LinearAlgebraOperations<T> Class

Finds the index of element having max.

Finds the index of element having max.

THE MODIFIED GIVENS TRANSFORMATION, H, TO THE 2 BY N MATRIX (DX^T) , WHERE **T INDICATES TRANSPOSE.

Performs one of the matrix-vector operations y := alpha*A*x + beta*y, or y := alpha*A^T*x + beta*y, where alpha and beta are scalars, x and y are vectors and A is an m by n band matrix, with kl sub-diagonals and ku super-diagonals.

Performs one of the matrix-vector operations y := alpha*A*x + beta*y, or y := alpha*A^T*x + beta*y, or y := alpha*A^H*x + beta*y, where alpha and beta are scalars, x and y are vectors and A is an m by n band matrix, with kl sub-diagonals and ku super-diagonals.

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 symmetric band matrix, with k super-diagonals.

Performs one of the matrix-vector operations x := A*x, or x := A^T*x, where x is an n element vector and A is an n by n unit, or non-unit, upper or lower triangular band matrix, with ( k + 1 ) diagonals.

Performs one of the matrix-vector operations x := A*x, or x := A^T*x, or x := A^H*x, where x is an n element vector and A is an n by n unit, or non-unit, upper or lower triangular band matrix, with ( k + 1 ) diagonals.

Solves one of the systems of equations A*x = b, or A^T*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 band matrix, with ( k + 1 ) diagonals.

Solves one of the systems of equations A*x = b, or A^T*x = b, or A^H*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 band matrix, with ( k + 1 ) diagonals.

Computes the sum of the absolute values of a complex number

Forms the dot product of a vector.

Performs the rank 1 operation A := alpha*x*y**H + A, where alpha is a scalar, x is an m element vector, y is an n element vector and A is an m by n matrix.

Copies a vector, x, to a vector, y.

Copies a vector, x, to a vector, y.

Copies all or part of a two-dimensional matrix A to another matrix B.

Determines a complex Givens rotation.

Construct givens plane rotation.

THE MODIFIED GIVENS TRANSFORMATION MATRIX H WHICH ZEROS THE SECOND COMPONENT OF THE 2-VECTOR (DSQRT(DD1)*DX1,DSQRT(DD2)*> DY2)**T.

Forms the dot product of two vectors.

Forms the dot product of two vectors.

Returns the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a real matrix A.

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 matrix.

Performs one of the matrix-matrix operations C := alpha*A*B + beta*C, or C := alpha*B*A + beta*C, where alpha and beta are scalars, A is an hermitian matrix and B and C are m by n matrices.

Performs the hermitian rank 1 operation A := alpha*x*x**H + A, where alpha is a real scalar, x is an n element vector and A is an n by n hermitian matrix.

Performs the hermitian rank 2 operation A := alpha*x*y**H + conjg( alpha )*y*x**H + A, where alpha is a scalar, x and y are n element vectors and A is an n by n hermitian matrix.

Performs one of the hermitian rank k operations C := alpha*A*A^H + beta*C, or C := alpha*A^H*A + beta*C, where alpha and beta are real scalars, C is an n by n hermitian matrix and A is an n by k matrix in the first case and a k by n matrix in the second case.

Performs one of the hermitian rank 2k operations C := alpha*A*B^H + conjg( alpha )*B*A^H + beta*C, or C := alpha*A^H*B + conjg( alpha )*B^H*A + beta*C, where alpha and beta are scalars with beta real, C is an n by n hermitian matrix and A and B are n by k matrices in the first case and k by n matrices in the second case.

Constant times a vector plus a vector.

Constant times a vector plus a vector.

Performs one of the matrix-vector operations y := alpha*A*x + beta*y, or y := alpha*A^T*x + beta*y, where alpha and beta are scalars, x and y are vectors and A is an m by n matrix.

Performs one of the matrix-vector operations y := alpha*A*x + beta*y, or y := alpha*A^T*x + beta*y, or y := alpha*A^H*x + beta*y, where alpha and beta are scalars, x and y are vectors and A is an m by n matrix.

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 ) = X^T, 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.

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 ) = X^T or op( X ) = X^H, 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.

Scales a vector by a constant.

Scales a vector by a constant.

Scales a vector by a constant.

Takes the sum of the absolute values.

Performs the rank 1 operation A := alpha*x*y**T + A, where alpha is a scalar, x is an m element vector, y is an n element vector and A is an m by n matrix.

Performs the rank 1 operation A := alpha*x*y**T + A, where alpha is a scalar, x is an m element vector, y is an n element vector and A is an m by n matrix.

Takes the sum of the absolute values.

Applies a plane rotation.

A plane rotation, where the cos and sin (c and s) are real and the vectors cx and cy are complex.

Swaps the elements of two vectors.

Interchanges two vectors.

Returns the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a real symmetric matrix A.

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 symmetric matrix.

Performs one of the matrix-matrix operations C := alpha*A*B + beta*C, or C := alpha*B*A + beta*C, where alpha and beta are scalars, A is a symmetric matrix and B and C are m by n matrices.

Performs one of the matrix-matrix operations C := alpha*A*B + beta*C, or C := alpha*B*A + beta*C, where alpha and beta are scalars, A is a symmetric matrix and B and C are m by n matrices.

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.

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.

Performs one of the symmetric rank k operations C := alpha*A*A^T + beta*C, or C := alpha*A^T*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.

Performs one of the symmetric rank k operations C := alpha*A*A^T + beta*C, or C := alpha*A^T*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.

Performs one of the symmetric rank 2k operations C := alpha*A*B^T + alpha*B*A^T + beta*C, or C := alpha*A^T*B + alpha*B^T*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.

Performs one of the symmetric rank 2k operations C := alpha*A*B^T + alpha*B*A^T + beta*C, or C := alpha*A^T*B + alpha*B^T*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.

Returns the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a trapezoidal or triangular matrix A.

Performs one of the matrix-vector operations x := A*x, or x := A^T*x, where x is an n element vector and A is an n by n unit, or non-unit, upper or lower triangular matrix.

Performs one of the matrix-vector operations x := A*x, or x := A^T*x, or x := A^H*x, where x is an n element vector and A is an n by n unit, or non-unit, upper or lower triangular matrix.

Performs one of the matrix-matrix operations B := alpha*op( A )*B, or B := alpha*B*op( A ), where alpha is a scalar, B is an m by n matrix, A is a unit, or non-unit, upper or lower triangular matrix and op( A ) is one of op( A ) = A or op( A ) = A^T.

Performs one of the matrix-matrix operations B := alpha*op( A )*B, or B := alpha*B*op( A ) where alpha is a scalar, B is an m by n matrix, A is a unit, or non-unit, upper or lower triangular matrix and op( A ) is one of op( A ) = A or op( A ) = A^T or op( A ) = A^H.

Solves one of the systems of equations A*x = b, or A^T*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.

Solves one of the systems of equations A*x = b, or A^T*x = b, or A^H*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.

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 ) = A^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 ) = A^T or op( A ) = A^H.

            Returns the euclidean norm of a vector via the function
            name, so that
               DNRM2 := sqrt( x'*x )
            

            Returns the euclidean norm of a vector via the function
            name, so that
               DZNRM2 := sqrt( x**H*x )