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complib/zsysvx(3) -- to a complex system of linear equations A * X = B,
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ZSYSVX uses the diagonal pivoting factorization to compute the solution to a complex system of linear equations A * X = B, where A is an N-by-N symmetric 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/zsytf2(3) -- the Bunch-Kaufman diagonal pivoting method
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ZSYTF2 computes the factorization of a complex symmetric matrix A using the Bunch-Kaufman diagonal pivoting method: A = U*D*U' or A = L*D*L' where U (or L) is a product of permutation and unit upper (lower) triangular matrices, U' is the transpose of U, and D is symmetric and block diagonal with 1-by-1 and 2-by-2 diagonal blocks. This is the unblocked version of the algorithm, calling Level 2 BLAS.... |
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complib/zsytrf(3) -- the Bunch-Kaufman diagonal pivoting method
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ZSYTRF computes the factorization of a complex symmetric matrix A using the Bunch-Kaufman diagonal pivoting method. The form of the factorization is A = U*D*U**T or A = L*D*L**T where U (or L) is a product of permutation and unit upper (lower) triangular matrices, and D is symmetric and block diagonal with with 1- by-1 and 2-by-2 diagonal blocks. This is the blocked version of the algorithm, calling Level 3 BLAS.... |
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complib/zsytri(3) -- compute the inverse of a complex symmetric indefinite matrix A using the factorization A = U*D*U**T or A = L*D
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ZSYTRI computes the inverse of a complex symmetric indefinite matrix A using the factorization A = U*D*U**T or A = L*D*L**T computed by ZSYTRF. |
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complib/zsytrs(3) -- solve a system of linear equations A*X = B with a complex symmetric matrix A using the factorization A = U*D*U
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ZSYTRS solves a system of linear equations A*X = B with a complex symmetric matrix A using the factorization A = U*D*U**T or A = L*D*L**T computed by ZSYTRF. |
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complib/ztbcon(3) -- band matrix A, in either the 1-norm or the infinity-norm
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ZTBCON estimates the reciprocal of the condition number of a triangular band 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/ztbrfs(3) -- provide error bounds and backward error estimates for the solution to a system of linear equations with a tria
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ZTBRFS provides error bounds and backward error estimates for the solution to a system of linear equations with a triangular band coefficient matrix. The solution matrix X must be computed by ZTBTRS or some other means before entering this routine. ZTBRFS does not do iterative refinement because doing so cannot improve the backward error. |
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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)) ). |
