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complib/dggrqf(3) -- a P-by-N matrix B
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DGGRQF computes a generalized RQ factorization of an M-by-N matrix A and a P-by-N matrix B: A = R*Q, B = Z*T*Q, 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 M <= N, R = ( 0 R12 ) M, or if M > N, R = ( R11 ) M-N, N-M M ( R21 ) N N where R12 or R21 is upper triangular, and if P >= N, T = ( T11 ) N , or if P < N, T = ( T11 T12 ) P, ( 0 ) P-N P N-P N where T11 is upper triangular. In particular, if B is square and nonsingular, the G... |
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complib/dggsvd(3) -- an M-by-N real matrix A and P-by-N real matrix B
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DGGSVD computes the generalized singular value decomposition (GSVD) of an M-by-N real matrix A and P-by-N real matrix B: U'*A*Q = D1*( 0 R ), V'*B*Q = D2*( 0 R ) where U, V and Q are orthogonal matrices, and Z' is the transpose of Z. Let K+L = the effective numerical rank of the matrix (A',B')', then R is a K+L-by-K+L nonsingular upper triangular matrix, D1 and D2 are M-by(K+L) and P-by-(K+L) "diagonal" matrices and of the following structures, respectively: If M-K-L >= 0, K L D1 = K ( I... |
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complib/dggsvp(3) -- U'*A*Q = K ( 0 A12 A13 ) if M-K-L >= 0
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DGGSVP computes orthogonal matrices U, V and Q such that L ( 0 0 A23 ) M-K-L ( 0 0 0 ) N-K-L K L = K ( 0 A12 A13 ) if M-K-L < 0; M-K ( 0 0 A23 ) N-K-L K L V'*B*Q = L ( 0 0 B13 ) P-L ( 0 0 0 ) where the K-by-K matrix A12 and L-by-L matrix B13 are nonsingular upper triangular; A23 is L-by-L upper triangular if M-K-L >= 0, otherwise A23 is (M-K)-by-L upper trapezoidal. K+L = the effective numerical rank of the (M+P)-by-N matrix (A',B')'. Z' denotes the transpose of Z. This decomposition is the... |
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standard/dglclose(3) -- closes the DGL server connection
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sid expects the identifier of the server you want to close. If sid is negative, then all graphics server connections are closed. Server identifiers are returned by dglopen. |
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standard/dglopen(3) -- opens a Graphics Library connection to a graphics server
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svname expects a pointer to the name of the graphics server to which you want to open a connection. For a successful connection, the client host must have permission to connect to the graphics server. Authentication is accomplished via the same mechanisms as for X clients. See xhost(1) for further details. The svname parameter has the following syntax: [[username ]password@]hostname[:server[.screen]] where hostname is an internet host name recognized by gethostname(3N). server and screen are ign... |
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complib/dgtcon(3) -- estimate the reciprocal of the condition number of a real tridiagonal matrix A using the LU factorization as c
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DGTCON estimates the reciprocal of the condition number of a real tridiagonal matrix A using the LU factorization as computed by DGTTRF. An estimate is obtained for norm(inv(A)), and the reciprocal of the condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))). |
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complib/dgtrfs(3) -- improve the computed solution to a system of linear equations when the coefficient matrix is tridiagonal, and
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DGTRFS improves the computed solution to a system of linear equations when the coefficient matrix is tridiagonal, and provides error bounds and backward error estimates for the solution. |
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complib/DGTSL(3) -- DGTSL given a general tridiagonal matrix and a right hand side will find the solution.
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On Entry N INTEGER is the order of the tridiagonal matrix. C DOUBLE PRECISION(N) is the subdiagonal of the tridiagonal matrix. C(2) through C(N) should contain the subdiagonal. On output C is destroyed. D DOUBLE PRECISION(N) is the diagonal of the tridiagonal matrix. On output D is destroyed. E DOUBLE PRECISION(N) is the superdiagonal of the tridiagonal matrix. E(1) through E(N-1) should contain the superdiagonal. On output E is destroyed. B DOUBLE PRECISION(N) is the right hand side vector. On ... |
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complib/dgtsv(3) -- solve the equation A*X = B,
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DGTSV solves the equation where A is an N-by-N tridiagonal matrix, by Gaussian elimination with partial pivoting. Note that the equation A'*X = B may be solved by interchanging the order of the arguments DU and DL. |
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complib/dgtsvx(3) -- system of linear equations A * X = B or A**T * X = B,
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DGTSVX uses the LU factorization to compute the solution to a real system of linear equations A * X = B or A**T * X = B, where A is a tridiagonal matrix of order N 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/dgttrf(3) -- compute an LU factorization of a real tridiagonal matrix A using elimination with partial pivoting and row int
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DGTTRF computes an LU factorization of a real tridiagonal matrix A using elimination with partial pivoting and row interchanges. The factorization has the form A = L * U where L is a product of permutation and unit lower bidiagonal matrices and U is upper triangular with nonzeros in only the main diagonal and first two superdiagonals. |
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complib/dgttrs(3) -- solve one of the systems of equations A*X = B or A'*X = B,
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DGTTRS solves one of the systems of equations A*X = B or A'*X = B, with a tridiagonal matrix A using the LU factorization computed by DGTTRF. |
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complib/dhgeqz(3) -- w(i) B ) = 0 In addition, the pair A,B may be reduced to generalized Schur form
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DHGEQZ implements a single-/double-shift version of the QZ method for finding the generalized eigenvalues B is upper triangular, and A is block upper triangular, where the diagonal blocks are either 1-by-1 or 2-by-2, the 2-by-2 blocks having complex generalized eigenvalues (see the description of the argument JOB.) If JOB='S', then the pair (A,B) is simultaneously reduced to Schur form by applying one orthogonal tranformation (usually called Q) on the left and another (usually called Z) on the... |
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complib/dhsein(3) -- use inverse iteration to find specified right and/or left eigenvectors of a real upper Hessenberg matrix H
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DHSEIN uses inverse iteration to find specified right and/or left eigenvectors of a real upper Hessenberg matrix H. The right eigenvector x and the left eigenvector y of the matrix H corresponding to an eigenvalue w are defined by: H * x = w * x, y**h * H = w * y**h where y**h denotes the conjugate transpose of the vector y. |
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complib/dhseqr(3) -- compute the eigenvalues of a real upper Hessenberg matrix H and, optionally, the matrices T and Z from the Sch
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DHSEQR computes the eigenvalues of a real upper Hessenberg matrix H and, optionally, the matrices T and Z from the Schur decomposition H = Z T Z**T, where T is an upper quasi-triangular matrix (the Schur form), and Z is the orthogonal matrix of Schur vectors. Optionally Z may be postmultiplied into an input orthogonal matrix Q, so that this routine can give the Schur factorization of a matrix A which has been reduced to the Hessenberg form H by the orthogonal matrix Q: A = Q*H*Q**T = (QZ)*T*(QZ)... |
