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SUBROUTINE <a name="CUNMHR.1"></a><a href="cunmhr.f.html#CUNMHR.1">CUNMHR</a>( SIDE, TRANS, M, N, ILO, IHI, A, LDA, TAU, C,
$ LDC, WORK, LWORK, INFO )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> -- LAPACK routine (version 3.1) --
</span><span class="comment">*</span><span class="comment"> Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
</span><span class="comment">*</span><span class="comment"> November 2006
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> .. Scalar Arguments ..
</span> CHARACTER SIDE, TRANS
INTEGER IHI, ILO, INFO, LDA, LDC, LWORK, M, N
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Array Arguments ..
</span> COMPLEX A( LDA, * ), C( LDC, * ), TAU( * ),
$ WORK( * )
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Purpose
</span><span class="comment">*</span><span class="comment"> =======
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> <a name="CUNMHR.20"></a><a href="cunmhr.f.html#CUNMHR.1">CUNMHR</a> overwrites the general complex M-by-N matrix C with
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> SIDE = 'L' SIDE = 'R'
</span><span class="comment">*</span><span class="comment"> TRANS = 'N': Q * C C * Q
</span><span class="comment">*</span><span class="comment"> TRANS = 'C': Q**H * C C * Q**H
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> where Q is a complex unitary matrix of order nq, with nq = m if
</span><span class="comment">*</span><span class="comment"> SIDE = 'L' and nq = n if SIDE = 'R'. Q is defined as the product of
</span><span class="comment">*</span><span class="comment"> IHI-ILO elementary reflectors, as returned by <a name="CGEHRD.28"></a><a href="cgehrd.f.html#CGEHRD.1">CGEHRD</a>:
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Q = H(ilo) H(ilo+1) . . . H(ihi-1).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Arguments
</span><span class="comment">*</span><span class="comment"> =========
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> SIDE (input) CHARACTER*1
</span><span class="comment">*</span><span class="comment"> = 'L': apply Q or Q**H from the Left;
</span><span class="comment">*</span><span class="comment"> = 'R': apply Q or Q**H from the Right.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> TRANS (input) CHARACTER*1
</span><span class="comment">*</span><span class="comment"> = 'N': apply Q (No transpose)
</span><span class="comment">*</span><span class="comment"> = 'C': apply Q**H (Conjugate transpose)
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> M (input) INTEGER
</span><span class="comment">*</span><span class="comment"> The number of rows of the matrix C. M >= 0.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> N (input) INTEGER
</span><span class="comment">*</span><span class="comment"> The number of columns of the matrix C. N >= 0.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> ILO (input) INTEGER
</span><span class="comment">*</span><span class="comment"> IHI (input) INTEGER
</span><span class="comment">*</span><span class="comment"> ILO and IHI must have the same values as in the previous call
</span><span class="comment">*</span><span class="comment"> of <a name="CGEHRD.52"></a><a href="cgehrd.f.html#CGEHRD.1">CGEHRD</a>. Q is equal to the unit matrix except in the
</span><span class="comment">*</span><span class="comment"> submatrix Q(ilo+1:ihi,ilo+1:ihi).
</span><span class="comment">*</span><span class="comment"> If SIDE = 'L', then 1 <= ILO <= IHI <= M, if M > 0, and
</span><span class="comment">*</span><span class="comment"> ILO = 1 and IHI = 0, if M = 0;
</span><span class="comment">*</span><span class="comment"> if SIDE = 'R', then 1 <= ILO <= IHI <= N, if N > 0, and
</span><span class="comment">*</span><span class="comment"> ILO = 1 and IHI = 0, if N = 0.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> A (input) COMPLEX array, dimension
</span><span class="comment">*</span><span class="comment"> (LDA,M) if SIDE = 'L'
</span><span class="comment">*</span><span class="comment"> (LDA,N) if SIDE = 'R'
</span><span class="comment">*</span><span class="comment"> The vectors which define the elementary reflectors, as
</span><span class="comment">*</span><span class="comment"> returned by <a name="CGEHRD.63"></a><a href="cgehrd.f.html#CGEHRD.1">CGEHRD</a>.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> LDA (input) INTEGER
</span><span class="comment">*</span><span class="comment"> The leading dimension of the array A.
</span><span class="comment">*</span><span class="comment"> LDA >= max(1,M) if SIDE = 'L'; LDA >= max(1,N) if SIDE = 'R'.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> TAU (input) COMPLEX array, dimension
</span><span class="comment">*</span><span class="comment"> (M-1) if SIDE = 'L'
</span><span class="comment">*</span><span class="comment"> (N-1) if SIDE = 'R'
</span><span class="comment">*</span><span class="comment"> TAU(i) must contain the scalar factor of the elementary
</span><span class="comment">*</span><span class="comment"> reflector H(i), as returned by <a name="CGEHRD.73"></a><a href="cgehrd.f.html#CGEHRD.1">CGEHRD</a>.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> C (input/output) COMPLEX array, dimension (LDC,N)
</span><span class="comment">*</span><span class="comment"> On entry, the M-by-N matrix C.
</span><span class="comment">*</span><span class="comment"> On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> LDC (input) INTEGER
</span><span class="comment">*</span><span class="comment"> The leading dimension of the array C. LDC >= max(1,M).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> WORK (workspace/output) COMPLEX array, dimension (MAX(1,LWORK))
</span><span class="comment">*</span><span class="comment"> On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> LWORK (input) INTEGER
</span><span class="comment">*</span><span class="comment"> The dimension of the array WORK.
</span><span class="comment">*</span><span class="comment"> If SIDE = 'L', LWORK >= max(1,N);
</span><span class="comment">*</span><span class="comment"> if SIDE = 'R', LWORK >= max(1,M).
</span><span class="comment">*</span><span class="comment"> For optimum performance LWORK >= N*NB if SIDE = 'L', and
</span><span class="comment">*</span><span class="comment"> LWORK >= M*NB if SIDE = 'R', where NB is the optimal
</span><span class="comment">*</span><span class="comment"> blocksize.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> If LWORK = -1, then a workspace query is assumed; the routine
</span><span class="comment">*</span><span class="comment"> only calculates the optimal size of the WORK array, returns
</span><span class="comment">*</span><span class="comment"> this value as the first entry of the WORK array, and no error
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