Linear Algebra Operations Extensions.Symmetric Rank Update Method
Definition
Assembly: Numerics.NET (in Numerics.NET.dll) Version: 9.0.3
Overload List
SymmetricRankUpdate<T>(ILinearAlgebraOperations<T>, MatrixTriangle, Int32, T, ReadOnlySpanSlice<T>, Span2D<T>)
Performs the symmetric rank 1 operation A := alpha*x*x**T + A, where alpha is a real scalar, x is an n element vector and A is an n by n symmetric matrix.
public static void SymmetricRankUpdate<T>(
this ILinearAlgebraOperations<T> operations,
MatrixTriangle uplo,
int n,
T alpha,
ReadOnlySpanSlice<T> x,
Span2D<T> a
)
Parameters
- operations ILinearAlgebraOperations<T>
- The object that performs the operation.
- uplo MatrixTriangle
On entry, UPLO specifies whether the upper or lower triangular part of the array A is to be referenced as follows: UPLO = 'U' or 'u' Only the upper triangular part of A is to be referenced. UPLO = 'L' or 'l' Only the lower triangular part of A is to be referenced.
- n Int32
On entry, N specifies the order of the matrix A. N must be at least zero.
- alpha T
ALPHA is DOUBLE PRECISION. On entry, ALPHA specifies the scalar alpha.
- x ReadOnlySpanSlice<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 vector x.
On entry, INCX specifies the increment for the elements of X. INCX must not be zero.
- a Span2D<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 part of the symmetric matrix and the strictly lower triangular part of A is not referenced. On exit, the upper triangular part of the array A is overwritten by the upper triangular part of the updated matrix. Before entry with UPLO = 'L' or 'l', the leading n by n lower triangular part of the array A must contain the lower triangular part of the symmetric matrix and the strictly upper triangular part of A is not referenced. On exit, the lower triangular part of the array A is overwritten by the lower triangular part of the updated matrix.
On entry, LDA specifies the first dimension of A as declared in the calling (sub) program. LDA must be at least max( 1, n ).
Type Parameters
- T
Usage Note
In Visual Basic and C#, you can call this method as an instance method on any object of type ILinearAlgebraOperations<T>. When you use instance method syntax to call this method, omit the first parameter. For more information, see Extension Methods (Visual Basic) or Extension Methods (C# Programming Guide).Remarks
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
SymmetricRankUpdate<T, TStorage, TStorage2D>(ILinearAlgebraOperations<T>, MatrixTriangle, Int32, T, TStorage, TStorage2D)
public static void SymmetricRankUpdate<T, TStorage, TStorage2D>(
this ILinearAlgebraOperations<T> operations,
MatrixTriangle storedTriangle,
int n,
T alpha,
TStorage x,
TStorage2D a
)
where TStorage : Object, IStorageSlice<T>
where TStorage2D : Object, IStorage2D<T>
Parameters
- operations ILinearAlgebraOperations<T>
- The linear algebra operations instance used to perform the calculation.
- storedTriangle MatrixTriangle
- Specifies whether the matrix is an upper or lower triangular matrix.
- n Int32
- The number of rows and columns in the matrix a.
- alpha T
- The scalar used to multiply the outer product.
- x TStorage
- A reference to a one-dimensional array containing the elements of the vector x.
- a TStorage2D
- A span that contains the elements of the matrix.
Type Parameters
- T
- TStorage
- TStorage2D
Usage Note
In Visual Basic and C#, you can call this method as an instance method on any object of type ILinearAlgebraOperations<T>. When you use instance method syntax to call this method, omit the first parameter. For more information, see Extension Methods (Visual Basic) or Extension Methods (C# Programming Guide).Remarks
This method is similar to the BLAS routine DSYR.
SymmetricRankUpdate<T>(ILinearAlgebraOperations<T>, MatrixTriangle, Int32, T, ReadOnlySpanSlice<T>, ReadOnlySpanSlice<T>, Span2D<T>)
Performs the symmetric rank 2 operation A := alpha*x*y**T + alpha*y*x**T + A, where alpha is a scalar, x and y are n element vectors and A is an n by n symmetric matrix.
public static void SymmetricRankUpdate<T>(
this ILinearAlgebraOperations<T> operations,
MatrixTriangle uplo,
int n,
T alpha,
ReadOnlySpanSlice<T> x,
ReadOnlySpanSlice<T> y,
Span2D<T> a
)
Parameters
- operations ILinearAlgebraOperations<T>
- The object that performs the operation.
- uplo MatrixTriangle
On entry, UPLO specifies whether the upper or lower triangular part of the array A is to be referenced as follows: UPLO = 'U' or 'u' Only the upper triangular part of A is to be referenced. UPLO = 'L' or 'l' Only the lower triangular part of A is to be referenced.
- n Int32
On entry, N specifies the order of the matrix A. N must be at least zero.
- alpha T
ALPHA is DOUBLE PRECISION. On entry, ALPHA specifies the scalar alpha.
- x ReadOnlySpanSlice<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 vector x.
On entry, INCX specifies the increment for the elements of X. INCX must not be zero.
- y ReadOnlySpanSlice<T>
Y is DOUBLE PRECISION array of dimension at least ( 1 + ( n - 1 )*abs( INCY ) ). Before entry, the incremented array Y must contain the n element vector y.
On entry, INCY specifies the increment for the elements of Y. INCY must not be zero.
- a Span2D<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 part of the symmetric matrix and the strictly lower triangular part of A is not referenced. On exit, the upper triangular part of the array A is overwritten by the upper triangular part of the updated matrix. Before entry with UPLO = 'L' or 'l', the leading n by n lower triangular part of the array A must contain the lower triangular part of the symmetric matrix and the strictly upper triangular part of A is not referenced. On exit, the lower triangular part of the array A is overwritten by the lower triangular part of the updated matrix.
On entry, LDA specifies the first dimension of A as declared in the calling (sub) program. LDA must be at least max( 1, n ).
Type Parameters
- T
Usage Note
In Visual Basic and C#, you can call this method as an instance method on any object of type ILinearAlgebraOperations<T>. When you use instance method syntax to call this method, omit the first parameter. For more information, see Extension Methods (Visual Basic) or Extension Methods (C# Programming Guide).Remarks
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
SymmetricRankUpdate<T, TStorage, TStorage2D>(ILinearAlgebraOperations<T>, MatrixTriangle, Int32, T, TStorage, TStorage, TStorage2D)
public static void SymmetricRankUpdate<T, TStorage, TStorage2D>(
this ILinearAlgebraOperations<T> operations,
MatrixTriangle storedTriangle,
int n,
T alpha,
TStorage x,
TStorage y,
TStorage2D a
)
where TStorage : Object, IStorageSlice<T>
where TStorage2D : Object, IStorage2D<T>
Parameters
- operations ILinearAlgebraOperations<T>
- The linear algebra operations instance used to perform the calculation.
- storedTriangle MatrixTriangle
- Specifies whether the matrix is an upper or lower triangular matrix.
- n Int32
- The number of rows and columns in the matrix a.
- alpha T
- The scalar used to multiply the outer product.
- x TStorage
- A reference to a one-dimensional array containing the elements of the vector x.
- y TStorage
- A reference to a one-dimensional array containing the elements of the vector y.
- a TStorage2D
- A span that contains the elements of the matrix.
Type Parameters
- T
- TStorage
- TStorage2D
Usage Note
In Visual Basic and C#, you can call this method as an instance method on any object of type ILinearAlgebraOperations<T>. When you use instance method syntax to call this method, omit the first parameter. For more information, see Extension Methods (Visual Basic) or Extension Methods (C# Programming Guide).Remarks
This method is similar to the BLAS routine DSYR2.
SymmetricRankUpdate<T>(ILinearAlgebraOperations<T>, MatrixTriangle, TransposeOperation, Int32, Int32, T, ReadOnlySpan2D<T>, T, Span2D<T>)
Performs one of the symmetric rank k operations C := alpha*A*AT + beta*C, or C := alpha*AT*A + beta*C, where alpha and beta are scalars, C is an n by n symmetric matrix and A is an n by k matrix in the first case and a k by n matrix in the second case.
public static void SymmetricRankUpdate<T>(
this ILinearAlgebraOperations<T> operations,
MatrixTriangle uplo,
TransposeOperation trans,
int n,
int k,
T alpha,
ReadOnlySpan2D<T> a,
T beta,
Span2D<T> c
)
Parameters
- operations ILinearAlgebraOperations<T>
- The object that performs the operation.
- uplo MatrixTriangle
On entry, UPLO specifies whether the upper or lower triangular part of the array C is to be referenced as follows: UPLO = 'U' or 'u' Only the upper triangular part of C is to be referenced. UPLO = 'L' or 'l' Only the lower triangular part of C is to be referenced.
- trans TransposeOperation
On entry, TRANS specifies the operation to be performed as follows: TRANS = 'N' or 'n' C := alpha*A*AT + beta*C. TRANS = 'T' or 't' C := alpha*AT*A + beta*C. TRANS = 'C' or 'c' C := alpha*AT*A + beta*C.
- n Int32
On entry, N specifies the order of the matrix C. N must be at least zero.
- k Int32
On entry with TRANS = 'N' or 'n', K specifies the number of columns of the matrix A, and on entry with TRANS = 'T' or 't' or 'C' or 'c', K specifies the number of rows of the matrix A. K must be at least zero.
- alpha T
ALPHA is DOUBLE PRECISION. On entry, ALPHA specifies the scalar alpha.
- a ReadOnlySpan2D<T>
A is DOUBLE PRECISION array of DIMENSION ( LDA, ka ), where ka is k when TRANS = 'N' or 'n', and is n otherwise. Before entry with TRANS = 'N' or 'n', the leading n by k part of the array A must contain the matrix A, otherwise the leading k by n part of the array A must contain the matrix A.
On entry, LDA specifies the first dimension of A as declared in the calling (sub) program. When TRANS = 'N' or 'n' then LDA must be at least max( 1, n ), otherwise LDA must be at least max( 1, k ).
- beta T
BETA is DOUBLE PRECISION. On entry, BETA specifies the scalar beta.
- c Span2D<T>
C is DOUBLE PRECISION array of DIMENSION ( LDC, n ). Before entry with UPLO = 'U' or 'u', the leading n by n upper triangular part of the array C must contain the upper triangular part of the symmetric matrix and the strictly lower triangular part of C is not referenced. On exit, the upper triangular part of the array C is overwritten by the upper triangular part of the updated matrix. Before entry with UPLO = 'L' or 'l', the leading n by n lower triangular part of the array C must contain the lower triangular part of the symmetric matrix and the strictly upper triangular part of C is not referenced. On exit, the lower triangular part of the array C is overwritten by the lower triangular part of the updated matrix.
On entry, LDC specifies the first dimension of C as declared in the calling (sub) program. LDC must be at least max( 1, n ).
Type Parameters
- T
Usage Note
In Visual Basic and C#, you can call this method as an instance method on any object of type ILinearAlgebraOperations<T>. When you use instance method syntax to call this method, omit the first parameter. For more information, see Extension Methods (Visual Basic) or Extension Methods (C# Programming Guide).Remarks
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
SymmetricRankUpdate<T, TStorage2D>(ILinearAlgebraOperations<T>, MatrixTriangle, TransposeOperation, Int32, Int32, T, TStorage2D, T, TStorage2D)
public static void SymmetricRankUpdate<T, TStorage2D>(
this ILinearAlgebraOperations<T> operations,
MatrixTriangle storedTriangle,
TransposeOperation trans,
int n,
int k,
T alpha,
TStorage2D a,
T beta,
TStorage2D c
)
where TStorage2D : Object, IStorage2D<T>
Parameters
- operations ILinearAlgebraOperations<T>
- The linear algebra operations instance used to perform the calculation.
- storedTriangle MatrixTriangle
- Specifies whether the elements of the matrix a are stored in the upper or lower triangular part.
- trans TransposeOperation
- Specifies the operation to be performed on the matrix a.
- n Int32
- The number of rows and columns in the matrix c.
- k Int32
- The number of columns in the matrix a transformed as specified by trans.
- alpha T
- The scalar used to multiply the matrix-matrix product.
- a TStorage2D
- A span that contains the elements of the first matrix.
- beta T
- The scalar used to multiply c.
- c TStorage2D
- A span that contains the elements of the third matrix.
Type Parameters
- T
- TStorage2D
Usage Note
In Visual Basic and C#, you can call this method as an instance method on any object of type ILinearAlgebraOperations<T>. When you use instance method syntax to call this method, omit the first parameter. For more information, see Extension Methods (Visual Basic) or Extension Methods (C# Programming Guide).SymmetricRankUpdate<T>(ILinearAlgebraOperations<T>, MatrixTriangle, TransposeOperation, Int32, Int32, T, ReadOnlySpan2D<T>, ReadOnlySpan2D<T>, T, Span2D<T>)
Performs one of the symmetric rank 2k operations C := alpha*A*BT + alpha*B*AT + beta*C, or C := alpha*AT*B + alpha*BT*A + beta*C, where alpha and beta are scalars, C is an n by n symmetric matrix and A and B are n by k matrices in the first case and k by n matrices in the second case.
public static void SymmetricRankUpdate<T>(
this ILinearAlgebraOperations<T> operations,
MatrixTriangle uplo,
TransposeOperation trans,
int n,
int k,
T alpha,
ReadOnlySpan2D<T> a,
ReadOnlySpan2D<T> b,
T beta,
Span2D<T> c
)
Parameters
- operations ILinearAlgebraOperations<T>
- The object that performs the operation.
- uplo MatrixTriangle
On entry, UPLO specifies whether the upper or lower triangular part of the array C is to be referenced as follows: UPLO = 'U' or 'u' Only the upper triangular part of C is to be referenced. UPLO = 'L' or 'l' Only the lower triangular part of C is to be referenced.
- trans TransposeOperation
On entry, TRANS specifies the operation to be performed as follows: TRANS = 'N' or 'n' C := alpha*A*BT + alpha*B*AT + beta*C. TRANS = 'T' or 't' C := alpha*AT*B + alpha*BT*A + beta*C. TRANS = 'C' or 'c' C := alpha*AT*B + alpha*BT*A + beta*C.
- n Int32
On entry, N specifies the order of the matrix C. N must be at least zero.
- k Int32
On entry with TRANS = 'N' or 'n', K specifies the number of columns of the matrices A and B, and on entry with TRANS = 'T' or 't' or 'C' or 'c', K specifies the number of rows of the matrices A and B. K must be at least zero.
- alpha T
ALPHA is DOUBLE PRECISION. On entry, ALPHA specifies the scalar alpha.
- a ReadOnlySpan2D<T>
A is DOUBLE PRECISION array of DIMENSION ( LDA, ka ), where ka is k when TRANS = 'N' or 'n', and is n otherwise. Before entry with TRANS = 'N' or 'n', the leading n by k part of the array A must contain the matrix A, otherwise the leading k by n part of the array A must contain the matrix A.
On entry, LDA specifies the first dimension of A as declared in the calling (sub) program. When TRANS = 'N' or 'n' then LDA must be at least max( 1, n ), otherwise LDA must be at least max( 1, k ).
- b ReadOnlySpan2D<T>
B is DOUBLE PRECISION array of DIMENSION ( LDB, kb ), where kb is k when TRANS = 'N' or 'n', and is n otherwise. Before entry with TRANS = 'N' or 'n', the leading n by k part of the array B must contain the matrix B, otherwise the leading k by n part of the array B must contain the matrix B.
On entry, LDB specifies the first dimension of B as declared in the calling (sub) program. When TRANS = 'N' or 'n' then LDB must be at least max( 1, n ), otherwise LDB must be at least max( 1, k ).
- beta T
BETA is DOUBLE PRECISION. On entry, BETA specifies the scalar beta.
- c Span2D<T>
C is DOUBLE PRECISION array of DIMENSION ( LDC, n ). Before entry with UPLO = 'U' or 'u', the leading n by n upper triangular part of the array C must contain the upper triangular part of the symmetric matrix and the strictly lower triangular part of C is not referenced. On exit, the upper triangular part of the array C is overwritten by the upper triangular part of the updated matrix. Before entry with UPLO = 'L' or 'l', the leading n by n lower triangular part of the array C must contain the lower triangular part of the symmetric matrix and the strictly upper triangular part of C is not referenced. On exit, the lower triangular part of the array C is overwritten by the lower triangular part of the updated matrix.
On entry, LDC specifies the first dimension of C as declared in the calling (sub) program. LDC must be at least max( 1, n ).
Type Parameters
- T
Usage Note
In Visual Basic and C#, you can call this method as an instance method on any object of type ILinearAlgebraOperations<T>. When you use instance method syntax to call this method, omit the first parameter. For more information, see Extension Methods (Visual Basic) or Extension Methods (C# Programming Guide).Remarks
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
SymmetricRankUpdate<T, TStorage2D>(ILinearAlgebraOperations<T>, MatrixTriangle, TransposeOperation, Int32, Int32, T, TStorage2D, TStorage2D, T, TStorage2D)
public static void SymmetricRankUpdate<T, TStorage2D>(
this ILinearAlgebraOperations<T> operations,
MatrixTriangle storedTriangle,
TransposeOperation trans,
int n,
int k,
T alpha,
TStorage2D a,
TStorage2D b,
T beta,
TStorage2D c
)
where TStorage2D : Object, IStorage2D<T>
Parameters
- operations ILinearAlgebraOperations<T>
- The linear algebra operations instance used to perform the calculation.
- storedTriangle MatrixTriangle
- Specifies whether the elements of the matrix a are stored in the upper or lower triangular part.
- trans TransposeOperation
- Specifies the operation to be performed on the matrix a.
- n Int32
- The number of rows and columns in the matrix c.
- k Int32
- The number of columns in the matrix a transformed as specified by trans.
- alpha T
- The scalar used to multiply the matrix-matrix product.
- a TStorage2D
- A span that contains the elements of the first matrix.
- b TStorage2D
- A span that contains the elements of the second matrix.
- beta T
- The scalar used to multiply c.
- c TStorage2D
- A span that contains the elements of the third matrix.
Type Parameters
- T
- TStorage2D