Annotation of rpl/lapack/lapack/ztzrzf.f, revision 1.9
1.9 ! bertrand 1: *> \brief \b ZTZRZF
! 2: *
! 3: * =========== DOCUMENTATION ===========
! 4: *
! 5: * Online html documentation available at
! 6: * http://www.netlib.org/lapack/explore-html/
! 7: *
! 8: *> \htmlonly
! 9: *> Download ZTZRZF + dependencies
! 10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/ztzrzf.f">
! 11: *> [TGZ]</a>
! 12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/ztzrzf.f">
! 13: *> [ZIP]</a>
! 14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/ztzrzf.f">
! 15: *> [TXT]</a>
! 16: *> \endhtmlonly
! 17: *
! 18: * Definition:
! 19: * ===========
! 20: *
! 21: * SUBROUTINE ZTZRZF( M, N, A, LDA, TAU, WORK, LWORK, INFO )
! 22: *
! 23: * .. Scalar Arguments ..
! 24: * INTEGER INFO, LDA, LWORK, M, N
! 25: * ..
! 26: * .. Array Arguments ..
! 27: * COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * )
! 28: * ..
! 29: *
! 30: *
! 31: *> \par Purpose:
! 32: * =============
! 33: *>
! 34: *> \verbatim
! 35: *>
! 36: *> ZTZRZF reduces the M-by-N ( M<=N ) complex upper trapezoidal matrix A
! 37: *> to upper triangular form by means of unitary transformations.
! 38: *>
! 39: *> The upper trapezoidal matrix A is factored as
! 40: *>
! 41: *> A = ( R 0 ) * Z,
! 42: *>
! 43: *> where Z is an N-by-N unitary matrix and R is an M-by-M upper
! 44: *> triangular matrix.
! 45: *> \endverbatim
! 46: *
! 47: * Arguments:
! 48: * ==========
! 49: *
! 50: *> \param[in] M
! 51: *> \verbatim
! 52: *> M is INTEGER
! 53: *> The number of rows of the matrix A. M >= 0.
! 54: *> \endverbatim
! 55: *>
! 56: *> \param[in] N
! 57: *> \verbatim
! 58: *> N is INTEGER
! 59: *> The number of columns of the matrix A. N >= M.
! 60: *> \endverbatim
! 61: *>
! 62: *> \param[in,out] A
! 63: *> \verbatim
! 64: *> A is COMPLEX*16 array, dimension (LDA,N)
! 65: *> On entry, the leading M-by-N upper trapezoidal part of the
! 66: *> array A must contain the matrix to be factorized.
! 67: *> On exit, the leading M-by-M upper triangular part of A
! 68: *> contains the upper triangular matrix R, and elements M+1 to
! 69: *> N of the first M rows of A, with the array TAU, represent the
! 70: *> unitary matrix Z as a product of M elementary reflectors.
! 71: *> \endverbatim
! 72: *>
! 73: *> \param[in] LDA
! 74: *> \verbatim
! 75: *> LDA is INTEGER
! 76: *> The leading dimension of the array A. LDA >= max(1,M).
! 77: *> \endverbatim
! 78: *>
! 79: *> \param[out] TAU
! 80: *> \verbatim
! 81: *> TAU is COMPLEX*16 array, dimension (M)
! 82: *> The scalar factors of the elementary reflectors.
! 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 >= max(1,M).
! 95: *> For optimum performance LWORK >= M*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: *> \par Contributors:
! 124: * ==================
! 125: *>
! 126: *> A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA
! 127: *
! 128: *> \par Further Details:
! 129: * =====================
! 130: *>
! 131: *> \verbatim
! 132: *>
! 133: *> The factorization is obtained by Householder's method. The kth
! 134: *> transformation matrix, Z( k ), which is used to introduce zeros into
! 135: *> the ( m - k + 1 )th row of A, is given in the form
! 136: *>
! 137: *> Z( k ) = ( I 0 ),
! 138: *> ( 0 T( k ) )
! 139: *>
! 140: *> where
! 141: *>
! 142: *> T( k ) = I - tau*u( k )*u( k )**H, u( k ) = ( 1 ),
! 143: *> ( 0 )
! 144: *> ( z( k ) )
! 145: *>
! 146: *> tau is a scalar and z( k ) is an ( n - m ) element vector.
! 147: *> tau and z( k ) are chosen to annihilate the elements of the kth row
! 148: *> of X.
! 149: *>
! 150: *> The scalar tau is returned in the kth element of TAU and the vector
! 151: *> u( k ) in the kth row of A, such that the elements of z( k ) are
! 152: *> in a( k, m + 1 ), ..., a( k, n ). The elements of R are returned in
! 153: *> the upper triangular part of A.
! 154: *>
! 155: *> Z is given by
! 156: *>
! 157: *> Z = Z( 1 ) * Z( 2 ) * ... * Z( m ).
! 158: *> \endverbatim
! 159: *>
! 160: * =====================================================================
1.1 bertrand 161: SUBROUTINE ZTZRZF( M, N, A, LDA, TAU, WORK, LWORK, INFO )
162: *
1.9 ! bertrand 163: * -- LAPACK computational routine (version 3.4.0) --
1.1 bertrand 164: * -- LAPACK is a software package provided by Univ. of Tennessee, --
165: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.9 ! bertrand 166: * November 2011
1.1 bertrand 167: *
168: * .. Scalar Arguments ..
169: INTEGER INFO, LDA, LWORK, M, N
170: * ..
171: * .. Array Arguments ..
172: COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * )
173: * ..
174: *
175: * =====================================================================
176: *
177: * .. Parameters ..
178: COMPLEX*16 ZERO
179: PARAMETER ( ZERO = ( 0.0D+0, 0.0D+0 ) )
180: * ..
181: * .. Local Scalars ..
182: LOGICAL LQUERY
1.8 bertrand 183: INTEGER I, IB, IWS, KI, KK, LDWORK, LWKMIN, LWKOPT,
184: $ M1, MU, NB, NBMIN, NX
1.1 bertrand 185: * ..
186: * .. External Subroutines ..
187: EXTERNAL XERBLA, ZLARZB, ZLARZT, ZLATRZ
188: * ..
189: * .. Intrinsic Functions ..
190: INTRINSIC MAX, MIN
191: * ..
192: * .. External Functions ..
193: INTEGER ILAENV
194: EXTERNAL ILAENV
195: * ..
196: * .. Executable Statements ..
197: *
198: * Test the input arguments
199: *
200: INFO = 0
201: LQUERY = ( LWORK.EQ.-1 )
202: IF( M.LT.0 ) THEN
203: INFO = -1
204: ELSE IF( N.LT.M ) THEN
205: INFO = -2
206: ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
207: INFO = -4
208: END IF
209: *
210: IF( INFO.EQ.0 ) THEN
211: IF( M.EQ.0 .OR. M.EQ.N ) THEN
212: LWKOPT = 1
1.8 bertrand 213: LWKMIN = 1
1.1 bertrand 214: ELSE
215: *
216: * Determine the block size.
217: *
218: NB = ILAENV( 1, 'ZGERQF', ' ', M, N, -1, -1 )
219: LWKOPT = M*NB
1.8 bertrand 220: LWKMIN = MAX( 1, M )
1.1 bertrand 221: END IF
222: WORK( 1 ) = LWKOPT
223: *
1.8 bertrand 224: IF( LWORK.LT.LWKMIN .AND. .NOT.LQUERY ) THEN
1.1 bertrand 225: INFO = -7
226: END IF
227: END IF
228: *
229: IF( INFO.NE.0 ) THEN
230: CALL XERBLA( 'ZTZRZF', -INFO )
231: RETURN
232: ELSE IF( LQUERY ) THEN
233: RETURN
234: END IF
235: *
236: * Quick return if possible
237: *
238: IF( M.EQ.0 ) THEN
239: RETURN
240: ELSE IF( M.EQ.N ) THEN
241: DO 10 I = 1, N
242: TAU( I ) = ZERO
243: 10 CONTINUE
244: RETURN
245: END IF
246: *
247: NBMIN = 2
248: NX = 1
249: IWS = M
250: IF( NB.GT.1 .AND. NB.LT.M ) THEN
251: *
252: * Determine when to cross over from blocked to unblocked code.
253: *
254: NX = MAX( 0, ILAENV( 3, 'ZGERQF', ' ', M, N, -1, -1 ) )
255: IF( NX.LT.M ) THEN
256: *
257: * Determine if workspace is large enough for blocked code.
258: *
259: LDWORK = M
260: IWS = LDWORK*NB
261: IF( LWORK.LT.IWS ) THEN
262: *
263: * Not enough workspace to use optimal NB: reduce NB and
264: * determine the minimum value of NB.
265: *
266: NB = LWORK / LDWORK
267: NBMIN = MAX( 2, ILAENV( 2, 'ZGERQF', ' ', M, N, -1,
268: $ -1 ) )
269: END IF
270: END IF
271: END IF
272: *
273: IF( NB.GE.NBMIN .AND. NB.LT.M .AND. NX.LT.M ) THEN
274: *
275: * Use blocked code initially.
276: * The last kk rows are handled by the block method.
277: *
278: M1 = MIN( M+1, N )
279: KI = ( ( M-NX-1 ) / NB )*NB
280: KK = MIN( M, KI+NB )
281: *
282: DO 20 I = M - KK + KI + 1, M - KK + 1, -NB
283: IB = MIN( M-I+1, NB )
284: *
285: * Compute the TZ factorization of the current block
286: * A(i:i+ib-1,i:n)
287: *
288: CALL ZLATRZ( IB, N-I+1, N-M, A( I, I ), LDA, TAU( I ),
289: $ WORK )
290: IF( I.GT.1 ) THEN
291: *
292: * Form the triangular factor of the block reflector
293: * H = H(i+ib-1) . . . H(i+1) H(i)
294: *
295: CALL ZLARZT( 'Backward', 'Rowwise', N-M, IB, A( I, M1 ),
296: $ LDA, TAU( I ), WORK, LDWORK )
297: *
298: * Apply H to A(1:i-1,i:n) from the right
299: *
300: CALL ZLARZB( 'Right', 'No transpose', 'Backward',
301: $ 'Rowwise', I-1, N-I+1, IB, N-M, A( I, M1 ),
302: $ LDA, WORK, LDWORK, A( 1, I ), LDA,
303: $ WORK( IB+1 ), LDWORK )
304: END IF
305: 20 CONTINUE
306: MU = I + NB - 1
307: ELSE
308: MU = M
309: END IF
310: *
311: * Use unblocked code to factor the last or only block
312: *
313: IF( MU.GT.0 )
314: $ CALL ZLATRZ( MU, N, N-M, A, LDA, TAU, WORK )
315: *
316: WORK( 1 ) = LWKOPT
317: *
318: RETURN
319: *
320: * End of ZTZRZF
321: *
322: END
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