CS201- Introduction to Programming- Lecture 43
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The document provides an overview of programming concepts focusing on matrices, including definitions, operations (addition, subtraction, multiplication, and transposition), and their corresponding rules for performing these operations. It also discusses designing a program with clear problem statements, analyzing the issues, and considering user interface components related to matrix operations. Lastly, it touches on memory allocation and interface methods like constructors and operators in matrix programming.
CS201- Introduction to Programming- Lecture 43
- 1. Introduction ttoo PPrrooggrraammmmiinngg LLeeccttuurree ## 4433
- 2. Math Library Complex number Matrix Quadratic equation and their solution …………….…
- 3. DDeessiiggnn RReecciippee TToo ddeessiiggnn aa pprrooggrraamm pprrooppeerrllyy,, wwee mmuusstt :: – AAnnaallyyzzee aa pprroobblleemm ssttaatteemmeenntt,, ttyyppiiccaallllyy eexxpprreesssseedd aass aa wwoorrdd pprroobblleemm – EExxpprreessss iittss eesssseennccee,, aabbssttrraaccttllyy aanndd wwiitthh eexxaammpplleess – FFoorrmmuullaattee ssttaatteemmeennttss aanndd ccoommmmeennttss iinn aa pprreecciissee llaanngguuaaggee ii..ee.. ccooddee – EEvvaalluuaattee aanndd rreevviissee tthhee aaccttiivviittiieess iinn lliigghhtt ooff cchheecckkss aanndd tteessttss aanndd – PPAAYY AATTTTEENNTTIIOONN TTOO DDEETTAAIILL
- 4. Matrix • Matrix is nothing but a two dimensional array of numbers • Normally, represented in the form of : • Rows • Columns
- 5. Example 1 2 3 4 5 6 7 8 9 10 11 12 A = Three Rows Four Columns
- 6. i & j are two Integers i representing the Row number j representing the Column number
- 7. Operations Performed with Matrix • Addition of two matrices. • Addition of a scalar and a matrix • Subtraction of two matrices • Subtraction of a scalar from a matrix • Multiplication of two matrices • Multiplication of a scalar with a matrix • Division of a scalar with a matrix • Transpose of a matrix
- 8. Interface
- 9. Addition of two Matrices Aij+Bij = Cij
- 10. Addition of two Matrices Size of two matrices must be same Number of rows and columns must be identical for the matrices to be addable
- 11. Example 1 2 3 5 6 7 9 10 11 - 3 6 8 7 4 7 9 10 1 = -2 -4 -5 -2 2 0 0 0 10 Cij = Aij - Bij
- 12. Adding a Scalar to the Matrix Ordinary number added to every element of the matrix
- 13. Subtracting a Scalar from a Matrix Ordinary number subtracted from every element of the matrix
- 14. Division of Matrix by a Scalar Divide every element of Matrix by a scalar number
- 15. Example Let : X be a Scalar number A be a Matrix C = Aij ij X
- 16. Multiplication of a scalar with a Matrix Example Let : X is a Scalar number A is a Matrix X * A X * Aij = Cij
- 17. Multiply two Matrices 1 2 * 2 4 5 6 1 2 = ( 1 ) ( 2 ) + ( 2 ) ( 1 ) ( 1 ) ( 4 ) + ( 2 ) ( 2 ) ( 5 ) ( 2 ) + ( 6 ) ( 1 ) ( 5 ) ( 4 ) + ( 6 ) ( 2 )
- 18. Rules Regarding Matrix Multiplication Number of columns of the 1st Matrix = Number of rows of the 2nd Matrix
- 19. Rules rreeggaarrddiinngg MMaattrriixx MMuullttiipplliiccaattiioonn FFiirrsstt mmaattrriixx hhaass – MM rroowwss – NN ccoolluummnnss SSeeccoonndd mmaattrriixx hhaass – NN rroowwss – PP ccoolluummnnss RReessuullttaanntt mmaattrriixx wwiillll hhaavvee – MM rroowwss – PP ccoolluummnnss
- 20. Transpose of a Matrix Interchange of rows and columns
- 21. Transpose of a Matrix Example 1 2 3 5 6 7 9 10 11 1 5 9 2 6 10 3 7 11
- 22. Transpose of a Non Square Matrix Size of matrix change after transpose A AT 3 ( Rows ) * 4 ( Columns ) Before 4 ( Rows ) * 3 ( Columns ) After
- 23. Next Phase of Analysis • Determine the Constants • Memory Allocation • What is it’s user interface
- 24. Interface
- 25. IInntteerrffaaccee CCoonnssttrruuccttoorr :: PPaarraammeetteerrss aarree NNuummbbeerr ooff rroowwss NNuummbbeerr ooff ccoolluummnnss DDiissppllaayy ffuunnccttiioonn PPlluuss ooppeerraattoorr :: mmeemmbbeerr ooppeerraattoorr ooff tthhee ccllaassss SSuubbttrraaccttiioonn ooppeerraattoorr :: mmeemmbbeerr ooppeerraattoorr ooff tthhee ccllaassss PPlluuss ooppeerraattoorr :: ffrriieenndd ooff tthhee ccllaassss SSuubbttrraaccttiioonn ooppeerraattoorr :: ffrriieenndd ooff tthhee ccllaassss
- 26. Plus Operator A + X X + A
- 27. Subtraction Operator A - X X – A
- 28. *
- 29. IInntteerrffaaccee MMuullttiipplliiccaattiioonn OOppeerraattoorr :: MMeemmbbeerr ooff tthhee CCllaassss MMuullttiipplliiccaattiioonn OOppeerraattoorr :: FFrriieenndd ooff tthhee CCllaassss DDiivviissiioonn OOppeerraattoorr :: MMeemmbbeerr ooff tthhee CCllaassss TTrraannssppoossee FFuunnccttiioonn :: MMeemmbbeerr ooff tthhee CCllaassss AAssssiiggnnmmeenntt OOppeerraattoorr :: MMeemmbbeerr ooff tthhee CCllaassss ++== ,, --== :: MMeemmbbeerrss ooff tthhee CCllaassss
- 30. Multiplication Operator A * X X * A
- 31. Assignment Operator A = B ( Member Operator )
- 32. Interface >> Extraction Operator : Friend Operator << Stream Insertion Operator : Friend Operator
- 33. Copy Constructor
- 34. CCooppyy CCoonnssttrruuccttoorr AAssssiiggnnmmeenntt OOppeerraattoorr MMeemmoorryy AAllllooccaattiioonn MMeemmoorryy DDeeaallllooccaattiioonn