LinearAlgebraOperationsExtensions Class

Finds the index of element having max.

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 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.

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.

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

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

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.

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-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.

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.

Applies a plane rotation.

Swaps the elements 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 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 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 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-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.

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 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.

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