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NAG[f08kec] NAG[nag_dgebrd] - Orthogonal reduction of real general rectangular matrix to bidiagonal form
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Calling Sequence
f08kec(a, d, e, tauq, taup, 'm'=m, 'n'=n, 'fail'=fail)
nag_dgebrd(. . .)
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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d - Vector(1..dim, datatype=float[8]);
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Note: the dimension, dim, of the array d must be at least  .
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On exit: the diagonal elements of the bidiagonal matrix  .
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e - Vector(1..dim, datatype=float[8]);
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Note: the dimension, dim, of the array e must be at least  .
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On exit: the off-diagonal elements of the bidiagonal matrix  .
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tauq - Vector(1..dim, datatype=float[8]);
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Note: the dimension, dim, of the array tauq must be at least  .
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On exit: further details of the matrix  .
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taup - Vector(1..dim, datatype=float[8]);
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Note: the dimension, dim, of the array taup must be at least  .
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On exit: further details of the matrix  .
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'm'=m - integer; (optional)
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Default value: the first dimension of the array a.
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On entry:  , the number of rows of the matrix  .
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Constraint:  . .
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'n'=n - integer; (optional)
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Default value: the second dimension of the array a.
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On entry:  , the number of columns 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_dgebrd (f08kec) reduces a real  by  matrix to bidiagonal form.
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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_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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Further Comments
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The total number of floating-point operations is approximately  if  or  if  .
If  , it can be more efficient to first call f08aec (nag_dgeqrf) to perform a  factorization of  , and then to call nag_dgebrd (f08kec) to reduce the factor  to bidiagonal form. This requires approximately  floating-point operations.
If  , it can be more efficient to first call f08ahc (nag_dgelqf) to perform an  factorization of  , and then to call nag_dgebrd (f08kec) to reduce the factor  to bidiagonal form. This requires approximately  operations.
To form the orthogonal matrices  and/or  nag_dgebrd (f08kec) may be followed by calls to f08kfc (nag_dorgbr):
to form the  by  orthogonal matrix 
nag_dorgbr ("Nag_FormQ",n,a,tauq,m='m','n'=m)
but note that the second dimension of the array a must be at least m, which may be larger than was required by nag_dgebrd (f08kec);
To apply  or  to a real rectangular matrix  , nag_dgebrd (f08kec) may be followed by a call to f08kgc (nag_dormbr).
The complex analogue of this function is f08ksc (nag_zgebrd).
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Examples
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m := 6:
n := 4:
a := Matrix([[-0.57, -1.28, -0.39, 0.25], [-1.93, 1.08, -0.31, -2.14], [2.3, 0.24, 0.4, -0.35], [-1.93, 0.64, -0.66, 0.08], [0.15, 0.3, 0.15, -2.13], [-0.02, 1.03, -1.43, 0.5]], datatype=float[8]):
d := Vector(4, datatype=float[8]):
e := Vector(3, datatype=float[8]):
tauq := Vector(4, datatype=float[8]):
taup := Vector(4, datatype=float[8]):
NAG:-f08kec(a, d, e, tauq, taup, 'm' = m, 'n' = n):
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