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QBasic => QB Discussion & Programming Help => Topic started by: farshad1360 on November 07, 2006, 01:48:37 PM



Title: help
Post by: farshad1360 on November 07, 2006, 01:48:37 PM
hello.
i am a beginner programmer and i need a precise source code for solving the system of linear equations and use it in my program as a subroutine.
please help me.
thank you.


Title: help
Post by: zoasterboy on November 07, 2006, 03:30:40 PM
This should probably be in the "newb qn" section.

Is this so that you can quickly do you algebra homework without actualy doing the problems?


Title: help
Post by: Skyler on November 07, 2006, 06:56:44 PM
Quote from: "zoasterboy"
This should probably be in the "newb qn" section.

And please don't title your message "help", title it something relevant, such as "Linear Equation Solver Needed".
Refresh my memory- a system of linear eqautions is two equations in the format
Code:
y = 2x + 2

which intersect in 0, 1, or infinite points, correct?


Title: help
Post by: zoasterboy on November 07, 2006, 07:23:11 PM
No, I think

Code:
y = 2x + 2


Is direct variation.

Ill take a look at my old algebra notes. I think it's somthing to do with a bunch of eqns that all intersect at one point, such as:

Code:


Acme TV service costs 30 bucks up front and 10 bucks a month

Emca TV service costs 70 bucks up front and 5 bucks a month

How many months untill Emca becomes a better deal than Acme? // this is the answer to the system of linear eqns



Or somthing along those lines.

Later when I find it ill post what they are.


Title: help
Post by: Antoni Gual on November 10, 2006, 02:04:18 PM
This is from Jean Debord's fbmath lib. http://sourceforge.net/projects/fbmath/
 I had only to rearrange the DIM lines to make it work to QB. The test code is mine.
Code:

DECLARE SUB lineq (a() AS DOUBLE, b() AS DOUBLE, det AS DOUBLE)
CONST MatErrDim = -3
' Non-compatible dimensions

' ------------------------------------------------------------------
' Machine-dependent constant
' ------------------------------------------------------------------

CONST MachEp = 2.220446049250313D-16
' Floating point precision: 2^(-52)

' ------------------------------------------------------------------
' Global variable
' ------------------------------------------------------------------

COMMON SHARED errcode AS INTEGER
' Error code from the latest function evaluation

' ******************************************************************
DATA 3.4,2.5,4.1,3.2
DATA 1.9,3.1
DIM det AS DOUBLE
DIM a(1, 1) AS DOUBLE
DIM b(1) AS DOUBLE
DIM i AS INTEGER, j AS INTEGER
FOR i = 0 TO 1
  FOR j = 0 TO 1
    READ a(i, j)
NEXT j, i
FOR i = 0 TO 1
  READ b(i)
NEXT

lineq a(), b(), det
IF errcode <> 0 THEN
  PRINT "error "; errcode
ELSE
 PRINT "results"
 FOR i = 0 TO 1
   PRINT b(i)
 NEXT
 PRINT "determinant "; det
END IF


SUB lineq (a() AS DOUBLE, b() AS DOUBLE, det AS DOUBLE)
' ------------------------------------------------------------------
' Solves the linear system A*X = B by Gauss-Jordan algorithm
' ------------------------------------------------------------------
' On input:
'   * A(L..N, L..N) is the system matrix
'   * B(L..N) is the constant vector
'
' On output:
'   * A(L..N, L..N) contains the inverse matrix
'   * B(L..N) contains the solution vector
'   * The determinant of the system matrix is returned in Det
'   * The error code is returned in the global variable ErrCode:
'       ErrCode = MatOk     ==> no error
'       ErrCode = MatErrDim ==> non-compatible dimensions
'       ErrCode = MatSing   ==> quasi-singular matrix
' ------------------------------------------------------------------

  DIM L AS INTEGER, N AS INTEGER     ' Bounds of A
  DIM i AS INTEGER, j AS INTEGER, K  AS INTEGER ' Loop variables
  DIM Ik AS INTEGER, Jk AS INTEGER   ' Pivot coordinates
  DIM Pvt AS DOUBLE      ' Pivot
  DIM T AS DOUBLE        ' Auxiliary variable

  L = LBOUND(a, 1)
  N = UBOUND(a, 1)
   
  IF LBOUND(b) <> L OR UBOUND(b) <> N THEN
    errcode = MatErrDim
    EXIT SUB
  END IF

  DIM PRow(L TO N) AS INTEGER  ' Stores line of pivot
  DIM PCol(L TO N) AS INTEGER  ' Stores column of pivot
  DIM MCol(L TO N) AS double  ' Stores a column of the matrix

  det = 1
  K = L

  DO WHILE K <= N
    ' Search for largest pivot in submatrix A[K..N, K..N]
    Pvt = a(K, K)
    Ik = K
    Jk = K
    FOR i = K TO N
      FOR j = K TO N
        IF ABS(a(i, j)) > ABS(Pvt) THEN
          Pvt = a(i, j)
          Ik = i
          Jk = j
        END IF
      NEXT j
    NEXT i

    ' Pivot too small ==> quasi-singular matrix
    IF ABS(Pvt) < MachEp THEN
      det = 0
      errcode = MatSing
      EXIT SUB
    END IF

    ' Save pivot position
    PRow(K) = Ik
    PCol(K) = Jk

    ' Update determinant
    det = det * Pvt
    IF Ik <> K THEN det = -det
    IF Jk <> K THEN det = -det

    ' Exchange current row (K) with pivot row (Ik)
    IF Ik <> K THEN
      FOR j = L TO N
        SWAP a(K, j), a(Ik, j)
      NEXT j
      SWAP b(K), b(Ik)
    END IF

    ' Exchange current column (K) with pivot column (Jk)
    IF Jk <> K THEN
      FOR i = L TO N
        SWAP a(i, K), a(i, Jk)
      NEXT i
    END IF

    ' Store col. K of A into MCol and set this col. to 0
    FOR i = L TO N
      IF i <> K THEN
        MCol(i) = a(i, K)
        a(i, K) = 0
      ELSE
        MCol(i) = 0
        a(i, K) = 1
      END IF
    NEXT i

    ' Transform pivot row
    FOR j = L TO N
      a(K, j) = a(K, j) / Pvt
    NEXT j
    b(K) = b(K) / Pvt
   
    ' Transform other rows
    FOR i = L TO N
      IF i <> K THEN
        T = MCol(i)
        FOR j = L TO N
          a(i, j) = a(i, j) - T * a(K, j)
        NEXT j
        b(i) = b(i) - T * b(K)
      END IF
    NEXT i

    K = K + 1
  LOOP

  ' Exchange rows of inverse matrix and solution vector
  FOR i = N TO L STEP -1
    Ik = PCol(i)
    IF Ik <> i THEN
      FOR j = L TO N
        SWAP a(i, j), a(Ik, j)
      NEXT j
      SWAP b(i), b(Ik)
    END IF
  NEXT i

  ' Exchange columns of inverse matrix
  FOR j = N TO L STEP -1
    Jk = PRow(j)
    IF Jk <> j THEN
      FOR i = L TO N
        SWAP a(i, j), a(i, Jk)
      NEXT i
    END IF
  NEXT j

  errcode = MatOk
END SUB


Title: help
Post by: Skyler on November 10, 2006, 06:12:54 PM
Quote from: "zoasterboy"
I think it's somthing to do with a bunch of eqns that all intersect at one point.

That's what I said.
If x = number of months, then
Acme = 10x + 30
or y = 10x + 30, which is a linear equation, like I said.