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November 15, 2017 19:39
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QR Decomposition in SAGE MATH (Givens rotation)
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| K = RR | |
| # Input matrix here | |
| A = matrix(K, [[-3, 32/5, 4 ], | |
| [4, 24/5, 3 ], | |
| [5, 6*sqrt(2), 5*sqrt(2)]]) | |
| m,n = (3,3) | |
| # Calculate r, c, s | |
| def givens(a,b): | |
| if b == 0: | |
| c = 1 | |
| s = 0 | |
| else: | |
| if abs(b) > abs(a): | |
| r = a / b; | |
| s = 1 / sqrt(1 + r**2) | |
| c = s*r | |
| else: | |
| r = b / a | |
| c = 1 / sqrt(1 + r**2) | |
| s = c*r | |
| return r, c, s | |
| Q = matrix(K,m,n,1) | |
| R = copy(A) | |
| # Calculate QR | |
| for j in range(0,n): | |
| for i in range(m-1, j, -1): | |
| r, c, s = givens(R[i-1,j], R[i,j]) | |
| R[i-1:i+1,j:n] = matrix([[c,s],[-s,c]]) * R[i-1:i+1,j:n] | |
| Q[i-1:i+1,:] = matrix([[c,s],[-s,c]]) * Q[i-1:i+1,:] | |
| Q = Q.transpose() | |
| print "-" * 10 | |
| print Q | |
| print R | |
| print Q * R | |
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