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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/zsrscl(3) -- multiplie an n-element complex vector x by the real scalar 1/a CDRSCL multiplies an n-element complex vector x by the real scalar 1/a. This is done without overflow or underflow as long as the final result x/a does not overflow or underflow. complib/zstedc(3) -- compute all eigenvalues and, optionally, eigenvectors of a symmetric tridiagonal matrix using the divide and c ZSTEDC computes all eigenvalues and, optionally, eigenvectors of a symmetric tridiagonal matrix using the divide and conquer method. The eigenvectors of a full or band complex Hermitian matrix can also be found if ZHETRD or ZHPTRD or ZHBTRD has been used to reduce this matrix to tridiagonal form. This code makes very mild assumptions about floating point arithmetic. It will work on machines with a guard digit in add/subtract, or on those binary machines without guard digits which subtract like t...
complib/zstein(3) -- compute the eigenvectors of a real symmetric tridiagonal matrix T corresponding to specified eigenvalues, usin
ZSTEIN computes the eigenvectors of a real symmetric tridiagonal matrix T corresponding to specified eigenvalues, using inverse iteration. The maximum number of iterations allowed for each eigenvector is specified by an internal parameter MAXITS (currently set to 5). Although the eigenvectors are real, they are stored in a complex array, which may be passed to ZUNMTR or ZUPMTR for back transformation to the eigenvectors of a complex Hermitian matrix which was reduced to tridiagonal form....
complib/zsteqr(3) -- compute all eigenvalues and, optionally, eigenvectors of a symmetric tridiagonal matrix using the implicit QL
ZSTEQR computes all eigenvalues and, optionally, eigenvectors of a symmetric tridiagonal matrix using the implicit QL or QR method. The eigenvectors of a full or band complex Hermitian matrix can also be found if ZHETRD or ZHPTRD or ZHBTRD has been used to reduce this matrix to tridiagonal form.
complib/zsycon(3) -- estimate the reciprocal of the condition number (in the 1-norm) of a complex symmetric matrix A using the fact
ZSYCON estimates the reciprocal of the condition number (in the 1-norm) of a complex symmetric matrix A using the factorization A = U*D*U**T or A = L*D*L**T computed by ZSYTRF. An estimate is obtained for norm(inv(A)), and the reciprocal of the condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).
complib/zsyr(3) -- perform the symmetric rank 1 operation A := alpha*x*( x' ) + A,
ZSYR performs the symmetric rank 1 operation where alpha is a complex scalar, x is an n element vector and A is an n by n symmetric matrix.
complib/zsyrfs(3) -- improve the computed solution to a system of linear equations when the coefficient matrix is symmetric indefin
ZSYRFS improves the computed solution to a system of linear equations when the coefficient matrix is symmetric indefinite, and provides error bounds and backward error estimates for the solution.
complib/zsysv(3) -- X = B,
ZSYSV computes 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 Nby-NRHS matrices. The diagonal pivoting method is used to factor A as A = U * D * U**T, if UPLO = 'U', or A = L * D * L**T, if UPLO = 'L', where U (or L) is a product of permutation and unit upper (lower) triangular matrices, and D is symmetric and block diagonal with 1-by-1 and 2-by-2 diagonal blocks. The factored form of A is then used to solve the system of...
complib/zsysvx(3) -- to a complex system of linear equations A * X = B,
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.
complib/zsytf2(3) -- the Bunch-Kaufman diagonal pivoting method
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....
complib/zsytrf(3) -- the Bunch-Kaufman diagonal pivoting method
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....
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
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.
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
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.
complib/ztbcon(3) -- band matrix A, in either the 1-norm or the infinity-norm
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)) ).
complib/ztbrfs(3) -- provide error bounds and backward error estimates for the solution to a system of linear equations with a tria
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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