Decomposition Operations<TReal, TComplex>.Band Cholesky Solve Method
Definition
Assembly: Numerics.NET (in Numerics.NET.dll) Version: 9.0.3
Overload List
Band | Solves a system of linear equations A*X = B with a symmetric positive definite band matrix A using the Cholesky factorization A = UT*U or A = L*LT computed by DPBTRF. |
Band | Solves a system of linear equations A*X = B with a Hermitian positive definite band matrix A using the Cholesky factorization A = UH *U or A = L*LH computed by ZPBTRF. |
Band | Solves a system of linear equations A*X = B with a Hermitian positive definite band matrix A using the Cholesky factorization A = UH *U or A = L*LH computed by ZPBTRF. |
Band | Solves a system of linear equations A*X = B with a symmetric positive definite band matrix A using the Cholesky factorization A = UT*U or A = L*LT computed by DPBTRF. |
Band | Solves a system of linear equations A*X = B with a Hermitian positive definite band matrix A using the Cholesky factorization A = UH *U or A = L*LH computed by ZPBTRF. |
Band | Solves a system of linear equations A*X = B with a symmetric positive definite band matrix A using the Cholesky factorization A = UT*U or A = L*LT 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 = UT*U or A = L*LT computed by DPBTRF.
public void BandCholeskySolve(
MatrixTriangle storedTriangle,
int n,
int kd,
int nrhs,
Array2D<TReal> ab,
Array2D<TReal> b,
out int info
)
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 = UT*U or A = L*LT 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 = UH *U or A = L*LH computed by ZPBTRF.
public void BandCholeskySolve(
MatrixTriangle uplo,
int n,
int kd,
int nrhs,
Array2D<TComplex> ab,
Array2D<TComplex> b,
out int info
)
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 = UH *U or A = L*LH 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 = UH *U or A = L*LH computed by ZPBTRF.
public void BandCholeskySolve(
MatrixTriangle uplo,
int n,
int kd,
int nrhs,
ReadOnlySpan2D<TComplex> ab,
Span2D<TComplex> b,
out int info
)
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 = UH *U or A = L*LH 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 = UT*U or A = L*LT computed by DPBTRF.
public void BandCholeskySolve(
MatrixTriangle storedTriangle,
int n,
int kd,
int nrhs,
Span2D<TReal> ab,
Span2D<TReal> b,
out int info
)
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 = UT*U or A = L*LT 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 = UH *U or A = L*LH 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
)
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 = UH *U or A = L*LH 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 = UT*U or A = L*LT 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
)
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 = UT*U or A = L*LT 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.