
complib/zgetri(3)  compute the inverse of a matrix using the LU factorization computed by ZGETRF

ZGETRI computes the inverse of a matrix using the LU factorization computed by ZGETRF. This method inverts U and then computes inv(A) by solving the system inv(A)*L = inv(U) for inv(A). 
complib/zgetrs(3)  A**H * X = B with a general NbyN matrix A using the LU factorization computed by ZGETRF

ZGETRS solves a system of linear equations A * X = B, A**T * X = B, or A**H * X = B with a general NbyN matrix A using the LU factorization computed by ZGETRF. 
complib/zggbak(3)  form the right or left eigenvectors of a complex generalized eigenvalue problem A*x = lambda*B*x, by backward

ZGGBAK forms the right or left eigenvectors of a complex generalized eigenvalue problem A*x = lambda*B*x, by backward transformation on the computed eigenvectors of the balanced pair of matrices output by ZGGBAL. 
complib/zggbal(3)  balance a pair of general complex matrices (A,B)

ZGGBAL balances a pair of general complex matrices (A,B). This involves, first, permuting A and B by similarity transformations to isolate eigenvalues in the first 1 to ILO$$1 and last IHI+1 to N elements on the diagonal; and second, applying a diagonal similarity transformation to rows and columns ILO to IHI to make the rows and columns as close in norm as possible. Both steps are optional. Balancing may reduce the 1norm of the matrices, and improve the accuracy of the computed eigenvalues an... 
complib/zggglm(3)  solve a general GaussMarkov linear model (GLM) problem

ZGGGLM solves a general GaussMarkov linear model (GLM) problem: minimize  y _2 subject to d = A*x + B*y x where A is an NbyM matrix, B is an NbyP matrix, and d is a given Nvector. It is assumed that M <= N <= M+P, and rank(A) = M and rank( A B ) = N. Under these assumptions, the constrained equation is always consistent, and there is a unique solution x and a minimal 2norm solution y, which is obtained using a generalized QR factorization of A and B. In particular, if matrix B is squar... 
complib/zgghrd(3)  reduce a pair of complex matrices (A,B) to generalized upper Hessenberg form using unitary transformations, wh

ZGGHRD reduces a pair of complex matrices (A,B) to generalized upper Hessenberg form using unitary transformations, where A is a general matrix and B is upper triangular: Q' * A * Z = H and Q' * B * Z = T, where H is upper Hessenberg, T is upper triangular, and Q and Z are unitary, and ' means conjugate transpose. The unitary matrices Q and Z are determined as products of Givens rotations. They may either be formed explicitly, or they may be postmultiplied into input matrices Q1 and Z1, so th... 
complib/zgglse(3)  solve the linear equalityconstrained least squares (LSE) problem

ZGGLSE solves the linear equalityconstrained least squares (LSE) problem: minimize  c  A*x _2 subject to B*x = d where A is an MbyN matrix, B is a PbyN matrix, c is a given Mvector, and d is a given Pvector. It is assumed that P <= N <= M+P, and rank(B) = P and rank( ( A ) ) = N. ( ( B ) ) These conditions ensure that the LSE problem has a unique solution, which is obtained using a GRQ factorization of the matrices B and A.... 
complib/zggqrf(3)  an NbyP matrix B

ZGGQRF computes a generalized QR factorization of an NbyM matrix A and an NbyP matrix B: A = Q*R, B = Q*T*Z, where Q is an NbyN unitary matrix, Z is a PbyP unitary matrix, and R and T assume one of the forms: if N >= M, R = ( R11 ) M , or if N < M, R = ( R11 R12 ) N, ( 0 ) NM N MN M where R11 is upper triangular, and if N <= P, T = ( 0 T12 ) N, or if N > P, T = ( T11 ) NP, PN N ( T21 ) P P where T12 or T21 is upper triangular. In particular, if B is square and nonsingular, the GQR fa... 
complib/zggrqf(3)  a PbyN matrix B

ZGGRQF computes a generalized RQ factorization of an MbyN matrix A and a PbyN matrix B: A = R*Q, B = Z*T*Q, where Q is an NbyN unitary matrix, Z is a PbyP unitary matrix, and R and T assume one of the forms: if M <= N, R = ( 0 R12 ) M, or if M > N, R = ( R11 ) MN, NM M ( R21 ) N N where R12 or R21 is upper triangular, and if P >= N, T = ( T11 ) N , or if P < N, T = ( T11 T12 ) P, ( 0 ) PN P NP N where T11 is upper triangular. In particular, if B is square and nonsingular, the GRQ fac... 
complib/zggsvd(3)  an MbyN complex matrix A and PbyN complex matrix B

ZGGSVD computes the generalized singular value decomposition (GSVD) of an MbyN complex matrix A and PbyN complex matrix B: U'*A*Q = D1*( 0 R ), V'*B*Q = D2*( 0 R ) where U, V and Q are unitary matrices, and Z' means the conjugate transpose of Z. Let K+L = the effective numerical rank of the matrix (A',B')', then R is a (K+L)by(K+L) nonsingular upper triangular matrix, D1 and D2 are Mby(K+L) and Pby(K+L) "diagonal" matrices and of the following structures, respectively: If MKL... 
complib/zggsvp(3)  U'*A*Q = K ( 0 A12 A13 ) if MKL >= 0

ZGGSVP computes unitary matrices U, V and Q such that L ( 0 0 A23 ) MKL ( 0 0 0 ) NKL K L = K ( 0 A12 A13 ) if MKL < 0; MK ( 0 0 A23 ) NKL K L V'*B*Q = L ( 0 0 B13 ) PL ( 0 0 0 ) where the KbyK matrix A12 and LbyL matrix B13 are nonsingular upper triangular; A23 is LbyL upper triangular if MKL >= 0, otherwise A23 is (MK)byL upper trapezoidal. K+L = the effective numerical rank of the (M+P)byN matrix (A',B')'. Z' denotes the conjugate transpose of Z. This decomposition... 
complib/zgtcon(3)  estimate the reciprocal of the condition number of a complex tridiagonal matrix A using the LU factorization a

ZGTCON estimates the reciprocal of the condition number of a complex tridiagonal matrix A using the LU factorization as computed by ZGTTRF. 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/zgtrfs(3)  improve the computed solution to a system of linear equations when the coefficient matrix is tridiagonal, and

ZGTRFS improves the computed solution to a system of linear equations when the coefficient matrix is tridiagonal, and provides error bounds and backward error estimates for the solution. 