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*> \ingroup complex16GBcomputational 154* 155* ===================================================================== 156 SUBROUTINE ZUNGBR( VECT, M, N, K, A, LDA, TAU, WORK, LWORK, INFO ) 157* 158* -- LAPACK computational routine -- 159* -- LAPACK is a software package provided by Univ. of Tennessee, -- 160* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 161* 162* .. Scalar Arguments .. 163 CHARACTER VECT 164 INTEGER INFO, K, LDA, LWORK, M, N 165* .. 166* .. Array Arguments .. 167 COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * ) 168* .. 169* 170* ===================================================================== 171* 172* .. Parameters .. 173 COMPLEX*16 ZERO, ONE 174 PARAMETER ( ZERO = ( 0.0D+0, 0.0D+0 ), 175 $ ONE = ( 1.0D+0, 0.0D+0 ) ) 176* .. 177* .. Local Scalars .. 178 LOGICAL LQUERY, WANTQ 179 INTEGER I, IINFO, J, LWKOPT, MN 180* .. 181* .. External Functions .. 182 LOGICAL LSAME 183 EXTERNAL LSAME 184* .. 185* .. External Subroutines .. 186 EXTERNAL XERBLA, ZUNGLQ, ZUNGQR 187* .. 188* .. Intrinsic Functions .. 189 INTRINSIC MAX, MIN 190* .. 191* .. Executable Statements .. 192* 193* Test the input arguments 194* 195 INFO = 0 196 WANTQ = LSAME( VECT, 'Q' ) 197 MN = MIN( M, N ) 198 LQUERY = ( LWORK.EQ.-1 ) 199 IF( .NOT.WANTQ .AND. .NOT.LSAME( VECT, 'P' ) ) THEN 200 INFO = -1 201 ELSE IF( M.LT.0 ) THEN 202 INFO = -2 203 ELSE IF( N.LT.0 .OR. ( WANTQ .AND. ( N.GT.M .OR. N.LT.MIN( M, 204 $ K ) ) ) .OR. ( .NOT.WANTQ .AND. ( M.GT.N .OR. M.LT. 205 $ MIN( N, K ) ) ) ) THEN 206 INFO = -3 207 ELSE IF( K.LT.0 ) THEN 208 INFO = -4 209 ELSE IF( LDA.LT.MAX( 1, M ) ) THEN 210 INFO = -6 211 ELSE IF( LWORK.LT.MAX( 1, MN ) .AND. .NOT.LQUERY ) THEN 212 INFO = -9 213 END IF 214* 215 IF( INFO.EQ.0 ) THEN 216 WORK( 1 ) = 1 217 IF( WANTQ ) THEN 218 IF( M.GE.K ) THEN 219 CALL ZUNGQR( M, N, K, A, LDA, TAU, WORK, -1, IINFO ) 220 ELSE 221 IF( M.GT.1 ) THEN 222 CALL ZUNGQR( M-1, M-1, M-1, A, LDA, TAU, WORK, -1, 223 $ IINFO ) 224 END IF 225 END IF 226 ELSE 227 IF( K.LT.N ) THEN 228 CALL ZUNGLQ( M, N, K, A, LDA, TAU, WORK, -1, IINFO ) 229 ELSE 230 IF( N.GT.1 ) THEN 231 CALL ZUNGLQ( N-1, N-1, N-1, A, LDA, TAU, WORK, -1, 232 $ IINFO ) 233 END IF 234 END IF 235 END IF 236 LWKOPT = DBLE( WORK( 1 ) ) 237 LWKOPT = MAX (LWKOPT, MN) 238 END IF 239* 240 IF( INFO.NE.0 ) THEN 241 CALL XERBLA( 'ZUNGBR', -INFO ) 242 RETURN 243 ELSE IF( LQUERY ) THEN 244 WORK( 1 ) = LWKOPT 245 RETURN 246 END IF 247* 248* Quick return if possible 249* 250 IF( M.EQ.0 .OR. N.EQ.0 ) THEN 251 WORK( 1 ) = 1 252 RETURN 253 END IF 254* 255 IF( WANTQ ) THEN 256* 257* Form Q, determined by a call to ZGEBRD to reduce an m-by-k 258* matrix 259* 260 IF( M.GE.K ) THEN 261* 262* If m >= k, assume m >= n >= k 263* 264 CALL ZUNGQR( M, N, K, A, LDA, TAU, WORK, LWORK, IINFO ) 265* 266 ELSE 267* 268* If m < k, assume m = n 269* 270* Shift the vectors which define the elementary reflectors one 271* column to the right, and set the first row and column of Q 272* to those of the unit matrix 273* 274 DO 20 J = M, 2, -1 275 A( 1, J ) = ZERO 276 DO 10 I = J + 1, M 277 A( I, J ) = A( I, J-1 ) 278 10 CONTINUE 279 20 CONTINUE 280 A( 1, 1 ) = ONE 281 DO 30 I = 2, M 282 A( I, 1 ) = ZERO 283 30 CONTINUE 284 IF( M.GT.1 ) THEN 285* 286* Form Q(2:m,2:m) 287* 288 CALL ZUNGQR( M-1, M-1, M-1, A( 2, 2 ), LDA, TAU, WORK, 289 $ LWORK, IINFO ) 290 END IF 291 END IF 292 ELSE 293* 294* Form P**H, determined by a call to ZGEBRD to reduce a k-by-n 295* matrix 296* 297 IF( K.LT.N ) THEN 298* 299* If k < n, assume k <= m <= n 300* 301 CALL ZUNGLQ( M, N, K, A, LDA, TAU, WORK, LWORK, IINFO ) 302* 303 ELSE 304* 305* If k >= n, assume m = n 306* 307* Shift the vectors which define the elementary reflectors one 308* row downward, and set the first row and column of P**H to 309* those of the unit matrix 310* 311 A( 1, 1 ) = ONE 312 DO 40 I = 2, N 313 A( I, 1 ) = ZERO 314 40 CONTINUE 315 DO 60 J = 2, N 316 DO 50 I = J - 1, 2, -1 317 A( I, J ) = A( I-1, J ) 318 50 CONTINUE 319 A( 1, J ) = ZERO 320 60 CONTINUE 321 IF( N.GT.1 ) THEN 322* 323* Form P**H(2:n,2:n) 324* 325 CALL ZUNGLQ( N-1, N-1, N-1, A( 2, 2 ), LDA, TAU, WORK, 326 $ LWORK, IINFO ) 327 END IF 328 END IF 329 END IF 330 WORK( 1 ) = LWKOPT 331 RETURN 332* 333* End of ZUNGBR 334* 335 END 336