energy that you're giving away Is your creative energy that is supposed to be used to get you wealthy But you're giving it away for free to women and think that you're getting over But really what you're doing is you're diminishing You're diminishing your creative energy That energy is supposed to be channeled to create And if you don't use it to create and you just use it to procreate or have sex or you know You know do all these things that make you feel good sexually That energy is better spent elsewhere, you know Creating something putting all that frustration anger Pent up energy into a project You know a lot of men who are very successful sometimes they practice celibacy for a while So that that energy builds up and gets them to that next level, you know It's like to some men it's a turn on to earn a bunch of money like dang. I just earned You know $40,000 in three days because I put all my energy and effort into you know this project and bam There it goes. You know, that's the orgasm. Damn. Look at my success A lot of men Don't know what to do with this energy.   Okay So anyway I'm reading some of these comments um Yeah, if like ladies Also the the type of man you choose to be with Shows who you are as well. So if you're if you're choosing players thugs Men that don't really have a lot of ambition in life and just want to play you and look good and talk sweet to you And you know all this kind of that that means that you don't take yourself seriously You know, you're dealing with men who not serious about life means you don't take your life seriously as well You're just in there, you know for the moment, but you have to remember one thing Women I don't want to say women have an expiration date, but we have a time clock And don't waste your youth on on guys who are not going anywhere, you know If you don't take yourself serious, you're not going to be attracted to serious men You know, you're going to be attracted to boys.   Did your sister take her life seriously? Do you want to be in the same position as they are? Did you see them struggle? Do you want to struggle? You know, do you want to take your life seriously get a serious man? You know, that's that's common sense But a lot of people will not think like that because they weren't taught So You have to retrain yourself to think do I take my life seriously, you know So, um Whoever's in here talking about god and jesus's stuff. Thank you. We don't need a pastor. This is not church, darling um If you like if you're if you find yourself in a situation where you're dating someone that's not going anywhere Anywhere and doesn't want to go anywhere politely leave the situation, you know politely leave and If he asks you why you're leaving and just say I I want a more serious life I'm taking myself more seriously now.  You can fit in where you get in, you know um Men who want to do good by their families, they will find a way, you know Seek I must this is for the uh, bible person Seek and you shall find if you're not looking you can't you're not gonna find it, you know So if your man is not even looking to better himself or looking to upgrade you guys lifestyle He's not going to find it. Make sure he's looking, you know, you look with him.  Take your man Make sure he sees that there's better better ways to live, you know Um, then when he sees women out with other men who are giving them everything that look worse than you He's gonna feel that you're like, dang, she could have this type of lifestyle if she really wanted to let me do something You know that girl is ugly and she got this rich dude. Dang my girl could get a rich dude.  Look at these girls in here I know I look 20 times better. Guess what? You don't know what you know, you don't know what goes on in the DM and the in my inbox, you know So You want to let him see that you deserve better and that you can get better if you really wanted to look I wait on you. I'm working with you.  Oh, I got her.  She cooks my food. She loves me, but don't ever think Like Beyonce say you don't ever think you're not irreplaceable So, yes Show him what you can have if you really wanted it, but let him know that you waiting on him to upgrade So you can have it with him. Okay This is key.  You don't say we should be here. Go there Yes, you should be there.  That's just silly. That's weird. Like this has nothing to do with religion There's all this has something to do with bettering your life through the type of men you choose 70 percent of black children that has nothing to do with Jesus though Like 70 percent of black children born out of marriage has nothing to do with religion. Okay Because Christianity was not our original religion anyway, so You know, so That's nothing to do with religion Okay Yes, I'm Someone says I'm an advocate for same-sex marriage. So And what's your point? I'm an advocate for a lot of stuff that you probably don't agree with so I Bye Felicia If you're here to judge and tell people to repent and all that stuff you want to wrong Because you know, we don't hear like we we in it to win it We're in it to win it Okay So You know, if you are smart you'd be collecting tithes and offerings since you're a church I know that's what I be doing The only way I'd ever be Christian again is if I was the first lady of a mega church.   We want somebody to add to us So we can take half their check when we divorce them So you got good luck with that I told you we in it to win it Someone keeps texting me like I want to talk to Okay 10 dollar someone is saying $10 an hour is not good for you hoes I made $10 an hour when I was 18 years old back before $10 an hour was even high. I mean was even low When I was working minimum wage was like 4 475 or 425 an hour And I was making 10.  So if you making that now as a grown man 30 years later, you got issues I'm sorry Hey the Christian trolling Anyway, it like for example If you're always envious Of other people And what they have and you're in a relationship and you're in a marriage and you can't have nice things And that's what you want. Okay. Remember it's all about what you want In life, you know If you want something You're not going to be happy to get it, right? So it's not about your morals. It's not about what's right or what's wrong It's about if you want something and you deserve to have it and you think you deserve to have it Until you have it.   Don't just hint around tell him look. I want a new purse It costs this much. Can you get it for me for my birthday? If his answer is no then say, okay fine. I'll find another way to get it.   Oh my friend gave it to me. Oh, my mom bought it for me.   Does he like her hairstyle? Does he like her makeup? Why is he looking at her? What is it about her that he likes, you know, uh, of course men are always gonna look but Look what he's looking at pay attention.  We're not looking at her. We're looking at her stuff Okay Men have always asked me that why do other women look at other women? We're not looking at them. We're looking at their stuff Look at that hair. Look at them nails. Look at that Purse look at them shoes. Look at them jeans, you know, that's what we're looking at. We're not looking at them Oh, they look nice in that thing that I want. Yes. We'll give them a compliment. Oh, she looks good in that We want that, you know Men are looking for a totally different reason.  Oh my god. I love her shoes. Oh my god. Look at that watch, you know And smile That's so cute. Where did you get that? Like I have so many people ask me where I get my stuff at in the grocery store Oh my god, where did you get that from and and then we go and tell them. Oh, yeah It's on sale. You know, you can order it online. You can buy it here. You can buy it there That's what women talk about stuff Okay And if you're a man and you don't realize that or understand that women like certain things Then, you know, you need to start realizing that now because that's what we're looking at Um, now there's someone that's not materialistic at all. They just don't care that they were wearing the same clothes every week by $10 purse at, you know Goodwill or or walmart and be perfectly happy, you know but They might want all your attention and all your time and be clingy to you And want you to be there and call them and text them and be there for you all the time That might be their wealth, you know, that might be Uh, what they want instead of material and men sometimes men can't even give women that You know, the non materialistic women want other things And sometimes men can't even give them that but then they want to complain about Materialistic women, you know, they want too much. They want too much And then the girl who doesn't want anything she wants too much time. She's too clingy, you know Uh, the woman that doesn't even want time. It just wants a commitment or she wants commitment, you know The easiest thing to give a woman is material That's why you know, it's It's very easy for a man with money to please most women.  It's hard to keep a woman happy by emotionally stroking her and saying, oh, baby, you're perfect. I love you I'm gonna give you all this attention. You know, I'm never gonna go out with my friends.  What type of woman do you want?  And she'll take a $10 hot dog and a Walmart purse Which one which one is easier to please in a piece, you know You have to think about these kind of things because some women, you know Some women want it all someone want the money the attention and everything so This person keeps texting me like a book I'm like 20 texts So Men like i'm just telling y'all what women want how to impress women how to impress us like it's not that hard You know three things, you know how men say you only think meet three things food sex and you know, uh, what else I forgot the third thing but Women just like nice things You know for you to be a good guy, you know not not miss over her and what Commitment that's all we want That's what most want you need to have something you need to be committed and you need to be decent Okay, that's it.  You can make your woman happy If you can't do those three things You're always gonna have issues, you know Uh Trump's wife. Okay, Melania. Yeah, she of course. She's a male order bride. Okay. She married for money She never thought she was gonna be the first lady. She don't even like donald trump She don't live in the same house with him. Okay She's just in it for the money period Lifestyle only she don't even like him And he probably knows that i'm sure she probably cusses him out every night And he probably can't even get it up no more. So really doesn't matter, you know The only reason donald trump gets married is for status. Okay, he doesn't need a wife It's status I can have any woman I want.  It's like an accessory wealthy man If you ever notice most super wealthy men always have a wife Because it's a status symbol You can't be super Wealthy and not have a wife. The wife is the the thing that most men If they could just have satisfied have, you know, this this wife, that's a status symbol That's the equivalent to having a Bentley a maybach, you know, you got all these things. Where's your wife?  Can you master a wife? Can you make a woman happy? That's the last thing you can do Can you make a woman happy? That's why all these millionaires and billionaires have wives Because that is the last thing that they can they have to master If you can master a woman you got it.  He has a wife He can provide all her needs. Look at her car. She's driving a Range Rover.  Oh, she earned that car because she don't ever go to work They're thinking look what her husband did for her. Oh my god. He's a good guy. He must be rich He must be smart. I wonder what he does for a living day.  They thought something was wrong with you. They looked down upon you I mean as a man, it's like where's your wife?    Or you have a very nice car and live in a nice house and she's still chasing behind you know Somebody else but you have more than them now, you know Success is always the best revenge. No matter who done your dirty, you know what I'm saying So men you can be successful as revenge as well. You know what I'm saying? I I feel that That has to be the best revenge for any man because first of all it boosts his ego It makes it makes him feel like yeah, you look at all this stuff you left You know, you this could have been you, you know, just like that silo video from a long time from a couple years ago uh, if you I see you driving round town with a girl I love and I'm like if you And then she was working at the diner and he got rich so, you know No matter what Make sure it's motivation to get you to that next level.  Who called you worthless take that and flip it into inspiration to get the ultimate revenge Okay, success. That's what I would do if I was a man And I didn't have a lot of money. I would figure out how to get some My success will be the best revenge upon any woman who ever Left me or whatever, you know, I would flip the script You know, some men aren't born knowing these things some men aren't perfect Some men weren't raised around, you know men that have success.    That's just saying, you know what? Um I'm gonna show the world who I am, you know what I can do. I can master this World I can master this matrix. I can master Anything because I'm confident in myself not not I'm afraid to do anything So I'm just gonna stay where I am and I'm gonna wait for someone to stoop down to my level You know, I'm gonna wait for something to drop from from somebody else, you know Pockets so that I can be okay.  Don't do it for a gold digger. Do it for your children in the future Do it for yourself. Do it for the best revenge ever Do it to make you feel successful like a man. Do it for the respect You know, don't do it for a woman Do it for the respect the recognition You know, and how it's gonna make you feel do it to make your parents proud, you know Don't do it for me. Don't do it for her. Don't do it for them. Do it for yourself and your parents, you know, your parents sacrifice a lot Only to see you be mediocre only to see you scrape and struggle no They want to see you do better than them if you're not doing better than your parents you messed up somewhere You messed up somewhere if you're not doing better than your parents are or were at your age, you need to get on it Mm-hmm And like a lot of these new guys, I know they're mad at me because I'm like you Women don't pay on dates and blah blah blah blah Think about this. Okay.   You really like her though.  Anyway, so I'm not saying don't pay or I'm not saying to pay But just know what you're setting yourself up for some women like being doormats Some women find find it as a turn on to Be a doormat to a man to let the man Cust them out because that's what they were raised around and they think that's love but You know, nothing good ever comes of nothing like that. So If you don't want to be a doormat Set your standards from the beginning and stick to them. Do not bend them. Okay Men the same thing, you know, if you have standards of a woman Don't bend don't bend your standards because you want some or you think she'll give it up Stick with your standards, you know, if you have a standard that you will not date certain type of women Then that's what you stick to because if you keep Going back on what you said and dating all these type of women that you said you don't want You're going to keep attracting more and more of those type of women, you know, because That's what you're entertaining. That's what you're working with That's that's the energy that you're working with that type of woman, you know, just like manifesting if you're manifesting something You're not going to do something against with your what you're manifesting because you don't want it to not come to you so You're going to only focus on what you want versus what you don't want and Men want different things out of different women, you know So focus on that get the type of woman you want Women same thing.  Where are you going to be in five years? You know, if he still says working and wherever he's working, um Then you already know he ain't even thought about it. So, you know Just getting him to think about it is the first step You know, ask him the questions. Where are you going to be in five years?  What is your plan? and Even if they didn't have a plan they're going to create one right then because Now that they've seen what you plan on doing they got to do something too Or else they know you're going to be gone. So Start talking about it And and the more you talk about it the more they'll think about it and the more they'll act towards it.   No, it means she wants to control you The one with the wallet has the more control So if i'm paying for stuff like if i'm rich if i'm a sugar mama And I have this cute guy, you know And he looks like a male model and I pay for trips and stuff and hawaii and blah blah blah blah blah I'm gonna have some say so i'm gonna have some say so where you go where you don't go What time you come home?   Look Get home right now Because if they don't get home, guess what they car getting took Their account is going to be empty.  She probably has a lot of control over you Okay, you might think you sneaking around and doing this and that but you know when she called and Just that phone ring, you know, you better answer You know what when I become an old widow and I'm like 85 or 55 or Probably 55. Yeah, I might have me a little young thing. I might use my all my money for my insurance and Stuff like that have me a little tenderoni a little tender Yeah, I'm gonna tell them what to do where to be where to go But I've earned that I'm I'm old My hood's gone. I got all this cash, you know, if I ever if I ever do that that would be my only way, you know, I'm old and I'm just be like these sugar daddies out here But I could that probably won't even really be my style. I probably get me a A nice regal a regal gentleman But I'm just saying if I was ever to pay for a man, it would be under those circumstances Sugar mama when I'm old my hood did and I got all this money to spend before I die Let's see. Okay Okay, someone says that they're Them being weak makes them Hate themselves. Okay being weak is a choice Do you think with emotion or do you think with logic? Okay You think with emotion and you make decisions based on how you feel about someone or how much you love someone Or how much you like being with someone? That's your mistake You think with logic Okay, what is this person doing for me? You know, what are their actions showing me?  You know, um, do they like me or are they using me? You know Make logical decisions. Don't be weak If you're weak, you'll always come out last You always be prey You know for the hunters You know, like when they see a herd of zebras The lion will always go off the small weak one Because they're easier to catch and control Okay, Angelina says she's 22 and 12 in the mind and believes in fairy tales. Well, I was too girl That's the good thing because you you can experience love the right way And then when you get the reality check and the wake up call Then you'll be able to make logical decisions based on, you know What happened to you, you know 22 years old That's when women are still looking for that prince charming everything fairy tale That's why I say if men want to date someone who loves them for them date women 25 and under Because you're still going to get that innocent fairy tale You know, I'm with you because I love you type woman But if you're you know, if you're wanting a woman who can hold her on pay half the bills and stuff like that You're probably going to want someone your own age But since they already know better than to fall for your tricks and things like that You have to go for the younger girl and pay for her because she ain't going to be able She's not going to be able to pay half your bills and stuff like that at that young age So it's kind of a choice Either you get a young dumb person.  I'm just saying inexperienced Or you get someone who knows better and knows the game and it's not going to play these games Unless they're winning them, you know Uh I met my husband at 22, you know, I thought everything was a fairy tale and uh blah blah blah blah, but I was still In logical thinking I'm like, okay in the fairy tale the prince was always rich He wouldn't broke. Okay. Y'all remember that you might have the fairy tale in your mind But you forgot that the prince was always rich in the fairy tale And the lady was always the princess or the queen at the end If you ain't no princess or no queen at the end and your man is not rich You are not thinking like a fairy tale fairy tales have fantasy as well as logic Okay So if you're only looking at one side of the fairy tale and not the other side of the fairy tale Then you're missing the whole point Okay, um So Even shrek had his own swamp and his own house Okay He didn't live with his mama. So Even though he wasn't rich he owned some stuff. He owned some land. He owned a swamp. He owned a house He had his own stuff. Okay So Even if the fairy tale Is fantasy The end game Is still the same get with somebody who can support you and who's stable.  You got to be very strategic in Relationships, especially when you're young when you're the most youthful and beautiful And have the best body and you have more power At your young age, you know what I'm saying? But if you can learn this stuff young, you're gonna get a hit quick Look at all the housewives on tv. Look at all those basketball wives on tv They knew the game from the start. Okay, they aimed high Okay, they aimed high Now you start aiming low at 22.  I'm old. Okay, but I benefited at my peak I benefited a lot at my peak. Okay Um And I was smart. I had an older sister who taught me the game Okay, I was I was schooled from a young age. I watched her And that's how I knew what I knew at a young age. That's how I knew not to fall in love with you know looks and You know things like that, but the fall in love with lifestyle because My sister took me to all these places, you know, nice places. She used to date millionaires She took me all this stuff and I couldn't just date anybody after that I couldn't just marry anybody after that. I just I couldn't you know, because I was so used to nice things I was used to valley parking. I was used to VIP. I was used to having money I was used to going in the store and not looking at prices I was used to that. So how can I go backwards? You know, get yourself used to that lifestyle hang out with people that have that lifestyle Put yourself in those environments so you can't move backwards even if you want it to You just won't be comfortable there, you know There was no way I could I could even marry Because how I felt about someone I needed them Sorry y'all somebody called I needed them to be able to provide. You know, I needed the lifestyle. I needed to drive nice cars I needed to have a nice house. I needed to be here. I needed to be there, you know So I needed to go on vacation. So that's what I looked for in a husband Okay, so I'm sorry. I'm gonna have to end it with you guys because I do have an appointment But thank you guys for tuning in. I do have a consultation and You know I'll see y'all on the next one thumbs up if y'all agree and I'll see y'all there. All right


Okay, so I've been following this video all day today on Twitter. It's been driving me crazy because it's just as you would expect and The Democrat Party media is just basically whipping up the shitstorm over these two lawful gun owners Who are clearly just defending their home from what looks and sounds like violent mobs That have been rampaging across the country for the last three weeks So, you know, it's not that hard to understand why these people might be out there With their weapons as this mob descends on their home. So and beyond that These people that the media is now going after and they're treating them like their racist nutcases They were well within the rights to defend their home especially after you know, everybody's seen these videos of these Protesters the rioters and looter, you know, I don't know how to differentiate them honestly But everybody saw these videos and these and these leaders from these groups saying oh, we're coming to the suburbs next be ready We're coming to the suburbs. That's not a new threat either. I mean, we've heard that threat in the past with past protest after Black people have been shot by police whether it was legitimate or not and these were just peaceful protesters I mean, even if they were peaceful their initial actions weren't peaceful busting through the gate and we got video of that as well Which I'll put up here in just a second But first just give me 30 seconds to tell you about this special offer from my subscribers What will your savings in retirement look like once we've declared victory over the virus many Americans use this little known IRS qualified loophole that allows Americans to buy gold and silver with their retirement accounts call today and request a free Investment kit below mentioned drone tech politics and get a free one ounce silver coin for qualified retirement account holders Must be over 40 to qualify call<PHONE_NUMBER> and get your free investment guide today So let's take a look at this video here real quick and then I want to talk a little bit about the media responses And I'm sure tonight There's no doubt they're gonna be going after these people apparently they're lawyers in st. Louis And so let's just check this out real quick. This is one of the videos. There's several videos Why are they still provoking these people? I don't understand not not the homeowners this mob. They should be moving on Let's get out of here instead They're provoking Yeah, that's ridiculous so According to the Breitbart article here the homeowner told Kmov4 that he came out armed because the protesters allegedly burst through a historic gate on the way to his property He said a mob of at least a hundred smashed through the historic wrought iron gates a Portland place Destroying them rushed towards my home where my family was having dinner outside and put us in fear of our lives Yeah, I think I would probably feel the exact same way But the media doesn't of course of course not because gun owners are bad Okay, so we saw the other video. This is them actually coming through the gate This is after they already buzzed through the gate right there. They've already And there's a sign right there that says this is private property these people don't care Yeah, I Giant mob burst through the gates of a private gated community With drums and chanting like I'd be a little nervous too especially after like I said everything that we've seen Okay, so we've seen that that's pretty much it Let's take a look at some of the media reactions now, which I promise you are utterly ridiculous I mean there are reasons to criticize these people although the guy's not really pointing it He's holding it I would probably do a little differently But I mean in the heat of the moment if he's outside eating and this Happens what do you do and I don't think you can blame these people I think the tactics of BLM and what the media is letting them get away with is Atrocious and it's actually a gonna hurt their movement in the long run So let's check out what the media said in response So here we have ABC news a couple pointed guns at protesters in St. Louis as a group marched toward the mayor's home to demand her resignation Well, that's all well and good and that and as far you know That might just be an after-the-fact story maybe that is what they went for but as far as I know protests require permits You got to get a permit to have a protest. You can't just burst on the people's property into a private neighborhood and Protest that's illegal any other group doing that would be arrested and charged for trespassing at the minimum Or how about Keith Boykin here from CNN Donald Trump this morning proudly retweeted the video of Ken and Karen Which are essentially racial slurs for white people at this point pointing their guns at black people in st. Louis Trump never misses an opportunity to fan the flames of white resentment and racial unrest He's projecting. That's what he's doing and guess what it wasn't just black people out there There were lots of white people too and like I said, I wouldn't appointed the guns I think they initially did that as the crowd especially guys with cameras kind of kick descended on them Eventually they stopped doing it But like I wouldn't have done that myself But I don't think that's any reason to attack these people and they were at their home And it was this protest so-called protest that was actually illegal. Okay, so how about Reuters here? Supposedly objective news source a couple was seen barefoot in brandishing firearms on protesters as they entered their neighborhood during a protest Against the st. Louis mayor.  It wasn't illegal protest It was a private neighborhood and none of these facts are in the headline. Maybe if you read the story. They're there I don't know. I'm not gonna do it right now, but that's the way a lot of these news organizations operate It's all you know, you read the headline. Most people just keep going. Oh here CBS News white couple aims guns at st. Louis protests What does the fact that they're white mean if it was what if it was black homeowners that had done it? Would they mention the fact that they were black not likely? I don't think they would And what was this guy up here just saying from CNN that it's Trump that's fanning the flames of racial resentment It's clearly the media doing that and members of the media and of course these people have become targets as you can see All the left-wing groups are gonna start targeting these people and it's just too bad Something may even happen to them who knows but it will be the media's fault and this kind of thing is only gonna spread Okay, the media is backing the mob and you have scared people who have nobody looking out for them The Republicans sure aren't doing anything or going out and to defend these people. So they're on their own No doubt no no reason for them not to be harmed and Feeling threatened at this point. So guys go ahead and check that video out for yourself Watch the news tonight. I guarantee you I guarantee you the media is just going to be demonizing and Insighting essentially is citing violence against these people just going down the Twitter feed here. You can see I mean You know the hill Trump shares video of white couple pointing guns at protesters like again What's the what's the fact that they're white have to do with anything? I really don't get it It's not just the left-wing lunatics threatening these people at this point the president of the leftist DC think tank Attack st. Louis homeowners says he would beat their brains in check this out Jerry Taylor He's the president and co-founder of this DC DNC think tank and he said if I were in that March and these racist lunatics were waving their guns at me What evidence do you have that they're racist at all their skin color?  You know, I don't they're gonna they're gonna make a big mistake here at some point and they're gonna awaken a sleeping dragon Like I don't think they understand what the backlash is going to be but if they continue this and they continue to escalate I don't see it in