Linear
Definition
Assembly: Extreme.Numerics (in Extreme.Numerics.dll) Version: 8.1.23
Overload List
| Multiply | Constant times a vector plus a vector. |
| Multiply | Constant times a vector plus a vector. |
| Multiply | Performs one of the matrix-vector operations y := alpha*A*x + beta*y, or y := alpha*AT*x + beta*y, where alpha and beta are scalars, x and y are vectors and A is an m by n matrix. |
| Multiply | Performs one of the matrix-vector operations y := alpha*A*x + beta*y, or y := alpha*AT*x + beta*y, or y := alpha*AH*x + beta*y, where alpha and beta are scalars, x and y are vectors and A is an m by n matrix. |
| Multiply | Performs one of the matrix-matrix operations C := alpha*op( A )*op( B ) + beta*C, where op( X ) is one of op( X ) = X or op( X ) = XT, alpha and beta are scalars, and A, B and C are matrices, with op( A ) an m by k matrix, op( B ) a k by n matrix and C an m by n matrix. |
| Multiply | Performs one of the matrix-matrix operations C := alpha*op( A )*op( B ) + beta*C, where op( X ) is one of op( X ) = X or op( X ) = XT or op( X ) = XH, alpha and beta are scalars, and A, B and C are matrices, with op( A ) an m by k matrix, op( B ) a k by n matrix and C an m by n matrix. |
MultiplyAndAddInPlace(Int32, T, ArraySlice<T>, ArraySlice<T>)
Constant times a vector plus a vector.
public virtual void MultiplyAndAddInPlace(
int n,
T da,
ArraySlice<T> dx,
ArraySlice<T> dy
)Parameters
- n Int32
- da T
- dx ArraySlice<T>
- dy ArraySlice<T>
Implements
ILinearAlgebraOperations<T>.MultiplyAndAddInPlace(Int32, T, ArraySlice<T>, ArraySlice<T>)Remarks
uses unrolled loops for increments equal to one.
Further Details:
jack dongarra, linpack, 3/11/78.
modified 12/3/93, array(1) declarations changed to array(*)
Authors: Univ. of Tennessee, Univ. of California Berkeley, Univ. of Colorado Denver, NAG Ltd.
Date: November 2011
MultiplyAndAddInPlace(Int32, Complex<T>, ArraySlice<Complex<T>>, ArraySlice<Complex<T>>)
Constant times a vector plus a vector.
public abstract void MultiplyAndAddInPlace(
int n,
Complex<T> za,
ArraySlice<Complex<T>> zx,
ArraySlice<Complex<T>> zy
)Parameters
- n Int32
- za Complex<T>
- zx ArraySlice<Complex<T>>
- zy ArraySlice<Complex<T>>
Implements
ILinearAlgebraOperations<T>.MultiplyAndAddInPlace(Int32, T, ArraySlice<T>, ArraySlice<T>)Remarks
Further Details:
jack dongarra, 3/11/78.
modified 12/3/93, array(1) declarations changed to array(*)
Authors: Univ. of Tennessee, Univ. of California Berkeley, Univ. of Colorado Denver, NAG Ltd.
Date: November 2011
MultiplyAndAddInPlace(TransposeOperation, Int32, Int32, T, Array2D<T>, ArraySlice<T>, T, ArraySlice<T>)
Performs one of the matrix-vector operations y := alpha*A*x + beta*y, or y := alpha*AT*x + beta*y, where alpha and beta are scalars, x and y are vectors and A is an m by n matrix.
public abstract void MultiplyAndAddInPlace(
TransposeOperation trans,
int m,
int n,
T alpha,
Array2D<T> a,
ArraySlice<T> x,
T beta,
ArraySlice<T> y
)Parameters
- trans TransposeOperation
On entry, TRANS specifies the operation to be performed as follows: TRANS = 'N' or 'n' y := alpha*A*x + beta*y. TRANS = 'T' or 't' y := alpha*AT*x + beta*y. TRANS = 'C' or 'c' y := alpha*AT*x + beta*y.- m Int32
On entry, M specifies the number of rows of the matrix A. M must be at least zero.- n Int32
On entry, N specifies the number of columns of the matrix A. N 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, n ). Before entry, the leading m by n part of the array A must contain the matrix of coefficients.On entry, LDA specifies the first dimension of A as declared in the calling (sub) program. LDA must be at least max( 1, m ).- x ArraySlice<T>
X is DOUBLE PRECISION array of DIMENSION at least ( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n' and at least ( 1 + ( m - 1 )*abs( INCX ) ) otherwise. Before entry, the incremented array X must contain the vector x.On entry, INCX specifies the increment for the elements of X. INCX must not be zero.- beta T
BETA is DOUBLE PRECISION. On entry, BETA specifies the scalar beta. When BETA is supplied as zero then Y need not be set on input.- y ArraySlice<T>
Y is DOUBLE PRECISION array of DIMENSION at least ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n' and at least ( 1 + ( n - 1 )*abs( INCY ) ) otherwise. Before entry with BETA non-zero, the incremented array Y must contain the vector y. On exit, Y is overwritten by the updated vector y.On entry, INCY specifies the increment for the elements of Y. INCY must not be zero.
Implements
ILinearAlgebraOperations<T>.MultiplyAndAddInPlace(TransposeOperation, Int32, Int32, T, Array2D<T>, ArraySlice<T>, T, ArraySlice<T>)Remarks
Further Details:
Level 2 LinearAlgebra routine.
The vector and matrix arguments are not referenced when N = 0, or M = 0
-- 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
MultiplyAndAddInPlace(TransposeOperation, Int32, Int32, Complex<T>, Array2D<Complex<T>>, ArraySlice<Complex<T>>, Complex<T>, ArraySlice<Complex<T>>)
Performs one of the matrix-vector operations y := alpha*A*x + beta*y, or y := alpha*AT*x + beta*y, or y := alpha*AH*x + beta*y, where alpha and beta are scalars, x and y are vectors and A is an m by n matrix.
public abstract void MultiplyAndAddInPlace(
TransposeOperation trans,
int m,
int n,
Complex<T> alpha,
Array2D<Complex<T>> a,
ArraySlice<Complex<T>> x,
Complex<T> beta,
ArraySlice<Complex<T>> y
)Parameters
- trans TransposeOperation
On entry, TRANS specifies the operation to be performed as follows: TRANS = 'N' or 'n' y := alpha*A*x + beta*y. TRANS = 'T' or 't' y := alpha*AT*x + beta*y. TRANS = 'C' or 'c' y := alpha*AH*x + beta*y.- m Int32
On entry, M specifies the number of rows of the matrix A. M must be at least zero.- n Int32
On entry, N specifies the number of columns of the matrix A. N 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, n ). Before entry, the leading m by n part of the array A must contain the matrix of coefficients.On entry, LDA specifies the first dimension of A as declared in the calling (sub) program. LDA must be at least max( 1, m ).- x ArraySlice<Complex<T>>
X is complex array of DIMENSION at least ( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n' and at least ( 1 + ( m - 1 )*abs( INCX ) ) otherwise. Before entry, the incremented array X must contain the vector x.On entry, INCX specifies the increment for the elements of X. INCX must not be zero.- beta Complex<T>
On entry, BETA specifies the scalar beta. When BETA is supplied as zero then Y need not be set on input.- y ArraySlice<Complex<T>>
Y is complex array of DIMENSION at least ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n' and at least ( 1 + ( n - 1 )*abs( INCY ) ) otherwise. Before entry with BETA non-zero, the incremented array Y must contain the vector y. On exit, Y is overwritten by the updated vector y.On entry, INCY specifies the increment for the elements of Y. INCY must not be zero.
Implements
ILinearAlgebraOperations<T>.MultiplyAndAddInPlace(TransposeOperation, Int32, Int32, T, Array2D<T>, ArraySlice<T>, T, ArraySlice<T>)Remarks
Further Details:
Level 2 LinearAlgebra routine.
The vector and matrix arguments are not referenced when N = 0, or M = 0
-- 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
MultiplyAndAddInPlace(TransposeOperation, TransposeOperation, Int32, Int32, Int32, T, Array2D<T>, Array2D<T>, T, Array2D<T>)
Performs one of the matrix-matrix operations C := alpha*op( A )*op( B ) + beta*C, where op( X ) is one of op( X ) = X or op( X ) = XT, alpha and beta are scalars, and A, B and C are matrices, with op( A ) an m by k matrix, op( B ) a k by n matrix and C an m by n matrix.
public abstract void MultiplyAndAddInPlace(
TransposeOperation transa,
TransposeOperation transb,
int m,
int n,
int k,
T alpha,
Array2D<T> a,
Array2D<T> b,
T beta,
Array2D<T> c
)Parameters
- 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.- transb TransposeOperation
On entry, TRANSB specifies the form of op( B ) to be used in the matrix multiplication as follows: TRANSB = 'N' or 'n', op( B ) = B. TRANSB = 'T' or 't', op( B ) = BT. TRANSB = 'C' or 'c', op( B ) = BT.- m Int32
On entry, M specifies the number of rows of the matrix op( A ) and of the matrix C. M must be at least zero.- n Int32
On entry, N specifies the number of columns of the matrix op( B ) and the number of columns of the matrix C. N must be at least zero.- k Int32
On entry, K specifies the number of columns of the matrix op( A ) and the number of rows of the matrix op( 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 TRANSA = 'N' or 'n', and is m otherwise. Before entry with TRANSA = 'N' or 'n', the leading m by k part of the array A must contain the matrix A, otherwise the leading k by m 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 TRANSA = 'N' or 'n' then LDA must be at least max( 1, m ), otherwise LDA must be at least max( 1, k ).- b Array2D<T>
B is DOUBLE PRECISION array of DIMENSION ( LDB, kb ), where kb is n when TRANSB = 'N' or 'n', and is k otherwise. Before entry with TRANSB = 'N' or 'n', the leading k by n part of the array B must contain the matrix B, otherwise the leading n by k 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 TRANSB = 'N' or 'n' then LDB must be at least max( 1, k ), otherwise LDB must be at least max( 1, n ).- beta T
BETA is DOUBLE PRECISION. On entry, BETA specifies the scalar beta. When BETA is supplied as zero then C need not be set on input.- c Array2D<T>
C is DOUBLE PRECISION array of DIMENSION ( LDC, n ). Before entry, the leading m by n part of the array C must contain the matrix C, except when beta is zero, in which case C need not be set on entry. On exit, the array C is overwritten by the m by n matrix ( alpha*op( A )*op( B ) + beta*C ).On entry, LDC specifies the first dimension of C as declared in the calling (sub) program. LDC must be at least max( 1, m ).
Implements
ILinearAlgebraOperations<T>.MultiplyAndAddInPlace(TransposeOperation, TransposeOperation, Int32, 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
MultiplyAndAddInPlace(TransposeOperation, TransposeOperation, Int32, Int32, Int32, Complex<T>, Array2D<Complex<T>>, Array2D<Complex<T>>, Complex<T>, Array2D<Complex<T>>)
Performs one of the matrix-matrix operations C := alpha*op( A )*op( B ) + beta*C, where op( X ) is one of op( X ) = X or op( X ) = XT or op( X ) = XH, alpha and beta are scalars, and A, B and C are matrices, with op( A ) an m by k matrix, op( B ) a k by n matrix and C an m by n matrix.
public abstract void MultiplyAndAddInPlace(
TransposeOperation transa,
TransposeOperation transb,
int m,
int n,
int k,
Complex<T> alpha,
Array2D<Complex<T>> a,
Array2D<Complex<T>> b,
Complex<T> beta,
Array2D<Complex<T>> c
)Parameters
- 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.- transb TransposeOperation
On entry, TRANSB specifies the form of op( B ) to be used in the matrix multiplication as follows: TRANSB = 'N' or 'n', op( B ) = B. TRANSB = 'T' or 't', op( B ) = BT. TRANSB = 'C' or 'c', op( B ) = BH.- m Int32
On entry, M specifies the number of rows of the matrix op( A ) and of the matrix C. M must be at least zero.- n Int32
On entry, N specifies the number of columns of the matrix op( B ) and the number of columns of the matrix C. N must be at least zero.- k Int32
On entry, K specifies the number of columns of the matrix op( A ) and the number of rows of the matrix op( 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 TRANSA = 'N' or 'n', and is m otherwise. Before entry with TRANSA = 'N' or 'n', the leading m by k part of the array A must contain the matrix A, otherwise the leading k by m 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 TRANSA = 'N' or 'n' then LDA must be at least max( 1, m ), otherwise LDA must be at least max( 1, k ).- b Array2D<Complex<T>>
B is complex array of DIMENSION ( LDB, kb ), where kb is n when TRANSB = 'N' or 'n', and is k otherwise. Before entry with TRANSB = 'N' or 'n', the leading k by n part of the array B must contain the matrix B, otherwise the leading n by k 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 TRANSB = 'N' or 'n' then LDB must be at least max( 1, k ), otherwise LDB must be at least max( 1, n ).- beta Complex<T>
On entry, BETA specifies the scalar beta. When BETA is supplied as zero then C need not be set on input.- c Array2D<Complex<T>>
C is complex array of DIMENSION ( LDC, n ). Before entry, the leading m by n part of the array C must contain the matrix C, except when beta is zero, in which case C need not be set on entry. On exit, the array C is overwritten by the m by n matrix ( alpha*op( A )*op( B ) + beta*C ).On entry, LDC specifies the first dimension of C as declared in the calling (sub) program. LDC must be at least max( 1, m ).
Implements
ILinearAlgebraOperations<T>.MultiplyAndAddInPlace(TransposeOperation, TransposeOperation, Int32, 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