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complib/zgeev(3) -- compute for an N-by-N complex nonsymmetric matrix A, the eigenvalues and, optionally, the left and/or right ei
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ZGEEV computes for an N-by-N complex nonsymmetric matrix A, the eigenvalues and, optionally, the left and/or right eigenvectors. The right eigenvector v(j) of A satisfies A * v(j) = lambda(j) * v(j) where lambda(j) is its eigenvalue. The left eigenvector u(j) of A satisfies u(j)**H * A = lambda(j) * u(j)**H where u(j)**H denotes the conjugate transpose of u(j). The computed eigenvectors are normalized to have Euclidean norm equal to 1 and largest component real.... |
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complib/zgeevx(3) -- compute for an N-by-N complex nonsymmetric matrix A, the eigenvalues and, optionally, the left and/or right ei
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ZGEEVX computes for an N-by-N complex nonsymmetric matrix A, the eigenvalues and, optionally, the left and/or right eigenvectors. Optionally also, it computes a balancing transformation to improve the conditioning of the eigenvalues and eigenvectors (ILO, IHI, SCALE, and ABNRM), reciprocal condition numbers for the eigenvalues (RCONDE), and reciprocal condition numbers for the right eigenvectors (RCONDV). The right eigenvector v(j) of A satisfies A * v(j) = lambda(j) * v(j) where lambda(j) is it... |
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complib/zgegs(3) -- compute for a pair of N-by-N complex nonsymmetric matrices A,
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DGEGS computes for a pair of N-by-N complex nonsymmetric matrices A, B: the generalized eigenvalues (alpha, beta), the complex Schur form (A, B), and optionally left and/or right Schur vectors (VSL and VSR). (If only the generalized eigenvalues are needed, use the driver ZGEGV instead.) 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 r... |
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complib/zgegv(3) -- B, the generalized eigenvalues (alpha, beta), and optionally,
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ZGEGV computes for a pair of N-by-N complex nonsymmetric matrices A and B, the generalized eigenvalues (alpha, 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 reference ... |
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complib/zgehd2(3) -- reduce a complex general matrix A to upper Hessenberg form H by a unitary similarity transformation
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ZGEHD2 reduces a complex general matrix A to upper Hessenberg form H by a unitary similarity transformation: Q' * A * Q = H . |
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complib/zgehrd(3) -- reduce a complex general matrix A to upper Hessenberg form H by a unitary similarity transformation
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ZGEHRD reduces a complex general matrix A to upper Hessenberg form H by a unitary similarity transformation: Q' * A * Q = H . |
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complib/zgelq2(3) -- compute an LQ factorization of a complex m by n matrix A
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ZGELQ2 computes an LQ factorization of a complex m by n matrix A: A = L * Q. |
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complib/zgelqf(3) -- compute an LQ factorization of a complex M-by-N matrix A
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ZGELQF computes an LQ factorization of a complex M-by-N matrix A: A = L * Q. |
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complib/zgels(3) -- involving an M-by-N matrix A, or its conjugate-transpose, using a QR or LQ factorization of A
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ZGELS solves overdetermined or underdetermined complex linear systems involving an M-by-N matrix A, or its conjugate-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 ... |
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complib/zgelss(3) -- compute the minimum norm solution to a complex linear least squares problem
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ZGELSS computes the minimum norm solution to a complex 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 whi... |
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complib/zgelsx(3) -- compute the minimum-norm solution to a complex linear least squares problem
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ZGELSX computes the minimum-norm solution to a complex 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/zgeql2(3) -- compute a QL factorization of a complex m by n matrix A
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ZGEQL2 computes a QL factorization of a complex m by n matrix A: A = Q * L. |
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complib/zgeqlf(3) -- compute a QL factorization of a complex M-by-N matrix A
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ZGEQLF computes a QL factorization of a complex M-by-N matrix A: A = Q * L. |
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complib/zgeqpf(3) -- compute a QR factorization with column pivoting of a complex Mby-N matrix A
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ZGEQPF computes a QR factorization with column pivoting of a complex Mby-N matrix A: A*P = Q*R. |
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complib/zgeqr2(3) -- compute a QR factorization of a complex m by n matrix A
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ZGEQR2 computes a QR factorization of a complex m by n matrix A: A = Q * R. |
