Sample 14 Linear algebra


DO
    SYSTEM(ScrollToLine=-2)
    DLG(B="How to solve a system of linear equations",
        B="How to calculate the DOT PRODUCT of matrices m23*m32",
        B="How to calculate the TRANSPOSED of a matrix",
        B="How to calculate the INVERSE of a matrix",
        B="How to calculate a UNITY matrix",
        B="How to calculate the DETERMINANT of a matrix",
        B='How to calculate the product "CONST*MATRIX"',
        B='How to element-wise ADD "m32a+m32b"',
        B='How to element-wise SUBTRACT "m32a-m32b"',
        B='QUIT HicEst')
    IF($txtRC == 'QUIT HicEst') SYSTEM(Quit=1)

        IF($txtRC == "How to solve a system of linear equations")
    DO
        DLG(NumEdit=n,SYM,BG=990, B="n as is",  B="Increase n", B="Decrease n", B="Exit")
        IF($txtRC == "Exit") EXIT
        n = n  + ($txtRC == "Increase n") - ($txtRC == "Decrease n")
        n = MAX(n, 1)
        ARRAY(Name=A, CLeaR=1, Name=invers, Clear=1, Name=b, CLeaR=1, Name=x, CLeaR=1)
        SET(A=(n,n), b=(n,1), x=(n,1))
        DO i = n
            b(i) = i
            DO j = n
                A(i,j) = RAN(1)
            ENDDO
        ENDDO
        IF(n <= 10)
            DLG(TI='Matrix A of "A*x=b"', Left=2/3, Hei=1/3, Top=0/3, Nr=1, Array=A)
            DLG(TI='Vector b of "A*x=b"', Left=2/3, Hei=1/3, Top=1/3, Nr=2, Array=b, TI='row,B(row),')
        ELSE
            DLG(Kill=1, Kill=3)
        ENDIF
        LINALG(Matrix=A, INVerse=invers, Constants=b, ToDo=invers*b, Result=x)
        DLG(TI='Vector x of "A*x=b"', Left=2/3, Hei=1/3, Top=2/3, Nr=3, Array=x, TI='row,x(row),')
        SYSTEM(ScrollToLine = 0)
    ENDDO

ELSEIF($txtRC == "How to calculate the DOT PRODUCT of matrices m23*m32")
    m23 = ((1,2,3), (4,5,6))
    m32 = ((11,12), (13,14), (15,16))
    DLG(TI='Matrix m23 of "m23*m32"', Left=2/3, Hei=1/3, Top=0/3, Nr=1, Array=m23)
    DLG(TI='Matrix m32 of "m23*m32"', Left=2/3, Hei=1/3, Top=1/3, Nr=2, Array=m32)
    LINALG(Matrix=m23, Matrix=m32, ToDo=m23*m32, Result=dotProd)
    SYSTEM(ScrollToLine = 1)
    DLG(TI='Dot product of "m23*m32"', Left=2/3, Hei=1/3, Top=2/3, Array=dotProd)

ELSEIF($txtRC == "How to calculate the TRANSPOSED of a matrix")
    m23 = ((1,2,3), (4,5,6))
    DLG(TI='Matrix m23 to be transposed', Nr=2, Left=2/3, Hei=1/3, Top=1/3, Array=m23)
    LINALG(Matrix=m23, Transpose=m32T)
    SYSTEM(ScrollToLine = 1)
    DLG(TI='The transposed matrix m32T', Left=2/3, Hei=1/3, Top=2/3, Array=m32T)

ELSEIF($txtRC == "How to calculate the INVERSE of a matrix")
    m33 = ((1,2,3), (4,5,6), (7,8,1))
    DLG(TI='Matrix m33 to be inversed', Nr=2, Left=2/3, Hei=1/3, Top=1/3, Array=m33)
    LINALG(Matrix=m33, Inverse=m33I)
    SYSTEM(ScrollToLine = 0)
    SYSTEM(ScrollToLine = 1)
    DLG(TI='The inversed matrix m33I', Left=2/3, Hei=1/3, Top=2/3, Array=m33I)

ELSEIF($txtRC == "How to calculate a UNITY matrix")
    SET(unity=(6,6))
    LINALG(Matrix=unity, Unity=uni)
    SYSTEM(ScrollToLine = 1)
    DLG(TI='The unity matrix for n=6', Left=2/3, Hei=1/3, Top=2/3, Array=uni)

ELSEIF($txtRC == "How to calculate the DETERMINANT of a matrix")
    d22 = ( (1,2), (3,4) )
    LINALG(Matrix=d22, DETerminant=det)
    SYSTEM(ScrollToLine = 1)
    DLG(TI='determinant(d22) = ' & det, Left=2/3, Hei=1/3, Top=2/3, Array=d22)

ELSEIF($txtRC == 'How to calculate the product "CONST*MATRIX"')
    m32 = ((1,2), (3,4), (5,6))
    DLG(TI='Matrix m32 of "const*m32"', Nr=2, Left=2/3, Hei=1/3, Top=1/3, Array=m32)
    LINALG(Matrix=m32, ToDo=1.2*m32, Result=m32C)
    SYSTEM(ScrollToLine = 1)
    DLG(TI='1.2*m32', Left=2/3, Hei=1/3, Top=2/3, Array=m32C)

ELSEIF($txtRC == 'How to element-wise ADD "m32a+m32b"')
    m32a = ((1,2), (3,4), (5,6))
    m32b = ((.2,.3), (.4,.5), (.6,.7))
    DLG(TI='Matrix m32a of "m32a+m32b"', Nr=1, Left=2/3, Hei=1/3, Top=0/3, Array=m32a)
    DLG(TI='Matrix m32b of "m32a+m32b"', Nr=2, Left=2/3, Hei=1/3, Top=1/3, Array=m32b)
    LINALG(Matrix=m32a, Matrix=m32b, ToDo=m32a+m32b, Result=m32eA)
    SYSTEM(ScrollToLine = 1)
    DLG(TI='Element-wise m32a+m32b', Left=2/3, Hei=1/3, Top=2/3, Array=m32eA)

ELSEIF($txtRC == 'How to element-wise SUBTRACT "m32a-m32b"')
    m32a = ((1,2), (3,4), (5,6))
    m32b = ((.2,.3), (.4,.5), (.6,.7))
    DLG(TI='Matrix m32a of "m32a-m32b"', Nr=1, Left=2/3, Hei=1/3, Top=0/3, Array=m32a)
    DLG(TI='Matrix m32b of "m32a-m32b"', Nr=2, Left=2/3, Hei=1/3, Top=1/3, Array=m32b)
    LINALG(Matrix=m32a, Matrix=m32b, ToDo=m32a-m32b, Result=m32eS)
    SYSTEM(ScrollToLine = 1)
    DLG(TI='Element-wise m32a-m32b', Left=2/3, Hei=1/3, Top=2/3, Array=m32eS)

ENDIF
DLG(Kill=1, Kill=2, Kill=3)
ENDDO
END

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