05-04-2022, 08:23 AM
(This post was last modified: 05-17-2022, 06:29 PM by TarotRedhand.)
The contents of this part are -
The code for which is -
And that's it.
TR
Code: (Select All)
' _FLOAT
SUB IdentityFMatrix(A##(), MatrixSize%)
SUB ZeroFMatrix(A##())
SUB ConFMatrix(A##())
SUB FMatrixNegate(A##())
SUB FMatrixTransPose(A##(), B##())
SUB FMatrixCopy(This##(), ToThis##())
SUB FMatrixPrint(A##())
SUB FMatrixFilePrint(A##(), FileNumber)
SUB FMatrixInput(A##())
SUB FMatrixFileInput(A##() , FileNum)
SUB FMatrixAdd(A##(), B##(), C##())
SUB FMatrixScalarAdd(A##(), B##, C##())
SUB FMatrixSubtract(A##(), B##(), C##())
SUB FMatrixScalarSubtract(A##(), B##, C##())
SUB FMatrixMultiply(A##(), B##(), C##())
SUB FMatrixScalarMultiply(A##(), B##, C##())
FUNCTION FMatrixMaximum##(A##())
FUNCTION FMatrixMinimum##(A##())
FUNCTION FMatrixMean##(A##())
FUNCTION FMatrixVariance##(A##())The code for which is -
Code: (Select All)
REM ******************************************************************
REM * This library deals with 2 dimensional arrays that are treated *
REM * as though they were mathematical matrices. I have included *
REM * all the routines that are associated with matrices that make *
REM * sense for the various TYPEs that are used. So for integers *
REM * and longs there no routines for mean, variance, inverse or *
REM * determinant. Also for singles and doubles I have left out *
REM * routines for inverse and determinant as their use is very *
REM * limited and specialised. *
REM ******************************************************************
REM ******************************************************************
REM * Private SUB only intended for use by the routines in this *
REM * library. *
REM ******************************************************************
SUB MatrixError(Where$, Fault$)
PRINT "Error in ";Where$;" - ";Fault$
STOP
END SUB ' | MatrixError
REM ******************************************************************
REM * _FLOAT floating point Matrices *
REM ******************************************************************
REM ******************************************************************
REM * A##() is REDIM'ed to be a square matrix with MatrixSize# rows *
REM * and MatrixSize# columns. All the elements of A##() are set to *
REM * zero except those where the row and the column are equal which *
REM * are set to one e.g. A##(1,1) = 1, A##(1,2) = 0. *
REM ******************************************************************
SUB IdentityFMatrix(A##(), MatrixSize&)
MatrixSize& = ABS(MatrixSize&)
REDIM A##(1 TO MatrixSize&, 1 TO MatrixSize&)
FOR Column& = 1 TO MatrixSize&
FOR Row& = 1 TO MatrixSize&
IF Row& = Column& THEN
A##(Row&,Column&) = 1.0
ELSE
A##(Row&,Column&) = 0.0
END IF
NEXT Row&
NEXT Column&
END SUB ' | IdentityFMatrix
REM ******************************************************************
REM * All the elements of A##() are set to zero. *
REM ******************************************************************
SUB ZeroFMatrix(A##())
ARowStart& = LBOUND(A##)
ARowEnd& = UBOUND(A##)
AColStart& = LBOUND(A##, 2)
AColEnd& = UBOUND(A##, 2)
FOR Column& = AColStart& To AColEnd&
FOR Row& = ARowStart& TO ARowEnd&
A##(Row&,Column&) = 0.0
NEXT Row&
NEXT Column&
END SUB ' | ZeroFMatrix
REM ******************************************************************
REM * All the elements of A##() are set to one. *
REM ******************************************************************
SUB ConFMatrix(A##())
ARowStart& = LBOUND(A##)
ARowEnd& = UBOUND(A##)
AColStart& = LBOUND(A##, 2)
AColEnd& = UBOUND(A##, 2)
FOR Column& = AColStart& To AColEnd&
FOR Row& = ARowStart& TO ARowEnd&
A##(Row&,Column&) = 1.0
NEXT Row&
NEXT Column&
END SUB ' | ConFMatrix
REM ******************************************************************
REM * LET A##() = -A##() e.g if A##(1,1) = 5 then after this routine *
REM * A##(1,1) = -5. *
REM ******************************************************************
SUB FMatrixNegate(A##())
ARowStart& = LBOUND(A##)
ARowEnd& = UBOUND(A##)
AColStart& = LBOUND(A##, 2)
AColEnd& = UBOUND(A##, 2)
FOR Column& = AColStart& To AColEnd&
FOR Row& = ARowStart& TO ARowEnd&
A##(Row&,Column&) = -A##(Row&,Column&)
NEXT Row&
NEXT Column&
END SUB ' | FMatrixNegate
REM ******************************************************************
REM * B##() is REDIM'ed to have the same number of columns as A##() *
REM * has rows and to have the same number of rows as A##() has *
REM * columns, and then the rows of A##() are copied to the columns *
REM * of B##(). *
REM ******************************************************************
SUB FMatrixTransPose(A##(), B##())
ARowStart& = LBOUND(A##)
AColStart& = LBOUND(A##, 2)
ARowEnd& = UBOUND(A##)
AColEnd& = UBOUND(A##, 2)
REDIM B##(AColStart& TO AColEnd&, ARowStart& TO ARowEnd&)
FOR P& = AColStart& TO AColEnd&
FOR Q& = ARowStart& TO ARowEnd&
B##(P&, Q&) = A##(Q&, P&)
NEXT Q&
NEXT P&
END SUB ' | FMatrixTransPose
REM ******************************************************************
REM * REDIM's ToThis##() to be the same size as This##() and then *
REM * copies the contents of This##() to ToThis##(). *
REM ******************************************************************
SUB FMatrixCopy(This##(), ToThis##())
RowStart& = LBOUND(This##)
RowFinish& = UBOUND(This##)
ColStart& = LBOUND(This##, 2)
ColFinish& = UBOUND(This##,2)
REDIM ToThis##(RowStart& TO RowFinish&, ColStart& TO ColFinish&)
FOR Column& = ColStart& TO ColFinish&
FOR Row& = RowStart& To RowFinish&
ToThis##(Row&,Column&) = This##(Row&,Column&)
NEXT Row&
NEXT Column&
END SUB ' | FMatrixCopy
REM ******************************************************************
REM * Display the contents of A##() on screen, formatted in columns. *
REM ******************************************************************
SUB FMatrixPrint(A##())
ARowStart& = LBOUND(A##)
ARowEnd& = UBOUND(A##)
AColStart& = LBOUND(A##, 2)
AColEnd& = UBOUND(A##, 2)
FOR Row& = ARowStart& TO ARowEnd&
FOR Column& = AColStart& To AColEnd&
PRINT A##(Row&,Column&);" ";
NEXT Column&
PRINT
NEXT Row&
END SUB ' | FMatrixPrint
REM ******************************************************************
REM * Saves the contents of A##() to the file specified by FileNumber *
REM ******************************************************************
SUB FMatrixFilePrint(A##(), FileNumber)
ARowStart& = LBOUND(A##)
PRINT #FileNumber, ARowStart&;" ";
ARowEnd& = UBOUND(A##)
PRINT #FileNumber, ARowEnd&;" ";
AColStart& = LBOUND(A##, 2)
PRINT #FileNumber, AColStart&;" ";
AColEnd& = UBOUND(A##, 2)
PRINT #FileNumber, AColEnd&;" ";
PRINT #FileNumber,
FOR Row& = ARowStart& TO ARowEnd&
FOR Column& = AColStart& To AColEnd&
PRINT #FileNumber, A##(Row&,Column&);" ";
NEXT Column&
PRINT #FileNumber,
NEXT Row&
END SUB ' | FMatrixFilePrint
REM ******************************************************************
REM * This routine is for the sadists and masochists among you in *
REM * that it inputs all the information necessary to create and *
REM * fill a matrix fromthe keyboard. *
REM ******************************************************************
SUB FMatrixInput(A##())
INPUT"Lowest subscript for A##(1):",A
INPUT"Highest subscript for A##(1):",B
INPUT"Lowest subscript for A##(2):",C
INPUT"Lowest subscript for A##(2):",D
REDIM A##(A TO B, C TO D)
PRINT
FOR Row& = A TO B
FOR Column& = C TO D
PRINT "Enter value for position ";Row&;", ";Column&;":";
INPUT A
A##(Row&,Column&) = FIX(A)
NEXT Column&
NEXT Row&
END SUB ' | FMatrixInput
REM ******************************************************************
REM * This routine reads all the information necessary to create and *
REM * fill a matrix ( A##() ) from a file specified by filenum. This *
REM * routine is the complement to IMatrixFilePrint and retrieves *
REM * the information in the same order as that routine writes it. *
REM ******************************************************************
SUB FMatrixFileInput(A##() , FileNum)
INPUT #FileNum, A
INPUT #FileNum, B
INPUT #FileNum, C
INPUT #FileNum, D
A = ABS(FIX(A))
B = ABS(FIX(B))
C = ABS(FIX(C))
D = ABS(FIX(D))
REDIM A##(A TO B, C TO D)
FOR Row& = A TO B
FOR Column& = C TO D
INPUT #FileNum, A##(Row&,Column&)
NEXT Column&
NEXT Row&
END SUB ' | FMatrixFileInput
REM ******************************************************************
REM * Matrix addition e.g. C##() = A##() + B##(). A##() and B##() must *
REM * have identical upper and lower bounds. C##() is REDIM'ed to be *
REM * the same size. Each element of C##() is assigned the result of *
REM * adding the equivalent elements in A##() and B##(). *
REM ******************************************************************
SUB FMatrixAdd(A##(), B##(), C##())
ID$ = "FMatrixAdd"
ARowStart& = LBOUND(A##)
BRowStart& = LBOUND(B##)
IF ARowStart& <> BRowStart& THEN
MatrixError ID$, "Lower bounds of A(1) and B(1) not identical##"
END IF
ARowEnd& = UBOUND(A##)
BRowEnd& = UBOUND(B##)
IF ARowEnd& <> BRowEnd& THEN
MatrixError ID$, "Upper bounds of A(1) and B(1) not identical##"
END IF
AColStart& = LBOUND(A##, 2)
BColStart& = LBOUND(B##, 2)
IF AColStart& <> BColStart& THEN
MatrixError ID$, "Lower bounds of A(2) and B(2) not identical##"
END IF
AColEnd& = UBOUND(A##, 2)
BColEnd& = UBOUND(B##, 2)
IF ARowEnd& <> BRowEnd& THEN
MatrixError ID$, "Upper bounds of A(1) and B(1) not identical##"
END IF
REDIM C##(ARowStart& TO ARowEnd&, AColStart& TO AColEnd&)
FOR Column& = AColStart& To AColEnd&
FOR Row& = ARowStart& TO ARowEnd&
C##(Row&,Column&) = A##(Row&,Column&) + B##(Row&,Column&)
NEXT Row&
NEXT Column&
END SUB ' | FMatrixAdd
REM ******************************************************************
REM * Matrix scalar addition e.g. C##() = A##() + B##. C##() is *
REM * REDIM'ed to be identical in size to A##(). Each element of *
REM * C##() is assigned the result of adding B# to the equivalent *
REM * elements in A##(). *
REM ******************************************************************
SUB FMatrixScalarAdd(A##(), B##, C##())
ARowStart& = LBOUND(A##)
ARowEnd& = UBOUND(A##)
AColStart& = LBOUND(A##, 2)
AColEnd& = UBOUND(A##, 2)
REDIM C##(ARowStart& TO ARowEnd&, AColStart& TO AColEnd&)
FOR Column& = AColStart& To AColEnd&
FOR Row& = ARowStart& TO ARowEnd&
C##(Row&,Column&) = A##(Row&,Column&) + B#
NEXT Row&
NEXT Column&
END SUB ' | FMatrixScalarAdd
REM ******************************************************************
REM * Matrix subtraction e.g. C##() = A##() - B##(). A##() and B##() *
REM * must have identical upper and lower bounds. C##() is REDIM'ed *
REM * to be the same size. Each element of C##() is assigned the *
REM * result of subtracting the equivalent element of B##() from the *
REM * equivalent element of A##(). *
REM ******************************************************************
SUB FMatrixSubtract(A##(), B##(), C##())
ID$ = "FMatrixSubtract"
ARowStart& = LBOUND(A##)
BRowStart& = LBOUND(B##)
IF ARowStart& <> BRowStart& THEN
MatrixError ID$, "Lower bounds of A(1) and B(1) not identical##"
END IF
ARowEnd& = UBOUND(A##)
BRowEnd& = UBOUND(B##)
IF ARowEnd& <> BRowEnd& THEN
MatrixError ID$, "Upper bounds of A(1) and B(1) not identical##"
END IF
AColStart& = LBOUND(A##, 2)
BColStart& = LBOUND(B##, 2)
IF AColStart& <> BColStart& THEN
MatrixError ID$, "Lower bounds of A(2) and B(2) not identical##"
END IF
AColEnd& = UBOUND(A##, 2)
BColEnd& = UBOUND(B##, 2)
IF ARowEnd& <> BRowEnd& THEN
MatrixError ID$, "Upper bounds of A(1) and B(1) not identical##"
END IF
REDIM C##(ARowStart& TO ARowEnd&, AColStart& TO AColEnd&)
FOR Column& = AColStart& To AColEnd&
FOR Row& = ARowStart& TO ARowEnd&
C##(Row&,Column&) = A##(Row&,Column&) - B##(Row&,Column&)
NEXT Row&
NEXT Column&
END SUB ' | FMatrixSubtract
REM ******************************************************************
REM * Matrix scalar subtraction e.g. C##() = A##() - B##. C##() is *
REM * REDIM'ed to be the same size as A##(). Each element of C##() is *
REM * assigned the result of subtracting B# from the equivalent of *
REM * A##(). *
REM ******************************************************************
SUB FMatrixScalarSubtract(A##(), B##, C##())
ARowStart& = LBOUND(A##)
ARowEnd& = UBOUND(A##)
AColStart& = LBOUND(A##, 2)
AColEnd& = UBOUND(A##, 2)
REDIM C##(ARowStart& TO ARowEnd&, AColStart& TO AColEnd&)
FOR Column& = AColStart& To AColEnd&
FOR Row& = ARowStart& TO ARowEnd&
C##(Row&,Column&) = A##(Row&,Column&) - B#
NEXT Row&
NEXT Column&
END SUB ' | FMatrixScalarSubtract
REM ******************************************************************
REM * Matrix multiplication e.g. C##() = A##() * B##(). As such it is *
REM * easier to direct you to look at the source code for this *
REM * routine rather than to try to explain it, other than to say *
REM * that C##() is REDIM'ed according to the standard matrix formula *
REM ******************************************************************
SUB FMatrixMultiply(A##(), B##(), C##())
ID$ = "FMatrixMultiply"
ARowStart& = LBOUND(A##)
BRowStart& = LBOUND(B##)
IF ARowStart& <> BRowStart& THEN
MatrixError ID$, "Lower bounds of A(1) and B(1) not identical##"
END IF
AColStart& = LBOUND(A##, 2)
BColStart& = LBOUND(B##, 2)
IF AColStart& <> BColStart& THEN
MatrixError ID$, "Lower bounds of A(2) and B(2) not identical##"
END IF
BRowEnd& = UBOUND(B##)
AColEnd& = UBOUND(A##, 2)
IF AColEnd& <> BRowEnd& THEN
MatrixError ID$, "Upper bounds of A(2) and B(1) not identical##"
END IF
ARowEnd& = UBOUND(A##)
BColEnd& = UBOUND(B##, 2)
REDIM C##(ARowStart& TO ARowEnd&, BColStart& TO BColEnd&)
FOR Row& = ARowStart& TO ARowEnd&
FOR Column& = BColStart& To BColEnd&
Sum## = 0.0
FOR Z& = AColStart& TO AColEnd&
Sum## = Sum## + (A##(Row&, Z&) * B##(Z&, Column&))
NEXT Z&
C##(Row&,Column&) = Sum##
NEXT Column&
NEXT Row&
END SUB ' | FMatrixMultiply
REM ******************************************************************
REM * Matrix scalar multiplication e.g. C##() = A##() * B##. C##() is *
REM * REDIM'ed to be the same size as A##(). Each element of C##() is *
REM * assigned the result of multiplying the equivalent element of *
REM * A##() by B##. *
REM ******************************************************************
SUB FMatrixScalarMultiply(A##(), B##, C##())
ARowStart& = LBOUND(A##)
AColStart& = LBOUND(A##, 2)
ARowEnd& = UBOUND(A##)
AColEnd& = UBOUND(A##, 2)
REDIM C##(ARowStart& TO ARowEnd&, AColStart& TO AColEnd&)
FOR Column& = AColStart& To AColEnd&
FOR Row& = ARowStart& TO ARowEnd&
C##(Row&,Column&) = A##(Row&,Column&) * B#
NEXT Row&
NEXT Column&
END SUB ' | FMatrixScalarMultiply
REM ******************************************************************
REM * Returns the maximum element contained in A##(). *
REM ******************************************************************
FUNCTION FMatrixMaximum##(A##())
MyMax## = -1.18E-4932
ARowStart& = LBOUND(A##)
ARowEnd& = UBOUND(A##)
AColStart& = LBOUND(A##, 2)
AColEnd& = UBOUND(A##, 2)
FOR Column& = AColStart& To AColEnd&
FOR Row& = ARowStart& TO ARowEnd&
IF MyMax## < A##(Row&, Column&) THEN
MyMax## = A##(Row&,Column&)
END IF
NEXT Row&
NEXT Column&
FMatrixMaximum## = MyMax##
END FUNCTION ' | FMatrixMaximum##
REM ******************************************************************
REM * Returns the minimum element contained in A##(). *
REM ******************************************************************
FUNCTION FMatrixMinimum##(A##())
MyMin## = 1.18E+4932
ARowStart& = LBOUND(A##)
ARowEnd& = UBOUND(A##)
AColStart& = LBOUND(A##, 2)
AColEnd& = UBOUND(A##, 2)
FOR Column& = AColStart& To AColEnd&
FOR Row& = ARowStart& TO ARowEnd&
IF MyMin## > A##(Row&, Column&) THEN
MyMin## = A##(Row&,Column&)
END IF
NEXT Row&
NEXT Column&
FMatrixMinimum## = MyMin##
END FUNCTION ' | FMatrixMinimum##
REM ******************************************************************
REM * Returns the Average of all the values contained in A##(). *
REM ******************************************************************
FUNCTION FMatrixMean##(A##())
Sum## = 0.0
ARowStart& = LBOUND(A##)
AColStart& = LBOUND(A##, 2)
ARowEnd& = UBOUND(A##)
AColEnd& = UBOUND(A##, 2)
FOR Column& = AColStart& TO AColEnd&
FOR Row& = ARowStart& TO ARowEnd&
Sum## = Sum## + A##(Row&,Column&)
NEXT Row&
NEXT Column&
MatrixSize## = (1.0 + ARowEnd& - ARowStart&) * (1.0 + AColEnd& - AColStart&)
FMatrixMean## = Sum## / MatrixSize##
END FUNCTION ' | FMatrixMean##
REM ******************************************************************
REM * Returns the variance of all the values contained in A##(). *
REM ******************************************************************
FUNCTION FMatrixVariance##(A##())
SumSquared## = 0.0
MyMean## = FMatrixMean##(A##())
ARowStart& = LBOUND(A##)
AColStart& = LBOUND(A##, 2)
ARowEnd& = UBOUND(A##)
AColEnd& = UBOUND(A##, 2)
FOR Column& = AColStart& TO AColEnd&
FOR Row& = ARowStart& TO ARowEnd&
Temp## = A##(Row&,Column&) - MyMean##
Temp## = Temp## * Temp##
SumSquared## = SumSquared## + Temp##
NEXT Row&
NEXT Column&
MatrixSize## = (1.0 + ARowEnd& - ARowStart&) * (1.0 + AColEnd& - AColStart&)
FMatrixVariance## = SumSquared## / (MatrixSize## - 1.0)
END FUNCTION ' | FMatrixVariance##And that's it.
TR