if ( UPPER ) then   U'*A*Q = U'*( A1 A2 )*Q = ( x 0 )  ( 0 A3 ) ( x x ) and  V'*B*Q = V'*( B1 B2 )*Q = ( x 0 )	( 0 B3 ) ( x x )  or if ( .NOT.UPPER ) then   U'*A*Q = U'*( A1 0 )*Q = ( x x )	( A2 A3 ) ( 0 x ) and  V'*B*Q = V'*( B1 0 )*Q = ( x x )  ( B2 B3 ) ( 0 x ) where   U = ( CSU SNU ), V = ( CSV SNV ),
zlahef		zlahef (3p)	- compute a partial factorization of a complex Hermitian matrix A using the Bunch-Kaufman diagonal pivoting method
zlahqr		zlahqr (3p)	- i an auxiliary routine called by ZHSEQR to update the eigenvalues and Schur decomposition already computed by ZHSEQR, by dealing with the Hessenberg submatrix in rows and columns ILO to IHI
zlahrd		zlahrd (3p)	- reduce the first NB columns of a complex general n-by-(n-k+1) matrix A so that elements below the k-th subdiagonal are zero
zlaic1		zlaic1 (3p)	- applie one step of incremental condition estimation in its simplest version
zlangb		zlangb (3p)	- return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of an n by n band matrix A, with kl sub-diagonals and ku super-diagonals
zlange		zlange (3p)	- return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex matrix A
zlangt		zlangt (3p)	- return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex tridiagonal matrix A
zlanhb		zlanhb (3p)	- return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of an n by n hermitian band matrix A, with k super-diagonals
zlanhe		zlanhe (3p)	- return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex hermitian matrix A
zlanhp		zlanhp (3p)	- return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex hermitian matrix A, supplied in packed form
zlanhs		zlanhs (3p)	- return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a Hessenberg matrix A
zlanht		zlanht (3p)	- return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex Hermitian tridiagonal matrix A
zlansb		zlansb (3p)	- return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of an n by n symmetric band matrix A, with k super-diagonals
zlansp		zlansp (3p)	- return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex symmetric matrix A, supplied in packed form
zlansy		zlansy (3p)	- return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex symmetric matrix A
zlantb		zlantb (3p)	- return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of an n by n triangular band matrix A, with ( k + 1 ) diagonals
zlantp		zlantp (3p)	- return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a triangular matrix A, supplied in packed form
zlantr		zlantr (3p)	- return the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a trapezoidal or triangular matrix A
zlapll		zlapll (3p)	- two column vectors X and Y, let   A = ( X Y )
zlapmt		zlapmt (3p)	- rearrange the columns of the M by N matrix X as specified by the permutation K(1),K(2),...,K(N) of the integers 1,...,N
zlaqgb		zlaqgb (3p)	- equilibrate a general M by N band matrix A with KL subdiagonals and KU superdiagonals using the row and scaling factors in the vectors R and C
zlaqge		zlaqge (3p)	- equilibrate a general M by N matrix A using the row and scaling factors in the vectors R and C
zlaqhb		zlaqhb (3p)	- equilibrate a symmetric band matrix A using the scaling factors in the vector S
zlaqhe		zlaqhe (3p)	- equilibrate a Hermitian matrix A using the scaling factors in the vector S
zlaqhp		zlaqhp (3p)	- equilibrate a Hermitian matrix A using the scaling factors in the vector S
zlaqsb		zlaqsb (3p)	- equilibrate a symmetric band matrix A using the scaling factors in the vector S
zlaqsp		zlaqsp (3p)	- equilibrate a symmetric matrix A using the scaling factors in the vector S
zlaqsy		zlaqsy (3p)	- equilibrate a symmetric matrix A using the scaling factors in the vector S
zlar2v		zlar2v (3p)	- applie a vector of complex plane rotations with real cosines from both sides to a sequence of 2-by-2 complex Hermitian matrices,
zlarf		zlarf (3p)	- applie a complex elementary reflector H to a complex M-by-N matrix C, from either the left or the right
zlarfb		zlarfb (3p)	- applie a complex block reflector H or its transpose H' to a complex M-by-N matrix C, from either the left or the right
zlarfg		zlarfg (3p)	- generate a complex elementary reflector H of order n, such that   H' * ( alpha ) = ( beta ), H' * H = I
zlarft		zlarft (3p)	- form the triangular factor T of a complex block reflector H of order n, which is defined as a product of k elementary reflectors
zlarfx		zlarfx (3p)	- applie a complex elementary reflector H to a complex m by n matrix C, from either the left or the right
zlargv		zlargv (3p)	- generate a vector of complex plane rotations with real cosines, determined by elements of the complex vectors x and y
zlarnv		zlarnv (3p)	- return a vector of n random complex numbers from a uniform or normal distribution
zlartg		zlartg (3p)	- generate a plane rotation so that   [ CS SN ] [ F ] [ R ]  [ __ ] 
zlartv		zlartv (3p)	- applie a vector of complex plane rotations with real cosines to elements of the complex vectors x and y
zlascl		zlascl (3p)	- multiply the M by N complex matrix A by the real scalar CTO/CFROM
zlaset		zlaset (3p)	- initialize a 2-D array A to BETA on the diagonal and ALPHA on the offdiagonals
zlasr		zlasr (3p)	- perform the transformation   A := P*A, when SIDE = 'L' or 'l' ( Left-hand side )   A := A*P', when SIDE = 'R' or 'r' ( Right-hand side )  where A is an m by n complex matrix and P is an orthogonal matrix,
zlassq		zlassq (3p)	- return the values scl and ssq such that   ( scl**2 )*ssq = x( 1 )**2 +...+ x( n )**2 + ( scale**2 )*sumsq,
zlaswp		zlaswp (3p)	- perform a series of row interchanges on the matrix A
zlasyf		zlasyf (3p)	- compute a partial factorization of a complex symmetric matrix A using the Bunch-Kaufman diagonal pivoting method
zlatbs		zlatbs (3p)	- solve one of the triangular systems	A * x = s*b, A**T * x = s*b, or A**H * x = s*b,
zlatps		zlatps (3p)	- solve one of the triangular systems	A * x = s*b, A**T * x = s*b, or A**H * x = s*b,
zlatrd		zlatrd (3p)	- reduce NB rows and columns of a complex Hermitian matrix A to Hermitian tridiagonal form by a unitary similarity transformation Q' * A * Q, and returns the matrices V and W which are needed to apply the transformation to the unreduced part of A
zlatrs		zlatrs (3p)	- solve one of the triangular systems	A * x = s*b, A**T * x = s*b, or A**H * x = s*b,
zlatzm		zlatzm (3p)	- applie a Householder matrix generated by ZTZRQF to a matrix
zlauu2		zlauu2 (3p)	- compute the product U * U' or L' * L, where the triangular factor U or L is stored in the upper or lower triangular part of the array A
zlauum		zlauum (3p)	- compute the product U * U' or L' * L, where the triangular factor U or L is stored in the upper or lower triangular part of the array A
zpbco		zpbco (3p)	- compute a Cholesky factorization and condition number of a symmetric positive definite matrix A in banded storage.  If the condition number is not needed then xPBFA is slightly faster.  It is typical to follow a call to xPBCO with a call to xPBSL to solve Ax = b or to xPBDI to compute the determinant of A.
zpbcon		zpbcon (3p)	- estimate the reciprocal of the condition number (in the 1-norm) of a complex Hermitian positive definite band matrix using the Cholesky factorization A = U**H*U or A = L*L**H computed by ZPBTRF
zpbdi		zpbdi