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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/zgelqf(3) -- compute an LQ factorization of a complex M-by-N matrix A ZGELQF computes an LQ factorization of a complex M-by-N matrix A: A = L * Q. complib/zgels(3) -- involving an M-by-N matrix A, or its conjugate-transpose, using a QR or LQ factorization of A 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 ...
complib/zgelss(3) -- compute the minimum norm solution to a complex linear least squares problem
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...
complib/zgelsx(3) -- compute the minimum-norm solution to a complex linear least squares problem
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 ]...
complib/zgeql2(3) -- compute a QL factorization of a complex m by n matrix A
ZGEQL2 computes a QL factorization of a complex m by n matrix A: A = Q * L.
complib/zgeqlf(3) -- compute a QL factorization of a complex M-by-N matrix A
ZGEQLF computes a QL factorization of a complex M-by-N matrix A: A = Q * L.
complib/zgeqpf(3) -- compute a QR factorization with column pivoting of a complex Mby-N matrix A
ZGEQPF computes a QR factorization with column pivoting of a complex Mby-N matrix A: A*P = Q*R.
complib/zgeqr2(3) -- compute a QR factorization of a complex m by n matrix A
ZGEQR2 computes a QR factorization of a complex m by n matrix A: A = Q * R.
complib/zgeqrf(3) -- compute a QR factorization of a complex M-by-N matrix A
ZGEQRF computes a QR factorization of a complex M-by-N matrix A: A = Q * R.
complib/zgerfs(3) -- improve the computed solution to a system of linear equations and provides error bounds and backward error est
ZGERFS improves the computed solution to a system of linear equations and provides error bounds and backward error estimates for the solution.
complib/zgerq2(3) -- compute an RQ factorization of a complex m by n matrix A
ZGERQ2 computes an RQ factorization of a complex m by n matrix A: A = R * Q.
complib/zgerqf(3) -- compute an RQ factorization of a complex M-by-N matrix A
ZGERQF computes an RQ factorization of a complex M-by-N matrix A: A = R * Q.
complib/zgesv(3) -- X = B,
ZGESV 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....
complib/zgesvd(3) -- compute the singular value decomposition (SVD) of a complex Mby-N matrix A, optionally computing the left and/
ZGESVD 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...
complib/zgesvx(3) -- system of linear equations A * X = B,
ZGESVX 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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