
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 1norm) of a complex symmetric matrix A using the fact

ZSYCON estimates the reciprocal of the condition number (in the 1norm) 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 NbyN symmetric matrix and X and B are NbyNRHS 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 1by1 and 2by2 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 NbyN symmetric matrix and X and B are NbyNRHS matrices. Error bounds on the solution and a condition estimate are also provided. 
complib/zsytf2(3)  the BunchKaufman diagonal pivoting method

ZSYTF2 computes the factorization of a complex symmetric matrix A using the BunchKaufman 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 1by1 and 2by2 diagonal blocks. This is the unblocked version of the algorithm, calling Level 2 BLAS.... 
complib/zsytrf(3)  the BunchKaufman diagonal pivoting method

ZSYTRF computes the factorization of a complex symmetric matrix A using the BunchKaufman 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 by1 and 2by2 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 1norm or the infinitynorm

ZTBCON estimates the reciprocal of the condition number of a triangular band matrix A, in either the 1norm or the infinitynorm. 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. 