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complib/CGEFA(3) -- CGEFA factors a complex matrix by Gaussian elimination. CGEFA is usually called by CGECO, but it can be called
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On Entry A COMPLEX(LDA, N) the matrix to be factored. LDA INTEGER the leading dimension of the array A . N INTEGER the order of the matrix A . On Return A an upper triangular matrix and the multipliers which were used to obtain it. The factorization can be written A = L*U where L is a product of permutation and unit lower triangular matrices and U is upper triangular. IPVT INTEGER(N) an integer vector of pivot indices. INFO INTEGER = 0 normal value. = K if U(K,K) .EQ. 0.0 . This is not an error ... |
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complib/cgegs(3) -- compute for a pair of N-by-N complex nonsymmetric matrices A,
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SGEGS 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 CGEGV 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/cgegv(3) -- B, the generalized eigenvalues (alpha, beta), and optionally,
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CGEGV 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/cgehd2(3) -- reduce a complex general matrix A to upper Hessenberg form H by a unitary similarity transformation
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CGEHD2 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/cgehrd(3) -- reduce a complex general matrix A to upper Hessenberg form H by a unitary similarity transformation
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CGEHRD 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/cgelq2(3) -- compute an LQ factorization of a complex m by n matrix A
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CGELQ2 computes an LQ factorization of a complex m by n matrix A: A = L * Q. |
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complib/cgelqf(3) -- compute an LQ factorization of a complex M-by-N matrix A
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CGELQF computes an LQ factorization of a complex M-by-N matrix A: A = L * Q. |
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complib/cgels(3) -- involving an M-by-N matrix A, or its conjugate-transpose, using a QR or LQ factorization of A
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CGELS 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/cgelss(3) -- compute the minimum norm solution to a complex linear least squares problem
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CGELSS 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/cgelsx(3) -- compute the minimum-norm solution to a complex linear least squares problem
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CGELSX 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/cgeql2(3) -- compute a QL factorization of a complex m by n matrix A
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CGEQL2 computes a QL factorization of a complex m by n matrix A: A = Q * L. |
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complib/cgeqlf(3) -- compute a QL factorization of a complex M-by-N matrix A
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CGEQLF computes a QL factorization of a complex M-by-N matrix A: A = Q * L. |
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complib/cgeqpf(3) -- compute a QR factorization with column pivoting of a complex Mby-N matrix A
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CGEQPF computes a QR factorization with column pivoting of a complex Mby-N matrix A: A*P = Q*R. |
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complib/cgeqr2(3) -- compute a QR factorization of a complex m by n matrix A
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CGEQR2 computes a QR factorization of a complex m by n matrix A: A = Q * R. |
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complib/cgeqrf(3) -- compute a QR factorization of a complex M-by-N matrix A
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CGEQRF computes a QR factorization of a complex M-by-N matrix A: A = Q * R. |
