Matlab

Introduction to Matlab 7 Lesson I

How to connect to you folders ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Marco Lattuada – Statistical and Numerical Methods for Chemical Engineers Matlab Introduction Course – Page #

Matlab 7.0.4 - 7.10 ,[object Object],[object Object],Marco Lattuada – Statistical and Numerical Methods for Chemical Engineers Matlab Introduction Course – Page # Matlab is an interatcive system for numerical computation ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Matlab 7.0.4 - 7.10 ,[object Object],Marco Lattuada – Statistical and Numerical Methods for Chemical Engineers Matlab Introduction Course – Page # ,[object Object],[object Object],[object Object]

Matlab Introduction Window Marco Lattuada – Statistical and Numerical Methods for Chemical Engineers Matlab Introduction Course – Page # File Structure Variable Editor Commands / Instructions Command History Variables / Structures Try it! Do not be too timid about your actions. All life is an experiment. The more you make, the better! Ralph Waldo Emerson

Variables Marco Lattuada – Statistical and Numerical Methods for Chemical Engineers Matlab Introduction Course – Page # Rules: ,[object Object],[object Object],[object Object],[object Object],Valid Examples a = 1 speed = 1500 BeamOutput_Type1 = v*Q*v’ name = ’John Smith’ Invalid Examples 2ndvariable = ’yes’ first one = 1 No need to specify the variable type

[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Variables Marco Lattuada – Statistical and Numerical Methods for Chemical Engineers Matlab Introduction Course – Page # By pressing “w”+↑, the command who is recalled… Why these are arrays??? Every variable is an array!!!

[object Object],[object Object],[object Object],[object Object],[object Object],Variables Marco Lattuada – Statistical and Numerical Methods for Chemical Engineers Matlab Introduction Course – Page # By pressing ↑ or ↓, one can recall the previous commands By using the “ ; “ symbol at the end of a command, the execution is performed, but the result is not shown in the command window

[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Vectors Marco Lattuada – Statistical and Numerical Methods for Chemical Engineers Matlab Introduction Course – Page # If everything is an array, what is a vector ??? You should see: Fast help by: >> help linspace

[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Vector's Arithmetic Marco Lattuada – Statistical and Numerical Methods for Chemical Engineers Matlab Introduction Course – Page # Addition/multiplication by constants Dot product of vectors Addition of vectors Your first matrix…  (3,1) ·(1,3) = (3,3) Error!  (1,3)·(1,3) = nothing Element-by-element operations Examples of functions returning element-by-element operations

[object Object],[object Object],[object Object],[object Object],[object Object],Vector's Arithmetic II Marco Lattuada – Statistical and Numerical Methods for Chemical Engineers Matlab Introduction Course – Page # (3,1)x(1,3)=(3,3) Matrix! (1,3)x(3,1)=(1,1) SCALAR (dot product) ! Never forget the rules for matrix multiplication!

[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Arrays/Matrices Marco Lattuada – Statistical and Numerical Methods for Chemical Engineers Matlab Introduction Course – Page #

[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Accessing Elements Marco Lattuada – Statistical and Numerical Methods for Chemical Engineers Matlab Introduction Course – Page #

[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Arithmetic with Matrices Marco Lattuada – Statistical and Numerical Methods for Chemical Engineers Matlab Introduction Course – Page # Addition/multiplication by constants Addition of matrices Transpose Elimination of columns/lines Product between matrices Square of matrix Square of matrix's elements E i,j = 2^A i,j Square-root of matrix's elements Square-root of matrix (try: >> (sqrtm(A))^2) Inverse of A (equal to: >> inv(A)) Remember: product between matrices is usually not commutative!

[object Object],[object Object],[object Object],[object Object],Matrix Division Marco Lattuada – Statistical and Numerical Methods for Chemical Engineers Matlab Introduction Course – Page # Two square matrices A divided by B, alternatively mrdevide(A,B) equivalent to A*inv(B) The two divisions are different, because the product between matrices is not commutative! alternatively mldevide(A,B) equivalent to inv(B)*A

[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Other Ways of Creating Matrices Marco Lattuada – Statistical and Numerical Methods for Chemical Engineers Matlab Introduction Course – Page #

[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Operators for Matrices Marco Lattuada – Statistical and Numerical Methods for Chemical Engineers Matlab Introduction Course – Page # min(A) = -max(-A) var(A), std(A), …

Exercises ,[object Object],[object Object],[object Object],Marco Lattuada – Statistical and Numerical Methods for Chemical Engineers Matlab Introduction Course – Page #

[object Object],[object Object],[object Object],Solution of Linear Algebraic Systems Marco Lattuada – Statistical and Numerical Methods for Chemical Engineers Matlab Introduction Course – Page # Shortcut

[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Structures in Matlab Marco Lattuada – Statistical and Numerical Methods for Chemical Engineers Matlab Introduction Course – Page # Structures are arrays whose names have dot-separated parts. They can be used to store information of different kinds together in a hierarchical structure.

[object Object],[object Object],Loops in Matlab Marco Lattuada – Statistical and Numerical Methods for Chemical Engineers Matlab Introduction Course – Page # ,[object Object],[object Object],[object Object]

[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Examples of Loops Marco Lattuada – Statistical and Numerical Methods for Chemical Engineers Matlab Introduction Course – Page # A technique is a trick that works Giancarlo Rota

While Loops in Matlab ,[object Object],[object Object],Marco Lattuada – Statistical and Numerical Methods for Chemical Engineers Matlab Introduction Course – Page # ,[object Object],[object Object],[object Object],The statement is executed as long as the expression is true The statements are executed an indefinite number of times

[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Examples of Loops Marco Lattuada – Statistical and Numerical Methods for Chemical Engineers Matlab Introduction Course – Page # Pre- allocate arrays Vectorize and use pre-defined functions 20 times faster 129 times faster Make it right before you make it faster Elements of Programming Style (1978)

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