算法介紹
矩陣求逆在程序中很常見，主要應用于求Billboard矩陣。按照定義的計算方法乘法運算，嚴重影響了性能。在需要大量Billboard矩陣運算時，矩陣求逆的優化能極大提高性能。這里要介紹的矩陣求逆算法稱為全選主元高斯-約旦法。
高斯-約旦法（全選主元）求逆的步驟如下：
首先，對于 k 從 0 到 n - 1 作如下幾步：
從第 k 行、第 k 列開始的右下角子陣中選取絕對值最大的元素，并記住次元素所在的行號和列號，在通過行交換和列交換將它交換到主元素位置上。這一步稱為全選主元。
m(k, k) = 1 / m(k, k)
m(k, j) = m(k, j) * m(k, k)，j = 0, 1, ..., n-1；j != k
m(i, j) = m(i, j) - m(i, k) * m(k, j)，i, j = 0, 1, ..., n-1；i, j != k
m(i, k) = -m(i, k) * m(k, k)，i = 0, 1, ..., n-1；i != k
最后，根據在全選主元過程中所記錄的行、列交換的信息進行恢復，恢復的原則如下：在全選主元過程中，先交換的行（列）后進行恢復；原來的行（列）交換用列（行）交換來恢復。
標簽：
算法
矩陣求逆
程序
上傳時間：
2015-04-09
上傳用戶：wang5829
The government of a small but important country has decided that the alphabet needs to be streamlined and reordered. Uppercase letters will be eliminated. They will issue a royal decree in the form of a String of B and A characters. The first character in the decree specifies whether a must come ( B )Before b in the new alphabet or ( A )After b . The second character determines the relative placement of b and c , etc. So, for example, "BAA" means that a must come Before b , b must come After c , and c must come After d .
Any letters beyond these requirements are to be excluded, so if the decree specifies k comparisons then the new alphabet will contain the first k+1 lowercase letters of the current alphabet.
Create a class Alphabet that contains the method choices that takes the decree as input and returns the number of possible new alphabets that conform to the decree. If more than 1,000,000,000 are possible, return -1.
Definition
標簽：
government
streamline
important
alphabet
上傳時間：
2015-06-09
上傳用戶：weixiao99
Hard-decision decoding scheme
Codeword length (n) : 31 symbols.
Message length (k) : 19 symbols.
Error correction capability (t) : 6 symbols
One symbol represents 5 bit.
Uses GF(2^5) with primitive polynomial p(x) = X^5 X^2 + 1
Generator polynomial, g(x) = a^15 a^21*X + a^6*X^2 + a^15*X^3 + a^25*X^4 + a^17*X^5 + a^18*X^6 + a^30*X^7 + a^20*X^8 + a^23*X^9 + a^27*X^10 + a^24*X^11 + X^12. Note: a = alpha, primitive element in GF(2^5) and a^i is root of g(x) for i = 19, 20, ..., 30.
Uses Verilog description with synthesizable RTL modelling.
Consists of 5 main blocks: SC (Syndrome Computation), KES (Key Equation Solver), CSEE (Chien Search and Error Evaluator), Controller and FIFO Register.
標簽：
symbols
length
Hard-decision
Codeword
上傳時間：
2014-07-08
上傳用戶：曹云鵬
