Algo358 Serial Number Full Torrent [Mac/Win]

by trisjaek
Published: June 8, 2022 (3 weeks ago)

Algo358 is a tool that works with the singular value decomposition of a complex matrix in C++ and C#
Implicates the function CSVD in C++ and C#:
void CSVD(complex a[][maxA], int m, int n, int p, int nu, int nv, float *s, complex u[][maxA], complex v[][maxA])
Singular Value Decomposition, a = u * s * Conj(Tran(v)), a is destroyed by CSVD. The diagonal matrix s is output as a vector, m must be >= n, if smaller, a should be filled with zero rows. This code is adapted from Collected Algorithms from ACM, Algorithm 358. The transformation Conj(Tran(u)) is applied to the p vectors given in columns n, n+1, …, n+p-1 of matrix a.

 

 

 

 

 

 

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(See:
Input: A complex matrix [X] m x n whose transpose is stored as [A].
The m-by-n matrix X must have m >= n. (If m Q:

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Singular Value Decomposition, a = u * s * Conj(Tran(v)), a is destroyed by CSVD. The diagonal matrix s is output as a vector, m must be >= n, if smaller, a should be filled with zero rows. This code is adapted from Collected Algorithms from ACM, Algorithm 358. The transformation Conj(Tran(u)) is applied to the p vectors given in columns n, n+1,., n+p-1 of matrix a.
The algorithm first computes the singular values and vectors of input matrix.

[x, s] = SVD(a)

Here, x and s are two arrays of length n+1. The array s is of the same size as the one returned by calling Hestfun(a,u,’p’,u,m) for matrix u.
Matrix u is a part of the block-diagonal matrix. In addition, it is the matrix with

[u, v] = QR(a)

We already found that the singular values of the block-diagonal matrix is given by (this is the result of Algo 358):

u = Diag(s).*Trans(u)

s(n+1:end-1) = Abs(s(n+1:end-1))

and the vectors (this is the result of Algo 358):

v = Trans(u)*s(1:end-1)

The matrix v is rectangular matrix of the same size as u, which means that v has two columns and n rows.
If we apply the transformations

a = Conv(a, w, n)
u = Conv(u, w, m)

The singular values (this is the result of Algo 358):

s = Conv(s, w, n+1)

and the vectors (this is the result of Algo 358)

v = Conv(v, w, m+1)

are the same as those of v, we conclude that this is the case.
The original matrix a remains unchanged.

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Complexity: n^3 log(n)
Maximum singular values and number of right singular vectors are output. These can be used in the computation of the SVD of a second matrix.

The algorithm tries to fit a power series to the function f(z) = z^N (N > 1) and is based on the minimization of the following quantity
[|f(z) – a_0 + a_1 z + cdots + a_N z^N|_2^2]
The optimal polynomial is then given by the formula
[frac{1}{N} a_0 + frac{1}{2! N} a_1 + frac{1}{3! N} a_2 + cdots + frac{1}{N!} a_N]

If a_N = 0, then
[frac{1}{N} a_0 + frac{1}{2! N} a_1 + cdots + frac{1}{N!} a_{N-1} = 0]
This implies
[a_1 + cdots + a_{N-1} = 0]
and the polynomial becomes
[f(z) = a_0 + frac{1}{2!} a_1 z + cdots + frac{1}{N!} a_N z^N]

This polynomial is very accurate for all z, but one must take care of the following cautions. First, the convergence radius of the series is 1, meaning that the coefficients of the power series must be positive and can never be negative. Second, the coefficients of the power series are no longer real because they are complex and an extra imaginary factor is introduced into the first term of the series. This causes some problems in the computation of the power series coefficients, in particular, they tend to be large in magnitude.

This algorithm works with the singular value decomposition of an NxN matrix a, input as complex numbers (the default). The algorithm takes the matrix as a single array and returns an NxN diagonal matrix as well as the top k singular vectors of a.

Complexity

Some examples

The following code prints the matrices U and V such that the singular value decomposition of M:

What’s New in the Algo358?

Singular value decomposition is a fundamental tool in data analysis and statistics. The decomposition is the equivalent of the eigenvector and eigenvalue decomposition of a square matrix with real or complex entries. It is used to compute the best “fit” linear transformations, often as a heuristic to solve a linear system of equations that has an ill-conditioned matrix. Singular value decomposition is also used in applications such as compression, k-means clustering, and data mining.
The Singular value decomposition of a square matrix a (of size m x m) is defined as follows: a = U D V, where a is a rectangular matrix, U is a m x m unitary matrix, V is a m x m unitary matrix, and D is a diagonal matrix with non-negative real entries on the diagonal. The diagonal elements of the diagonal matrix D are the “singular values” of the matrix a. If a = U * D * V’, then the matrix U is a left unitary matrix and V is a right unitary matrix.
The singular values of a matrix are closely related to the eigenvalues of the matrix’s cofactor matrix, which is a matrix obtained by multiplying the transpose of the original matrix by its inverse. The product of the singular values is the sum of the eigenvalues of the cofactor matrix.
The Singular value decomposition of a rectangular matrix can be represented by the following pseudocode:
U
for i from 1 to n do
for j from i+1 to m do
a[i,j] = 0
a[i,j] = 1
end for
for j from 1 to p do
a[i,j] = 0
end for
end for
D
for j from 1 to n do
D[j,j] = sqrt(a[j,j])
end for
end for
V
for i from 1 to m do
for j from 1 to n do
a[i,j] = 0
end for
a[i,j] = 1
end for
end for
end for
There are a number of possible algorithms for obtaining a factorization of a matrix, but most of these algorithms have complexity O(n3) and are very slow. See the survey by Martin [1] and the references in that paper.
The algorithm given here has complexity O(n3) (O

System Requirements For Algo358:

As always, we recommend testing on your local machine before installing on a server, but for non-trivial installations, we require the following equipment.
GPU: Geforce GTX 970
CPU: Intel® Core i7 2600K
RAM: 16GB
Disk Space: 12GB
CGI-BIN environment variable must be set for PHP 5.4:
If your cgi-bin folder is outside of the /var/www/html/ directory then you will need to change the $PHP_CGI

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