DecompositionOperations<TReal, TComplex>.BandLUSolve Method

public void BandLUSolve(
	TransposeOperation trans,
	int n,
	int kl,
	int ku,
	int nrhs,
	Array2D<TReal> ab,
	Array1D<int> ipiv,
	Array2D<TReal> b,
	out int info
)

Public Sub BandLUSolve ( 
	trans As TransposeOperation,
	n As Integer,
	kl As Integer,
	ku As Integer,
	nrhs As Integer,
	ab As Array2D(Of TReal),
	ipiv As Array1D(Of Integer),
	b As Array2D(Of TReal),
	<OutAttribute> ByRef info As Integer
)

public:
void BandLUSolve(
	TransposeOperation trans, 
	int n, 
	int kl, 
	int ku, 
	int nrhs, 
	Array2D<TReal> ab, 
	Array1D<int> ipiv, 
	Array2D<TReal> b, 
	[OutAttribute] int% info
)

member BandLUSolve : 
        trans : TransposeOperation * 
        n : int * 
        kl : int * 
        ku : int * 
        nrhs : int * 
        ab : Array2D<'TReal> * 
        ipiv : Array1D<int> * 
        b : Array2D<'TReal> * 
        info : int byref -> unit 

Parameters

trans  TransposeOperation

            Specifies the form of the system of equations.
            = 'N':  A * X = B  (No transpose)
            = 'T':  AT* X = B  (Transpose)
            = 'C':  AT* X = B  (Conjugate transpose = Transpose)
            

n  Int32

            The order of the matrix A.  N >= 0.
            

kl  Int32

            The number of subdiagonals within the band of A.  KL >= 0.
            

ku  Int32

            The number of superdiagonals within the band of A.  KU >= 0.
            

nrhs  Int32

            The number of right hand sides, i.e., the number of columns
            of the matrix B.  NRHS >= 0.
            

ab  Array2D<TReal>

            AB is TReal array, dimension (LDAB,N)
            Details of the LU factorization of the band matrix A, as
            computed by DGBTRF.  U is stored as an upper triangular band
            matrix with KL+KU superdiagonals in rows 1 to KL+KU+1, and
            the multipliers used during the factorization are stored in
            rows KL+KU+2 to 2*KL+KU+1.
            

            The leading dimension of the array AB.  LDAB >= 2*KL+KU+1.
            

ipiv  Array1D<Int32>

            Dimension (N)
            The pivot indices; for 1 <= i <= N, row i of the matrix was
            interchanged with row IPIV(i).
            

b  Array2D<TReal>

            B is TReal array, dimension (LDB,NRHS)
            On entry, the right hand side matrix B.
            On exit, the solution matrix X.
            

            The leading dimension of the array B.  LDB >= max(1,N).
            

info  Int32

            = 0:  successful exit
            < 0: if INFO = -i, the i-th argument had an illegal value
            

This method corresponds to the LAPACK routine ?GBTRS.

public void BandLUSolve(
	TransposeOperation trans,
	int n,
	int kl,
	int ku,
	int nrhs,
	Array2D<TComplex> ab,
	Array1D<int> ipiv,
	Array2D<TComplex> b,
	out int info
)

Public Sub BandLUSolve ( 
	trans As TransposeOperation,
	n As Integer,
	kl As Integer,
	ku As Integer,
	nrhs As Integer,
	ab As Array2D(Of TComplex),
	ipiv As Array1D(Of Integer),
	b As Array2D(Of TComplex),
	<OutAttribute> ByRef info As Integer
)

public:
void BandLUSolve(
	TransposeOperation trans, 
	int n, 
	int kl, 
	int ku, 
	int nrhs, 
	Array2D<TComplex> ab, 
	Array1D<int> ipiv, 
	Array2D<TComplex> b, 
	[OutAttribute] int% info
)

member BandLUSolve : 
        trans : TransposeOperation * 
        n : int * 
        kl : int * 
        ku : int * 
        nrhs : int * 
        ab : Array2D<'TComplex> * 
        ipiv : Array1D<int> * 
        b : Array2D<'TComplex> * 
        info : int byref -> unit 

Parameters

trans  TransposeOperation

            Specifies the form of the system of equations.
            = 'N':  A * X = B     (No transpose)
            = 'T':  AT * X = B  (Transpose)
            = 'C':  AH * X = B  (Conjugate transpose)
            

n  Int32

            The order of the matrix A.  N >= 0.
            

kl  Int32

            The number of subdiagonals within the band of A.  KL >= 0.
            

ku  Int32

            The number of superdiagonals within the band of A.  KU >= 0.
            

nrhs  Int32

            The number of right hand sides, i.e., the number of columns
            of the matrix B.  NRHS >= 0.
            

ab  Array2D<TComplex>

            AB is TComplex array, dimension (LDAB,N)
            Details of the LU factorization of the band matrix A, as
            computed by ZGBTRF.  U is stored as an upper triangular band
            matrix with KL+KU superdiagonals in rows 1 to KL+KU+1, and
            the multipliers used during the factorization are stored in
            rows KL+KU+2 to 2*KL+KU+1.
            

            The leading dimension of the array AB.  LDAB >= 2*KL+KU+1.
            

ipiv  Array1D<Int32>

            Dimension (N)
            The pivot indices; for 1 <= i <= N, row i of the matrix was
            interchanged with row IPIV(i).
            

b  Array2D<TComplex>

            B is TComplex array, dimension (LDB,NRHS)
            On entry, the right hand side matrix B.
            On exit, the solution matrix X.
            

            The leading dimension of the array B.  LDB >= max(1,N).
            

info  Int32

            = 0:  successful exit
            < 0:  if INFO = -i, the i-th argument had an illegal value
            

Authors: 
             Univ. of Tennessee,
             Univ. of California Berkeley,
             Univ. of Colorado Denver,
             NAG Ltd.
Date:  November 2011

public void BandLUSolve(
	TransposeOperation trans,
	int n,
	int kl,
	int ku,
	int nrhs,
	Span2D<TReal> ab,
	Span<int> ipiv,
	Span2D<TReal> b,
	out int info
)

Public Sub BandLUSolve ( 
	trans As TransposeOperation,
	n As Integer,
	kl As Integer,
	ku As Integer,
	nrhs As Integer,
	ab As Span2D(Of TReal),
	ipiv As Span(Of Integer),
	b As Span2D(Of TReal),
	<OutAttribute> ByRef info As Integer
)

public:
void BandLUSolve(
	TransposeOperation trans, 
	int n, 
	int kl, 
	int ku, 
	int nrhs, 
	Span2D<TReal> ab, 
	Span<int> ipiv, 
	Span2D<TReal> b, 
	[OutAttribute] int% info
)

member BandLUSolve : 
        trans : TransposeOperation * 
        n : int * 
        kl : int * 
        ku : int * 
        nrhs : int * 
        ab : Span2D<'TReal> * 
        ipiv : Span<int> * 
        b : Span2D<'TReal> * 
        info : int byref -> unit 

Parameters

trans  TransposeOperation

            Specifies the form of the system of equations.
            = 'N':  A * X = B  (No transpose)
            = 'T':  AT* X = B  (Transpose)
            = 'C':  AT* X = B  (Conjugate transpose = Transpose)
            

n  Int32

            The order of the matrix A.  N >= 0.
            

kl  Int32

            The number of subdiagonals within the band of A.  KL >= 0.
            

ku  Int32

            The number of superdiagonals within the band of A.  KU >= 0.
            

nrhs  Int32

            The number of right hand sides, i.e., the number of columns
            of the matrix B.  NRHS >= 0.
            

ab  Span2D<TReal>

            AB is TReal array, dimension (LDAB,N)
            Details of the LU factorization of the band matrix A, as
            computed by DGBTRF.  U is stored as an upper triangular band
            matrix with KL+KU superdiagonals in rows 1 to KL+KU+1, and
            the multipliers used during the factorization are stored in
            rows KL+KU+2 to 2*KL+KU+1.
            

            The leading dimension of the array AB.  LDAB >= 2*KL+KU+1.
            

ipiv  Span<Int32>

            Dimension (N)
            The pivot indices; for 1 <= i <= N, row i of the matrix was
            interchanged with row IPIV(i).
            

b  Span2D<TReal>

            B is TReal array, dimension (LDB,NRHS)
            On entry, the right hand side matrix B.
            On exit, the solution matrix X.
            

            The leading dimension of the array B.  LDB >= max(1,N).
            

info  Int32

            = 0:  successful exit
            < 0: if INFO = -i, the i-th argument had an illegal value
            

This method corresponds to the LAPACK routine ?GBTRS.

public void BandLUSolve(
	TransposeOperation trans,
	int n,
	int kl,
	int ku,
	int nrhs,
	Span2D<TComplex> ab,
	Span<int> ipiv,
	Span2D<TComplex> b,
	out int info
)

Public Sub BandLUSolve ( 
	trans As TransposeOperation,
	n As Integer,
	kl As Integer,
	ku As Integer,
	nrhs As Integer,
	ab As Span2D(Of TComplex),
	ipiv As Span(Of Integer),
	b As Span2D(Of TComplex),
	<OutAttribute> ByRef info As Integer
)

public:
void BandLUSolve(
	TransposeOperation trans, 
	int n, 
	int kl, 
	int ku, 
	int nrhs, 
	Span2D<TComplex> ab, 
	Span<int> ipiv, 
	Span2D<TComplex> b, 
	[OutAttribute] int% info
)

member BandLUSolve : 
        trans : TransposeOperation * 
        n : int * 
        kl : int * 
        ku : int * 
        nrhs : int * 
        ab : Span2D<'TComplex> * 
        ipiv : Span<int> * 
        b : Span2D<'TComplex> * 
        info : int byref -> unit 

Parameters

trans  TransposeOperation

            Specifies the form of the system of equations.
            = 'N':  A * X = B     (No transpose)
            = 'T':  AT * X = B  (Transpose)
            = 'C':  AH * X = B  (Conjugate transpose)
            

n  Int32

            The order of the matrix A.  N >= 0.
            

kl  Int32

            The number of subdiagonals within the band of A.  KL >= 0.
            

ku  Int32

            The number of superdiagonals within the band of A.  KU >= 0.
            

nrhs  Int32

            The number of right hand sides, i.e., the number of columns
            of the matrix B.  NRHS >= 0.
            

ab  Span2D<TComplex>

            AB is TComplex array, dimension (LDAB,N)
            Details of the LU factorization of the band matrix A, as
            computed by ZGBTRF.  U is stored as an upper triangular band
            matrix with KL+KU superdiagonals in rows 1 to KL+KU+1, and
            the multipliers used during the factorization are stored in
            rows KL+KU+2 to 2*KL+KU+1.
            

            The leading dimension of the array AB.  LDAB >= 2*KL+KU+1.
            

ipiv  Span<Int32>

            Dimension (N)
            The pivot indices; for 1 <= i <= N, row i of the matrix was
            interchanged with row IPIV(i).
            

b  Span2D<TComplex>

            B is TComplex array, dimension (LDB,NRHS)
            On entry, the right hand side matrix B.
            On exit, the solution matrix X.
            

            The leading dimension of the array B.  LDB >= max(1,N).
            

info  Int32

            = 0:  successful exit
            < 0:  if INFO = -i, the i-th argument had an illegal value
            

Authors: 
             Univ. of Tennessee,
             Univ. of California Berkeley,
             Univ. of Colorado Denver,
             NAG Ltd.
Date:  November 2011

public abstract void BandLUSolve(
	TransposeOperation trans,
	int n,
	int kl,
	int ku,
	int nrhs,
	Span<TReal> ab,
	int ldab,
	Span<int> ipiv,
	Span<TReal> b,
	int ldb,
	out int info
)

Public MustOverride Sub BandLUSolve ( 
	trans As TransposeOperation,
	n As Integer,
	kl As Integer,
	ku As Integer,
	nrhs As Integer,
	ab As Span(Of TReal),
	ldab As Integer,
	ipiv As Span(Of Integer),
	b As Span(Of TReal),
	ldb As Integer,
	<OutAttribute> ByRef info As Integer
)

public:
virtual void BandLUSolve(
	TransposeOperation trans, 
	int n, 
	int kl, 
	int ku, 
	int nrhs, 
	Span<TReal> ab, 
	int ldab, 
	Span<int> ipiv, 
	Span<TReal> b, 
	int ldb, 
	[OutAttribute] int% info
) abstract

abstract BandLUSolve : 
        trans : TransposeOperation * 
        n : int * 
        kl : int * 
        ku : int * 
        nrhs : int * 
        ab : Span<'TReal> * 
        ldab : int * 
        ipiv : Span<int> * 
        b : Span<'TReal> * 
        ldb : int * 
        info : int byref -> unit 

Parameters

trans  TransposeOperation

            Specifies the form of the system of equations.
            = 'N':  A * X = B  (No transpose)
            = 'T':  AT* X = B  (Transpose)
            = 'C':  AT* X = B  (Conjugate transpose = Transpose)
            

n  Int32

            The order of the matrix A.  N >= 0.
            

kl  Int32

            The number of subdiagonals within the band of A.  KL >= 0.
            

ku  Int32

            The number of superdiagonals within the band of A.  KU >= 0.
            

nrhs  Int32

            The number of right hand sides, i.e., the number of columns
            of the matrix B.  NRHS >= 0.
            

ab  Span<TReal>

            AB is TReal array, dimension (LDAB,N)
            Details of the LU factorization of the band matrix A, as
            computed by DGBTRF.  U is stored as an upper triangular band
            matrix with KL+KU superdiagonals in rows 1 to KL+KU+1, and
            the multipliers used during the factorization are stored in
            rows KL+KU+2 to 2*KL+KU+1.
            

ldab  Int32

            The leading dimension of the array AB.  LDAB >= 2*KL+KU+1.
            

ipiv  Span<Int32>

            Dimension (N)
            The pivot indices; for 1 <= i <= N, row i of the matrix was
            interchanged with row IPIV(i).
            

b  Span<TReal>

            B is TReal array, dimension (LDB,NRHS)
            On entry, the right hand side matrix B.
            On exit, the solution matrix X.
            

ldb  Int32

            The leading dimension of the array B.  LDB >= max(1,N).
            

info  Int32

            = 0:  successful exit
            < 0: if INFO = -i, the i-th argument had an illegal value
            

This method corresponds to the LAPACK routine ?GBTRS.

public abstract void BandLUSolve(
	TransposeOperation trans,
	int n,
	int kl,
	int ku,
	int nrhs,
	Span<TComplex> ab,
	int ldab,
	Span<int> ipiv,
	Span<TComplex> b,
	int ldb,
	out int info
)

Public MustOverride Sub BandLUSolve ( 
	trans As TransposeOperation,
	n As Integer,
	kl As Integer,
	ku As Integer,
	nrhs As Integer,
	ab As Span(Of TComplex),
	ldab As Integer,
	ipiv As Span(Of Integer),
	b As Span(Of TComplex),
	ldb As Integer,
	<OutAttribute> ByRef info As Integer
)

public:
virtual void BandLUSolve(
	TransposeOperation trans, 
	int n, 
	int kl, 
	int ku, 
	int nrhs, 
	Span<TComplex> ab, 
	int ldab, 
	Span<int> ipiv, 
	Span<TComplex> b, 
	int ldb, 
	[OutAttribute] int% info
) abstract

abstract BandLUSolve : 
        trans : TransposeOperation * 
        n : int * 
        kl : int * 
        ku : int * 
        nrhs : int * 
        ab : Span<'TComplex> * 
        ldab : int * 
        ipiv : Span<int> * 
        b : Span<'TComplex> * 
        ldb : int * 
        info : int byref -> unit 

Parameters

trans  TransposeOperation

            Specifies the form of the system of equations.
            = 'N':  A * X = B     (No transpose)
            = 'T':  AT * X = B  (Transpose)
            = 'C':  AH * X = B  (Conjugate transpose)
            

n  Int32

            The order of the matrix A.  N >= 0.
            

kl  Int32

            The number of subdiagonals within the band of A.  KL >= 0.
            

ku  Int32

            The number of superdiagonals within the band of A.  KU >= 0.
            

nrhs  Int32

            The number of right hand sides, i.e., the number of columns
            of the matrix B.  NRHS >= 0.
            

ab  Span<TComplex>

            AB is TComplex array, dimension (LDAB,N)
            Details of the LU factorization of the band matrix A, as
            computed by ZGBTRF.  U is stored as an upper triangular band
            matrix with KL+KU superdiagonals in rows 1 to KL+KU+1, and
            the multipliers used during the factorization are stored in
            rows KL+KU+2 to 2*KL+KU+1.
            

ldab  Int32

            The leading dimension of the array AB.  LDAB >= 2*KL+KU+1.
            

ipiv  Span<Int32>

            Dimension (N)
            The pivot indices; for 1 <= i <= N, row i of the matrix was
            interchanged with row IPIV(i).
            

b  Span<TComplex>

            B is TComplex array, dimension (LDB,NRHS)
            On entry, the right hand side matrix B.
            On exit, the solution matrix X.
            

ldb  Int32

            The leading dimension of the array B.  LDB >= max(1,N).
            

info  Int32

            = 0:  successful exit
            < 0:  if INFO = -i, the i-th argument had an illegal value
            

Authors: 
             Univ. of Tennessee,
             Univ. of California Berkeley,
             Univ. of Colorado Denver,
             NAG Ltd.
Date:  November 2011

Reference