MagickExport size_t GetOptimalKernelWidth2D(const double radius,
const double sigma)
{
double
alpha,
beta,
gamma,
normalize,
value;
size_t
width;
ssize_t
j,
u,
v;
(void) LogMagickEvent(TraceEvent,GetMagickModule(),"...");
if (radius > MagickEpsilon)
return((size_t) (2.0*ceil(radius)+1.0));
gamma=fabs(sigma);
if (gamma <= MagickEpsilon)
return(3UL);
alpha=MagickEpsilonReciprocal(2.0*gamma*gamma);
beta=(double) MagickEpsilonReciprocal((MagickRealType) Magick2PI*gamma*gamma);
for (width=5; ; )
{
normalize=0.0;
j=(ssize_t) width/2;
for (v=(-j); v <= j; v++)
for (u=(-j); u <= j; u++)
normalize+=exp(-((double) (u*u+v*v))*alpha)*beta;
value=exp(-((double) (j*j))*alpha)*beta/normalize;
if ((value < QuantumScale) || (value < MagickEpsilon))
break;
width+=2;
}
return((size_t) (width-2));
}
/*
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %
% %
% %
% R e a d P A N G O I m a g e %
% %
% %
% %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% ReadPANGOImage() reads an image in the Pango Markup Language Format.
%
% The format of the ReadPANGOImage method is:
%
% Image *ReadPANGOImage(const ImageInfo *image_info,
% ExceptionInfo *exception)
%
% A description of each parameter follows:
%
% o image_info: the image info.
%
% o exception: return any errors or warnings in this structure.
%
*/
static Image *ReadPANGOImage(const ImageInfo *image_info,
ExceptionInfo *exception)
{
cairo_font_options_t
*font_options;
cairo_surface_t
*surface;
char
*caption,
*property;
cairo_t
*cairo_image;
const char
*option;
DrawInfo
*draw_info;
Image
*image;
MagickBooleanType
status;
PangoAlignment
align;
PangoContext
*context;
PangoFontMap
*fontmap;
PangoGravity
gravity;
PangoLayout
*layout;
PangoRectangle
extent;
PixelPacket
fill_color;
RectangleInfo
page;
register unsigned char
*p;
size_t
stride;
ssize_t
y;
unsigned char
*pixels;
/*
Initialize Image structure.
*/
assert(image_info != (const ImageInfo *) NULL);
assert(image_info->signature == MagickSignature);
if (image_info->debug != MagickFalse)
(void) LogMagickEvent(TraceEvent,GetMagickModule(),"%s",
image_info->filename);
assert(exception != (ExceptionInfo *) NULL);
assert(exception->signature == MagickSignature);
image=AcquireImage(image_info);
(void) ResetImagePage(image,"0x0+0+0");
/*
Format caption.
*/
option=GetImageOption(image_info,"filename");
if (option == (const char *) NULL)
property=InterpretImageProperties(image_info,image,image_info->filename);
else
if (LocaleNCompare(option,"pango:",6) == 0)
property=InterpretImageProperties(image_info,image,option+6);
else
property=InterpretImageProperties(image_info,image,option);
(void) SetImageProperty(image,"caption",property);
property=DestroyString(property);
caption=ConstantString(GetImageProperty(image,"caption"));
/*
Get context.
*/
fontmap=pango_cairo_font_map_new();
pango_cairo_font_map_set_resolution(PANGO_CAIRO_FONT_MAP(fontmap),
image->x_resolution);
font_options=cairo_font_options_create();
option=GetImageOption(image_info,"pango:hinting");
if (option != (const char *) NULL)
{
if (LocaleCompare(option,"none") != 0)
cairo_font_options_set_hint_style(font_options,CAIRO_HINT_STYLE_NONE);
if (LocaleCompare(option,"full") != 0)
cairo_font_options_set_hint_style(font_options,CAIRO_HINT_STYLE_FULL);
}
context=pango_font_map_create_context(fontmap);
pango_cairo_context_set_font_options(context,font_options);
cairo_font_options_destroy(font_options);
option=GetImageOption(image_info,"pango:language");
if (option != (const char *) NULL)
pango_context_set_language(context,pango_language_from_string(option));
draw_info=CloneDrawInfo(image_info,(DrawInfo *) NULL);
pango_context_set_base_dir(context,draw_info->direction ==
RightToLeftDirection ? PANGO_DIRECTION_RTL : PANGO_DIRECTION_LTR);
switch (draw_info->gravity)
{
case NorthGravity:
{
gravity=PANGO_GRAVITY_NORTH;
break;
}
case NorthWestGravity:
case WestGravity:
case SouthWestGravity:
{
gravity=PANGO_GRAVITY_WEST;
break;
}
case NorthEastGravity:
case EastGravity:
case SouthEastGravity:
{
gravity=PANGO_GRAVITY_EAST;
break;
}
case SouthGravity:
{
gravity=PANGO_GRAVITY_SOUTH;
break;
}
default:
{
gravity=PANGO_GRAVITY_AUTO;
break;
}
}
pango_context_set_base_gravity(context,gravity);
option=GetImageOption(image_info,"pango:gravity-hint");
if (option != (const char *) NULL)
{
if (LocaleCompare(option,"line") == 0)
pango_context_set_gravity_hint(context,PANGO_GRAVITY_HINT_LINE);
if (LocaleCompare(option,"natural") == 0)
pango_context_set_gravity_hint(context,PANGO_GRAVITY_HINT_NATURAL);
if (LocaleCompare(option,"strong") == 0)
pango_context_set_gravity_hint(context,PANGO_GRAVITY_HINT_STRONG);
}
/*
Configure layout.
*/
layout=pango_layout_new(context);
option=GetImageOption(image_info,"pango:auto-dir");
if (option != (const char *) NULL)
pango_layout_set_auto_dir(layout,1);
option=GetImageOption(image_info,"pango:ellipsize");
if (option != (const char *) NULL)
{
if (LocaleCompare(option,"end") == 0)
pango_layout_set_ellipsize(layout,PANGO_ELLIPSIZE_END);
if (LocaleCompare(option,"middle") == 0)
pango_layout_set_ellipsize(layout,PANGO_ELLIPSIZE_MIDDLE);
if (LocaleCompare(option,"none") == 0)
pango_layout_set_ellipsize(layout,PANGO_ELLIPSIZE_NONE);
if (LocaleCompare(option,"start") == 0)
pango_layout_set_ellipsize(layout,PANGO_ELLIPSIZE_START);
}
option=GetImageOption(image_info,"pango:justify");
if ((option != (const char *) NULL) && (IsMagickTrue(option) != MagickFalse))
pango_layout_set_justify(layout,1);
option=GetImageOption(image_info,"pango:single-paragraph");
if ((option != (const char *) NULL) && (IsMagickTrue(option) != MagickFalse))
pango_layout_set_single_paragraph_mode(layout,1);
option=GetImageOption(image_info,"pango:wrap");
if (option != (const char *) NULL)
{
if (LocaleCompare(option,"char") == 0)
pango_layout_set_wrap(layout,PANGO_WRAP_CHAR);
if (LocaleCompare(option,"word") == 0)
pango_layout_set_wrap(layout,PANGO_WRAP_WORD);
if (LocaleCompare(option,"word-char") == 0)
pango_layout_set_wrap(layout,PANGO_WRAP_WORD_CHAR);
}
option=GetImageOption(image_info,"pango:indent");
if (option != (const char *) NULL)
pango_layout_set_indent(layout,(int) ((StringToLong(option)*
image->x_resolution*PANGO_SCALE+36)/72.0+0.5));
switch (draw_info->align)
{
case CenterAlign: align=PANGO_ALIGN_CENTER; break;
case RightAlign: align=PANGO_ALIGN_RIGHT; break;
case LeftAlign: align=PANGO_ALIGN_LEFT; break;
default:
{
if (draw_info->gravity == CenterGravity)
{
align=PANGO_ALIGN_CENTER;
break;
}
align=PANGO_ALIGN_LEFT;
break;
}
}
if ((align != PANGO_ALIGN_CENTER) &&
(draw_info->direction == RightToLeftDirection))
align=(PangoAlignment) (PANGO_ALIGN_LEFT+PANGO_ALIGN_RIGHT-align);
pango_layout_set_alignment(layout,align);
if (draw_info->font != (char *) NULL)
{
PangoFontDescription
*description;
/*
Set font.
*/
description=pango_font_description_from_string(draw_info->font);
pango_font_description_set_size(description,(int) (PANGO_SCALE*
draw_info->pointsize+0.5));
pango_layout_set_font_description(layout,description);
pango_font_description_free(description);
}
option=GetImageOption(image_info,"pango:markup");
if ((option != (const char *) NULL) && (IsMagickTrue(option) == MagickFalse))
pango_layout_set_text(layout,caption,-1);
else
{
GError
*error;
error=(GError *) NULL;
if (pango_parse_markup(caption,-1,0,NULL,NULL,NULL,&error) == 0)
(void) ThrowMagickException(exception,GetMagickModule(),CoderError,
error->message,"`%s'",image_info->filename);
pango_layout_set_markup(layout,caption,-1);
}
pango_layout_context_changed(layout);
page.x=0;
page.y=0;
if (image_info->page != (char *) NULL)
(void) ParseAbsoluteGeometry(image_info->page,&page);
if (image->columns == 0)
{
pango_layout_get_pixel_extents(layout,NULL,&extent);
image->columns=extent.x+extent.width+2*page.x;
}
else
{
image->columns-=2*page.x;
pango_layout_set_width(layout,(int) ((PANGO_SCALE*image->columns*
image->x_resolution+36.0)/72.0+0.5));
}
if (image->rows == 0)
{
pango_layout_get_pixel_extents(layout,NULL,&extent);
image->rows=extent.y+extent.height+2*page.y;
}
else
{
image->rows-=2*page.y;
pango_layout_set_height(layout,(int) ((PANGO_SCALE*image->rows*
image->y_resolution+36.0)/72.0+0.5));
}
/*
Render markup.
*/
stride=(size_t) cairo_format_stride_for_width(CAIRO_FORMAT_ARGB32,
image->columns);
pixels=(unsigned char *) AcquireQuantumMemory(image->rows,stride*
sizeof(*pixels));
if (pixels == (unsigned char *) NULL)
{
draw_info=DestroyDrawInfo(draw_info);
caption=DestroyString(caption);
ThrowReaderException(ResourceLimitError,"MemoryAllocationFailed");
}
surface=cairo_image_surface_create_for_data(pixels,CAIRO_FORMAT_ARGB32,
image->columns,image->rows,stride);
cairo_image=cairo_create(surface);
cairo_set_operator(cairo_image,CAIRO_OPERATOR_CLEAR);
cairo_paint(cairo_image);
cairo_set_operator(cairo_image,CAIRO_OPERATOR_OVER);
cairo_translate(cairo_image,page.x,page.y);
pango_cairo_show_layout(cairo_image,layout);
cairo_destroy(cairo_image);
cairo_surface_destroy(surface);
g_object_unref(layout);
g_object_unref(fontmap);
/*
Convert surface to image.
*/
(void) SetImageBackgroundColor(image);
p=pixels;
for (y=0; y < (ssize_t) image->rows; y++)
{
register PixelPacket
*q;
register ssize_t
x;
q=GetAuthenticPixels(image,0,y,image->columns,1,exception);
if (q == (PixelPacket *) NULL)
break;
for (x=0; x < (ssize_t) image->columns; x++)
{
double
gamma;
fill_color.blue=ScaleCharToQuantum(*p++);
fill_color.green=ScaleCharToQuantum(*p++);
fill_color.red=ScaleCharToQuantum(*p++);
fill_color.opacity=QuantumRange-ScaleCharToQuantum(*p++);
/*
Disassociate alpha.
*/
gamma=1.0-QuantumScale*fill_color.opacity;
gamma=MagickEpsilonReciprocal(gamma);
fill_color.blue*=gamma;
fill_color.green*=gamma;
fill_color.red*=gamma;
MagickCompositeOver(&fill_color,fill_color.opacity,q,(MagickRealType)
q->opacity,q);
q++;
}
if (SyncAuthenticPixels(image,exception) == MagickFalse)
break;
if (image->previous == (Image *) NULL)
{
status=SetImageProgress(image,LoadImageTag,(MagickOffsetType) y,
image->rows);
if (status == MagickFalse)
break;
}
}
/*
Relinquish resources.
*/
pixels=(unsigned char *) RelinquishMagickMemory(pixels);
draw_info=DestroyDrawInfo(draw_info);
caption=DestroyString(caption);
return(GetFirstImageInList(image));
}
/*
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %
% %
% %
% S e t I m a g e A l p h a C h a n n e l %
% %
% %
% %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% SetImageAlphaChannel() activates, deactivates, resets, or sets the alpha
% channel.
%
% The format of the SetImageAlphaChannel method is:
%
% MagickBooleanType SetImageAlphaChannel(Image *image,
% const AlphaChannelType alpha_type)
%
% A description of each parameter follows:
%
% o image: the image.
%
% o alpha_type: The alpha channel type: ActivateAlphaChannel,
% CopyAlphaChannel, DeactivateAlphaChannel, ExtractAlphaChannel,
% OpaqueAlphaChannel, ResetAlphaChannel, SetAlphaChannel,
% ShapeAlphaChannel, and TransparentAlphaChannel.
%
*/
MagickExport MagickBooleanType SetImageAlphaChannel(Image *image,
const AlphaChannelType alpha_type)
{
MagickBooleanType
status;
assert(image != (Image *) NULL);
if (image->debug != MagickFalse)
(void) LogMagickEvent(TraceEvent,GetMagickModule(),"...");
assert(image->signature == MagickSignature);
status=MagickTrue;
switch (alpha_type)
{
case ActivateAlphaChannel:
{
image->matte=MagickTrue;
break;
}
case BackgroundAlphaChannel:
{
CacheView
*image_view;
ExceptionInfo
*exception;
IndexPacket
index;
MagickBooleanType
status;
MagickPixelPacket
background;
PixelPacket
pixel;
ssize_t
y;
/*
Set transparent pixels to background color.
*/
if (image->matte == MagickFalse)
break;
if (SetImageStorageClass(image,DirectClass) == MagickFalse)
break;
GetMagickPixelPacket(image,&background);
SetMagickPixelPacket(image,&image->background_color,(const IndexPacket *)
NULL,&background);
if (image->colorspace == CMYKColorspace)
ConvertRGBToCMYK(&background);
index=0;
SetPixelPacket(image,&background,&pixel,&index);
status=MagickTrue;
exception=(&image->exception);
image_view=AcquireAuthenticCacheView(image,exception);
#if defined(MAGICKCORE_OPENMP_SUPPORT)
#pragma omp parallel for schedule(static,4) shared(status) \
dynamic_number_threads(image,image->columns,image->rows,1)
#endif
for (y=0; y < (ssize_t) image->rows; y++)
{
register IndexPacket
*restrict indexes;
register PixelPacket
*restrict q;
register ssize_t
x;
if (status == MagickFalse)
continue;
q=GetCacheViewAuthenticPixels(image_view,0,y,image->columns,1,
exception);
if (q == (PixelPacket *) NULL)
{
status=MagickFalse;
continue;
}
for (x=0; x < (ssize_t) image->columns; x++)
{
if (q->opacity == TransparentOpacity)
{
SetPixelRed(q,pixel.red);
SetPixelGreen(q,pixel.green);
SetPixelBlue(q,pixel.blue);
}
q++;
}
if (image->colorspace == CMYKColorspace)
{
indexes=GetCacheViewAuthenticIndexQueue(image_view);
for (x=0; x < (ssize_t) image->columns; x++)
SetPixelIndex(indexes+x,index);
}
if (SyncCacheViewAuthenticPixels(image_view,exception) == MagickFalse)
status=MagickFalse;
}
image_view=DestroyCacheView(image_view);
return(status);
}
case CopyAlphaChannel:
case ShapeAlphaChannel:
{
/*
Special usage case for SeparateImageChannel(): copy grayscale color to
the alpha channel.
*/
status=SeparateImageChannel(image,GrayChannels);
image->matte=MagickTrue; /* make sure transparency is now on! */
if (alpha_type == ShapeAlphaChannel)
{
MagickPixelPacket
background;
/*
Reset all color channels to background color.
*/
GetMagickPixelPacket(image,&background);
SetMagickPixelPacket(image,&(image->background_color),(IndexPacket *)
NULL,&background);
(void) LevelColorsImage(image,&background,&background,MagickTrue);
}
break;
}
case DeactivateAlphaChannel:
{
image->matte=MagickFalse;
break;
}
case ExtractAlphaChannel:
{
status=SeparateImageChannel(image,TrueAlphaChannel);
image->matte=MagickFalse;
break;
}
case RemoveAlphaChannel:
case FlattenAlphaChannel:
{
CacheView
*image_view;
ExceptionInfo
*exception;
IndexPacket
index;
MagickBooleanType
status;
MagickPixelPacket
background;
PixelPacket
pixel;
ssize_t
y;
/*
Flatten image pixels over the background pixels.
*/
if (image->matte == MagickFalse)
break;
if (SetImageStorageClass(image,DirectClass) == MagickFalse)
break;
GetMagickPixelPacket(image,&background);
SetMagickPixelPacket(image,&image->background_color,(const IndexPacket *)
NULL,&background);
if (image->colorspace == CMYKColorspace)
ConvertRGBToCMYK(&background);
index=0;
SetPixelPacket(image,&background,&pixel,&index);
status=MagickTrue;
exception=(&image->exception);
image_view=AcquireAuthenticCacheView(image,exception);
#if defined(MAGICKCORE_OPENMP_SUPPORT)
#pragma omp parallel for schedule(static,4) shared(status) \
dynamic_number_threads(image,image->columns,image->rows,1)
#endif
for (y=0; y < (ssize_t) image->rows; y++)
{
register IndexPacket
*restrict indexes;
register PixelPacket
*restrict q;
register ssize_t
x;
if (status == MagickFalse)
continue;
q=GetCacheViewAuthenticPixels(image_view,0,y,image->columns,1,
exception);
if (q == (PixelPacket *) NULL)
{
status=MagickFalse;
continue;
}
for (x=0; x < (ssize_t) image->columns; x++)
{
MagickRealType
gamma,
opacity;
gamma=1.0-QuantumScale*QuantumScale*q->opacity*pixel.opacity;
opacity=(MagickRealType) QuantumRange*(1.0-gamma);
gamma=MagickEpsilonReciprocal(gamma);
q->red=ClampToQuantum(gamma*MagickOver_((MagickRealType) q->red,
(MagickRealType) q->opacity,(MagickRealType) pixel.red,
(MagickRealType) pixel.opacity));
q->green=ClampToQuantum(gamma*MagickOver_((MagickRealType) q->green,
(MagickRealType) q->opacity,(MagickRealType) pixel.green,
(MagickRealType) pixel.opacity));
q->blue=ClampToQuantum(gamma*MagickOver_((MagickRealType) q->blue,
(MagickRealType) q->opacity,(MagickRealType) pixel.blue,
(MagickRealType) pixel.opacity));
q->opacity=ClampToQuantum(opacity);
q++;
}
if (image->colorspace == CMYKColorspace)
{
indexes=GetCacheViewAuthenticIndexQueue(image_view);
for (x=0; x < (ssize_t) image->columns; x++)
SetPixelIndex(indexes+x,index);
}
if (SyncCacheViewAuthenticPixels(image_view,exception) == MagickFalse)
status=MagickFalse;
}
image_view=DestroyCacheView(image_view);
return(status);
}
case ResetAlphaChannel: /* deprecated */
case OpaqueAlphaChannel:
{
status=SetImageOpacity(image,OpaqueOpacity);
break;
}
case SetAlphaChannel:
{
if (image->matte == MagickFalse)
status=SetImageOpacity(image,OpaqueOpacity);
break;
}
case TransparentAlphaChannel:
{
status=SetImageOpacity(image,TransparentOpacity);
break;
}
case UndefinedAlphaChannel:
break;
}
if (status == MagickFalse)
return(status);
return(SyncImagePixelCache(image,&image->exception));
}
/*
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %
% %
% %
% G a u s s J o r d a n E l i m i n a t i o n %
% %
% %
% %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% GaussJordanElimination() returns a matrix in reduced row echelon form,
% while simultaneously reducing and thus solving the augumented results
% matrix.
%
% See also http://en.wikipedia.org/wiki/Gauss-Jordan_elimination
%
% The format of the GaussJordanElimination method is:
%
% MagickBooleanType GaussJordanElimination(double **matrix,
% double **vectors,const size_t rank,const size_t number_vectors)
%
% A description of each parameter follows:
%
% o matrix: the matrix to be reduced, as an 'array of row pointers'.
%
% o vectors: the additional matrix argumenting the matrix for row reduction.
% Producing an 'array of column vectors'.
%
% o rank: The size of the square matrix (both rows and columns).
% Also represents the number terms that need to be solved.
%
% o number_vectors: Number of vectors columns, argumenting the above matrix.
% Usally 1, but can be more for more complex equation solving.
%
% Note that the 'matrix' is given as a 'array of row pointers' of rank size.
% That is values can be assigned as matrix[row][column] where 'row' is
% typically the equation, and 'column' is the term of the equation.
% That is the matrix is in the form of a 'row first array'.
%
% However 'vectors' is a 'array of column pointers' which can have any number
% of columns, with each column array the same 'rank' size as 'matrix'.
% It is assigned vector[column][row] where 'column' is the specific
% 'result' and 'row' is the 'values' for that answer. After processing
% the same vector array contains the 'weights' (answers) for each of the
% 'separatable' results.
%
% This allows for simpler handling of the results, especially is only one
% column 'vector' is all that is required to produce the desired solution
% for that specific set of equations.
%
% For example, the 'vectors' can consist of a pointer to a simple array of
% doubles. when only one set of simultanious equations is to be solved from
% the given set of coefficient weighted terms.
%
% double **matrix = AcquireMagickMatrix(8UL,8UL);
% double coefficents[8];
% ...
% GaussJordanElimination(matrix, &coefficents, 8UL, 1UL);
%
% However by specifing more 'columns' (as an 'array of vector columns'),
% you can use this function to solve multiple sets of 'separable' equations.
%
% For example a distortion function where u = U(x,y) v = V(x,y)
% And the functions U() and V() have separate coefficents, but are being
% generated from a common x,y->u,v data set.
%
% Another example is generation of a color gradient from a set of colors
% at specific coordients, such as a list x,y -> r,g,b,a
%
% See LeastSquaresAddTerms() below for such an example.
%
% You can also use the 'vectors' to generate an inverse of the given 'matrix'
% though as a 'column first array' rather than a 'row first array' (matrix
% is transposed).
%
% For details of this process see...
% http://en.wikipedia.org/wiki/Gauss-Jordan_elimination
%
*/
MagickPrivate MagickBooleanType GaussJordanElimination(double **matrix,
double **vectors,const size_t rank,const size_t number_vectors)
{
#define GaussJordanSwap(x,y) \
{ \
if ((x) != (y)) \
{ \
(x)+=(y); \
(y)=(x)-(y); \
(x)=(x)-(y); \
} \
}
double
max,
scale;
register ssize_t
i,
j,
k;
ssize_t
column,
*columns,
*pivots,
row,
*rows;
columns=(ssize_t *) AcquireQuantumMemory(rank,sizeof(*columns));
rows=(ssize_t *) AcquireQuantumMemory(rank,sizeof(*rows));
pivots=(ssize_t *) AcquireQuantumMemory(rank,sizeof(*pivots));
if ((rows == (ssize_t *) NULL) || (columns == (ssize_t *) NULL) ||
(pivots == (ssize_t *) NULL))
{
if (pivots != (ssize_t *) NULL)
pivots=(ssize_t *) RelinquishMagickMemory(pivots);
if (columns != (ssize_t *) NULL)
columns=(ssize_t *) RelinquishMagickMemory(columns);
if (rows != (ssize_t *) NULL)
rows=(ssize_t *) RelinquishMagickMemory(rows);
return(MagickFalse);
}
(void) ResetMagickMemory(columns,0,rank*sizeof(*columns));
(void) ResetMagickMemory(rows,0,rank*sizeof(*rows));
(void) ResetMagickMemory(pivots,0,rank*sizeof(*pivots));
column=0;
row=0;
for (i=0; i < (ssize_t) rank; i++)
{
max=0.0;
for (j=0; j < (ssize_t) rank; j++)
if (pivots[j] != 1)
{
for (k=0; k < (ssize_t) rank; k++)
if (pivots[k] != 0)
{
if (pivots[k] > 1)
return(MagickFalse);
}
else
if (fabs(matrix[j][k]) >= max)
{
max=fabs(matrix[j][k]);
row=j;
column=k;
}
}
pivots[column]++;
if (row != column)
{
for (k=0; k < (ssize_t) rank; k++)
GaussJordanSwap(matrix[row][k],matrix[column][k]);
for (k=0; k < (ssize_t) number_vectors; k++)
GaussJordanSwap(vectors[k][row],vectors[k][column]);
}
rows[i]=row;
columns[i]=column;
if (matrix[column][column] == 0.0)
return(MagickFalse); /* singularity */
scale=MagickEpsilonReciprocal(matrix[column][column]);
matrix[column][column]=1.0;
for (j=0; j < (ssize_t) rank; j++)
matrix[column][j]*=scale;
for (j=0; j < (ssize_t) number_vectors; j++)
vectors[j][column]*=scale;
for (j=0; j < (ssize_t) rank; j++)
if (j != column)
{
scale=matrix[j][column];
matrix[j][column]=0.0;
for (k=0; k < (ssize_t) rank; k++)
matrix[j][k]-=scale*matrix[column][k];
for (k=0; k < (ssize_t) number_vectors; k++)
vectors[k][j]-=scale*vectors[k][column];
}
}
for (j=(ssize_t) rank-1; j >= 0; j--)
if (columns[j] != rows[j])
for (i=0; i < (ssize_t) rank; i++)
GaussJordanSwap(matrix[i][rows[j]],matrix[i][columns[j]]);
pivots=(ssize_t *) RelinquishMagickMemory(pivots);
rows=(ssize_t *) RelinquishMagickMemory(rows);
columns=(ssize_t *) RelinquishMagickMemory(columns);
return(MagickTrue);
}
