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NAG[f07bec] NAG[nag_dgbtrs] - Solution of real band system of linear equations, multiple right-hand sides, matrix already factorized by f07bdc (nag_dgbtrf)
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Calling Sequence
f07bec(trans, kl, ku, nrhs, ab, ipiv, b, 'n'=n, 'fail'=fail)
nag_dgbtrs(. . .)
Parameters
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trans - String;
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On entry: indicates the form of the equations.
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Constraint:   "Nag_NoTrans", "Nag_Trans" or "Nag_ConjTrans". .
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kl - integer;
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On entry: ![k[l]](/support/helpjp/helpview.aspx?si=10216/file08133/math53.png) , the number of subdiagonals within the band of the matrix  .
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Constraint:  . .
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ku - integer;
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On entry: ![k[u]](/support/helpjp/helpview.aspx?si=10216/file08133/math68.png) , the number of superdiagonals within the band of the matrix  .
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Constraint:  . .
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nrhs - integer;
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On entry:  , the number of right-hand sides.
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Constraint:  . .
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ab - 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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b - 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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'n'=n - integer; (optional)
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Default value: the second dimension of the array ab.
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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_dgbtrs (f07bec) solves a real band system of linear equations with multiple right-hand sides,
where  has been factorized by f07bdc (nag_dgbtrf).
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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:  .
"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 ![2n(2,k[l],+,k[u])r](/support/helpjp/helpview.aspx?si=10216/file08133/math370.png) , assuming ![`≫`(n, k[l])](/support/helpjp/helpview.aspx?si=10216/file08133/math372.png) and ![`≫`(n, k[u])](/support/helpjp/helpview.aspx?si=10216/file08133/math374.png) .
This function may be followed by a call to f07bhc (nag_dgbrfs) to refine the solution and return an error estimate.
The complex analogue of this function is f07bsc (nag_zgbtrs).
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Examples
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trans := "Nag_NoTrans":
n := 4:
kl := 1:
ku := 2:
nrhs := 2:
ab := Matrix([[0, -6.98, 2.46, -2.73, -2.13], [0.0329512893982808, 2.56, 2.46, 4.07, 0], [0.9605233703438396, -5.932930470988539, -3.839143870881089, 0, 0], [0.8056726812110376, -0.7269066639923109, 0, 0, 0]], datatype=float[8], order='C_order'):
ipiv := Vector([2, 3, 3, 4], datatype=integer[kernelopts('wordsize')/8]):
b := Matrix([[4.42, -36.01], [27.13, -31.67], [-6.14, -1.16], [10.5, -25.82]], datatype=float[8], order='C_order'):
NAG:-f07bec(trans, kl, ku, nrhs, ab, ipiv, b, 'n' = n):
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