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complib/cgerqf(3) -- compute an RQ factorization of a complex M-by-N matrix A
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CGERQF computes an RQ factorization of a complex M-by-N matrix A: A = R * Q. |
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complib/CGESL(3) -- CGESL solves the complex system A * X = B or CTRANS(A) * X = B using the factors computed by CGECO or CGEFA.
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On Entry A COMPLEX(LDA, N) the output from CGECO or CGEFA. LDA INTEGER the leading dimension of the array A . N INTEGER the order of the matrix A . IPVT INTEGER(N) the pivot vector from CGECO or CGEFA. B COMPLEX(N) the right hand side vector. JOB INTEGER = 0 to solve A*X = B , = nonzero to solve CTRANS(A)*X = B where CTRANS(A) is the conjugate transpose. On Return B the solution vector X . Error Condition A division by zero will occur if the input factor contains a zero on the diagonal. Technica... |
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complib/cgesv(3) -- X = B,
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CGESV computes the solution to a complex system of linear equations A * X = B, where A is an N-by-N matrix and X and B are N-by-NRHS matrices. The LU decomposition with partial pivoting and row interchanges is used to factor A as A = P * L * U, where P is a permutation matrix, L is unit lower triangular, and U is upper triangular. The factored form of A is then used to solve the system of equations A * X = B.... |
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complib/cgesvd(3) -- compute the singular value decomposition (SVD) of a complex Mby-N matrix A, optionally computing the left and/
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CGESVD computes the singular value decomposition (SVD) of a complex Mby-N matrix A, optionally computing the left and/or right singular vectors. The SVD is written A = U * SIGMA * conjugate-transpose(V) where SIGMA is an M-by-N matrix which is zero except for its min(m,n) diagonal elements, U is an M-by-M unitary matrix, and V is an N-by-N unitary matrix. The diagonal elements of SIGMA are the singular values of A; they are real and non-negative, and are returned in descending order. The first m... |
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complib/cgesvx(3) -- system of linear equations A * X = B,
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CGESVX uses the LU factorization to compute the solution to a complex system of linear equations A * X = B, where A is an N-by-N matrix and X and B are N-by-NRHS matrices. Error bounds on the solution and a condition estimate are also provided. |
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complib/cgetf2(3) -- compute an LU factorization of a general m-by-n matrix A using partial pivoting with row interchanges
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CGETF2 computes an LU factorization of a general m-by-n matrix A using partial pivoting with row interchanges. The factorization has the form A = P * L * U where P is a permutation matrix, L is lower triangular with unit diagonal elements (lower trapezoidal if m > n), and U is upper triangular (upper trapezoidal if m < n). This is the right-looking Level 2 BLAS version of the algorithm. |
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complib/cgetrf(3) -- compute an LU factorization of a general M-by-N matrix A using partial pivoting with row interchanges
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CGETRF computes an LU factorization of a general M-by-N matrix A using partial pivoting with row interchanges. The factorization has the form A = P * L * U where P is a permutation matrix, L is lower triangular with unit diagonal elements (lower trapezoidal if m > n), and U is upper triangular (upper trapezoidal if m < n). This is the right-looking Level 3 BLAS version of the algorithm. |
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complib/cgetri(3) -- compute the inverse of a matrix using the LU factorization computed by CGETRF
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CGETRI computes the inverse of a matrix using the LU factorization computed by CGETRF. This method inverts U and then computes inv(A) by solving the system inv(A)*L = inv(U) for inv(A). |
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complib/cgetrs(3) -- A**H * X = B with a general N-by-N matrix A using the LU factorization computed by CGETRF
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CGETRS solves a system of linear equations A * X = B, A**T * X = B, or A**H * X = B with a general N-by-N matrix A using the LU factorization computed by CGETRF. |
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complib/cggbak(3) -- form the right or left eigenvectors of a complex generalized eigenvalue problem A*x = lambda*B*x, by backward
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CGGBAK forms the right or left eigenvectors of a complex generalized eigenvalue problem A*x = lambda*B*x, by backward transformation on the computed eigenvectors of the balanced pair of matrices output by CGGBAL. |
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complib/cggbal(3) -- balance a pair of general complex matrices (A,B)
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CGGBAL balances a pair of general complex matrices (A,B). This involves, first, permuting A and B by similarity transformations to isolate eigenvalues in the first 1 to ILO$-$1 and last IHI+1 to N elements on the diagonal; and second, applying a diagonal similarity transformation to rows and columns ILO to IHI to make the rows and columns as close in norm as possible. Both steps are optional. Balancing may reduce the 1-norm of the matrices, and improve the accuracy of the computed eigenvalues an... |
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complib/cggglm(3) -- solve a general Gauss-Markov linear model (GLM) problem
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CGGGLM solves a general Gauss-Markov linear model (GLM) problem: minimize || y ||_2 subject to d = A*x + B*y x where A is an N-by-M matrix, B is an N-by-P matrix, and d is a given Nvector. It is assumed that M <= N <= M+P, and rank(A) = M and rank( A B ) = N. Under these assumptions, the constrained equation is always consistent, and there is a unique solution x and a minimal 2-norm solution y, which is obtained using a generalized QR factorization of A and B. In particular, if matrix B is squar... |
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complib/cgghrd(3) -- reduce a pair of complex matrices (A,B) to generalized upper Hessenberg form using unitary transformations, wh
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CGGHRD reduces a pair of complex matrices (A,B) to generalized upper Hessenberg form using unitary transformations, where A is a general matrix and B is upper triangular: Q' * A * Z = H and Q' * B * Z = T, where H is upper Hessenberg, T is upper triangular, and Q and Z are unitary, and ' means conjugate transpose. The unitary matrices Q and Z are determined as products of Givens rotations. They may either be formed explicitly, or they may be postmultiplied into input matrices Q1 and Z1, so th... |
