Provides subroutines implementing various root-finding algorithms, as well as a global bracket finder.
A root finder using the hybrid bisection-secant algorithm. Returns a computed value of the root within xleft and xright once error < maxerr or has run maximum number of iterations.
| Type | Intent | Optional | Attributes | Name | ||||||||||||||||
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| real(kind=8), | intent(out) | :: | error | A real variable in which an estimate of the error in the computed root will be stored and returned. |
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public pure function fnctn(x)The Fortran function for which the root will be found. Must take only one real argument, return a real argument. Arguments
Return Value real(kind=8) |
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| real(kind=8), | intent(in) | :: | maxerr | A real value which specifies the the maximum allowable error in the computed root. The subroutine terminates once the error passes below this level. |
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| integer, | intent(in) | :: | maxsteps | An integer value for the maximum number of iterations applied to the algorithm before terminating. |
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| integer, | intent(out) | :: | steps | Returns the number of iterations needed before error falls below maxerr (or returns maxsteps if that many iterations occur first). |
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| real(kind=8), | intent(out) | :: | xcur | A real variable in which the computed value of the root will be returned. |
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| real(kind=8), | intent(inout) | :: | xleft | A real value specifying lower bound within which to search for root. |
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| real(kind=8), | intent(inout) | :: | xright | A real value specifying upper bound within which to search for root. |
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A subroutine which finds the values of all roots of a function (or as many as will fit into the provided arrays) within a given range of values. This subroutine uses the hybrid bisection-secant root-finding algorithm.
| Type | Intent | Optional | Attributes | Name | ||||||||||||||||
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| real(kind=8), | intent(inout) | :: | dx | The initial size of increment to use when examining function. Minimum interval will be 0.01 of this. |
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| real(kind=8), | intent(out), | dimension(:) | :: | error | A real array in which an estimate of the error in each computed root will be stored and returned. |
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public pure function fnctn(x)The Fortran function for which the root will be found. Must take only one real argument, return a real argument. Arguments
Return Value real(kind=8) |
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| real(kind=8), | intent(in) | :: | maxerr | A real value which specifies the the maximum allowable error in the computed root. The subroutine terminates once the error passes below this level. |
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| integer, | intent(in) | :: | maxsteps | An integer value for the maximum number of iterations applied to the algorithm before terminating. |
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| integer, | intent(out) | :: | numroots | An integer value which will return the number of roots for which brackets were found. A negative number indicates that an error occurred. |
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| real(kind=8), | intent(out), | dimension(:) | :: | roots | A real array in which the computed values of each root will be returned. |
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| integer, | intent(out), | dimension(:) | :: | steps | An integer array in which the number of iterations needed before error falls below maxerr for each root is stored and returned. |
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| logical, | intent(in) | :: | verbose | A logical variable which specifies whether to print progress to stdout as brackets found and at each iteration as root found. Also says whether to print a warning if 'dx' set to 'dxmin' during 'globrack' routine and if maximum number of iterations reached while finding root. |
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| real(kind=8), | intent(in) | :: | xmax | The upper limit of the range on which the subroutine will search for roots and brackets. |
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| real(kind=8), | intent(in) | :: | xmin | The lower limit of the range on which the subroutine will search for roots and brackets. |
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A global bracket finder. For a given function it finds values on each side of each of the function's roots within a given range.
| Type | Intent | Optional | Attributes | Name | ||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| real(kind=8), | intent(out), | dimension(:,:) | :: | brackets | A 2 by n real array in which the left and right brackets will be stored and returned. Will find up to n sets of brackets. |
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| real(kind=8), | intent(inout) | :: | dx | The initial size of increment to use when examining function. Minimum interval will be 0.01 of this. |
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public pure function fnctn(x)The Fortran function for which the brackets will be found. Must take only one real argument, return a real argument. Arguments
Return Value real(kind=8) |
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| integer, | intent(out) | :: | numroots | An integer value which will return the number of roots for which brackets were found. A negative number indicates that an error occurred. |
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| logical, | intent(in) | :: | verbose | A logical variable which specifies whether to print to stdout any bracket values which are found and warning messages when 'dx' set to 'dxmin'. |
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| real(kind=8), | intent(in) | :: | xmax | The upper limit of the range on which the subroutine will search for roots and brackets. |
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| real(kind=8), | intent(in) | :: | xmin | The lower limit of the range on which the subroutine will search for roots and brackets. |
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