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Hollow isosceles triangle # Console

There are a lot of examples to create a triangle in C#
but now i need a hollow one here fore there are a lot of examples in C or C++ but i need one in C# console , can some body give me a few examples
*
* * *
* * * *
* * * * *
* * * * * *
int i, j;
for (i = 0; i < 5; i++)
{
for (j = 5 - i; j > 0; j--)
Console.Write(" ");
for (j = 0; j <= 2 * i; j++)
Console.Write("*");
Console.WriteLine();
}
*
* *
* *
* *
* * * * * *

This Works...But if the value is greater than that s printable on a single line it breaks into next line. The maximum possible value without line break is 40. Till 40 it works well and good in my system. For larger values you have to increase the width of command prompt. It can be done using commands or by changing the width in properties of command prompt.
int i, j,n=5;
for (i = 0; i < n; i++)
{
for (j = n - i; j > 0; j--)
Console.Write(" ");
for (j = 0; j <= 2 * i; j++)
{
if (j < 2 * i && j > 0&&i!=(n-1))
Console.Write(" ");
else
Console.Write("*");
}
Console.WriteLine();
}

Try this:
void Main()
{
Int32 totalLines = 9;
for (Int32 i = 0; i <= totalLines; ++i)
Console.WriteLine(Line(i, totalLines));
}
String Line(Int32 i, Int32 totalLines)
{
Int32 charCount = 2 * totalLines + 1;
Int32 center = charCount / 2;
// Last line is filled completely
if (i == totalLines) return new String(Enumerable.Repeat('*', charCount).ToArray());
Char[] chars = Enumerable.Repeat(' ', charCount).ToArray();
chars[center-i] = '*';
chars[center+i] = '*';
return new String(chars);
}
This will only work with monospace fonts.

Sobel image processing

My algorithm output is wrong. I tried many solutions, but nothing comes out.
View my result.
SourceImage
I'm sorry Lena
for (int x = 1; x < fimage.Bitmap.Width - 1; x++)
{
for (int y = 1; y < fimage.Bitmap.Height - 1; y++)
{
double sumX = 0, sumY = 0, sum = 0;
for ( int i = -1; i <= 1; i++ )
{
for ( int j = -1; j <= 1; j++ )
{
sumX += fimage[y + i, x + j].R * kernel1[i + 1, j + 1];
sumY += fimage[y + i, x + j].R * kernel2[i + 1, j + 1];
}
}
sum = Math.Sqrt(sumX * sumX + sumY * sumY);
sum = sum > 255 ? 255 : sum < 0 ? 0 : sum;
fimage[x, y] = Color.FromArgb((byte)sum, (byte)sum, (byte)sum);
}
}

Two things that are fishy:
for ( int j = -1; j <= 1; j++ )
{
sumX += fimage[y + i, x + j].R * kernel1[i + 1, j + 1];
sumY += fimage[y + i, x + j].R * kernel2[i + 1, j + 1];
}
You only respect the red component of the image here, why is that?
The other major thing is changing the input picture while iterating through it:
sum = Math.Sqrt(sumX * sumX + sumY * sumY);
sum = sum > 255 ? 255 : sum < 0 ? 0 : sum;
fimage[x, y] = Color.FromArgb((byte)sum, (byte)sum, (byte)sum);
You should save the value to a different output image (create a new Bitmap(fimage.Width, fimage.Height) with the dimensions from the source image). That could explain the weird diagonal symmetry in your picture, where there's basically a symteric copy of the other side.

GammaLn NameSpace In C#

I purchased the book Numerical Methods, Algorithms and Tools in C# by Waldemar Dos Passos.
On page 463, there is the method:
public static double FactorialLn(int n)
{
if(n < 0)
{
throw new Exception("Input value must be > 0");
}
else
{
return GammaLn(n+1.0);
}
}
I found the namespace where the function GammaLn resides: MicrosoftResearch.Infer.Maths
but Visual Studio 2010 does not recognize it and I was unable to find it in the .NET reference.
Please help me get the program to compile.
Thank you in advance.
I finally found the dource code of the GammaLn method itself here: http://seungwon.tistory.com/9
One does need nothing else when one possesses the very real thing, as Andrey correctly pointed out, but until then ...
I reproduce the method here for future reference, in case the site above stops from functioning.
/// <summary>
/// http://seungwon.tistory.com/9
/// GammaLn函数
/// </summary>
/// <param name="x"></param>
/// <returns></returns>
public static double GammaLn(double x)
{
double result = 0.0;
double d1 = -5.772156649015328605195174e-1;
double[,] p1 = {{4.945235359296727046734888e0},{ 2.018112620856775083915565e2},
{2.290838373831346393026739e3},{ 1.131967205903380828685045e4},
{2.855724635671635335736389e4},{ 3.848496228443793359990269e4},
{2.637748787624195437963534e4},{ 7.225813979700288197698961e3}};
double[,] q1 = {{6.748212550303777196073036e1},{ 1.113332393857199323513008e3},
{7.738757056935398733233834e3},{ 2.763987074403340708898585e4},
{5.499310206226157329794414e4},{ 6.161122180066002127833352e4},
{3.635127591501940507276287e4},{ 8.785536302431013170870835e3}};
double d2 = 4.227843350984671393993777e-1;
double[,] p2 = {{4.974607845568932035012064e0},{ 5.424138599891070494101986e2},
{1.550693864978364947665077e4},{ 1.847932904445632425417223e5},
{1.088204769468828767498470e6},{ 3.338152967987029735917223e6},
{5.106661678927352456275255e6},{ 3.074109054850539556250927e6}};
double[,] q2 = {{1.830328399370592604055942e2},{ 7.765049321445005871323047e3},
{1.331903827966074194402448e5},{ 1.136705821321969608938755e6},
{5.267964117437946917577538e6},{ 1.346701454311101692290052e7},
{1.782736530353274213975932e7},{ 9.533095591844353613395747e6}};
double d4 = 1.791759469228055000094023e0;
double[,] p4 = {{1.474502166059939948905062e4},{ 2.426813369486704502836312e6},
{1.214755574045093227939592e8},{ 2.663432449630976949898078e9},
{2.940378956634553899906876e10},{ 1.702665737765398868392998e11},
{4.926125793377430887588120e11},{5.606251856223951465078242e11}};
double[,] q4 = {{2.690530175870899333379843e3},{ 6.393885654300092398984238e5},
{4.135599930241388052042842e7},{ 1.120872109616147941376570e9},
{1.488613728678813811542398e10},{1.016803586272438228077304e11},
{3.417476345507377132798597e11},{ 4.463158187419713286462081e11}};
double[,] c = {{-1.910444077728e-03},{ 8.4171387781295e-04},
{-5.952379913043012e-04},{ 7.93650793500350248e-04},
{-2.777777777777681622553e-03},{ 8.333333333333333331554247e-02},
{ 5.7083835261e-03}};
double eps = 2.2204e-016;
if (x <= 0)
{
//报错！
}
else
{
double xden = 0.0;
double xnum = 0.0;
result = x;
if (x > 0 && x <= eps)
{
result = -Math.Log(x);
}
else if ((x > eps) && (x <= 0.5))
{
double y = x;
xden = 1;
xnum = 0;
for (int i = 0; i < 8; i++)
{
xnum = xnum * y + p1[i, 0];
xden = xden * y + q1[i, 0];
}
result = -Math.Log(y) + (y * (d1 + y * (xnum / xden)));
}
else if ((x > 0.5) && (x <= 0.6796875))
{
double xm1 = (x - 0.5) - 0.5;
xden = 1;
xnum = 0;
for (int i = 0; i < 8; i++)
{
xnum = xnum * xm1 + p2[i, 0];
xden = xden * xm1 + q2[i, 0];
}
result = -Math.Log(x) + xm1 * (d2 + xm1 * (xnum / xden));
}
else if ((x > 0.6796875) && (x <= 1.5))
{
double xm1 = (x - 0.5) - 0.5;
xden = 1;
xnum = 0;
for (int i = 0; i < 8; i++)
{
xnum = xnum * xm1 + p1[i, 0];
xden = xden * xm1 + q1[i, 0];
}
result = xm1 * (d1 + xm1 * (xnum / xden));
}
else if ((x > 1.5) && (x <= 4))
{
double xm2 = x - 2;
xden = 1;
xnum = 0;
for (int i = 0; i < 8; i++)
{
xnum = xnum * xm2 + p2[i, 0];
xden = xden * xm2 + q2[i, 0];
}
result = xm2 * (d2 + xm2 * (xnum / xden));
}
else if ((x > 4) && (x <= 12))
{
double xm4 = x - 4;
xden = -1;
xnum = 0;
for (int i = 0; i < 8; i++)
{
xnum = xnum * xm4 + p4[i, 0];
xden = xden * xm4 + q4[i, 0];
}
result = d4 + xm4 * (xnum / xden);
}
else if (x > 12)
{
double y = x;
double r = c[6, 0];// 等于：double r = repmat(c[6, 0], 1)[0,0];
double ysq = y * y;
for (int i = 0; i < 6; i++)
{
r = r / ysq + c[i, 0];
}
r = r / y;
double corr = Math.Log(y);
double spi = 0.9189385332046727417803297;
result = r + spi - 0.5 * corr + y * (corr - 1);
}
}
return result;
}

Writing stars with specific shape

i want to write a shape with " * " and " | " the shape is below.
The program must take height and width from user.Width is column number without ' | '.I tried to write but confused.My code sometimes works great and sometimes being stupid.For example when i enter height : 13, width : 4 it writes one more,if witdh is 1 it enters infinite loop.While trying to solve it became too conflicted.Must i fix it or rewrite ? Here is the code : height =10, width = 5
|*____|
|_*___|
|__*__|
|___*_|
|____*|
|___*_|
|__*__|
|_*___|
|*____|
|_*___|
private static void Function()
{
int height, width;
if (width == 2)
while (height > 0)
{
FirstPart(width, height);
height -= width;
}
else
while (height > 0)
{
if (height > 1)
{
FirstPart(width, height);
height -= width;
}
if (height > 0)
{
SecondPart(width, height);
height -= width - 2;
}
}
}
private static void FirstPart(int width,int height)
{
if(height > width)
for (int i = 0; i < width; i++)
{
for (int j = 0; j < width+2; j++)
{
if (j == 0 || j == width + 1)
Console.Write("|");
else
if (i + 1 == j)
Console.Write("*");
else
Console.Write(" ");
}
Console.WriteLine();
}
else
for (int i = 0; i < height; i++)
{
for (int j = 0; j < width + 2; j++)
{
if (j == 0 || j == width + 1)
Console.Write("|");
else
if (i + 1 == j)
Console.Write("*");
else
Console.Write(" ");
}
Console.WriteLine();
}
}
private static void SecondPart(int width,int height)
{
if(height > width)
for (int i = 0; i < width-2; i++)
{
for (int j = 0; j < width+2; j++)
{
if (j == 0 || j == width + 1)
Console.Write("|");
else
if (i + j == width-1)
Console.Write("*");
else
Console.Write(" ");
}
Console.WriteLine();
}
else
for (int i = 0; i < height; i++)
{
for (int j = 0; j < width + 2; j++)
{
if (j == 0 || j == width + 1)
Console.Write("|");
else
if (i + j == width - 1)
Console.Write("*");
else
Console.Write(" ");
}
Console.WriteLine();
}
}

private static void WriteStars(int width, int height)
{
int j = 0;
for (int i = 0; i < height; i++)
{
Console.Write("|");
for (int f = 0; f < width; f++)
{
if (f == Math.Abs(j))
{
Console.Write("*");
}
else
{
Console.Write(" ");
}
}
j++;
if (Math.Abs(j) == width - 1)
{
j *= -1;
}
Console.WriteLine("|");
}
}
Probably going to get downvoted for giving you a complete answer, but maybe it'll show you one correct approach and you can learn something from it...

I see a
while (Height > 0)
so your infinite loop is coming from Height never getting less or equal to 0.

It's better to rewrite. When you do, decouple the code into several functions so that one function draws a single line, and another one calls the former to draw all the lines.

void WriteStars(int Width,int Height)
{
int _sp=1; //Star Pos
bool _left = false;
for(int i =0;i<Height;i++)
{
Console.Write("|");
int j;
for(j=1;j<Width-1;j++)
{
if(j==_sp)
{
Console.Write("*");
if(_left)
{
_sp--;
}
else
{
_sp++;
}
j++;
break;
}
else
{
Console.Write("_");
}
}
for(;j<Width-1;j++)
{
Console.Write("_");
}
Console.WriteLine("|");
if(_sp==0)
{
_left = false;
}
else if(_sp==Width)
{
_left = true;
}
}
}
Try if it works, wrote it right here.

even shorter:
static void Variante_2(int height, int width)
{
byte[][] arr = new byte[height][];
int pos = 0;
int mov = 1;
for (int line = 0; line < height; line++)
{
arr[line] = new byte[width];
for (int col = 0; col < width; col++) { arr[line][col] = 45; }
arr[line][pos] = 42;
pos += mov;
if (pos == 0 || pos == (width - 1)) { mov *= -1; }
Console.WriteLine("|" + ASCIIEncoding.ASCII.GetString(arr[line]) + "|");
}
string temp = Console.ReadLine();
}

and it is possible to do it with less code:
static void Variante_3(int height, int width)
{
int pos = 1;
int mov = 1;
for (int line = 0; line < height; line++)
{
Console.WriteLine("|" + "*".PadLeft(pos, '_') + "|".PadLeft(width - pos, '_'));
pos += mov;
if (pos == 1 || pos == (width - 1)) { mov *= -1; }
}
string temp = Console.ReadLine();
}
Sorry to all not doing others homework, but I couldn´t sleep without showing this g

Calculating an NxN matrix determinant in C#

How do you calculate the determinant of an NxN matrix C# ?

The OP posted another question asking specifically about 4x4 matrices, which has been closed as an exact duplicate of this question. Well, if you're not looking for a general solution but instead are constrained to 4x4 matrices alone, then you can use this ugly looking but tried-and-true code:
public double GetDeterminant() {
var m = _values;
return
m[12] * m[9] * m[6] * m[3] - m[8] * m[13] * m[6] * m[3] -
m[12] * m[5] * m[10] * m[3] + m[4] * m[13] * m[10] * m[3] +
m[8] * m[5] * m[14] * m[3] - m[4] * m[9] * m[14] * m[3] -
m[12] * m[9] * m[2] * m[7] + m[8] * m[13] * m[2] * m[7] +
m[12] * m[1] * m[10] * m[7] - m[0] * m[13] * m[10] * m[7] -
m[8] * m[1] * m[14] * m[7] + m[0] * m[9] * m[14] * m[7] +
m[12] * m[5] * m[2] * m[11] - m[4] * m[13] * m[2] * m[11] -
m[12] * m[1] * m[6] * m[11] + m[0] * m[13] * m[6] * m[11] +
m[4] * m[1] * m[14] * m[11] - m[0] * m[5] * m[14] * m[11] -
m[8] * m[5] * m[2] * m[15] + m[4] * m[9] * m[2] * m[15] +
m[8] * m[1] * m[6] * m[15] - m[0] * m[9] * m[6] * m[15] -
m[4] * m[1] * m[10] * m[15] + m[0] * m[5] * m[10] * m[15];
}
It assumes you store your vector data in a 16-element array called _values (of double in this case, but float would work too), in the following order:
0, 1, 2, 3,
4, 5, 6, 7,
8, 9, 10, 11,
12, 13, 14, 15

Reduce to upper triangular form, then make a nested loop where you multiply all the values at position i == j together. There you have it.

The standard method is LU decomposition. You may want to use a library instead of coding it yourself. I don't know about C#, but the 40-year standard is LAPACK.

This solution is achieved using row operations. I took an identity matrix of the same dimensions as of my target matrix and then converted the target matrix to the identity matrix such that, every operation which is performed on target matrix, must also be performed to the identity matrix. In last, the target matrix will become identity matrix and the identity matrix will hold the inverse of the target matrix.
private static double determinant(double[,] matrix, int size)
{
double[] diviser = new double[size];// this will be used to make 0 all the elements of a row except (i,i)th value.
double[] temp = new double[size]; // this will hold the modified ith row after divided by (i,i)th value.
Boolean flag = false; // this will limit the operation to be performed only when loop n != loop i
double determinant = 1;
if (varifyRowsAndColumns(matrix, size)) // verifies that no rows or columns are similar or multiple of another row or column
for (int i = 0; i < size; i++)
{
int count = 0;
//this will hold the values to be multiplied by temp matrix
double[] multiplier = new double[size - 1];
diviser[i] = matrix[i, i];
//if(i,i)th value is 0, determinant shall be 0
if (diviser[i] == 0)
{
determinant = 0;
break;
}
/*
* whole ith row will be divided by (i,i)th value and result will be stored in temp matrix.
* this will generate 1 at (i,i)th position in temp matrix i.e. ith row of matrix
*/
for (int j = 0; j < size; j++)
{
temp[j] = matrix[i, j] / diviser[i];
}
//setting up multiplier to be used for multiplying the ith row of temp matrix
for (int o = 0; o < size; o++)
if (o != i)
multiplier[count++] = matrix[o, i];
count = 0;
//for creating 0s at every other position than (i,i)th
for (int n = 0; n < size; n++)
{
for (int k = 0; k < size; k++)
{
if (n != i)
{
flag = true;
matrix[n, k] -= (temp[k] * multiplier[count]);
}
}
if (flag)
count++;
flag = false;
}
}
else determinant = 0;
//if determinant is not 0, (i,i)th element will be multiplied and the result will be determinant
if (determinant != 0)
for (int i = 0; i < size; i++)
{
determinant *= matrix[i, i];
}
return determinant;
}
private static Boolean varifyRowsAndColumns(double[,] matrix, int size)
{
List<double[]> rows = new List<double[]>();
List<double[]> columns = new List<double[]>();
for (int j = 0; j < size; j++)
{
double[] temp = new double[size];
for (int k = 0; k < size; k++)
{
temp[j] = matrix[j, k];
}
rows.Add(temp);
}
for (int j = 0; j < size; j++)
{
double[] temp = new double[size];
for (int k = 0; k < size; k++)
{
temp[j] = matrix[k, j];
}
columns.Add(temp);
}
if (!RowsAndColumnsComparison(rows, size))
return false;
if (!RowsAndColumnsComparison(columns, size))
return false;
return true;
}
private static Boolean RowsAndColumnsComparison(List<double[]> rows, int size)
{
int countEquals = 0;
int countMod = 0;
int countMod2 = 0;
for (int i = 0; i < rows.Count; i++)
{
for (int j = 0; j < rows.Count; j++)
{
if (i != j)
{
double min = returnMin(rows.ElementAt(i), rows.ElementAt(j));
double max = returnMax(rows.ElementAt(i), rows.ElementAt(j));
for (int l = 0; l < size; l++)
{
if (rows.ElementAt(i)[l] == rows.ElementAt(j)[l])
countEquals++;
for (int m = (int)min; m <= max; m++)
{
if (rows.ElementAt(i)[l] % m == 0 && rows.ElementAt(j)[l] % m == 0)
countMod++;
if (rows.ElementAt(j)[l] % m == 0 && rows.ElementAt(i)[l] % m == 0)
countMod2++;
}
}
if (countEquals == size)
{
return false;
// one row is equal to another row. determinant is zero
}
if (countMod == size)
{
return false;
}
if (countMod2 == size)
{
return false;
}
}
}
}
return true;
}
private static double returnMin(double[] row1, double[] row2)
{
double min1 = row1[0];
double min2 = row2[0];
for (int i = 1; i < row1.Length; i++)
if (min1 > row1[i])
min1 = row1[i];
for (int i = 1; i < row2.Length; i++)
if (min2 > row2[i])
min2 = row2[i];
if (min1 < min2)
return min1;
else return min2;
}
private static double returnMax(double[] col1, double[] col2)
{
double max1 = col1[0];
double max2 = col2[0];
for (int i = 1; i < col1.Length; i++)
if (max1 < col1[i])
max1 = col1[i];
for (int i = 1; i < col2.Length; i++)
if (max2 < col2[i])
max2 = col2[i];
if (max1 > max2)
return max1;
else return max2;
}