Annotation of rpl/lapack/lapack/zungtr.f, revision 1.8
1.8 ! bertrand 1: *> \brief \b ZUNGTR
! 2: *
! 3: * =========== DOCUMENTATION ===========
! 4: *
! 5: * Online html documentation available at
! 6: * http://www.netlib.org/lapack/explore-html/
! 7: *
! 8: *> \htmlonly
! 9: *> Download ZUNGTR + dependencies
! 10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zungtr.f">
! 11: *> [TGZ]</a>
! 12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zungtr.f">
! 13: *> [ZIP]</a>
! 14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zungtr.f">
! 15: *> [TXT]</a>
! 16: *> \endhtmlonly
! 17: *
! 18: * Definition:
! 19: * ===========
! 20: *
! 21: * SUBROUTINE ZUNGTR( UPLO, N, A, LDA, TAU, WORK, LWORK, INFO )
! 22: *
! 23: * .. Scalar Arguments ..
! 24: * CHARACTER UPLO
! 25: * INTEGER INFO, LDA, LWORK, N
! 26: * ..
! 27: * .. Array Arguments ..
! 28: * COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * )
! 29: * ..
! 30: *
! 31: *
! 32: *> \par Purpose:
! 33: * =============
! 34: *>
! 35: *> \verbatim
! 36: *>
! 37: *> ZUNGTR generates a complex unitary matrix Q which is defined as the
! 38: *> product of n-1 elementary reflectors of order N, as returned by
! 39: *> ZHETRD:
! 40: *>
! 41: *> if UPLO = 'U', Q = H(n-1) . . . H(2) H(1),
! 42: *>
! 43: *> if UPLO = 'L', Q = H(1) H(2) . . . H(n-1).
! 44: *> \endverbatim
! 45: *
! 46: * Arguments:
! 47: * ==========
! 48: *
! 49: *> \param[in] UPLO
! 50: *> \verbatim
! 51: *> UPLO is CHARACTER*1
! 52: *> = 'U': Upper triangle of A contains elementary reflectors
! 53: *> from ZHETRD;
! 54: *> = 'L': Lower triangle of A contains elementary reflectors
! 55: *> from ZHETRD.
! 56: *> \endverbatim
! 57: *>
! 58: *> \param[in] N
! 59: *> \verbatim
! 60: *> N is INTEGER
! 61: *> The order of the matrix Q. N >= 0.
! 62: *> \endverbatim
! 63: *>
! 64: *> \param[in,out] A
! 65: *> \verbatim
! 66: *> A is COMPLEX*16 array, dimension (LDA,N)
! 67: *> On entry, the vectors which define the elementary reflectors,
! 68: *> as returned by ZHETRD.
! 69: *> On exit, the N-by-N unitary matrix Q.
! 70: *> \endverbatim
! 71: *>
! 72: *> \param[in] LDA
! 73: *> \verbatim
! 74: *> LDA is INTEGER
! 75: *> The leading dimension of the array A. LDA >= N.
! 76: *> \endverbatim
! 77: *>
! 78: *> \param[in] TAU
! 79: *> \verbatim
! 80: *> TAU is COMPLEX*16 array, dimension (N-1)
! 81: *> TAU(i) must contain the scalar factor of the elementary
! 82: *> reflector H(i), as returned by ZHETRD.
! 83: *> \endverbatim
! 84: *>
! 85: *> \param[out] WORK
! 86: *> \verbatim
! 87: *> WORK is COMPLEX*16 array, dimension (MAX(1,LWORK))
! 88: *> On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
! 89: *> \endverbatim
! 90: *>
! 91: *> \param[in] LWORK
! 92: *> \verbatim
! 93: *> LWORK is INTEGER
! 94: *> The dimension of the array WORK. LWORK >= N-1.
! 95: *> For optimum performance LWORK >= (N-1)*NB, where NB is
! 96: *> the optimal blocksize.
! 97: *>
! 98: *> If LWORK = -1, then a workspace query is assumed; the routine
! 99: *> only calculates the optimal size of the WORK array, returns
! 100: *> this value as the first entry of the WORK array, and no error
! 101: *> message related to LWORK is issued by XERBLA.
! 102: *> \endverbatim
! 103: *>
! 104: *> \param[out] INFO
! 105: *> \verbatim
! 106: *> INFO is INTEGER
! 107: *> = 0: successful exit
! 108: *> < 0: if INFO = -i, the i-th argument had an illegal value
! 109: *> \endverbatim
! 110: *
! 111: * Authors:
! 112: * ========
! 113: *
! 114: *> \author Univ. of Tennessee
! 115: *> \author Univ. of California Berkeley
! 116: *> \author Univ. of Colorado Denver
! 117: *> \author NAG Ltd.
! 118: *
! 119: *> \date November 2011
! 120: *
! 121: *> \ingroup complex16OTHERcomputational
! 122: *
! 123: * =====================================================================
1.1 bertrand 124: SUBROUTINE ZUNGTR( UPLO, N, A, LDA, TAU, WORK, LWORK, INFO )
125: *
1.8 ! bertrand 126: * -- LAPACK computational routine (version 3.4.0) --
1.1 bertrand 127: * -- LAPACK is a software package provided by Univ. of Tennessee, --
128: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.8 ! bertrand 129: * November 2011
1.1 bertrand 130: *
131: * .. Scalar Arguments ..
132: CHARACTER UPLO
133: INTEGER INFO, LDA, LWORK, N
134: * ..
135: * .. Array Arguments ..
136: COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * )
137: * ..
138: *
139: * =====================================================================
140: *
141: * .. Parameters ..
142: COMPLEX*16 ZERO, ONE
143: PARAMETER ( ZERO = ( 0.0D+0, 0.0D+0 ),
144: $ ONE = ( 1.0D+0, 0.0D+0 ) )
145: * ..
146: * .. Local Scalars ..
147: LOGICAL LQUERY, UPPER
148: INTEGER I, IINFO, J, LWKOPT, NB
149: * ..
150: * .. External Functions ..
151: LOGICAL LSAME
152: INTEGER ILAENV
153: EXTERNAL LSAME, ILAENV
154: * ..
155: * .. External Subroutines ..
156: EXTERNAL XERBLA, ZUNGQL, ZUNGQR
157: * ..
158: * .. Intrinsic Functions ..
159: INTRINSIC MAX
160: * ..
161: * .. Executable Statements ..
162: *
163: * Test the input arguments
164: *
165: INFO = 0
166: LQUERY = ( LWORK.EQ.-1 )
167: UPPER = LSAME( UPLO, 'U' )
168: IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
169: INFO = -1
170: ELSE IF( N.LT.0 ) THEN
171: INFO = -2
172: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
173: INFO = -4
174: ELSE IF( LWORK.LT.MAX( 1, N-1 ) .AND. .NOT.LQUERY ) THEN
175: INFO = -7
176: END IF
177: *
178: IF( INFO.EQ.0 ) THEN
179: IF( UPPER ) THEN
180: NB = ILAENV( 1, 'ZUNGQL', ' ', N-1, N-1, N-1, -1 )
181: ELSE
182: NB = ILAENV( 1, 'ZUNGQR', ' ', N-1, N-1, N-1, -1 )
183: END IF
184: LWKOPT = MAX( 1, N-1 )*NB
185: WORK( 1 ) = LWKOPT
186: END IF
187: *
188: IF( INFO.NE.0 ) THEN
189: CALL XERBLA( 'ZUNGTR', -INFO )
190: RETURN
191: ELSE IF( LQUERY ) THEN
192: RETURN
193: END IF
194: *
195: * Quick return if possible
196: *
197: IF( N.EQ.0 ) THEN
198: WORK( 1 ) = 1
199: RETURN
200: END IF
201: *
202: IF( UPPER ) THEN
203: *
204: * Q was determined by a call to ZHETRD with UPLO = 'U'
205: *
206: * Shift the vectors which define the elementary reflectors one
207: * column to the left, and set the last row and column of Q to
208: * those of the unit matrix
209: *
210: DO 20 J = 1, N - 1
211: DO 10 I = 1, J - 1
212: A( I, J ) = A( I, J+1 )
213: 10 CONTINUE
214: A( N, J ) = ZERO
215: 20 CONTINUE
216: DO 30 I = 1, N - 1
217: A( I, N ) = ZERO
218: 30 CONTINUE
219: A( N, N ) = ONE
220: *
221: * Generate Q(1:n-1,1:n-1)
222: *
223: CALL ZUNGQL( N-1, N-1, N-1, A, LDA, TAU, WORK, LWORK, IINFO )
224: *
225: ELSE
226: *
227: * Q was determined by a call to ZHETRD with UPLO = 'L'.
228: *
229: * Shift the vectors which define the elementary reflectors one
230: * column to the right, and set the first row and column of Q to
231: * those of the unit matrix
232: *
233: DO 50 J = N, 2, -1
234: A( 1, J ) = ZERO
235: DO 40 I = J + 1, N
236: A( I, J ) = A( I, J-1 )
237: 40 CONTINUE
238: 50 CONTINUE
239: A( 1, 1 ) = ONE
240: DO 60 I = 2, N
241: A( I, 1 ) = ZERO
242: 60 CONTINUE
243: IF( N.GT.1 ) THEN
244: *
245: * Generate Q(2:n,2:n)
246: *
247: CALL ZUNGQR( N-1, N-1, N-1, A( 2, 2 ), LDA, TAU, WORK,
248: $ LWORK, IINFO )
249: END IF
250: END IF
251: WORK( 1 ) = LWKOPT
252: RETURN
253: *
254: * End of ZUNGTR
255: *
256: END
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