Linear
Definition
Assembly: Extreme.Numerics (in Extreme.Numerics.dll) Version: 8.1.23
Overload List
| Symmetric | 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. |
| Symmetric | 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. |
| Symmetric | 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. |
| Symmetric | 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. |
| Symmetric | 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. |
| Symmetric | 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. |
SymmetricRankUpdate(MatrixTriangle, Int32, T, ArraySlice<T>, Array2D<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 abstract void SymmetricRankUpdate(
MatrixTriangle uplo,
int n,
T alpha,
ArraySlice<T> x,
Array2D<T> a
)Parameters
- 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 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 vector x.On entry, INCX specifies the increment for the elements of X. INCX must not be 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 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 ).
Implements
ILinearAlgebraOperations<T>.SymmetricRankUpdate(MatrixTriangle, Int32, T, ArraySlice<T>, Array2D<T>)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(MatrixTriangle, Int32, T, ArraySlice<T>, ArraySlice<T>, Array2D<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 abstract void SymmetricRankUpdate(
MatrixTriangle uplo,
int n,
T alpha,
ArraySlice<T> x,
ArraySlice<T> y,
Array2D<T> a
)Parameters
- 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 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 vector x.On entry, INCX specifies the increment for the elements of X. INCX must not be zero.- y ArraySlice<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 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 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 ).
Implements
ILinearAlgebraOperations<T>.SymmetricRankUpdate(MatrixTriangle, Int32, T, ArraySlice<T>, ArraySlice<T>, Array2D<T>)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(MatrixTriangle, TransposeOperation, Int32, Int32, T, Array2D<T>, T, Array2D<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 abstract void SymmetricRankUpdate(
MatrixTriangle uplo,
TransposeOperation trans,
int n,
int k,
T alpha,
Array2D<T> a,
T beta,
Array2D<T> c
)Parameters
- 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 Array2D<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 Array2D<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 ).
Implements
ILinearAlgebraOperations<T>.SymmetricRankUpdate(MatrixTriangle, TransposeOperation, Int32, Int32, T, Array2D<T>, T, Array2D<T>)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(MatrixTriangle, TransposeOperation, Int32, Int32, Complex<T>, Array2D<Complex<T>>, Complex<T>, Array2D<Complex<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 abstract void SymmetricRankUpdate(
MatrixTriangle uplo,
TransposeOperation trans,
int n,
int k,
Complex<T> alpha,
Array2D<Complex<T>> a,
Complex<T> beta,
Array2D<Complex<T>> c
)Parameters
- 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.- 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', K specifies the number of rows of the matrix A. K must be at least zero.- alpha Complex<T>
On entry, ALPHA specifies the scalar alpha.- a Array2D<Complex<T>>
A is complex 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 Complex<T>
On entry, BETA specifies the scalar beta.- c Array2D<Complex<T>>
C is complex 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 ).
Implements
ILinearAlgebraOperations<T>.SymmetricRankUpdate(MatrixTriangle, TransposeOperation, Int32, Int32, T, Array2D<T>, T, Array2D<T>)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(MatrixTriangle, TransposeOperation, Int32, Int32, T, Array2D<T>, Array2D<T>, T, Array2D<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 abstract void SymmetricRankUpdate(
MatrixTriangle uplo,
TransposeOperation trans,
int n,
int k,
T alpha,
Array2D<T> a,
Array2D<T> b,
T beta,
Array2D<T> c
)Parameters
- 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 Array2D<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 Array2D<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 Array2D<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 ).
Implements
ILinearAlgebraOperations<T>.SymmetricRankUpdate(MatrixTriangle, TransposeOperation, Int32, Int32, T, Array2D<T>, Array2D<T>, T, Array2D<T>)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(MatrixTriangle, TransposeOperation, Int32, Int32, Complex<T>, Array2D<Complex<T>>, Array2D<Complex<T>>, Complex<T>, Array2D<Complex<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 abstract void SymmetricRankUpdate(
MatrixTriangle uplo,
TransposeOperation trans,
int n,
int k,
Complex<T> alpha,
Array2D<Complex<T>> a,
Array2D<Complex<T>> b,
Complex<T> beta,
Array2D<Complex<T>> c
)Parameters
- 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.- 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', K specifies the number of rows of the matrices A and B. K must be at least zero.- alpha Complex<T>
On entry, ALPHA specifies the scalar alpha.- a Array2D<Complex<T>>
A is complex 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 Array2D<Complex<T>>
B is complex 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 Complex<T>
On entry, BETA specifies the scalar beta.- c Array2D<Complex<T>>
C is complex 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 ).
Implements
ILinearAlgebraOperations<T>.SymmetricRankUpdate(MatrixTriangle, TransposeOperation, Int32, Int32, T, Array2D<T>, Array2D<T>, T, Array2D<T>)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