Linear
Definition
Assembly: Extreme.Numerics (in Extreme.Numerics.dll) Version: 8.1.23
Overload List
| Triangular | Solves one of the systems of equations A*x = b, or AT*x = b, where b and x are n element vectors and A is an n by n unit, or non-unit, upper or lower triangular matrix. |
| Triangular | Solves one of the systems of equations A*x = b, or AT*x = b, or AH*x = b, where b and x are n element vectors and A is an n by n unit, or non-unit, upper or lower triangular matrix. |
| Triangular | Solves one of the matrix equations op( A )*X = alpha*B, or X*op( A ) = alpha*B, where alpha is a scalar, X and B are m by n matrices, A is a unit, or non-unit, upper or lower triangular matrix and op( A ) is one of op( A ) = A or op( A ) = AT. |
| Triangular | Solves one of the matrix equations op( A )*X = alpha*B, or X*op( A ) = alpha*B, where alpha is a scalar, X and B are m by n matrices, A is a unit, or non-unit, upper or lower triangular matrix and op( A ) is one of op( A ) = A or op( A ) = AT or op( A ) = AH. |
TriangularSolveInPlace(MatrixTriangle, TransposeOperation, MatrixDiagonal, Int32, Array2D<T>, ArraySlice<T>)
Solves one of the systems of equations A*x = b, or AT*x = b, where b and x are n element vectors and A is an n by n unit, or non-unit, upper or lower triangular matrix.
public abstract void TriangularSolveInPlace(
MatrixTriangle uplo,
TransposeOperation trans,
MatrixDiagonal diag,
int n,
Array2D<T> a,
ArraySlice<T> x
)Parameters
- uplo MatrixTriangle
On entry, UPLO specifies whether the matrix is an upper or lower triangular matrix as follows: UPLO = 'U' or 'u' A is an upper triangular matrix. UPLO = 'L' or 'l' A is a lower triangular matrix.- trans TransposeOperation
On entry, TRANS specifies the equations to be solved as follows: TRANS = 'N' or 'n' A*x = b. TRANS = 'T' or 't' AT*x = b. TRANS = 'C' or 'c' AT*x = b.- diag MatrixDiagonal
On entry, DIAG specifies whether or not A is unit triangular as follows: DIAG = 'U' or 'u' A is assumed to be unit triangular. DIAG = 'N' or 'n' A is not assumed to be unit triangular.- n Int32
On entry, N specifies the order of the matrix A. N must be at least zero.- a Array2D<T>
A is DOUBLE PRECISION array of DIMENSION ( LDA, n ). Before entry with UPLO = 'U' or 'u', the leading n by n upper triangular part of the array A must contain the upper triangular matrix and the strictly lower triangular part of A is not referenced. Before entry with UPLO = 'L' or 'l', the leading n by n lower triangular part of the array A must contain the lower triangular matrix and the strictly upper triangular part of A is not referenced. Note that when DIAG = 'U' or 'u', the diagonal elements of A are not referenced either, but are assumed to be unity.On entry, LDA specifies the first dimension of A as declared in the calling (sub) program. LDA must be at least max( 1, n ).- x ArraySlice<T>
X is DOUBLE PRECISION array of dimension at least ( 1 + ( n - 1 )*abs( INCX ) ). Before entry, the incremented array X must contain the n element right-hand side vector b. On exit, X is overwritten with the solution vector x.On entry, INCX specifies the increment for the elements of X. INCX must not be zero. 2 LinearAlgebra routine. itten on 22-October-1986. ack Dongarra, Argonne National Lab. Jeremy Du Croz, Nag Central Office. Sven Hammarling, Nag Central Office. Richard Hanson, Sandia National Labs.
Implements
ILinearAlgebraOperations<T>.TriangularSolveInPlace(MatrixTriangle, TransposeOperation, MatrixDiagonal, Int32, Array2D<T>, ArraySlice<T>)Remarks
No test for singularity or near-singularity is included in this
routine. Such tests must be performed before calling this routine.
Authors: Univ. of Tennessee, Univ. of California Berkeley, Univ. of Colorado Denver, NAG Ltd.
Date: November 2011
TriangularSolveInPlace(MatrixTriangle, TransposeOperation, MatrixDiagonal, Int32, Array2D<Complex<T>>, ArraySlice<Complex<T>>)
Solves one of the systems of equations A*x = b, or AT*x = b, or AH*x = b, where b and x are n element vectors and A is an n by n unit, or non-unit, upper or lower triangular matrix.
public abstract void TriangularSolveInPlace(
MatrixTriangle uplo,
TransposeOperation trans,
MatrixDiagonal diag,
int n,
Array2D<Complex<T>> a,
ArraySlice<Complex<T>> x
)Parameters
- uplo MatrixTriangle
On entry, UPLO specifies whether the matrix is an upper or lower triangular matrix as follows: UPLO = 'U' or 'u' A is an upper triangular matrix. UPLO = 'L' or 'l' A is a lower triangular matrix.- trans TransposeOperation
On entry, TRANS specifies the equations to be solved as follows: TRANS = 'N' or 'n' A*x = b. TRANS = 'T' or 't' AT*x = b. TRANS = 'C' or 'c' AH*x = b.- diag MatrixDiagonal
On entry, DIAG specifies whether or not A is unit triangular as follows: DIAG = 'U' or 'u' A is assumed to be unit triangular. DIAG = 'N' or 'n' A is not assumed to be unit triangular.- n Int32
On entry, N specifies the order of the matrix A. N must be at least zero.- a Array2D<Complex<T>>
A is complex array of DIMENSION ( LDA, n ). Before entry with UPLO = 'U' or 'u', the leading n by n upper triangular part of the array A must contain the upper triangular matrix and the strictly lower triangular part of A is not referenced. Before entry with UPLO = 'L' or 'l', the leading n by n lower triangular part of the array A must contain the lower triangular matrix and the strictly upper triangular part of A is not referenced. Note that when DIAG = 'U' or 'u', the diagonal elements of A are not referenced either, but are assumed to be unity.On entry, LDA specifies the first dimension of A as declared in the calling (sub) program. LDA must be at least max( 1, n ).- x ArraySlice<Complex<T>>
X is complex array of dimension at least ( 1 + ( n - 1 )*abs( INCX ) ). Before entry, the incremented array X must contain the n element right-hand side vector b. On exit, X is overwritten with the solution vector x.On entry, INCX specifies the increment for the elements of X. INCX must not be zero.
Implements
ILinearAlgebraOperations<T>.TriangularSolveInPlace(MatrixTriangle, TransposeOperation, MatrixDiagonal, Int32, Array2D<T>, ArraySlice<T>)Remarks
No test for singularity or near-singularity is included in this
routine. Such tests must be performed before calling this routine.
Further Details:
Level 2 LinearAlgebra routine.
-- Written on 22-October-1986.
Jack Dongarra, Argonne National Lab.
Jeremy Du Croz, Nag Central Office.
Sven Hammarling, Nag Central Office.
Richard Hanson, Sandia National Labs.
Authors: Univ. of Tennessee, Univ. of California Berkeley, Univ. of Colorado Denver, NAG Ltd.
Date: November 2011
TriangularSolveInPlace(MatrixOperationSide, MatrixTriangle, TransposeOperation, MatrixDiagonal, Int32, Int32, T, Array2D<T>, Array2D<T>)
Solves one of the matrix equations op( A )*X = alpha*B, or X*op( A ) = alpha*B, where alpha is a scalar, X and B are m by n matrices, A is a unit, or non-unit, upper or lower triangular matrix and op( A ) is one of op( A ) = A or op( A ) = AT.
public abstract void TriangularSolveInPlace(
MatrixOperationSide side,
MatrixTriangle uplo,
TransposeOperation transa,
MatrixDiagonal diag,
int m,
int n,
T alpha,
Array2D<T> a,
Array2D<T> b
)Parameters
- side MatrixOperationSide
On entry, SIDE specifies whether op( A ) appears on the left or right of X as follows: SIDE = 'L' or 'l' op( A )*X = alpha*B. SIDE = 'R' or 'r' X*op( A ) = alpha*B.- uplo MatrixTriangle
On entry, UPLO specifies whether the matrix A is an upper or lower triangular matrix as follows: UPLO = 'U' or 'u' A is an upper triangular matrix. UPLO = 'L' or 'l' A is a lower triangular matrix.- transa TransposeOperation
On entry, TRANSA specifies the form of op( A ) to be used in the matrix multiplication as follows: TRANSA = 'N' or 'n' op( A ) = A. TRANSA = 'T' or 't' op( A ) = AT. TRANSA = 'C' or 'c' op( A ) = AT.- diag MatrixDiagonal
On entry, DIAG specifies whether or not A is unit triangular as follows: DIAG = 'U' or 'u' A is assumed to be unit triangular. DIAG = 'N' or 'n' A is not assumed to be unit triangular.- m Int32
On entry, M specifies the number of rows of B. M must be at least zero.- n Int32
On entry, N specifies the number of columns of B. N must be at least zero.- alpha T
ALPHA is DOUBLE PRECISION. On entry, ALPHA specifies the scalar alpha. When alpha is zero then A is not referenced and B need not be set before entry.- a Array2D<T>
A is DOUBLE PRECISION array of DIMENSION ( LDA, k ), where k is m when SIDE = 'L' or 'l' and k is n when SIDE = 'R' or 'r'. Before entry with UPLO = 'U' or 'u', the leading k by k upper triangular part of the array A must contain the upper triangular matrix and the strictly lower triangular part of A is not referenced. Before entry with UPLO = 'L' or 'l', the leading k by k lower triangular part of the array A must contain the lower triangular matrix and the strictly upper triangular part of A is not referenced. Note that when DIAG = 'U' or 'u', the diagonal elements of A are not referenced either, but are assumed to be unity.On entry, LDA specifies the first dimension of A as declared in the calling (sub) program. When SIDE = 'L' or 'l' then LDA must be at least max( 1, m ), when SIDE = 'R' or 'r' then LDA must be at least max( 1, n ).- b Array2D<T>
B is DOUBLE PRECISION array of DIMENSION ( LDB, n ). Before entry, the leading m by n part of the array B must contain the right-hand side matrix B, and on exit is overwritten by the solution matrix X.On entry, LDB specifies the first dimension of B as declared in the calling (sub) program. LDB must be at least max( 1, m ).
Implements
ILinearAlgebraOperations<T>.TriangularSolveInPlace(MatrixOperationSide, MatrixTriangle, TransposeOperation, MatrixDiagonal, Int32, Int32, T, Array2D<T>, Array2D<T>)Remarks
The matrix X is overwritten on B.
Further Details:
Level 3 LinearAlgebra routine.
-- Written on 8-February-1989.
Jack Dongarra, Argonne National Laboratory.
Iain Duff, AERE Harwell.
Jeremy Du Croz, Numerical Algorithms Group Ltd.
Sven Hammarling, Numerical Algorithms Group Ltd.
Authors: Univ. of Tennessee, Univ. of California Berkeley, Univ. of Colorado Denver, NAG Ltd.
Date: November 2011
TriangularSolveInPlace(MatrixOperationSide, MatrixTriangle, TransposeOperation, MatrixDiagonal, Int32, Int32, Complex<T>, Array2D<Complex<T>>, Array2D<Complex<T>>)
Solves one of the matrix equations op( A )*X = alpha*B, or X*op( A ) = alpha*B, where alpha is a scalar, X and B are m by n matrices, A is a unit, or non-unit, upper or lower triangular matrix and op( A ) is one of op( A ) = A or op( A ) = AT or op( A ) = AH.
public abstract void TriangularSolveInPlace(
MatrixOperationSide side,
MatrixTriangle uplo,
TransposeOperation transa,
MatrixDiagonal diag,
int m,
int n,
Complex<T> alpha,
Array2D<Complex<T>> a,
Array2D<Complex<T>> b
)Parameters
- side MatrixOperationSide
On entry, SIDE specifies whether op( A ) appears on the left or right of X as follows: SIDE = 'L' or 'l' op( A )*X = alpha*B. SIDE = 'R' or 'r' X*op( A ) = alpha*B.- uplo MatrixTriangle
On entry, UPLO specifies whether the matrix A is an upper or lower triangular matrix as follows: UPLO = 'U' or 'u' A is an upper triangular matrix. UPLO = 'L' or 'l' A is a lower triangular matrix.- transa TransposeOperation
On entry, TRANSA specifies the form of op( A ) to be used in the matrix multiplication as follows: TRANSA = 'N' or 'n' op( A ) = A. TRANSA = 'T' or 't' op( A ) = AT. TRANSA = 'C' or 'c' op( A ) = AH.- diag MatrixDiagonal
On entry, DIAG specifies whether or not A is unit triangular as follows: DIAG = 'U' or 'u' A is assumed to be unit triangular. DIAG = 'N' or 'n' A is not assumed to be unit triangular.- m Int32
On entry, M specifies the number of rows of B. M must be at least zero.- n Int32
On entry, N specifies the number of columns of B. N must be at least zero.- alpha Complex<T>
On entry, ALPHA specifies the scalar alpha. When alpha is zero then A is not referenced and B need not be set before entry.- a Array2D<Complex<T>>
A is complex array of DIMENSION ( LDA, k ), where k is m when SIDE = 'L' or 'l' and k is n when SIDE = 'R' or 'r'. Before entry with UPLO = 'U' or 'u', the leading k by k upper triangular part of the array A must contain the upper triangular matrix and the strictly lower triangular part of A is not referenced. Before entry with UPLO = 'L' or 'l', the leading k by k lower triangular part of the array A must contain the lower triangular matrix and the strictly upper triangular part of A is not referenced. Note that when DIAG = 'U' or 'u', the diagonal elements of A are not referenced either, but are assumed to be unity.On entry, LDA specifies the first dimension of A as declared in the calling (sub) program. When SIDE = 'L' or 'l' then LDA must be at least max( 1, m ), when SIDE = 'R' or 'r' then LDA must be at least max( 1, n ).- b Array2D<Complex<T>>
B is complex array of DIMENSION ( LDB, n ). Before entry, the leading m by n part of the array B must contain the right-hand side matrix B, and on exit is overwritten by the solution matrix X.On entry, LDB specifies the first dimension of B as declared in the calling (sub) program. LDB must be at least max( 1, m ).
Implements
ILinearAlgebraOperations<T>.TriangularSolveInPlace(MatrixOperationSide, MatrixTriangle, TransposeOperation, MatrixDiagonal, Int32, Int32, T, Array2D<T>, Array2D<T>)Remarks
The matrix X is overwritten on B.
Further Details:
Level 3 LinearAlgebra routine.
-- Written on 8-February-1989.
Jack Dongarra, Argonne National Laboratory.
Iain Duff, AERE Harwell.
Jeremy Du Croz, Numerical Algorithms Group Ltd.
Sven Hammarling, Numerical Algorithms Group Ltd.
Authors: Univ. of Tennessee, Univ. of California Berkeley, Univ. of Colorado Denver, NAG Ltd.
Date: November 2011