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complib/ztzrqf(3) -- reduce the M-by-N ( M<=N ) complex upper trapezoidal matrix A to upper triangular form by means of unitary tra
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ZTZRQF reduces the M-by-N ( 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 N-by-N unitary matrix and R is an M-by-M upper triangular matrix. |
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complib/zung2l(3) -- generate an m by n complex matrix Q with orthonormal columns,
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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. |
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complib/zung2r(3) -- generate an m by n complex matrix Q with orthonormal columns,
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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. |
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complib/zungbr(3) -- generate one of the complex unitary matrices Q or P**H determined by ZGEBRD when reducing a complex matrix A t
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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 M-by-K 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(m-1) and ZUNGBR returns Q as an M-by-M matri... |
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complib/zunghr(3) -- product of IHI-ILO elementary reflectors of order N, as returned by ZGEHRD
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ZUNGHR generates a complex unitary matrix Q which is defined as the product of IHI-ILO elementary reflectors of order N, as returned by ZGEHRD: Q = H(ilo) H(ilo+1) . . . H(ihi-1). |
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complib/zungl2(3) -- generate an m-by-n complex matrix Q with orthonormal rows,
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ZUNGL2 generates an m-by-n 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. |
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complib/zunglq(3) -- generate an M-by-N complex matrix Q with orthonormal rows,
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ZUNGLQ generates an M-by-N 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. |
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complib/zungql(3) -- generate an M-by-N complex matrix Q with orthonormal columns,
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ZUNGQL 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. |
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complib/zungqr(3) -- generate an M-by-N complex matrix Q with orthonormal columns,
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ZUNGQR 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. |
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complib/zungr2(3) -- generate an m by n complex matrix Q with orthonormal rows,
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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. |
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complib/zungrq(3) -- generate an M-by-N complex matrix Q with orthonormal rows,
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ZUNGRQ 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. |
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complib/zungtr(3) -- product of n-1 elementary reflectors of order N, as returned by ZHETRD
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ZUNGTR generates a complex unitary matrix Q which is defined as the product of n-1 elementary reflectors of order N, as returned by ZHETRD: if UPLO = 'U', Q = H(n-1) . . . H(2) H(1), if UPLO = 'L', Q = H(1) H(2) . . . H(n-1). |
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complib/zunm2l(3) -- overwrite the general complex m-by-n matrix C with Q * C if SIDE = 'L' and TRANS = 'N', or Q'* C if SIDE = 'L'
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ZUNM2L overwrites the general complex m-by-n 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'. |
