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complib/dgegv(3) -- the generalized eigenvalues (alphar +/- alphai*i, beta), and optionally, the left and/or right generalized eig
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DGEGV computes for a pair of n-by-n real nonsymmetric matrices A and B, the generalized eigenvalues (alphar +/- alphai*i, beta), and optionally, the left and/or right generalized eigenvectors (VL and VR). A generalized eigenvalue for a pair of matrices (A,B) is, roughly speaking, a scalar w or a ratio alpha/beta = w, such that A - w*B is singular. It is usually represented as the pair (alpha,beta), as there is a reasonable interpretation for beta=0, and even for both being zero. A good beginning... |
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complib/dgehd2(3) -- reduce a real general matrix A to upper Hessenberg form H by an orthogonal similarity transformation
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DGEHD2 reduces a real general matrix A to upper Hessenberg form H by an orthogonal similarity transformation: Q' * A * Q = H . |
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complib/dgehrd(3) -- reduce a real general matrix A to upper Hessenberg form H by an orthogonal similarity transformation
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DGEHRD reduces a real general matrix A to upper Hessenberg form H by an orthogonal similarity transformation: Q' * A * Q = H . |
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complib/dgelq2(3) -- compute an LQ factorization of a real m by n matrix A
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DGELQ2 computes an LQ factorization of a real m by n matrix A: A = L * Q. |
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complib/dgelqf(3) -- compute an LQ factorization of a real M-by-N matrix A
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DGELQF computes an LQ factorization of a real M-by-N matrix A: A = L * Q. |
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complib/dgels(3) -- involving an M-by-N matrix A, or its transpose, using a QR or LQ factorization of A
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DGELS solves overdetermined or underdetermined real linear systems involving an M-by-N matrix A, or its transpose, using a QR or LQ factorization of A. It is assumed that A has full rank. The following options are provided: 1. If TRANS = 'N' and m >= n: find the least squares solution of an overdetermined system, i.e., solve the least squares problem minimize || B - A*X ||. 2. If TRANS = 'N' and m < n: find the minimum norm solution of an underdetermined system A * X = B. 3. If TRANS = 'T'... |
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complib/dgelss(3) -- compute the minimum norm solution to a real linear least squares problem
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DGELSS computes the minimum norm solution to a real linear least squares problem: Minimize 2-norm(| b - A*x |). using the singular value decomposition (SVD) of A. A is an M-by-N matrix which may be rank-deficient. Several right hand side vectors b and solution vectors x can be handled in a single call; they are stored as the columns of the M-by-NRHS right hand side matrix B and the N-by-NRHS solution matrix X. The effective rank of A is determined by treating as zero those singular values which ... |
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complib/dgelsx(3) -- compute the minimum-norm solution to a real linear least squares problem
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DGELSX computes the minimum-norm solution to a real linear least squares problem: minimize || A * X - B || using a complete orthogonal factorization of A. A is an M-by-N matrix which may be rank-deficient. Several right hand side vectors b and solution vectors x can be handled in a single call; they are stored as the columns of the M-by-NRHS right hand side matrix B and the N-by-NRHS solution matrix X. The routine first computes a QR factorization with column pivoting: A * P = Q * [ R11 R12 ] [ ... |
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complib/dgeql2(3) -- compute a QL factorization of a real m by n matrix A
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DGEQL2 computes a QL factorization of a real m by n matrix A: A = Q * L. |
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complib/dgeqlf(3) -- compute a QL factorization of a real M-by-N matrix A
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DGEQLF computes a QL factorization of a real M-by-N matrix A: A = Q * L. |
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complib/dgeqpf(3) -- compute a QR factorization with column pivoting of a real M-by-N matrix A
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DGEQPF computes a QR factorization with column pivoting of a real M-by-N matrix A: A*P = Q*R. |
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complib/dgeqr2(3) -- compute a QR factorization of a real m by n matrix A
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DGEQR2 computes a QR factorization of a real m by n matrix A: A = Q * R. |
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complib/dgeqrf(3) -- compute a QR factorization of a real M-by-N matrix A
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DGEQRF computes a QR factorization of a real M-by-N matrix A: A = Q * R. |
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complib/dgerfs(3) -- improve the computed solution to a system of linear equations and provides error bounds and backward error est
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DGERFS improves the computed solution to a system of linear equations and provides error bounds and backward error estimates for the solution. |
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complib/dgerq2(3) -- compute an RQ factorization of a real m by n matrix A
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DGERQ2 computes an RQ factorization of a real m by n matrix A: A = R * Q. |
