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complib/ztbtrs(3) -- or A**H * X = B,
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ZTBTRS solves a triangular system of the form where A is a triangular band matrix of order N, and B is an N-by-NRHS matrix. A check is made to verify that A is nonsingular. |
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complib/ztgevc(3) -- compute some or all of the right and/or left generalized eigenvectors of a pair of complex upper triangular ma
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ZTGEVC computes some or all of the right and/or left generalized eigenvectors of a pair of complex upper triangular matrices (A,B). The right generalized eigenvector x and the left generalized eigenvector y of (A,B) corresponding to a generalized eigenvalue w are defined by: (A - wB) * x = 0 and y**H * (A - wB) = 0 where y**H denotes the conjugate tranpose of y. If an eigenvalue w is determined by zero diagonal elements of both A and B, a unit vector is returned as the corresponding eigenvector.... |
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complib/ztgsja(3) -- compute the generalized singular value decomposition (GSVD) of two complex upper triangular (or trapezoidal) m
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ZTGSJA computes the generalized singular value decomposition (GSVD) of two complex upper triangular (or trapezoidal) matrices A and B. On entry, it is assumed that matrices A and B have the following forms, which may be obtained by the preprocessing subroutine ZGGSVP from a general M-by-N matrix A and P-by-N matrix B: N-K-L K L A = K ( 0 A12 A13 ) if M-K-L >= 0; L ( 0 0 A23 ) M-K-L ( 0 0 0 ) N-K-L K L A = K ( 0 A12 A13 ) if M-K-L < 0; M-K ( 0 0 A23 ) N-K-L K L B = L ( 0 0 B13 ) P-L ( 0 0 0 ) whe... |
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complib/ztpcon(3) -- triangular matrix A, in either the 1-norm or the infinity-norm
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ZTPCON estimates the reciprocal of the condition number of a packed triangular matrix A, in either the 1-norm or the infinity-norm. The norm of A is computed and an estimate is obtained for norm(inv(A)), then the reciprocal of the condition number is computed as RCOND = 1 / ( norm(A) * norm(inv(A)) ). |
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complib/ztprfs(3) -- provide error bounds and backward error estimates for the solution to a system of linear equations with a tria
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ZTPRFS provides error bounds and backward error estimates for the solution to a system of linear equations with a triangular packed coefficient matrix. The solution matrix X must be computed by ZTPTRS or some other means before entering this routine. ZTPRFS does not do iterative refinement because doing so cannot improve the backward error. |
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complib/ztptri(3) -- compute the inverse of a complex upper or lower triangular matrix A stored in packed format
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ZTPTRI computes the inverse of a complex upper or lower triangular matrix A stored in packed format. |
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complib/ztptrs(3) -- or A**H * X = B,
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ZTPTRS solves a triangular system of the form where A is a triangular matrix of order N stored in packed format, and B is an N-by-NRHS matrix. A check is made to verify that A is nonsingular. |
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complib/ztrcon(3) -- matrix A, in either the 1-norm or the infinity-norm
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ZTRCON estimates the reciprocal of the condition number of a triangular matrix A, in either the 1-norm or the infinity-norm. The norm of A is computed and an estimate is obtained for norm(inv(A)), then the reciprocal of the condition number is computed as RCOND = 1 / ( norm(A) * norm(inv(A)) ). |
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complib/ztrevc(3) -- compute some or all of the right and/or left eigenvectors of a complex upper triangular matrix T
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ZTREVC computes some or all of the right and/or left eigenvectors of a complex upper triangular matrix T. The right eigenvector x and the left eigenvector y of T corresponding to an eigenvalue w are defined by: T*x = w*x, y'*T = w*y' where y' denotes the conjugate transpose of the vector y. If all eigenvectors are requested, the routine may either return the matrices X and/or Y of right or left eigenvectors of T, or the products Q*X and/or Q*Y, where Q is an input unitary matrix. If T was obt... |
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complib/ztrexc(3) -- reorder the Schur factorization of a complex matrix A = Q*T*Q**H, so that the diagonal element of T with row i
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ZTREXC reorders the Schur factorization of a complex matrix A = Q*T*Q**H, so that the diagonal element of T with row index IFST is moved to row ILST. The Schur form T is reordered by a unitary similarity transformation Z**H*T*Z, and optionally the matrix Q of Schur vectors is updated by postmultplying it with Z. |
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complib/ztrrfs(3) -- provide error bounds and backward error estimates for the solution to a system of linear equations with a tria
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ZTRRFS provides error bounds and backward error estimates for the solution to a system of linear equations with a triangular coefficient matrix. The solution matrix X must be computed by ZTRTRS or some other means before entering this routine. ZTRRFS does not do iterative refinement because doing so cannot improve the backward error. |
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complib/ztrsen(3) -- reorder the Schur factorization of a complex matrix A = Q*T*Q**H, so that a selected cluster of eigenvalues ap
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ZTRSEN reorders the Schur factorization of a complex matrix A = Q*T*Q**H, so that a selected cluster of eigenvalues appears in the leading positions on the diagonal of the upper triangular matrix T, and the leading columns of Q form an orthonormal basis of the corresponding right invariant subspace. Optionally the routine computes the reciprocal condition numbers of the cluster of eigenvalues and/or the invariant subspace.... |
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complib/ztrsna(3) -- estimate reciprocal condition numbers for specified eigenvalues and/or right eigenvectors of a complex upper t
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ZTRSNA estimates reciprocal condition numbers for specified eigenvalues and/or right eigenvectors of a complex upper triangular matrix T (or of any matrix Q*T*Q**H with Q unitary). |
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complib/ztrsyl(3) -- solve the complex Sylvester matrix equation
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ZTRSYL solves the complex Sylvester matrix equation: op(A)*X + X*op(B) = scale*C or op(A)*X - X*op(B) = scale*C, where op(A) = A or A**H, and A and B are both upper triangular. A is Mby-M and B is N-by-N; the right hand side C and the solution X are M-byN; and scale is an output scale factor, set <= 1 to avoid overflow in X. |
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complib/ztrti2(3) -- compute the inverse of a complex upper or lower triangular matrix
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ZTRTI2 computes the inverse of a complex upper or lower triangular matrix. This is the Level 2 BLAS version of the algorithm. |
