Decomposition Operations<TReal, TComplex>.LUSolve Method
Definition
Namespace: Numerics.NET.LinearAlgebra.Implementation
Assembly: Numerics.NET (in Numerics.NET.dll) Version: 9.0.3
Assembly: Numerics.NET (in Numerics.NET.dll) Version: 9.0.3
Overload List
LUSolve( | Solves a system of linear equations with a general N-by-N matrix A using the LU decomposition computed by LUDecompose(Int32, Int32, Span<TReal>, Int32, Span<Int32>, Int32). |
LUSolve( | ZGETRS solves a system of linear equations A * X = B or A' * X = B with a general N-by-N matrix A using the LU decomposition computed by ZGETRF. Arguments ========= TRANS (input) CHARACTER*1 Specifies the form of the system of equations: = 'N': A * X = B (No transpose) = TransposeOperation.Transpose: A'* X = B (Transpose) = 'C': A'* X = B (Conjugate transpose = Transpose) N (input) INTEGER The elementOrder of the matrix A. N >= 0. NRHS (input) INTEGER The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0. A (input) DOUBLE PRECISION array, dimension (LDA,N) The factors L and U from the decomposition A = P*L*U as computed by ZGETRF. LDA (input) INTEGER The leading dimension of the array A. LDA >= Max(1,N). IPIV (input) INTEGER array, dimension (N) The pivot indexes from ZGETRF; for 1< =i< =N, row i of the matrix was interchanged with row IPIVi. B (input/output) DOUBLE PRECISION array, dimension (LDB,NRHS) On entry, the right hand side matrix B. On exit, the solution matrix X. LDB (input) INTEGER The leading dimension of the array B. LDB >= Max(1,N). INFO (output) INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value ===================================================================== |
LUSolve( | Solves a system of linear equations with a general N-by-N matrix A using the LU decomposition computed by LUDecompose(Int32, Int32, Span<TReal>, Int32, Span<Int32>, Int32). |
LUSolve( | ZGETRS solves a system of linear equations A * X = B or A' * X = B with a general N-by-N matrix A using the LU decomposition computed by ZGETRF. Arguments ========= TRANS (input) CHARACTER*1 Specifies the form of the system of equations: = 'N': A * X = B (No transpose) = TransposeOperation.Transpose: A'* X = B (Transpose) = 'C': A'* X = B (Conjugate transpose = Transpose) N (input) INTEGER The elementOrder of the matrix A. N >= 0. NRHS (input) INTEGER The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0. A (input) DOUBLE PRECISION array, dimension (LDA,N) The factors L and U from the decomposition A = P*L*U as computed by ZGETRF. LDA (input) INTEGER The leading dimension of the array A. LDA >= Max(1,N). IPIV (input) INTEGER array, dimension (N) The pivot indexes from ZGETRF; for 1< =i< =N, row i of the matrix was interchanged with row IPIVi. B (input/output) DOUBLE PRECISION array, dimension (LDB,NRHS) On entry, the right hand side matrix B. On exit, the solution matrix X. LDB (input) INTEGER The leading dimension of the array B. LDB >= Max(1,N). INFO (output) INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value ===================================================================== |
LUSolve( | Solves a system of linear equations with a general N-by-N matrix A using the LU decomposition computed by LUDecompose(Int32, Int32, Span<TReal>, Int32, Span<Int32>, Int32). |
LUSolve( | ZGETRS solves a system of linear equations A * X = B or A' * X = B with a general N-by-N matrix A using the LU decomposition computed by ZGETRF. Arguments ========= TRANS (input) CHARACTER*1 Specifies the form of the system of equations: = 'N': A * X = B (No transpose) = TransposeOperation.Transpose: A'* X = B (Transpose) = 'C': A'* X = B (Conjugate transpose = Transpose) N (input) INTEGER The elementOrder of the matrix A. N >= 0. NRHS (input) INTEGER The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0. A (input) DOUBLE PRECISION array, dimension (LDA,N) The factors L and U from the decomposition A = P*L*U as computed by ZGETRF. LDA (input) INTEGER The leading dimension of the array A. LDA >= Max(1,N). IPIV (input) INTEGER array, dimension (N) The pivot indexes from ZGETRF; for 1< =i< =N, row i of the matrix was interchanged with row IPIVi. B (input/output) DOUBLE PRECISION array, dimension (LDB,NRHS) On entry, the right hand side matrix B. On exit, the solution matrix X. LDB (input) INTEGER The leading dimension of the array B. LDB >= Max(1,N). INFO (output) INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value ===================================================================== |
LUSolve(TransposeOperation, Int32, Int32, Array2D<TReal>, Array1D<Int32>, Array2D<TReal>, Int32)
Solves a system of linear equations
with a general N-by-N matrix A using the LU decomposition computed
by LUDecompose(Int32, Int32, Span<TReal>, Int32, Span<Int32>, Int32).
public void LUSolve(
TransposeOperation trans,
int n,
int nrhs,
Array2D<TReal> a,
Array1D<int> ipiv,
Array2D<TReal> b,
out int info
)
Parameters
- trans TransposeOperation
- A TransposeOperation value that specifies whether the regular or the transposed system should be solved.
- n Int32
- An integer specifying the number of rows and columns of the matrix a. Must be greater than or equal to zero.
- nrhs Int32
- An integer specifying the number of columns in the right-hand side matrix b. Must be greater than or equal to zero.
- a Array2D<TReal>
- TReal array specifying the n-by-n matrix containing the lower and upper triangular factors as computed by LUDecompose(Int32, Int32, Span<TReal>, Int32, Span<Int32>, Int32).
- ipiv Array1D<Int32>
- Integer array that contains the pivot indexes computed by LUDecompose(Int32, Int32, Span<TReal>, Int32, Span<Int32>, Int32).
- b Array2D<TReal>
- TReal array specifying the nrhs-by-n matrix containing the right-hand sides. On exit, this matrix is overwritten with the solution.
- info Int32
- Reference to an integer containing a result code. Zero indicates success. Greater than zero indicates U(i,i) is exactly zero. The decomposition has been completed, but the factor U is exactly singular, and division by zero will occur if it is used to solve a system of equations.
LUSolve(TransposeOperation, Int32, Int32, Array2D<TComplex>, Array1D<Int32>, Array2D<TComplex>, Int32)
ZGETRS solves a system of linear equations
A * X = B or A' * X = B
with a general N-by-N matrix A using the LU decomposition computed
by ZGETRF.
Arguments
=========
TRANS (input) CHARACTER*1
Specifies the form of the system of equations:
= 'N': A * X = B (No transpose)
= TransposeOperation.Transpose: A'* X = B (Transpose)
= 'C': A'* X = B (Conjugate transpose = Transpose)
N (input) INTEGER
The elementOrder of the matrix A. N >= 0.
NRHS (input) INTEGER
The number of right hand sides, i.e., the number of columns
of the matrix B. NRHS >= 0.
A (input) DOUBLE PRECISION array, dimension (LDA,N)
The factors L and U from the decomposition A = P*L*U
as computed by ZGETRF.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= Max(1,N).
IPIV (input) INTEGER array, dimension (N)
The pivot indexes from ZGETRF; for 1< =i< =N, row i of the
matrix was interchanged with row IPIVi.
B (input/output) DOUBLE PRECISION array, dimension (LDB,NRHS)
On entry, the right hand side matrix B.
On exit, the solution matrix X.
LDB (input) INTEGER
The leading dimension of the array B. LDB >= Max(1,N).
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
=====================================================================
public void LUSolve(
TransposeOperation trans,
int n,
int nrhs,
Array2D<TComplex> a,
Array1D<int> ipiv,
Array2D<TComplex> b,
out int info
)
Parameters
LUSolve(TransposeOperation, Int32, Int32, Span2D<TReal>, Span<Int32>, Span2D<TReal>, Int32)
Solves a system of linear equations
with a general N-by-N matrix A using the LU decomposition computed
by LUDecompose(Int32, Int32, Span<TReal>, Int32, Span<Int32>, Int32).
public void LUSolve(
TransposeOperation trans,
int n,
int nrhs,
Span2D<TReal> a,
Span<int> ipiv,
Span2D<TReal> b,
out int info
)
Parameters
- trans TransposeOperation
- A TransposeOperation value that specifies whether the regular or the transposed system should be solved.
- n Int32
- An integer specifying the number of rows and columns of the matrix a. Must be greater than or equal to zero.
- nrhs Int32
- An integer specifying the number of columns in the right-hand side matrix b. Must be greater than or equal to zero.
- a Span2D<TReal>
- TReal array specifying the n-by-n matrix containing the lower and upper triangular factors as computed by LUDecompose(Int32, Int32, Span<TReal>, Int32, Span<Int32>, Int32).
- ipiv Span<Int32>
- Integer array that contains the pivot indexes computed by LUDecompose(Int32, Int32, Span<TReal>, Int32, Span<Int32>, Int32).
- b Span2D<TReal>
- TReal array specifying the nrhs-by-n matrix containing the right-hand sides. On exit, this matrix is overwritten with the solution.
- info Int32
- Reference to an integer containing a result code. Zero indicates success. Greater than zero indicates U(i,i) is exactly zero. The decomposition has been completed, but the factor U is exactly singular, and division by zero will occur if it is used to solve a system of equations.
LUSolve(TransposeOperation, Int32, Int32, Span2D<TComplex>, Span<Int32>, Span2D<TComplex>, Int32)
ZGETRS solves a system of linear equations
A * X = B or A' * X = B
with a general N-by-N matrix A using the LU decomposition computed
by ZGETRF.
Arguments
=========
TRANS (input) CHARACTER*1
Specifies the form of the system of equations:
= 'N': A * X = B (No transpose)
= TransposeOperation.Transpose: A'* X = B (Transpose)
= 'C': A'* X = B (Conjugate transpose = Transpose)
N (input) INTEGER
The elementOrder of the matrix A. N >= 0.
NRHS (input) INTEGER
The number of right hand sides, i.e., the number of columns
of the matrix B. NRHS >= 0.
A (input) DOUBLE PRECISION array, dimension (LDA,N)
The factors L and U from the decomposition A = P*L*U
as computed by ZGETRF.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= Max(1,N).
IPIV (input) INTEGER array, dimension (N)
The pivot indexes from ZGETRF; for 1< =i< =N, row i of the
matrix was interchanged with row IPIVi.
B (input/output) DOUBLE PRECISION array, dimension (LDB,NRHS)
On entry, the right hand side matrix B.
On exit, the solution matrix X.
LDB (input) INTEGER
The leading dimension of the array B. LDB >= Max(1,N).
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
=====================================================================
public void LUSolve(
TransposeOperation trans,
int n,
int nrhs,
Span2D<TComplex> a,
Span<int> ipiv,
Span2D<TComplex> b,
out int info
)
Parameters
LUSolve(TransposeOperation, Int32, Int32, Span<TReal>, Int32, Span<Int32>, Span<TReal>, Int32, Int32)
Solves a system of linear equations
with a general N-by-N matrix A using the LU decomposition computed
by LUDecompose(Int32, Int32, Span<TReal>, Int32, Span<Int32>, Int32).
public abstract void LUSolve(
TransposeOperation trans,
int n,
int nrhs,
Span<TReal> a,
int lda,
Span<int> ipiv,
Span<TReal> b,
int ldb,
out int info
)
Parameters
- trans TransposeOperation
- A TransposeOperation value that specifies whether the regular or the transposed system should be solved.
- n Int32
- An integer specifying the number of rows and columns of the matrix a. Must be greater than or equal to zero.
- nrhs Int32
- An integer specifying the number of columns in the right-hand side matrix b. Must be greater than or equal to zero.
- a Span<TReal>
- TReal array specifying the n-by-n matrix containing the lower and upper triangular factors as computed by LUDecompose(Int32, Int32, Span<TReal>, Int32, Span<Int32>, Int32).
- lda Int32
- The leading dimension of the matrix a.
- ipiv Span<Int32>
- Integer array that contains the pivot indexes computed by LUDecompose(Int32, Int32, Span<TReal>, Int32, Span<Int32>, Int32).
- b Span<TReal>
- TReal array specifying the nrhs-by-n matrix containing the right-hand sides. On exit, this matrix is overwritten with the solution.
- ldb Int32
- The leading dimension of the matrix b.
- info Int32
- Reference to an integer containing a result code. Zero indicates success. Greater than zero indicates U(i,i) is exactly zero. The decomposition has been completed, but the factor U is exactly singular, and division by zero will occur if it is used to solve a system of equations.
LUSolve(TransposeOperation, Int32, Int32, Span<TComplex>, Int32, Span<Int32>, Span<TComplex>, Int32, Int32)
ZGETRS solves a system of linear equations
A * X = B or A' * X = B
with a general N-by-N matrix A using the LU decomposition computed
by ZGETRF.
Arguments
=========
TRANS (input) CHARACTER*1
Specifies the form of the system of equations:
= 'N': A * X = B (No transpose)
= TransposeOperation.Transpose: A'* X = B (Transpose)
= 'C': A'* X = B (Conjugate transpose = Transpose)
N (input) INTEGER
The elementOrder of the matrix A. N >= 0.
NRHS (input) INTEGER
The number of right hand sides, i.e., the number of columns
of the matrix B. NRHS >= 0.
A (input) DOUBLE PRECISION array, dimension (LDA,N)
The factors L and U from the decomposition A = P*L*U
as computed by ZGETRF.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= Max(1,N).
IPIV (input) INTEGER array, dimension (N)
The pivot indexes from ZGETRF; for 1< =i< =N, row i of the
matrix was interchanged with row IPIVi.
B (input/output) DOUBLE PRECISION array, dimension (LDB,NRHS)
On entry, the right hand side matrix B.
On exit, the solution matrix X.
LDB (input) INTEGER
The leading dimension of the array B. LDB >= Max(1,N).
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
=====================================================================
public abstract void LUSolve(
TransposeOperation trans,
int n,
int nrhs,
Span<TComplex> a,
int lda,
Span<int> ipiv,
Span<TComplex> b,
int ldb,
out int info
)