DecompositionOperations<TReal, TComplex>.BandCholeskySolve Method

Definition

Namespace: Numerics.NET.LinearAlgebra.Implementation
Assembly: Numerics.NET (in Numerics.NET.dll) Version: 9.0.4

Overload List

BandCholeskySolve(MatrixTriangle, Int32, Int32, Int32, Array2D<TReal>, Array2D<TReal>, Int32)	Solves a system of linear equations AX = B with a symmetric positive definite band matrix A using the Cholesky factorization A = U^TU or A = L*L^T computed by DPBTRF.
BandCholeskySolve(MatrixTriangle, Int32, Int32, Int32, Array2D<TComplex>, Array2D<TComplex>, Int32)	Solves a system of linear equations AX = B with a Hermitian positive definite band matrix A using the Cholesky factorization A = U^H U or A = L*L^H computed by ZPBTRF.
BandCholeskySolve(MatrixTriangle, Int32, Int32, Int32, ReadOnlySpan2D<TComplex>, Span2D<TComplex>, Int32)	Solves a system of linear equations AX = B with a Hermitian positive definite band matrix A using the Cholesky factorization A = U^H U or A = L*L^H computed by ZPBTRF.
BandCholeskySolve(MatrixTriangle, Int32, Int32, Int32, Span2D<TReal>, Span2D<TReal>, Int32)	Solves a system of linear equations AX = B with a symmetric positive definite band matrix A using the Cholesky factorization A = U^TU or A = L*L^T computed by DPBTRF.
BandCholeskySolve(MatrixTriangle, Int32, Int32, Int32, ReadOnlySpan<TComplex>, Int32, Span<TComplex>, Int32, Int32)	Solves a system of linear equations AX = B with a Hermitian positive definite band matrix A using the Cholesky factorization A = U^H U or A = L*L^H computed by ZPBTRF.
BandCholeskySolve(MatrixTriangle, Int32, Int32, Int32, Span<TReal>, Int32, Span<TReal>, Int32, Int32)	Solves a system of linear equations AX = B with a symmetric positive definite band matrix A using the Cholesky factorization A = U^TU or A = L*L^T computed by DPBTRF.

BandCholeskySolve(MatrixTriangle, Int32, Int32, Int32, Array2D<TReal>, Array2D<TReal>, Int32)

Solves a system of linear equations A*X = B with a symmetric positive definite band matrix A using the Cholesky factorization A = U^T*U or A = L*L^T computed by DPBTRF.

public void BandCholeskySolve(
	MatrixTriangle storedTriangle,
	int n,
	int kd,
	int nrhs,
	Array2D<TReal> ab,
	Array2D<TReal> b,
	out int info
)

Visual Basic

Public Sub BandCholeskySolve ( 
	storedTriangle As MatrixTriangle,
	n As Integer,
	kd As Integer,
	nrhs As Integer,
	ab As Array2D(Of TReal),
	b As Array2D(Of TReal),
	<OutAttribute> ByRef info As Integer
)

C++/CLI

public:
void BandCholeskySolve(
	MatrixTriangle storedTriangle, 
	int n, 
	int kd, 
	int nrhs, 
	Array2D<TReal> ab, 
	Array2D<TReal> b, 
	[OutAttribute] int% info
)

member BandCholeskySolve : 
        storedTriangle : MatrixTriangle * 
        n : int * 
        kd : int * 
        nrhs : int * 
        ab : Array2D<'TReal> * 
        b : Array2D<'TReal> * 
        info : int byref -> unit

Parameters

storedTriangle MatrixTriangle

            = 'U':  Upper triangular factor stored in AB;
            = 'L':  Lower triangular factor stored in AB.

n Int32

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

kd Int32

            The number of superdiagonals of the matrix A if UPLO = 'U',
            or the number of subdiagonals if UPLO = 'L'.  KD >= 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)
            The triangular factor U or L from the Cholesky factorization
            A = U^T*U or A = L*L^T of the band matrix A, stored in the
            first KD+1 rows of the array.  The j-th column of U or L is
            stored in the j-th column of the array AB as follows:
            if UPLO ='U', AB(kd+1+i-j,j) = U(i,j) for max(1,j-kd)<=i<=j;
            if UPLO ='L', AB(1+i-j,j)    = L(i,j) for j<=i<=min(n,j+kd).

            The leading dimension of the array AB.  LDAB >= KD+1.

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

Remarks

This method corresponds to the LAPACK routine ?PBTRS.

BandCholeskySolve(MatrixTriangle, Int32, Int32, Int32, Array2D<TComplex>, Array2D<TComplex>, Int32)

Solves a system of linear equations A*X = B with a Hermitian positive definite band matrix A using the Cholesky factorization A = U^H *U or A = L*L^H computed by ZPBTRF.

public void BandCholeskySolve(
	MatrixTriangle uplo,
	int n,
	int kd,
	int nrhs,
	Array2D<TComplex> ab,
	Array2D<TComplex> b,
	out int info
)

Visual Basic

Public Sub BandCholeskySolve ( 
	uplo As MatrixTriangle,
	n As Integer,
	kd As Integer,
	nrhs As Integer,
	ab As Array2D(Of TComplex),
	b As Array2D(Of TComplex),
	<OutAttribute> ByRef info As Integer
)

C++/CLI

public:
void BandCholeskySolve(
	MatrixTriangle uplo, 
	int n, 
	int kd, 
	int nrhs, 
	Array2D<TComplex> ab, 
	Array2D<TComplex> b, 
	[OutAttribute] int% info
)

member BandCholeskySolve : 
        uplo : MatrixTriangle * 
        n : int * 
        kd : int * 
        nrhs : int * 
        ab : Array2D<'TComplex> * 
        b : Array2D<'TComplex> * 
        info : int byref -> unit

Parameters

uplo MatrixTriangle

            = 'U':  Upper triangular factor stored in AB;
            = 'L':  Lower triangular factor stored in AB.

n Int32

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

kd Int32

            The number of superdiagonals of the matrix A if UPLO = 'U',
            or the number of subdiagonals if UPLO = 'L'.  KD >= 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)
            The triangular factor U or L from the Cholesky factorization
            A = U^H *U or A = L*L^H of the band matrix A, stored in the
            first KD+1 rows of the array.  The j-th column of U or L is
            stored in the j-th column of the array AB as follows:
            if UPLO ='U', AB(kd+1+i-j,j) = U(i,j) for max(1,j-kd)<=i<=j;
            if UPLO ='L', AB(1+i-j,j)    = L(i,j) for j<=i<=min(n,j+kd).

            The leading dimension of the array AB.  LDAB >= KD+1.

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

Remarks

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

Date: November 2011

BandCholeskySolve(MatrixTriangle, Int32, Int32, Int32, ReadOnlySpan2D<TComplex>, Span2D<TComplex>, Int32)

Solves a system of linear equations A*X = B with a Hermitian positive definite band matrix A using the Cholesky factorization A = U^H *U or A = L*L^H computed by ZPBTRF.

public void BandCholeskySolve(
	MatrixTriangle uplo,
	int n,
	int kd,
	int nrhs,
	ReadOnlySpan2D<TComplex> ab,
	Span2D<TComplex> b,
	out int info
)

Visual Basic

Public Sub BandCholeskySolve ( 
	uplo As MatrixTriangle,
	n As Integer,
	kd As Integer,
	nrhs As Integer,
	ab As ReadOnlySpan2D(Of TComplex),
	b As Span2D(Of TComplex),
	<OutAttribute> ByRef info As Integer
)

C++/CLI

public:
void BandCholeskySolve(
	MatrixTriangle uplo, 
	int n, 
	int kd, 
	int nrhs, 
	ReadOnlySpan2D<TComplex> ab, 
	Span2D<TComplex> b, 
	[OutAttribute] int% info
)

member BandCholeskySolve : 
        uplo : MatrixTriangle * 
        n : int * 
        kd : int * 
        nrhs : int * 
        ab : ReadOnlySpan2D<'TComplex> * 
        b : Span2D<'TComplex> * 
        info : int byref -> unit

Parameters

uplo MatrixTriangle

            = 'U':  Upper triangular factor stored in AB;
            = 'L':  Lower triangular factor stored in AB.

n Int32

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

kd Int32

            The number of superdiagonals of the matrix A if UPLO = 'U',
            or the number of subdiagonals if UPLO = 'L'.  KD >= 0.

nrhs Int32

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

ab ReadOnlySpan2D<TComplex>

            AB is TComplex array, dimension (LDAB,N)
            The triangular factor U or L from the Cholesky factorization
            A = U^H *U or A = L*L^H of the band matrix A, stored in the
            first KD+1 rows of the array.  The j-th column of U or L is
            stored in the j-th column of the array AB as follows:
            if UPLO ='U', AB(kd+1+i-j,j) = U(i,j) for max(1,j-kd)<=i<=j;
            if UPLO ='L', AB(1+i-j,j)    = L(i,j) for j<=i<=min(n,j+kd).

            The leading dimension of the array AB.  LDAB >= KD+1.

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

Remarks

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

Date: November 2011

BandCholeskySolve(MatrixTriangle, Int32, Int32, Int32, Span2D<TReal>, Span2D<TReal>, Int32)

Solves a system of linear equations A*X = B with a symmetric positive definite band matrix A using the Cholesky factorization A = U^T*U or A = L*L^T computed by DPBTRF.

public void BandCholeskySolve(
	MatrixTriangle storedTriangle,
	int n,
	int kd,
	int nrhs,
	Span2D<TReal> ab,
	Span2D<TReal> b,
	out int info
)

Visual Basic

Public Sub BandCholeskySolve ( 
	storedTriangle As MatrixTriangle,
	n As Integer,
	kd As Integer,
	nrhs As Integer,
	ab As Span2D(Of TReal),
	b As Span2D(Of TReal),
	<OutAttribute> ByRef info As Integer
)

C++/CLI

public:
void BandCholeskySolve(
	MatrixTriangle storedTriangle, 
	int n, 
	int kd, 
	int nrhs, 
	Span2D<TReal> ab, 
	Span2D<TReal> b, 
	[OutAttribute] int% info
)

member BandCholeskySolve : 
        storedTriangle : MatrixTriangle * 
        n : int * 
        kd : int * 
        nrhs : int * 
        ab : Span2D<'TReal> * 
        b : Span2D<'TReal> * 
        info : int byref -> unit

Parameters

storedTriangle MatrixTriangle

            = 'U':  Upper triangular factor stored in AB;
            = 'L':  Lower triangular factor stored in AB.

n Int32

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

kd Int32

            The number of superdiagonals of the matrix A if UPLO = 'U',
            or the number of subdiagonals if UPLO = 'L'.  KD >= 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)
            The triangular factor U or L from the Cholesky factorization
            A = U^T*U or A = L*L^T of the band matrix A, stored in the
            first KD+1 rows of the array.  The j-th column of U or L is
            stored in the j-th column of the array AB as follows:
            if UPLO ='U', AB(kd+1+i-j,j) = U(i,j) for max(1,j-kd)<=i<=j;
            if UPLO ='L', AB(1+i-j,j)    = L(i,j) for j<=i<=min(n,j+kd).

            The leading dimension of the array AB.  LDAB >= KD+1.

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

Remarks

This method corresponds to the LAPACK routine ?PBTRS.

BandCholeskySolve(MatrixTriangle, Int32, Int32, Int32, ReadOnlySpan<TComplex>, Int32, Span<TComplex>, Int32, Int32)

Solves a system of linear equations A*X = B with a Hermitian positive definite band matrix A using the Cholesky factorization A = U^H *U or A = L*L^H computed by ZPBTRF.

public abstract void BandCholeskySolve(
	MatrixTriangle uplo,
	int n,
	int kd,
	int nrhs,
	ReadOnlySpan<TComplex> ab,
	int ldab,
	Span<TComplex> b,
	int ldb,
	out int info
)

Visual Basic

Public MustOverride Sub BandCholeskySolve ( 
	uplo As MatrixTriangle,
	n As Integer,
	kd As Integer,
	nrhs As Integer,
	ab As ReadOnlySpan(Of TComplex),
	ldab As Integer,
	b As Span(Of TComplex),
	ldb As Integer,
	<OutAttribute> ByRef info As Integer
)

C++/CLI

public:
virtual void BandCholeskySolve(
	MatrixTriangle uplo, 
	int n, 
	int kd, 
	int nrhs, 
	ReadOnlySpan<TComplex> ab, 
	int ldab, 
	Span<TComplex> b, 
	int ldb, 
	[OutAttribute] int% info
) abstract

abstract BandCholeskySolve : 
        uplo : MatrixTriangle * 
        n : int * 
        kd : int * 
        nrhs : int * 
        ab : ReadOnlySpan<'TComplex> * 
        ldab : int * 
        b : Span<'TComplex> * 
        ldb : int * 
        info : int byref -> unit

Parameters

uplo MatrixTriangle

            = 'U':  Upper triangular factor stored in AB;
            = 'L':  Lower triangular factor stored in AB.

n Int32

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

kd Int32

            The number of superdiagonals of the matrix A if UPLO = 'U',
            or the number of subdiagonals if UPLO = 'L'.  KD >= 0.

nrhs Int32

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

ab ReadOnlySpan<TComplex>

            AB is TComplex array, dimension (LDAB,N)
            The triangular factor U or L from the Cholesky factorization
            A = U^H *U or A = L*L^H of the band matrix A, stored in the
            first KD+1 rows of the array.  The j-th column of U or L is
            stored in the j-th column of the array AB as follows:
            if UPLO ='U', AB(kd+1+i-j,j) = U(i,j) for max(1,j-kd)<=i<=j;
            if UPLO ='L', AB(1+i-j,j)    = L(i,j) for j<=i<=min(n,j+kd).

ldab Int32

            The leading dimension of the array AB.  LDAB >= KD+1.

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

Remarks

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

Date: November 2011

BandCholeskySolve(MatrixTriangle, Int32, Int32, Int32, Span<TReal>, Int32, Span<TReal>, Int32, Int32)

Solves a system of linear equations A*X = B with a symmetric positive definite band matrix A using the Cholesky factorization A = U^T*U or A = L*L^T computed by DPBTRF.

public abstract void BandCholeskySolve(
	MatrixTriangle storedTriangle,
	int n,
	int kd,
	int nrhs,
	Span<TReal> ab,
	int ldab,
	Span<TReal> b,
	int ldb,
	out int info
)

Visual Basic

Public MustOverride Sub BandCholeskySolve ( 
	storedTriangle As MatrixTriangle,
	n As Integer,
	kd As Integer,
	nrhs As Integer,
	ab As Span(Of TReal),
	ldab As Integer,
	b As Span(Of TReal),
	ldb As Integer,
	<OutAttribute> ByRef info As Integer
)

C++/CLI

public:
virtual void BandCholeskySolve(
	MatrixTriangle storedTriangle, 
	int n, 
	int kd, 
	int nrhs, 
	Span<TReal> ab, 
	int ldab, 
	Span<TReal> b, 
	int ldb, 
	[OutAttribute] int% info
) abstract

abstract BandCholeskySolve : 
        storedTriangle : MatrixTriangle * 
        n : int * 
        kd : int * 
        nrhs : int * 
        ab : Span<'TReal> * 
        ldab : int * 
        b : Span<'TReal> * 
        ldb : int * 
        info : int byref -> unit

Parameters

storedTriangle MatrixTriangle

            = 'U':  Upper triangular factor stored in AB;
            = 'L':  Lower triangular factor stored in AB.

n Int32

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

kd Int32

            The number of superdiagonals of the matrix A if UPLO = 'U',
            or the number of subdiagonals if UPLO = 'L'.  KD >= 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)
            The triangular factor U or L from the Cholesky factorization
            A = U^T*U or A = L*L^T of the band matrix A, stored in the
            first KD+1 rows of the array.  The j-th column of U or L is
            stored in the j-th column of the array AB as follows:
            if UPLO ='U', AB(kd+1+i-j,j) = U(i,j) for max(1,j-kd)<=i<=j;
            if UPLO ='L', AB(1+i-j,j)    = L(i,j) for j<=i<=min(n,j+kd).

ldab Int32

            The leading dimension of the array AB.  LDAB >= KD+1.

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

Remarks

This method corresponds to the LAPACK routine ?PBTRS.

DecompositionOperations<TReal, TComplex>.BandCholeskySolve Method

Definition

Overload List

BandCholeskySolve(MatrixTriangle, Int32, Int32, Int32, Array2D<TReal>, Array2D<TReal>, Int32)

Parameters

Remarks

BandCholeskySolve(MatrixTriangle, Int32, Int32, Int32, Array2D<TComplex>, Array2D<TComplex>, Int32)

Parameters

Remarks

BandCholeskySolve(MatrixTriangle, Int32, Int32, Int32, ReadOnlySpan2D<TComplex>, Span2D<TComplex>, Int32)

Parameters

Remarks

BandCholeskySolve(MatrixTriangle, Int32, Int32, Int32, Span2D<TReal>, Span2D<TReal>, Int32)

Parameters

Remarks

BandCholeskySolve(MatrixTriangle, Int32, Int32, Int32, ReadOnlySpan<TComplex>, Int32, Span<TComplex>, Int32, Int32)

Parameters

Remarks

BandCholeskySolve(MatrixTriangle, Int32, Int32, Int32, Span<TReal>, Int32, Span<TReal>, Int32, Int32)

Parameters

Remarks

See Also

Reference