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complib/zhegst(3) -- reduce a complex Hermitian-definite generalized eigenproblem to standard form
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ZHEGST reduces a complex Hermitian-definite generalized eigenproblem to standard form. If ITYPE = 1, the problem is A*x = lambda*B*x, and A is overwritten by inv(U**H)*A*inv(U) or inv(L)*A*inv(L**H) If ITYPE = 2 or 3, the problem is A*B*x = lambda*x or B*A*x = lambda*x, and A is overwritten by U*A*U**H or L**H*A*L. B must have been previously factorized as U**H*U or L*L**H by ZPOTRF. |
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complib/zhegv(3) -- a complex generalized Hermitian-definite eigenproblem, of the form A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x
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ZHEGV computes all the eigenvalues, and optionally, the eigenvectors of a complex generalized Hermitian-definite eigenproblem, of the form A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x. Here A and B are assumed to be Hermitian and B is also positive definite. |
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complib/zherfs(3) -- improve the computed solution to a system of linear equations when the coefficient matrix is Hermitian indefin
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ZHERFS improves the computed solution to a system of linear equations when the coefficient matrix is Hermitian indefinite, and provides error bounds and backward error estimates for the solution. |
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complib/zhesv(3) -- X = B,
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ZHESV computes the solution to a complex system of linear equations A * X = B, where A is an N-by-N Hermitian matrix and X and B are Nby-NRHS matrices. The diagonal pivoting method is used to factor A as A = U * D * U**H, if UPLO = 'U', or A = L * D * L**H, if UPLO = 'L', where U (or L) is a product of permutation and unit upper (lower) triangular matrices, and D is Hermitian 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... |
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complib/zhesvx(3) -- to a complex system of linear equations A * X = B,
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ZHESVX 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 Hermitian 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/zhetd2(3) -- reduce a complex Hermitian matrix A to real symmetric tridiagonal form T by a unitary similarity transformatio
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ZHETD2 reduces a complex Hermitian matrix A to real symmetric tridiagonal form T by a unitary similarity transformation: Q' * A * Q = T. |
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complib/zhetf2(3) -- the Bunch-Kaufman diagonal pivoting method
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ZHETF2 computes the factorization of a complex Hermitian 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 conjugate transpose of U, and D is Hermitian 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/zhetrd(3) -- reduce a complex Hermitian matrix A to real symmetric tridiagonal form T by a unitary similarity transformatio
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ZHETRD reduces a complex Hermitian matrix A to real symmetric tridiagonal form T by a unitary similarity transformation: Q**H * A * Q = T. |
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complib/zhetrf(3) -- the Bunch-Kaufman diagonal pivoting method
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ZHETRF computes the factorization of a complex Hermitian matrix A using the Bunch-Kaufman diagonal pivoting method. The form of the factorization is A = U*D*U**H or A = L*D*L**H where U (or L) is a product of permutation and unit upper (lower) triangular matrices, and D is Hermitian and block diagonal 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/zhetri(3) -- compute the inverse of a complex Hermitian indefinite matrix A using the factorization A = U*D*U**H or A = L*D
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ZHETRI computes the inverse of a complex Hermitian indefinite matrix A using the factorization A = U*D*U**H or A = L*D*L**H computed by ZHETRF. |
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complib/zhetrs(3) -- solve a system of linear equations A*X = B with a complex Hermitian matrix A using the factorization A = U*D*U
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ZHETRS solves a system of linear equations A*X = B with a complex Hermitian matrix A using the factorization A = U*D*U**H or A = L*D*L**H computed by ZHETRF. |
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complib/zhgeqz(3) -- w(i) B ) = 0 If JOB='S', then the pair (A,B) is simultaneously reduced to Schur form (i.e., A and B are both u
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ZHGEQZ implements a single-shift version of the QZ method for finding the generalized eigenvalues w(i)=ALPHA(i)/BETA(i) of the equation A are then ALPHA(1),...,ALPHA(N), and of B are BETA(1),...,BETA(N). If JOB='S' and COMPQ and COMPZ are 'V' or 'I', then the unitary transformations used to reduce (A,B) are accumulated into the arrays Q and Z s.t.: Q(in) A(in) Z(in)* = Q(out) A(out) Z(out)* Q(in) B(in) Z(in)* = Q(out) B(out) Z(out)* Ref: C.B. Moler & G.W. Stewart, "An Algorithm for Genera... |
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complib/zhpcon(3) -- estimate the reciprocal of the condition number of a complex Hermitian packed matrix A using the factorization
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ZHPCON estimates the reciprocal of the condition number of a complex Hermitian packed matrix A using the factorization A = U*D*U**H or A = L*D*L**H computed by ZHPTRF. 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/zhpev(3) -- compute all the eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix in packed storage
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ZHPEV computes all the eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix in packed storage. |
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complib/zhpevd(3) -- compute all the eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A in packed storage
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ZHPEVD computes all the eigenvalues and, optionally, eigenvectors of a complex Hermitian matrix A in packed storage. If eigenvectors are desired, it uses a divide and conquer algorithm. The divide and conquer algorithm 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 the Cray X-MP, Cray Y-MP, Cray C-90, or Cray-2. It could conceivably fail on hexadecimal o... |
