Annotation of rpl/lapack/lapack/zungbr.f, revision 1.9
1.9 ! bertrand 1: *> \brief \b ZUNGBR
! 2: *
! 3: * =========== DOCUMENTATION ===========
! 4: *
! 5: * Online html documentation available at
! 6: * http://www.netlib.org/lapack/explore-html/
! 7: *
! 8: *> \htmlonly
! 9: *> Download ZUNGBR + dependencies
! 10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zungbr.f">
! 11: *> [TGZ]</a>
! 12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zungbr.f">
! 13: *> [ZIP]</a>
! 14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zungbr.f">
! 15: *> [TXT]</a>
! 16: *> \endhtmlonly
! 17: *
! 18: * Definition:
! 19: * ===========
! 20: *
! 21: * SUBROUTINE ZUNGBR( VECT, M, N, K, A, LDA, TAU, WORK, LWORK, INFO )
! 22: *
! 23: * .. Scalar Arguments ..
! 24: * CHARACTER VECT
! 25: * INTEGER INFO, K, LDA, LWORK, M, N
! 26: * ..
! 27: * .. Array Arguments ..
! 28: * COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * )
! 29: * ..
! 30: *
! 31: *
! 32: *> \par Purpose:
! 33: * =============
! 34: *>
! 35: *> \verbatim
! 36: *>
! 37: *> ZUNGBR generates one of the complex unitary matrices Q or P**H
! 38: *> determined by ZGEBRD when reducing a complex matrix A to bidiagonal
! 39: *> form: A = Q * B * P**H. Q and P**H are defined as products of
! 40: *> elementary reflectors H(i) or G(i) respectively.
! 41: *>
! 42: *> If VECT = 'Q', A is assumed to have been an M-by-K matrix, and Q
! 43: *> is of order M:
! 44: *> if m >= k, Q = H(1) H(2) . . . H(k) and ZUNGBR returns the first n
! 45: *> columns of Q, where m >= n >= k;
! 46: *> if m < k, Q = H(1) H(2) . . . H(m-1) and ZUNGBR returns Q as an
! 47: *> M-by-M matrix.
! 48: *>
! 49: *> If VECT = 'P', A is assumed to have been a K-by-N matrix, and P**H
! 50: *> is of order N:
! 51: *> if k < n, P**H = G(k) . . . G(2) G(1) and ZUNGBR returns the first m
! 52: *> rows of P**H, where n >= m >= k;
! 53: *> if k >= n, P**H = G(n-1) . . . G(2) G(1) and ZUNGBR returns P**H as
! 54: *> an N-by-N matrix.
! 55: *> \endverbatim
! 56: *
! 57: * Arguments:
! 58: * ==========
! 59: *
! 60: *> \param[in] VECT
! 61: *> \verbatim
! 62: *> VECT is CHARACTER*1
! 63: *> Specifies whether the matrix Q or the matrix P**H is
! 64: *> required, as defined in the transformation applied by ZGEBRD:
! 65: *> = 'Q': generate Q;
! 66: *> = 'P': generate P**H.
! 67: *> \endverbatim
! 68: *>
! 69: *> \param[in] M
! 70: *> \verbatim
! 71: *> M is INTEGER
! 72: *> The number of rows of the matrix Q or P**H to be returned.
! 73: *> M >= 0.
! 74: *> \endverbatim
! 75: *>
! 76: *> \param[in] N
! 77: *> \verbatim
! 78: *> N is INTEGER
! 79: *> The number of columns of the matrix Q or P**H to be returned.
! 80: *> N >= 0.
! 81: *> If VECT = 'Q', M >= N >= min(M,K);
! 82: *> if VECT = 'P', N >= M >= min(N,K).
! 83: *> \endverbatim
! 84: *>
! 85: *> \param[in] K
! 86: *> \verbatim
! 87: *> K is INTEGER
! 88: *> If VECT = 'Q', the number of columns in the original M-by-K
! 89: *> matrix reduced by ZGEBRD.
! 90: *> If VECT = 'P', the number of rows in the original K-by-N
! 91: *> matrix reduced by ZGEBRD.
! 92: *> K >= 0.
! 93: *> \endverbatim
! 94: *>
! 95: *> \param[in,out] A
! 96: *> \verbatim
! 97: *> A is COMPLEX*16 array, dimension (LDA,N)
! 98: *> On entry, the vectors which define the elementary reflectors,
! 99: *> as returned by ZGEBRD.
! 100: *> On exit, the M-by-N matrix Q or P**H.
! 101: *> \endverbatim
! 102: *>
! 103: *> \param[in] LDA
! 104: *> \verbatim
! 105: *> LDA is INTEGER
! 106: *> The leading dimension of the array A. LDA >= M.
! 107: *> \endverbatim
! 108: *>
! 109: *> \param[in] TAU
! 110: *> \verbatim
! 111: *> TAU is COMPLEX*16 array, dimension
! 112: *> (min(M,K)) if VECT = 'Q'
! 113: *> (min(N,K)) if VECT = 'P'
! 114: *> TAU(i) must contain the scalar factor of the elementary
! 115: *> reflector H(i) or G(i), which determines Q or P**H, as
! 116: *> returned by ZGEBRD in its array argument TAUQ or TAUP.
! 117: *> \endverbatim
! 118: *>
! 119: *> \param[out] WORK
! 120: *> \verbatim
! 121: *> WORK is COMPLEX*16 array, dimension (MAX(1,LWORK))
! 122: *> On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
! 123: *> \endverbatim
! 124: *>
! 125: *> \param[in] LWORK
! 126: *> \verbatim
! 127: *> LWORK is INTEGER
! 128: *> The dimension of the array WORK. LWORK >= max(1,min(M,N)).
! 129: *> For optimum performance LWORK >= min(M,N)*NB, where NB
! 130: *> is the optimal blocksize.
! 131: *>
! 132: *> If LWORK = -1, then a workspace query is assumed; the routine
! 133: *> only calculates the optimal size of the WORK array, returns
! 134: *> this value as the first entry of the WORK array, and no error
! 135: *> message related to LWORK is issued by XERBLA.
! 136: *> \endverbatim
! 137: *>
! 138: *> \param[out] INFO
! 139: *> \verbatim
! 140: *> INFO is INTEGER
! 141: *> = 0: successful exit
! 142: *> < 0: if INFO = -i, the i-th argument had an illegal value
! 143: *> \endverbatim
! 144: *
! 145: * Authors:
! 146: * ========
! 147: *
! 148: *> \author Univ. of Tennessee
! 149: *> \author Univ. of California Berkeley
! 150: *> \author Univ. of Colorado Denver
! 151: *> \author NAG Ltd.
! 152: *
! 153: *> \date November 2011
! 154: *
! 155: *> \ingroup complex16GBcomputational
! 156: *
! 157: * =====================================================================
1.1 bertrand 158: SUBROUTINE ZUNGBR( VECT, M, N, K, A, LDA, TAU, WORK, LWORK, INFO )
159: *
1.9 ! bertrand 160: * -- LAPACK computational routine (version 3.4.0) --
1.1 bertrand 161: * -- LAPACK is a software package provided by Univ. of Tennessee, --
162: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.9 ! bertrand 163: * November 2011
1.1 bertrand 164: *
165: * .. Scalar Arguments ..
166: CHARACTER VECT
167: INTEGER INFO, K, LDA, LWORK, M, N
168: * ..
169: * .. Array Arguments ..
170: COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * )
171: * ..
172: *
173: * =====================================================================
174: *
175: * .. Parameters ..
176: COMPLEX*16 ZERO, ONE
177: PARAMETER ( ZERO = ( 0.0D+0, 0.0D+0 ),
178: $ ONE = ( 1.0D+0, 0.0D+0 ) )
179: * ..
180: * .. Local Scalars ..
181: LOGICAL LQUERY, WANTQ
182: INTEGER I, IINFO, J, LWKOPT, MN, NB
183: * ..
184: * .. External Functions ..
185: LOGICAL LSAME
186: INTEGER ILAENV
187: EXTERNAL LSAME, ILAENV
188: * ..
189: * .. External Subroutines ..
190: EXTERNAL XERBLA, ZUNGLQ, ZUNGQR
191: * ..
192: * .. Intrinsic Functions ..
193: INTRINSIC MAX, MIN
194: * ..
195: * .. Executable Statements ..
196: *
197: * Test the input arguments
198: *
199: INFO = 0
200: WANTQ = LSAME( VECT, 'Q' )
201: MN = MIN( M, N )
202: LQUERY = ( LWORK.EQ.-1 )
203: IF( .NOT.WANTQ .AND. .NOT.LSAME( VECT, 'P' ) ) THEN
204: INFO = -1
205: ELSE IF( M.LT.0 ) THEN
206: INFO = -2
207: ELSE IF( N.LT.0 .OR. ( WANTQ .AND. ( N.GT.M .OR. N.LT.MIN( M,
208: $ K ) ) ) .OR. ( .NOT.WANTQ .AND. ( M.GT.N .OR. M.LT.
209: $ MIN( N, K ) ) ) ) THEN
210: INFO = -3
211: ELSE IF( K.LT.0 ) THEN
212: INFO = -4
213: ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
214: INFO = -6
215: ELSE IF( LWORK.LT.MAX( 1, MN ) .AND. .NOT.LQUERY ) THEN
216: INFO = -9
217: END IF
218: *
219: IF( INFO.EQ.0 ) THEN
1.9 ! bertrand 220: WORK( 1 ) = 1
1.1 bertrand 221: IF( WANTQ ) THEN
1.9 ! bertrand 222: IF( M.GE.K ) THEN
! 223: CALL ZUNGQR( M, N, K, A, LDA, TAU, WORK, -1, IINFO )
! 224: ELSE
! 225: IF( M.GT.1 ) THEN
! 226: CALL ZUNGQR( M-1, M-1, M-1, A( 2, 2 ), LDA, TAU, WORK,
! 227: $ -1, IINFO )
! 228: END IF
! 229: END IF
1.1 bertrand 230: ELSE
1.9 ! bertrand 231: IF( K.LT.N ) THEN
! 232: CALL ZUNGLQ( M, N, K, A, LDA, TAU, WORK, -1, IINFO )
! 233: ELSE
! 234: IF( N.GT.1 ) THEN
! 235: CALL ZUNGLQ( N-1, N-1, N-1, A( 2, 2 ), LDA, TAU, WORK,
! 236: $ -1, IINFO )
! 237: END IF
! 238: END IF
1.1 bertrand 239: END IF
1.9 ! bertrand 240: LWKOPT = WORK( 1 )
1.1 bertrand 241: END IF
242: *
243: IF( INFO.NE.0 ) THEN
244: CALL XERBLA( 'ZUNGBR', -INFO )
245: RETURN
246: ELSE IF( LQUERY ) THEN
247: RETURN
248: END IF
249: *
250: * Quick return if possible
251: *
252: IF( M.EQ.0 .OR. N.EQ.0 ) THEN
253: WORK( 1 ) = 1
254: RETURN
255: END IF
256: *
257: IF( WANTQ ) THEN
258: *
259: * Form Q, determined by a call to ZGEBRD to reduce an m-by-k
260: * matrix
261: *
262: IF( M.GE.K ) THEN
263: *
264: * If m >= k, assume m >= n >= k
265: *
266: CALL ZUNGQR( M, N, K, A, LDA, TAU, WORK, LWORK, IINFO )
267: *
268: ELSE
269: *
270: * If m < k, assume m = n
271: *
272: * Shift the vectors which define the elementary reflectors one
273: * column to the right, and set the first row and column of Q
274: * to those of the unit matrix
275: *
276: DO 20 J = M, 2, -1
277: A( 1, J ) = ZERO
278: DO 10 I = J + 1, M
279: A( I, J ) = A( I, J-1 )
280: 10 CONTINUE
281: 20 CONTINUE
282: A( 1, 1 ) = ONE
283: DO 30 I = 2, M
284: A( I, 1 ) = ZERO
285: 30 CONTINUE
286: IF( M.GT.1 ) THEN
287: *
288: * Form Q(2:m,2:m)
289: *
290: CALL ZUNGQR( M-1, M-1, M-1, A( 2, 2 ), LDA, TAU, WORK,
291: $ LWORK, IINFO )
292: END IF
293: END IF
294: ELSE
295: *
1.8 bertrand 296: * Form P**H, determined by a call to ZGEBRD to reduce a k-by-n
1.1 bertrand 297: * matrix
298: *
299: IF( K.LT.N ) THEN
300: *
301: * If k < n, assume k <= m <= n
302: *
303: CALL ZUNGLQ( M, N, K, A, LDA, TAU, WORK, LWORK, IINFO )
304: *
305: ELSE
306: *
307: * If k >= n, assume m = n
308: *
309: * Shift the vectors which define the elementary reflectors one
1.8 bertrand 310: * row downward, and set the first row and column of P**H to
1.1 bertrand 311: * those of the unit matrix
312: *
313: A( 1, 1 ) = ONE
314: DO 40 I = 2, N
315: A( I, 1 ) = ZERO
316: 40 CONTINUE
317: DO 60 J = 2, N
318: DO 50 I = J - 1, 2, -1
319: A( I, J ) = A( I-1, J )
320: 50 CONTINUE
321: A( 1, J ) = ZERO
322: 60 CONTINUE
323: IF( N.GT.1 ) THEN
324: *
1.8 bertrand 325: * Form P**H(2:n,2:n)
1.1 bertrand 326: *
327: CALL ZUNGLQ( N-1, N-1, N-1, A( 2, 2 ), LDA, TAU, WORK,
328: $ LWORK, IINFO )
329: END IF
330: END IF
331: END IF
332: WORK( 1 ) = LWKOPT
333: RETURN
334: *
335: * End of ZUNGBR
336: *
337: END
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