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subroutine fpsysy(a,n,g)
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c subroutine fpsysy solves a linear n x n symmetric system
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c on input, vector g contains the right hand side ; on output it will
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c contain the solution (b).
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c decomposition of the symmetric matrix (a) = (l) * (d) *(l)'
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c with (l) a unit lower triangular matrix and (d) a diagonal
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a(k,1) = a(k,1)/a(1,1)
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fac = fac-a(j,j)*a(k,j)*a(i,j)
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if(k.gt.i) a(k,i) = fac/a(i,i)
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c solve the system (l)*(d)*(l)'*(b) = (g).
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c first step : solve (l)*(d)*(c) = (g).
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fac = fac-g(j)*a(j,j)*a(i,j)
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c second step : solve (l)'*(b) = (c)