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NAG[f08njc] NAG[nag_dgebak] - Transform eigenvectors of real balanced matrix to those of original matrix supplied to f08nhc (nag_dgebal)
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Calling Sequence
f08njc(job, side, ilo, ihi, scale, v, 'n'=n, 'm'=m, 'fail'=fail)
nag_dgebak(. . .)
Parameters
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job - String;
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Constraint:   "Nag_DoNothing", "Nag_Permute", "Nag_Scale" or "Nag_DoBoth". .
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side - String;
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On entry: indicates whether left or right eigenvectors are to be transformed.
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 The left eigenvectors are transformed.
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 The right eigenvectors are transformed.
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Constraint:   "Nag_LeftSide" or "Nag_RightSide". .
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ilo - integer;
ihi - integer;
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if  ,  ;
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scale - Vector(1..dim, datatype=float[8]);
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Note: the dimension, dim, of the array scale must be at least  .
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On entry: details of the permutations and/or the scaling factors used to balance the original real non-symmetric matrix, as returned by f08nhc (nag_dgebal).
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v - 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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On entry: the matrix of left or right eigenvectors to be transformed.
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On exit: the transformed eigenvectors.
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'n'=n - integer; (optional)
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Default value: the first dimension of the array v.
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On entry:  , the number of rows of the matrix of eigenvectors.
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Constraint:  . .
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'm'=m - integer; (optional)
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Default value: the second dimension of the array v.
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On entry:  , the number of columns of the matrix of eigenvectors.
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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_dgebak (f08njc) transforms eigenvectors of a balanced matrix to those of the original real non-symmetric matrix.
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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:  .
On entry,  . Constraint:  .
"NE_INT_3"
On entry,  ,  ,  . Constraint: if  ,  and  .
On entry,  ,  ,  . Constraint: if  ,  .
"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.
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Accuracy
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The errors are negligible.
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Further Comments
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The total number of floating-point operations is approximately proportional to  .
The complex analogue of this function is f08nwc (nag_zgebak).
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Examples
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job := "Nag_DoBoth":
side := "Nag_RightSide":
n := 4:
ilo := 2:
ihi := 4:
m := 4:
scale := Vector([3, 8, 8, 1], datatype=float[8]):
v := Matrix([[1, -0.4314180584465899, -0.9999999999999999, -1], [0, 1, -0.247654150974541, 0.08591655381643529], [0, -0.4910063736255747, -0.146105421622948, -0.4768657196218895], [0, -0.8751224464247366, -0.1307439268438695, 0.236243720668051]], datatype=float[8]):
NAG:-f08njc(job, side, ilo, ihi, scale, v, 'n' = n, 'm' = m):
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