QR decomposition: Difference between revisions

 

=={{header|Rascal}}==

This function applies the Gram Schmidt algorithm. Q is printed in the console, R can be printed or visualized.

 

public rel[real, real, real] matrixTranspose(rel[real x, real y, real v] matrix){

return {<y, x, v> | <x, y, v> <- matrix};

 

//a function to normalize an element of a matrix by the normalization of a column

normalized = 1.0/nroot((0.0 | it + v*v | <x,y,v> <- column), 2);

return matrixMultiplybyN(element, normalized);

 

//a function that takes the dot product, see also Rosetta Code problem "Dot product"

public real matrixDotproduct(rel[real x, real y, real v] column1, rel[real x, real y, real v] column2){

return (0.0 | it + v1*v2 | <x1,y1,v1> <- column1, <x2,y2,v2> <- column2, y1==y2);

 

//a function to subtract two columns

public rel[real,real,real] matrixSubtract(rel[real x, real y, real v] column1, rel[real x, real y, real v] column2){

return {<x1,y1,v1-v2> | <x1,y1,v1> <- column1, <x2,y2,v2> <- column2, y1==y2};

 

//a function to multiply a column by a number

public rel[real,real,real] matrixMultiplybyN(rel[real x, real y, real v] column, real n){

return {<x,y,v*n> | <x,y,v> <- column};

 

//a function to perform matrix multiplication, see also Rosetta Code problem "Matrix multiplication".

points = [box(text("<v>"), align(0.3333*(x+1),0.3333*(y+1)),shrink(0.25)) | <x,y,v> <- matrix];

render(overlay([*points], aspectRatio(1.0)));

 

//a matrix, given by a relation of <x-coordinate, y-coordinate, value>.

}

See R in picture</pre>

 

=={{header|Tcl}}==