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NAG[f08lsc] NAG[nag_zgbbrd] - Reduction of complex rectangular band matrix to upper bidiagonal form
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Calling Sequence
f08lsc(vect, m, kl, ku, ab, d, e, q, pt, c, 'n'=n, 'ncc'=ncc, 'fail'=fail)
nag_zgbbrd(. . .)
Parameters
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m - integer;
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On entry:  , the number of rows of the matrix  .
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Constraint:  . .
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kl - integer;
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On entry: ![k[l]](/support/helpjp/helpview.aspx?si=10444/file08271/math77.png) , the number of subdiagonals within the band of  .
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Constraint:  . .
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ku - integer;
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On entry: ![k[u]](/support/helpjp/helpview.aspx?si=10444/file08271/math92.png) , the number of superdiagonals within the band of  .
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Constraint:  . .
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ab - Matrix(1..dim1, 1..dim2, datatype=complex[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 exit:  is overwritten by values generated during the reduction.
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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 superdiagonal elements of the bidiagonal matrix  .
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q - Matrix(1..dim1, 1..dim2, datatype=complex[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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If   "Nag_DoNotForm" or "Nag_FormP", q is not referenced.
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pt - Matrix(1..dim1, 1..dim2, datatype=complex[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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c - Matrix(1..dim1, 1..dim2, datatype=complex[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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'n'=n - integer; (optional)
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Default value: the second dimension of the array ab.
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On entry:  , the number of columns of the matrix  .
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Constraint:  . .
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'ncc'=ncc - integer; (optional)
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Default value: the second dimension of the array c.
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On entry: ![n[C]](/support/helpjp/helpview.aspx?si=10444/file08271/math338.png) , 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_zgbbrd (f08lsc) reduces a complex  by  band matrix to real upper 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:  .
On entry,  . Constraint:  .
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 real floating-point operations is approximately the sum of:
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/k](/support/helpjp/helpview.aspx?si=10444/file08271/math500.png) , if  is updated, and
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where ![k = k[l]+k[u]](/support/helpjp/helpview.aspx?si=10444/file08271/math513.png) , assuming  . For this section we assume that  .
The real analogue of this function is f08lec (nag_dgbbrd).
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Examples
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vect := "Nag_DoNotForm":
m := 6:
n := 4:
ncc := 0:
kl := 2:
ku := 1:
ab := Matrix([[0 +0*I , 0 +0*I , 0.96 -0.8100000000000001*I , -0.03 +0.96*I ], [0 +0*I , -0.98 +1.98*I , -1.2 +0.19*I , -0.66 +0.42*I ], [0.62 -0.46*I , 1.01 +0.02*I , 0.63 -0.17*I , -1.11 +0.6*I ], [0.19 -0.54*I , -0.98 -0.36*I , 0.22 -0.2*I , 0 +0*I ], [-0.17 -0.46*I , 1.47 +1.59*I , 0 +0*I , 0 +0*I ], [0.26 +0.26*I , 0 +0*I , 0 +0*I , 0 +0*I ]], datatype=complex[8], order='C_order'):
d := Vector(4, datatype=float[8]):
e := Vector(3, datatype=float[8]):
q := Matrix(1, 1, datatype=complex[8], order='C_order'):
pt := Matrix(1, 1, datatype=complex[8], order='C_order'):
c := Matrix([[0 +0*I ]], datatype=complex[8], order='C_order'):
NAG:-f08lsc(vect, m, kl, ku, ab, d, e, q, pt, c, 'ncc' = ncc):
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