Linear
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
| Band | Performs the matrix-vector operation y := alpha*A*x + beta*y, where alpha and beta are scalars, x and y are n element vectors and A is an n by n hermitian band matrix, with k super-diagonals. |
| Band | Performs the matrix-vector operation y := alpha*A*x + beta*y, where alpha and beta are scalars, x and y are n element vectors and A is an n by n hermitian band matrix, with k super-diagonals. |
| Band | Performs the matrix-vector operation y := alpha*A*x + beta*y, where alpha and beta are scalars, x, incx and y are n element vectors and A is an n by n hermitian band matrix, with k super-diagonals. |
BandHermitianMultiplyAndAddInPlace(MatrixTriangle, Int32, Int32, Complex<T>, Array2D<Complex<T>>, ArraySlice<Complex<T>>, Complex<T>, ArraySlice<Complex<T>>)
Performs the matrix-vector operation y := alpha*A*x + beta*y, where alpha and beta are scalars, x and y are n element vectors and A is an n by n hermitian band matrix, with k super-diagonals.
public void BandHermitianMultiplyAndAddInPlace(
MatrixTriangle uplo,
int n,
int k,
Complex<T> alpha,
Array2D<Complex<T>> a,
ArraySlice<Complex<T>> x,
Complex<T> beta,
ArraySlice<Complex<T>> y
)Parameters
- uplo MatrixTriangle
On entry, UPLO specifies whether the upper or lower triangular part of the band matrix A is being supplied as follows: UPLO = 'U' or 'u' The upper triangular part of A is being supplied. UPLO = 'L' or 'l' The lower triangular part of A is being supplied.- n Int32
On entry, N specifies the order of the matrix A. N must be at least zero.- k Int32
On entry, K specifies the number of super-diagonals of the matrix A. K must satisfy 0 .le. K.- alpha Complex<T>
On entry, ALPHA specifies the scalar alpha.- a Array2D<Complex<T>>
A is complex array of DIMENSION ( LDA, n ). Before entry with UPLO = 'U' or 'u', the leading ( k + 1 ) by n part of the array A must contain the upper triangular band part of the hermitian matrix, supplied column by column, with the leading diagonal of the matrix in row ( k + 1 ) of the array, the first super-diagonal starting at position 2 in row k, and so on. The top left k by k triangle of the array A is not referenced. The following program segment will transfer the upper triangular part of a hermitian band matrix from conventional full matrix storage to band storage: DO 20, J = 1, N M = K + 1 - J DO 10, I = MAX( 1, J - K ), J A( M + I, J ) = matrix( I, J ) 10 CONTINUE 20 CONTINUE Before entry with UPLO = 'L' or 'l', the leading ( k + 1 ) by n part of the array A must contain the lower triangular band part of the hermitian matrix, supplied column by column, with the leading diagonal of the matrix in row 1 of the array, the first sub-diagonal starting at position 1 in row 2, and so on. The bottom right k by k triangle of the array A is not referenced. The following program segment will transfer the lower triangular part of a hermitian band matrix from conventional full matrix storage to band storage: DO 20, J = 1, N M = 1 - J DO 10, I = J, MIN( N, J + K ) A( M + I, J ) = matrix( I, J ) 10 CONTINUE 20 CONTINUE Note that the imaginary parts of the diagonal elements need not be set and are assumed to be zero.On entry, LDA specifies the first dimension of A as declared in the calling (sub) program. LDA must be at least ( k + 1 ).- 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 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.- y ArraySlice<Complex<T>>
Y is complex array of DIMENSION at least ( 1 + ( n - 1 )*abs( INCY ) ). Before entry, 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.
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
BandHermitianMultiplyAndAddInPlace(MatrixTriangle, Int32, Int32, Complex<T>, ReadOnlySpan2D<Complex<T>>, ReadOnlySpanSlice<Complex<T>>, Complex<T>, SpanSlice<Complex<T>>)
Performs the matrix-vector operation y := alpha*A*x + beta*y, where alpha and beta are scalars, x and y are n element vectors and A is an n by n hermitian band matrix, with k super-diagonals.
public void BandHermitianMultiplyAndAddInPlace(
MatrixTriangle uplo,
int n,
int k,
Complex<T> alpha,
ReadOnlySpan2D<Complex<T>> a,
ReadOnlySpanSlice<Complex<T>> x,
Complex<T> beta,
SpanSlice<Complex<T>> y
)Parameters
- uplo MatrixTriangle
On entry, UPLO specifies whether the upper or lower triangular part of the band matrix A is being supplied as follows: UPLO = 'U' or 'u' The upper triangular part of A is being supplied. UPLO = 'L' or 'l' The lower triangular part of A is being supplied.- n Int32
On entry, N specifies the order of the matrix A. N must be at least zero.- k Int32
On entry, K specifies the number of super-diagonals of the matrix A. K must satisfy 0 .le. K.- alpha Complex<T>
On entry, ALPHA specifies the scalar alpha.- a ReadOnlySpan2D<Complex<T>>
A is complex array of DIMENSION ( LDA, n ). Before entry with UPLO = 'U' or 'u', the leading ( k + 1 ) by n part of the array A must contain the upper triangular band part of the hermitian matrix, supplied column by column, with the leading diagonal of the matrix in row ( k + 1 ) of the array, the first super-diagonal starting at position 2 in row k, and so on. The top left k by k triangle of the array A is not referenced. The following program segment will transfer the upper triangular part of a hermitian band matrix from conventional full matrix storage to band storage: DO 20, J = 1, N M = K + 1 - J DO 10, I = MAX( 1, J - K ), J A( M + I, J ) = matrix( I, J ) 10 CONTINUE 20 CONTINUE Before entry with UPLO = 'L' or 'l', the leading ( k + 1 ) by n part of the array A must contain the lower triangular band part of the hermitian matrix, supplied column by column, with the leading diagonal of the matrix in row 1 of the array, the first sub-diagonal starting at position 1 in row 2, and so on. The bottom right k by k triangle of the array A is not referenced. The following program segment will transfer the lower triangular part of a hermitian band matrix from conventional full matrix storage to band storage: DO 20, J = 1, N M = 1 - J DO 10, I = J, MIN( N, J + K ) A( M + I, J ) = matrix( I, J ) 10 CONTINUE 20 CONTINUE Note that the imaginary parts of the diagonal elements need not be set and are assumed to be zero.On entry, LDA specifies the first dimension of A as declared in the calling (sub) program. LDA must be at least ( k + 1 ).- x ReadOnlySpanSlice<Complex<T>>
X is complex array of DIMENSION at least ( 1 + ( n - 1 )*abs( INCX ) ). 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.- y SpanSlice<Complex<T>>
Y is complex array of DIMENSION at least ( 1 + ( n - 1 )*abs( INCY ) ). Before entry, 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.
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
BandHermitianMultiplyAndAddInPlace(MatrixTriangle, Int32, Int32, Complex<T>, ReadOnlySpan<Complex<T>>, Int32, ReadOnlySpan<Complex<T>>, Int32, Complex<T>, Span<Complex<T>>, Int32)
Performs the matrix-vector operation y := alpha*A*x + beta*y, where alpha and beta are scalars, x, incx and y are n element vectors and A is an n by n hermitian band matrix, with k super-diagonals.
public abstract void BandHermitianMultiplyAndAddInPlace(
MatrixTriangle uplo,
int n,
int k,
Complex<T> alpha,
ReadOnlySpan<Complex<T>> a,
int lda,
ReadOnlySpan<Complex<T>> x,
int incx,
Complex<T> beta,
Span<Complex<T>> y,
int incy
)Parameters
- uplo MatrixTriangle
On entry, UPLO specifies whether the upper or lower triangular part of the band matrix A is being supplied as follows: UPLO = 'U' or 'u' The upper triangular part of A is being supplied. UPLO = 'L' or 'l' The lower triangular part of A is being supplied.- n Int32
On entry, N specifies the order of the matrix A. N must be at least zero.- k Int32
On entry, K specifies the number of super-diagonals of the matrix A. K must satisfy 0 .le. K.- alpha Complex<T>
On entry, ALPHA specifies the scalar alpha.- a ReadOnlySpan<Complex<T>>
A is complex array of DIMENSION ( LDA, n ). Before entry with UPLO = 'U' or 'u', the leading ( k + 1 ) by n part of the array A must contain the upper triangular band part of the hermitian matrix, supplied column by column, with the leading diagonal of the matrix in row ( k + 1 ) of the array, the first super-diagonal starting at position 2 in row k, and so on. The top left k by k triangle of the array A is not referenced. The following program segment will transfer the upper triangular part of a hermitian band matrix from conventional full matrix storage to band storage: DO 20, J = 1, N M = K + 1 - J DO 10, I = MAX( 1, J - K ), J A( M + I, J ) = matrix( I, J ) 10 CONTINUE 20 CONTINUE Before entry with UPLO = 'L' or 'l', the leading ( k + 1 ) by n part of the array A must contain the lower triangular band part of the hermitian matrix, supplied column by column, with the leading diagonal of the matrix in row 1 of the array, the first sub-diagonal starting at position 1 in row 2, and so on. The bottom right k by k triangle of the array A is not referenced. The following program segment will transfer the lower triangular part of a hermitian band matrix from conventional full matrix storage to band storage: DO 20, J = 1, N M = 1 - J DO 10, I = J, MIN( N, J + K ) A( M + I, J ) = matrix( I, J ) 10 CONTINUE 20 CONTINUE Note that the imaginary parts of the diagonal elements need not be set and are assumed to be zero.- lda Int32
On entry, LDA specifies the first dimension of A as declared in the calling (sub) program. LDA must be at least ( k + 1 ).- x ReadOnlySpan<Complex<T>>
X is complex array of DIMENSION at least ( 1 + ( n - 1 )*abs( INCX ) ). Before entry, the incremented array X must contain the vector x.- incx Int32
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.- y Span<Complex<T>>
Y is complex array of DIMENSION at least ( 1 + ( n - 1 )*abs( INCY ) ). Before entry, the incremented array Y must contain the vector y. On exit, Y is overwritten by the updated vector y.- incy Int32
On entry, INCY specifies the increment for the elements of Y. INCY must not be zero.
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