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{
This file is part of the Numlib package.
Copyright (c) 1986-2000 by
Kees van Ginneken, Wil Kortsmit and Loek van Reij of the
Computational centre of the Eindhoven University of Technology
FPC port Code by Marco van de Voort (marco@freepascal.org)
documentation by Michael van Canneyt (Michael@freepascal.org)
This unit contains some basic matrix operations.
See the file COPYING.FPC, included in this distribution,
for details about the copyright.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.
**********************************************************************}
Unit omv;
{$I direct.inc}
interface
uses typ;
{Calculates inproduct of vectors a and b which have N elements. The first
element is passed in a and b}
Function omvinp(Var a, b: ArbFloat; n: ArbInt): ArbFloat;
{Multiplication of two matrices C=AxB }
Procedure omvmmm(Var a: ArbFloat; m, n, rwa: ArbInt;
Var b: ArbFloat; k, rwb: ArbInt;
Var c: ArbFloat; rwc: ArbInt);
{Multiplication of a matrix(A) with a vector(B), C=A x B}
Procedure omvmmv(Var a: ArbFloat; m, n, rwidth: ArbInt; Var b, c: ArbFloat);
{Calculate 1-Norm of matrix A}
Function omvn1m(Var a: ArbFloat; m, n, rwidth: ArbInt): ArbFloat;
{Calculate 1-Norm of vector A}
Function omvn1v(Var a: ArbFloat; n: ArbInt): ArbFloat;
{Calculate 2-Norm of vector A}
Function omvn2v(Var a: ArbFloat; n: ArbInt): ArbFloat;
{Calculate Frobenius-Norm of mxn matrix A}
Function omvnfm(Var a: ArbFloat; m, n, rwidth: ArbInt): ArbFloat;
{Calculates maximum (infinite) norm of mxn matrix a}
Function omvnmm(Var a: ArbFloat; m, n, rwidth: ArbInt): ArbFloat;
{Calculates maximum (infinite) norm of n-Vector }
Function omvnmv(Var a: ArbFloat; n: ArbInt): ArbFloat;
{Transponate mxn matrix A (which was declared rwa bytes wide), put
it to C (rwc was declared elements wide)}
Procedure omvtrm(Var a: ArbFloat; m, n, rwa: ArbInt; Var c: ArbFloat;
rwc: ArbInt);
IMPLEMENTATION
Function omvinp(Var a, b: ArbFloat; n: ArbInt): ArbFloat;
Var pa, pb : ^arfloat1;
i : ArbInt;
s : ArbFloat;
Begin
If n<1 Then
exit(0);
pa := @a;
pb := @b;
s := 0;
For i:=1 To n Do
Begin
s := s+pa^[i]*pb^[i]
End; {i}
omvinp := s
End; {omvinp}
Procedure omvmmm(Var a: ArbFloat; m, n, rwa: ArbInt;
Var b: ArbFloat; k, rwb: ArbInt;
Var c: ArbFloat; rwc: ArbInt);
Var pa, pb, pc : ^arfloat1;
i, j, l, inda, indc : ArbInt;
s : ArbFloat;
Begin
If (m<1) Or (n<1) Or (k<1) Then
exit;
pa := @a;
pb := @b;
pc := @c;
For i:=1 To m Do
Begin
inda := (i-1)*rwa;
indc := (i-1)*rwc;
For j:=1 To k Do
Begin
s := 0;
For l:=1 To n Do
s := s+pa^[inda+l]*pb^[(l-1)*rwb+j];
pc^[indc+j] := s
End {j}
End; {i}
End; {omvmmm}
Procedure omvmmv(Var a: ArbFloat; m, n, rwidth: ArbInt; Var b, c: ArbFloat);
Var pa, pb, pc : ^arfloat1;
i, ind : ArbInt;
Begin
If (m<1) Or (n<1) Then
exit;
pa := @a;
pb := @b;
pc := @c;
ind := 0;
For i:=1 To m Do
Begin
pc^[i] := omvinp(pa^[ind+1], pb^[1], n);
ind := ind+rwidth
End; {i}
End; {omvmmv}
Function omvn1m(Var a: ArbFloat; m, n, rwidth: ArbInt): ArbFloat;
Var pa : ^arfloat1;
i, j : ArbInt;
norm, normc : ArbFloat;
Begin
If (m<1) Or (n<1) Then
exit;
pa := @a;
norm := 0;
For j:=1 To n Do
Begin
normc := 0;
For i:=1 To m Do
normc := normc+abs(pa^[j+(i-1)*rwidth]);
If norm<normc Then
norm := normc
End;
omvn1m := norm
End {omvn1m};
Function omvn1v(Var a: ArbFloat; n: ArbInt): ArbFloat;
Var pa : ^arfloat1;
i : ArbInt;
norm : ArbFloat;
Begin
If n<1 Then
exit;
pa := @a;
norm := 0;
For i:=1 To n Do
norm := norm+abs(pa^[i]);
omvn1v := norm
End {omvn1v};
Function omvn2v(Var a: ArbFloat; n: ArbInt): ArbFloat;
Var pa : ^arfloat1;
i : ArbInt;
norm : ArbFloat;
Begin
If n<1 Then
exit;
pa := @a;
norm := 0;
For i:=1 To n Do
norm := norm+sqr(pa^[i]);
omvn2v := sqrt(norm)
End {omvn2v};
Function omvnfm(Var a: ArbFloat; m, n, rwidth: ArbInt): ArbFloat;
Var pa : ^arfloat1;
i, j, k : ArbInt;
norm : ArbFloat;
Begin
If (m<1) Or (n<1) Then
exit;
pa := @a;
norm := 0;
k := 0;
For i:=1 To m Do
Begin
For j:=1 To n Do
norm := norm+sqr(pa^[j+k]);
k := k+rwidth
End;
omvnfm := sqrt(norm)
End {omvnfm};
Function omvnmm(Var a: ArbFloat; m, n, rwidth: ArbInt): ArbFloat;
Var pa : ^arfloat1;
i, k : ArbInt;
normr, norm : ArbFloat;
Begin
If (m<1) Or (n<1) Then
exit;
pa := @a;
norm := 0;
k := 0;
For i:=1 To m Do
Begin
normr := omvn1v(pa^[1+k], n);
If norm<normr Then
norm := normr;
k := k+rwidth
End;
omvnmm := norm
End {omvnmm};
Function omvnmv(Var a: ArbFloat; n: ArbInt): ArbFloat;
Var pa : ^arfloat1;
i : ArbInt;
norm, aa : ArbFloat;
Begin
If (n<1) Then
exit;
pa := @a;
norm := 0;
For i:=1 To n Do
Begin
aa := abs(pa^[i]);
If aa>norm Then
norm := aa
End;
omvnmv := norm
End {omvnmv};
Procedure omvtrm(Var a: ArbFloat; m, n, rwa: ArbInt;
Var c: ArbFloat; rwc: ArbInt);
Var pa, pc : ^arfloat1;
ind, i, j : ArbInt;
Begin
If (m<1) Or (n<1) Then
exit;
pa := @a;
pc := @c;
ind := 0;
For i:=1 To m Do
Begin
For j:=1 To n Do
pc^[(j-1)*rwc+i] := pa^[ind+j];
ind := ind+rwa
End; {i}
End; {omvtrm}
End.
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