
complib/ztzrqf(3)  reduce the MbyN ( M<=N ) complex upper trapezoidal matrix A to upper triangular form by means of unitary tra

ZTZRQF reduces the MbyN ( M<=N ) complex upper trapezoidal matrix A to upper triangular form by means of unitary transformations. The upper trapezoidal matrix A is factored as A = ( R 0 ) * Z, where Z is an NbyN unitary matrix and R is an MbyM upper triangular matrix. 
complib/zung2l(3)  generate an m by n complex matrix Q with orthonormal columns,

ZUNG2L generates an m by n complex matrix Q with orthonormal columns, which is defined as the last n columns of a product of k elementary reflectors of order m Q = H(k) . . . H(2) H(1) as returned by ZGEQLF. 
complib/zung2r(3)  generate an m by n complex matrix Q with orthonormal columns,

ZUNG2R generates an m by n complex matrix Q with orthonormal columns, which is defined as the first n columns of a product of k elementary reflectors of order m Q = H(1) H(2) . . . H(k) as returned by ZGEQRF. 
complib/zungbr(3)  generate one of the complex unitary matrices Q or P**H determined by ZGEBRD when reducing a complex matrix A t

ZUNGBR generates one of the complex unitary matrices Q or P**H determined by ZGEBRD when reducing a complex matrix A to bidiagonal form: A = Q * B * P**H. Q and P**H are defined as products of elementary reflectors H(i) or G(i) respectively. If VECT = 'Q', A is assumed to have been an MbyK matrix, and Q is of order M: if m >= k, Q = H(1) H(2) . . . H(k) and ZUNGBR returns the first n columns of Q, where m >= n >= k; if m < k, Q = H(1) H(2) . . . H(m1) and ZUNGBR returns Q as an MbyM matri... 
complib/zunghr(3)  product of IHIILO elementary reflectors of order N, as returned by ZGEHRD

ZUNGHR generates a complex unitary matrix Q which is defined as the product of IHIILO elementary reflectors of order N, as returned by ZGEHRD: Q = H(ilo) H(ilo+1) . . . H(ihi1). 
complib/zungl2(3)  generate an mbyn complex matrix Q with orthonormal rows,

ZUNGL2 generates an mbyn complex matrix Q with orthonormal rows, which is defined as the first m rows of a product of k elementary reflectors of order n Q = H(k)' . . . H(2)' H(1)' as returned by ZGELQF. 
complib/zunglq(3)  generate an MbyN complex matrix Q with orthonormal rows,

ZUNGLQ generates an MbyN complex matrix Q with orthonormal rows, which is defined as the first M rows of a product of K elementary reflectors of order N Q = H(k)' . . . H(2)' H(1)' as returned by ZGELQF. 
complib/zungql(3)  generate an MbyN complex matrix Q with orthonormal columns,

ZUNGQL generates an MbyN complex matrix Q with orthonormal columns, which is defined as the last N columns of a product of K elementary reflectors of order M Q = H(k) . . . H(2) H(1) as returned by ZGEQLF. 
complib/zungqr(3)  generate an MbyN complex matrix Q with orthonormal columns,

ZUNGQR generates an MbyN complex matrix Q with orthonormal columns, which is defined as the first N columns of a product of K elementary reflectors of order M Q = H(1) H(2) . . . H(k) as returned by ZGEQRF. 
complib/zungr2(3)  generate an m by n complex matrix Q with orthonormal rows,

ZUNGR2 generates an m by n complex matrix Q with orthonormal rows, which is defined as the last m rows of a product of k elementary reflectors of order n Q = H(1)' H(2)' . . . H(k)' as returned by ZGERQF. 
complib/zungrq(3)  generate an MbyN complex matrix Q with orthonormal rows,

ZUNGRQ generates an MbyN complex matrix Q with orthonormal rows, which is defined as the last M rows of a product of K elementary reflectors of order N Q = H(1)' H(2)' . . . H(k)' as returned by ZGERQF. 
complib/zungtr(3)  product of n1 elementary reflectors of order N, as returned by ZHETRD

ZUNGTR generates a complex unitary matrix Q which is defined as the product of n1 elementary reflectors of order N, as returned by ZHETRD: if UPLO = 'U', Q = H(n1) . . . H(2) H(1), if UPLO = 'L', Q = H(1) H(2) . . . H(n1). 
complib/zunm2l(3)  overwrite the general complex mbyn matrix C with Q * C if SIDE = 'L' and TRANS = 'N', or Q'* C if SIDE = 'L'

ZUNM2L overwrites the general complex mbyn matrix C with where Q is a complex unitary matrix defined as the product of k elementary reflectors Q = H(k) . . . H(2) H(1) as returned by ZGEQLF. Q is of order m if SIDE = 'L' and of order n if SIDE = 'R'. 