本文主要是介绍Sweet Snippet 之矩阵求逆，希望对大家解决编程问题提供一定的参考价值，需要的开发者们随着小编来一起学习吧！
矩阵求逆的简单实现
矩阵求逆有很多种方法,使用伴随矩阵可能是相对易于编码的方式,在此简单列一下实现(Lua):
-- matrix store is table in row order
-- e.g. 2 x 2 matrix is stored as table { m11, m12, m21, m22 }-- determinant 2 with scalar elements
function det2s(e11, e12, e21, e22)return e11 * e22 - e21 * e12
end-- determinant 3 with scalar elements
function det3s(e11, e12, e13, e21, e22, e23, e31, e32, e33)return e11 * det2s(e22, e23, e32, e33) - e12 * det2s(e21, e23, e31, e33) + e13 * det2s(e21, e22, e31, e32)
end-- determinant 2
function det2(m2)return det2s(table.unpack(m2))
end-- determinant 3
function det3(m3)return det3s(table.unpack(m3))
end-- multiply 2
function mul2(lm2, rm2)if lm2 and rm2 and #lm2 == #rm2 and #lm2 == 4 thenlocal m2 = {}m2[1] = lm2[1] * rm2[1] + lm2[2] * rm2[3]m2[2] = lm2[1] * rm2[2] + lm2[2] * rm2[4]m2[3] = lm2[3] * rm2[1] + lm2[4] * rm2[3]m2[4] = lm2[3] * rm2[2] + lm2[4] * rm2[4]return m2end
end-- multiply 3
function mul3(lm3, rm3)if lm3 and rm3 and #lm3 == #rm3 and #lm3 == 9 thenlocal m3 = {}m3[1] = lm3[1] * rm3[1] + lm3[2] * rm3[4] + lm3[3] * rm3[7]m3[2] = lm3[1] * rm3[2] + lm3[2] * rm3[5] + lm3[3] * rm3[8]m3[3] = lm3[1] * rm3[3] + lm3[2] * rm3[6] + lm3[3] * rm3[9]m3[4] = lm3[4] * rm3[1] + lm3[5] * rm3[4] + lm3[6] * rm3[7]m3[5] = lm3[4] * rm3[2] + lm3[5] * rm3[5] + lm3[6] * rm3[8]m3[6] = lm3[4] * rm3[3] + lm3[5] * rm3[6] + lm3[6] * rm3[9]m3[7] = lm3[7] * rm3[1] + lm3[8] * rm3[4] + lm3[9] * rm3[7]m3[8] = lm3[7] * rm3[2] + lm3[8] * rm3[5] + lm3[9] * rm3[8]m3[9] = lm3[7] * rm3[3] + lm3[8] * rm3[6] + lm3[9] * rm3[9]return m3end
end-- transpose 2
function trp2(m2)if m2 and #m2 == 4 thenlocal trp_m2 = {}trp_m2[1] = m2[1]trp_m2[2] = m2[3]trp_m2[3] = m2[2]trp_m2[4] = m2[4]return trp_m2end
end-- transpose 3
function trp3(m3)if m3 and #m3 == 9 thenlocal trp_m3 = {}trp_m3[1] = m3[1]trp_m3[2] = m3[4]trp_m3[3] = m3[7]trp_m3[4] = m3[2]trp_m3[5] = m3[5]trp_m3[6] = m3[8]trp_m3[7] = m3[3]trp_m3[8] = m3[6]trp_m3[9] = m3[9]return trp_m3end
end-- inverse 2
function inv2(m2)local det = det2(m2)if det and det ~= 0 thenlocal inv_m2 = {}local adjm = { m2[4], m2[3], m2[2], m2[1] }adjm = trp2(adjm)inv_m2[1] = adjm[1] / detinv_m2[2] = -adjm[2] / detinv_m2[3] = -adjm[3] / detinv_m2[4] = adjm[4] / detreturn inv_m2end
end-- inverse 3
function inv3(m3)local det = det3(m3)if det and det ~= 0 thenlocal inv_m3 = {}local adjm = { det2s(m3[5], m3[6], m3[8], m3[9]),det2s(m3[4], m3[6], m3[7], m3[9]),det2s(m3[4], m3[5], m3[7], m3[8]),det2s(m3[2], m3[3], m3[8], m3[9]),det2s(m3[1], m3[3], m3[7], m3[9]),det2s(m3[1], m3[2], m3[7], m3[8]),det2s(m3[2], m3[3], m3[5], m3[6]),det2s(m3[1], m3[3], m3[4], m3[6]),det2s(m3[1], m3[2], m3[4], m3[5]),}adjm = trp3(adjm)inv_m3[1] = adjm[1] / detinv_m3[2] = -adjm[2] / detinv_m3[3] = adjm[3] / detinv_m3[4] = -adjm[4] / detinv_m3[5] = adjm[5] / detinv_m3[6] = -adjm[6] / detinv_m3[7] = adjm[7] / detinv_m3[8] = -adjm[8] / detinv_m3[9] = adjm[9] / detreturn inv_m3end
end
有兴趣的朋友可以求解下矩阵:
local m3 =
{ 1, 2, 3, 4, 5, 6, 7, 8, 9
}
的逆矩阵,结果可能会出人意料哦~
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