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NAG[f07bsc] NAG[nag_zgbtrs] - Solution of complex band system of linear equations, multiple right-hand sides, matrix already factorized by f07brc (nag_zgbtrf)
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Calling Sequence
f07bsc(trans, kl, ku, ab, ipiv, b, 'n'=n, 'nrhs'=nrhs, 'fail'=fail)
nag_zgbtrs(. . .)
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=10109/file08137/math58.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=10109/file08137/math73.png) , the number of superdiagonals within the band of the matrix  .
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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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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=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 order of the matrix  .
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Constraint:  . .
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'nrhs'=nrhs - integer; (optional)
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Default value: the second dimension of the array b.
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On entry:  , the number of right-hand sides.
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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_zgbtrs (f07bsc) solves a complex band system of linear equations with multiple right-hand sides,
where  has been factorized by f07brc (nag_zgbtrf).
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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 real floating-point operations is approximately ![8n(2,k[l],+,k[u])r](/support/helpjp/helpview.aspx?si=10109/file08137/math389.png) , assuming ![`≫`(n, k[l])](/support/helpjp/helpview.aspx?si=10109/file08137/math391.png) and ![`≫`(n, k[u])](/support/helpjp/helpview.aspx?si=10109/file08137/math393.png) .
This function may be followed by a call to f07bvc (nag_zgbrfs) to refine the solution and return an error estimate.
The real analogue of this function is f07bec (nag_dgbtrs).
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Examples
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trans := "Nag_NoTrans":
n := 4:
kl := 1:
ku := 2:
nrhs := 2:
ab := Matrix([[0 +0*I , 0 +6.3*I , -1.48 -1.75*I , -3.99 +4.01*I , 0.59 -0.48*I ], [0.3587301587301587 +0.2619047619047619*I , -0.77 +2.83*I , -1.06 +1.94*I , 3.33 -1.04*I , 0 +0*I ], [0.2314260728743743 +0.6357648842047455*I , 4.930266941175471 -3.008563740627192*I , -1.769209381609681 -1.858747281945787*I , 0 +0*I , 0 +0*I ], [0.7604226619635511 +0.2429442589267133*I , 0.4337749265901603 +0.123252818156083*I , 0 +0*I , 0 +0*I , 0 +0*I ]], datatype=complex[8], order='C_order'):
ipiv := Vector([2, 3, 3, 4], datatype=integer[kernelopts('wordsize')/8]):
b := Matrix([[-1.06 +21.5*I , 12.85 +2.84*I ], [-22.72 -53.9*I , -70.22 +21.57*I ], [28.24 -38.6*I , -20.73 -1.23*I ], [-34.56 +16.73*I , 26.01 +31.97*I ]], datatype=complex[8], order='C_order'):
NAG:-f07bsc(trans, kl, ku, ab, ipiv, b, 'n' = n, 'nrhs' = nrhs):
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