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NAG[f07ajc] NAG[nag_dgetri] - Inverse of real matrix, matrix already factorized by f07adc (nag_dgetrf)
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Calling Sequence
f07ajc(a, ipiv, 'n'=n, 'fail'=fail)
nag_dgetri(. . .)
Parameters
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a - Matrix(1..dim1, 1..dim2, datatype=float[8], order=order);
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Note: this array may be supplied in Fortran_order or C_order , as specified by order. All array parameters must use a consistent order.
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ipiv - Vector(1..dim, datatype=integer[kernelopts('wordsize')/8]);
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Note: the dimension, dim, of the array ipiv must be at least  .
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'n'=n - integer; (optional)
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Default value: the dimension of the array a.
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On entry:  , the order of the matrix  .
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Constraint:  . .
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'fail'=fail - table; (optional)
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The NAG error argument, see the documentation for NagError.
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Description
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Purpose
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nag_dgetri (f07ajc) computes the inverse of a real matrix  , where  has been factorized by f07adc (nag_dgetrf).
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Error Indicators and Warnings
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"NE_ALLOC_FAIL"
Dynamic memory allocation failed.
"NE_BAD_PARAM"
On entry, argument  had an illegal value.
"NE_INT"
On entry,  . Constraint:  .
"NE_INTERNAL_ERROR"
An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please consult NAG for assistance.
"NE_SINGULAR"
Element  of the diagonal is zero.  is singular, and the inverse of  cannot be computed.
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Accuracy
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The computed inverse  satisfies a bound of the form:
where  is a modest linear function of  , and  is the machine precision.
Note that a similar bound for  cannot be guaranteed, although it is almost always satisfied. See Du Croz and Higham (1992).
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Further Comments
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The total number of floating-point operations is approximately  .
The complex analogue of this function is f07awc (nag_zgetri).
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Examples
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>
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n := 4:
a := Matrix([[5.25, -2.95, -0.95, -3.8], [0.3428571428571429, 3.891428571428571, 2.375714285714285, 0.4128571428571428], [0.300952380952381, -0.4631179637787567, -1.513859275575135, 0.2948206069505628], [-0.2114285714285714, -0.3298825256975037, 0.004723367663983707, 0.1313732394878517]], datatype=float[8]):
ipiv := Vector([2, 2, 3, 4], datatype=integer[kernelopts('wordsize')/8]):
NAG:-f07ajc(a, ipiv, 'n' = n):
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