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 Section All Sections 1 - General Commands 2 - System Calls 3 - Subroutines 4 - Special Files 5 - File Formats 6 - Games 7 - Macros and Conventions 8 - Maintenance Commands 9 - Kernel Interface n - New Commands
 complib/dgerqf(3) -- compute an RQ factorization of a real M-by-N matrix A DGERQF computes an RQ factorization of a real M-by-N matrix A: A = R * Q. complib/DGESL(3) -- DGESL solves the double precision system A * X = B or TRANS(A) * X = B using the factors computed by DGECO or On Entry A DOUBLE PRECISION(LDA, N) the output from DGECO or DGEFA. LDA INTEGER the leading dimension of the array A . N INTEGER the order of the matrix A . IPVT INTEGER(N) the pivot vector from DGECO or DGEFA. B DOUBLE PRECISION(N) the right hand side vector. JOB INTEGER = 0 to solve A*X = B , = nonzero to solve TRANS(A)*X = B where TRANS(A) is the 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. Te...
complib/dgesv(3) -- = B,
DGESV computes the solution to a real 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....
complib/dgesvd(3) -- compute the singular value decomposition (SVD) of a real M-by-N matrix A, optionally computing the left and/or
DGESVD computes the singular value decomposition (SVD) of a real M-by-N matrix A, optionally computing the left and/or right singular vectors. The SVD is written A = U * SIGMA * 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 orthogonal matrix, and V is an N-by-N orthogonal 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 min(m,n...
complib/dgesvx(3) -- system of linear equations A * X = B,
DGESVX uses the LU factorization to compute the solution to a real 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.
complib/dgetf2(3) -- compute an LU factorization of a general m-by-n matrix A using partial pivoting with row interchanges
DGETF2 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.
complib/dgetrf(3) -- compute an LU factorization of a general M-by-N matrix A using partial pivoting with row interchanges
DGETRF 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.
complib/dgetri(3) -- compute the inverse of a matrix using the LU factorization computed by DGETRF
DGETRI computes the inverse of a matrix using the LU factorization computed by DGETRF. This method inverts U and then computes inv(A) by solving the system inv(A)*L = inv(U) for inv(A).
complib/dgetrs(3) -- a general N-by-N matrix A using the LU factorization computed by DGETRF
DGETRS solves a system of linear equations A * X = B or A' * X = B with a general N-by-N matrix A using the LU factorization computed by DGETRF.
complib/dggbak(3) -- form the right or left eigenvectors of a real generalized eigenvalue problem A*x = lambda*B*x, by backward tra
DGGBAK forms the right or left eigenvectors of a real generalized eigenvalue problem A*x = lambda*B*x, by backward transformation on the computed eigenvectors of the balanced pair of matrices output by DGGBAL.
complib/dggbal(3) -- balance a pair of general real matrices (A,B)
DGGBAL balances a pair of general real 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 and/o...
complib/dggglm(3) -- solve a general Gauss-Markov linear model (GLM) problem
DGGGLM 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...
complib/dgghrd(3) -- reduce a pair of real matrices (A,B) to generalized upper Hessenberg form using orthogonal transformations, wh
DGGHRD reduces a pair of real matrices (A,B) to generalized upper Hessenberg form using orthogonal 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 orthogonal, and ' means transpose. The orthogonal 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 that Q...
complib/dgglse(3) -- solve the linear equality-constrained least squares (LSE) problem
DGGLSE solves the linear equality-constrained least squares (LSE) problem: minimize || c - A*x ||_2 subject to B*x = d where A is an M-by-N matrix, B is a P-by-N matrix, c is a given M-vector, and d is a given P-vector. It is assumed that P <= N <= M+P, and rank(B) = P and rank( ( A ) ) = N. ( ( B ) ) These conditions ensure that the LSE problem has a unique solution, which is obtained using a GRQ factorization of the matrices B and A....
complib/dggqrf(3) -- an N-by-P matrix B
DGGQRF computes a generalized QR factorization of an N-by-M matrix A and an N-by-P matrix B: A = Q*R, B = Q*T*Z, where Q is an N-by-N orthogonal matrix, Z is a P-by-P orthogonal matrix, and R and T assume one of the forms: if N >= M, R = ( R11 ) M , or if N < M, R = ( R11 R12 ) N, ( 0 ) N-M N M-N M where R11 is upper triangular, and if N <= P, T = ( 0 T12 ) N, or if N > P, T = ( T11 ) N-P, P-N N ( T21 ) P P where T12 or T21 is upper triangular. In particular, if B is square and nonsingular, the ...
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