Annotation of rpl/lapack/lapack/zunghr.f, revision 1.8
1.8 ! bertrand 1: *> \brief \b ZUNGHR
! 2: *
! 3: * =========== DOCUMENTATION ===========
! 4: *
! 5: * Online html documentation available at
! 6: * http://www.netlib.org/lapack/explore-html/
! 7: *
! 8: *> \htmlonly
! 9: *> Download ZUNGHR + dependencies
! 10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zunghr.f">
! 11: *> [TGZ]</a>
! 12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zunghr.f">
! 13: *> [ZIP]</a>
! 14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zunghr.f">
! 15: *> [TXT]</a>
! 16: *> \endhtmlonly
! 17: *
! 18: * Definition:
! 19: * ===========
! 20: *
! 21: * SUBROUTINE ZUNGHR( N, ILO, IHI, A, LDA, TAU, WORK, LWORK, INFO )
! 22: *
! 23: * .. Scalar Arguments ..
! 24: * INTEGER IHI, ILO, INFO, LDA, LWORK, N
! 25: * ..
! 26: * .. Array Arguments ..
! 27: * COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * )
! 28: * ..
! 29: *
! 30: *
! 31: *> \par Purpose:
! 32: * =============
! 33: *>
! 34: *> \verbatim
! 35: *>
! 36: *> ZUNGHR generates a complex unitary matrix Q which is defined as the
! 37: *> product of IHI-ILO elementary reflectors of order N, as returned by
! 38: *> ZGEHRD:
! 39: *>
! 40: *> Q = H(ilo) H(ilo+1) . . . H(ihi-1).
! 41: *> \endverbatim
! 42: *
! 43: * Arguments:
! 44: * ==========
! 45: *
! 46: *> \param[in] N
! 47: *> \verbatim
! 48: *> N is INTEGER
! 49: *> The order of the matrix Q. N >= 0.
! 50: *> \endverbatim
! 51: *>
! 52: *> \param[in] ILO
! 53: *> \verbatim
! 54: *> ILO is INTEGER
! 55: *> \endverbatim
! 56: *>
! 57: *> \param[in] IHI
! 58: *> \verbatim
! 59: *> IHI is INTEGER
! 60: *>
! 61: *> ILO and IHI must have the same values as in the previous call
! 62: *> of ZGEHRD. Q is equal to the unit matrix except in the
! 63: *> submatrix Q(ilo+1:ihi,ilo+1:ihi).
! 64: *> 1 <= ILO <= IHI <= N, if N > 0; ILO=1 and IHI=0, if N=0.
! 65: *> \endverbatim
! 66: *>
! 67: *> \param[in,out] A
! 68: *> \verbatim
! 69: *> A is COMPLEX*16 array, dimension (LDA,N)
! 70: *> On entry, the vectors which define the elementary reflectors,
! 71: *> as returned by ZGEHRD.
! 72: *> On exit, the N-by-N unitary matrix Q.
! 73: *> \endverbatim
! 74: *>
! 75: *> \param[in] LDA
! 76: *> \verbatim
! 77: *> LDA is INTEGER
! 78: *> The leading dimension of the array A. LDA >= max(1,N).
! 79: *> \endverbatim
! 80: *>
! 81: *> \param[in] TAU
! 82: *> \verbatim
! 83: *> TAU is COMPLEX*16 array, dimension (N-1)
! 84: *> TAU(i) must contain the scalar factor of the elementary
! 85: *> reflector H(i), as returned by ZGEHRD.
! 86: *> \endverbatim
! 87: *>
! 88: *> \param[out] WORK
! 89: *> \verbatim
! 90: *> WORK is COMPLEX*16 array, dimension (MAX(1,LWORK))
! 91: *> On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
! 92: *> \endverbatim
! 93: *>
! 94: *> \param[in] LWORK
! 95: *> \verbatim
! 96: *> LWORK is INTEGER
! 97: *> The dimension of the array WORK. LWORK >= IHI-ILO.
! 98: *> For optimum performance LWORK >= (IHI-ILO)*NB, where NB is
! 99: *> the optimal blocksize.
! 100: *>
! 101: *> If LWORK = -1, then a workspace query is assumed; the routine
! 102: *> only calculates the optimal size of the WORK array, returns
! 103: *> this value as the first entry of the WORK array, and no error
! 104: *> message related to LWORK is issued by XERBLA.
! 105: *> \endverbatim
! 106: *>
! 107: *> \param[out] INFO
! 108: *> \verbatim
! 109: *> INFO is INTEGER
! 110: *> = 0: successful exit
! 111: *> < 0: if INFO = -i, the i-th argument had an illegal value
! 112: *> \endverbatim
! 113: *
! 114: * Authors:
! 115: * ========
! 116: *
! 117: *> \author Univ. of Tennessee
! 118: *> \author Univ. of California Berkeley
! 119: *> \author Univ. of Colorado Denver
! 120: *> \author NAG Ltd.
! 121: *
! 122: *> \date November 2011
! 123: *
! 124: *> \ingroup complex16OTHERcomputational
! 125: *
! 126: * =====================================================================
1.1 bertrand 127: SUBROUTINE ZUNGHR( N, ILO, IHI, A, LDA, TAU, WORK, LWORK, INFO )
128: *
1.8 ! bertrand 129: * -- LAPACK computational routine (version 3.4.0) --
1.1 bertrand 130: * -- LAPACK is a software package provided by Univ. of Tennessee, --
131: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.8 ! bertrand 132: * November 2011
1.1 bertrand 133: *
134: * .. Scalar Arguments ..
135: INTEGER IHI, ILO, INFO, LDA, LWORK, N
136: * ..
137: * .. Array Arguments ..
138: COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * )
139: * ..
140: *
141: * =====================================================================
142: *
143: * .. Parameters ..
144: COMPLEX*16 ZERO, ONE
145: PARAMETER ( ZERO = ( 0.0D+0, 0.0D+0 ),
146: $ ONE = ( 1.0D+0, 0.0D+0 ) )
147: * ..
148: * .. Local Scalars ..
149: LOGICAL LQUERY
150: INTEGER I, IINFO, J, LWKOPT, NB, NH
151: * ..
152: * .. External Subroutines ..
153: EXTERNAL XERBLA, ZUNGQR
154: * ..
155: * .. External Functions ..
156: INTEGER ILAENV
157: EXTERNAL ILAENV
158: * ..
159: * .. Intrinsic Functions ..
160: INTRINSIC MAX, MIN
161: * ..
162: * .. Executable Statements ..
163: *
164: * Test the input arguments
165: *
166: INFO = 0
167: NH = IHI - ILO
168: LQUERY = ( LWORK.EQ.-1 )
169: IF( N.LT.0 ) THEN
170: INFO = -1
171: ELSE IF( ILO.LT.1 .OR. ILO.GT.MAX( 1, N ) ) THEN
172: INFO = -2
173: ELSE IF( IHI.LT.MIN( ILO, N ) .OR. IHI.GT.N ) THEN
174: INFO = -3
175: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
176: INFO = -5
177: ELSE IF( LWORK.LT.MAX( 1, NH ) .AND. .NOT.LQUERY ) THEN
178: INFO = -8
179: END IF
180: *
181: IF( INFO.EQ.0 ) THEN
182: NB = ILAENV( 1, 'ZUNGQR', ' ', NH, NH, NH, -1 )
183: LWKOPT = MAX( 1, NH )*NB
184: WORK( 1 ) = LWKOPT
185: END IF
186: *
187: IF( INFO.NE.0 ) THEN
188: CALL XERBLA( 'ZUNGHR', -INFO )
189: RETURN
190: ELSE IF( LQUERY ) THEN
191: RETURN
192: END IF
193: *
194: * Quick return if possible
195: *
196: IF( N.EQ.0 ) THEN
197: WORK( 1 ) = 1
198: RETURN
199: END IF
200: *
201: * Shift the vectors which define the elementary reflectors one
202: * column to the right, and set the first ilo and the last n-ihi
203: * rows and columns to those of the unit matrix
204: *
205: DO 40 J = IHI, ILO + 1, -1
206: DO 10 I = 1, J - 1
207: A( I, J ) = ZERO
208: 10 CONTINUE
209: DO 20 I = J + 1, IHI
210: A( I, J ) = A( I, J-1 )
211: 20 CONTINUE
212: DO 30 I = IHI + 1, N
213: A( I, J ) = ZERO
214: 30 CONTINUE
215: 40 CONTINUE
216: DO 60 J = 1, ILO
217: DO 50 I = 1, N
218: A( I, J ) = ZERO
219: 50 CONTINUE
220: A( J, J ) = ONE
221: 60 CONTINUE
222: DO 80 J = IHI + 1, N
223: DO 70 I = 1, N
224: A( I, J ) = ZERO
225: 70 CONTINUE
226: A( J, J ) = ONE
227: 80 CONTINUE
228: *
229: IF( NH.GT.0 ) THEN
230: *
231: * Generate Q(ilo+1:ihi,ilo+1:ihi)
232: *
233: CALL ZUNGQR( NH, NH, NH, A( ILO+1, ILO+1 ), LDA, TAU( ILO ),
234: $ WORK, LWORK, IINFO )
235: END IF
236: WORK( 1 ) = LWKOPT
237: RETURN
238: *
239: * End of ZUNGHR
240: *
241: END
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