Annotation of rpl/lapack/lapack/zggqrf.f, revision 1.9
1.9 ! bertrand 1: *> \brief \b ZGGQRF
! 2: *
! 3: * =========== DOCUMENTATION ===========
! 4: *
! 5: * Online html documentation available at
! 6: * http://www.netlib.org/lapack/explore-html/
! 7: *
! 8: *> \htmlonly
! 9: *> Download ZGGQRF + dependencies
! 10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zggqrf.f">
! 11: *> [TGZ]</a>
! 12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zggqrf.f">
! 13: *> [ZIP]</a>
! 14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zggqrf.f">
! 15: *> [TXT]</a>
! 16: *> \endhtmlonly
! 17: *
! 18: * Definition:
! 19: * ===========
! 20: *
! 21: * SUBROUTINE ZGGQRF( N, M, P, A, LDA, TAUA, B, LDB, TAUB, WORK,
! 22: * LWORK, INFO )
! 23: *
! 24: * .. Scalar Arguments ..
! 25: * INTEGER INFO, LDA, LDB, LWORK, M, N, P
! 26: * ..
! 27: * .. Array Arguments ..
! 28: * COMPLEX*16 A( LDA, * ), B( LDB, * ), TAUA( * ), TAUB( * ),
! 29: * $ WORK( * )
! 30: * ..
! 31: *
! 32: *
! 33: *> \par Purpose:
! 34: * =============
! 35: *>
! 36: *> \verbatim
! 37: *>
! 38: *> ZGGQRF computes a generalized QR factorization of an N-by-M matrix A
! 39: *> and an N-by-P matrix B:
! 40: *>
! 41: *> A = Q*R, B = Q*T*Z,
! 42: *>
! 43: *> where Q is an N-by-N unitary matrix, Z is a P-by-P unitary matrix,
! 44: *> and R and T assume one of the forms:
! 45: *>
! 46: *> if N >= M, R = ( R11 ) M , or if N < M, R = ( R11 R12 ) N,
! 47: *> ( 0 ) N-M N M-N
! 48: *> M
! 49: *>
! 50: *> where R11 is upper triangular, and
! 51: *>
! 52: *> if N <= P, T = ( 0 T12 ) N, or if N > P, T = ( T11 ) N-P,
! 53: *> P-N N ( T21 ) P
! 54: *> P
! 55: *>
! 56: *> where T12 or T21 is upper triangular.
! 57: *>
! 58: *> In particular, if B is square and nonsingular, the GQR factorization
! 59: *> of A and B implicitly gives the QR factorization of inv(B)*A:
! 60: *>
! 61: *> inv(B)*A = Z**H * (inv(T)*R)
! 62: *>
! 63: *> where inv(B) denotes the inverse of the matrix B, and Z**H denotes the
! 64: *> conjugate transpose of matrix Z.
! 65: *> \endverbatim
! 66: *
! 67: * Arguments:
! 68: * ==========
! 69: *
! 70: *> \param[in] N
! 71: *> \verbatim
! 72: *> N is INTEGER
! 73: *> The number of rows of the matrices A and B. N >= 0.
! 74: *> \endverbatim
! 75: *>
! 76: *> \param[in] M
! 77: *> \verbatim
! 78: *> M is INTEGER
! 79: *> The number of columns of the matrix A. M >= 0.
! 80: *> \endverbatim
! 81: *>
! 82: *> \param[in] P
! 83: *> \verbatim
! 84: *> P is INTEGER
! 85: *> The number of columns of the matrix B. P >= 0.
! 86: *> \endverbatim
! 87: *>
! 88: *> \param[in,out] A
! 89: *> \verbatim
! 90: *> A is COMPLEX*16 array, dimension (LDA,M)
! 91: *> On entry, the N-by-M matrix A.
! 92: *> On exit, the elements on and above the diagonal of the array
! 93: *> contain the min(N,M)-by-M upper trapezoidal matrix R (R is
! 94: *> upper triangular if N >= M); the elements below the diagonal,
! 95: *> with the array TAUA, represent the unitary matrix Q as a
! 96: *> product of min(N,M) elementary reflectors (see Further
! 97: *> Details).
! 98: *> \endverbatim
! 99: *>
! 100: *> \param[in] LDA
! 101: *> \verbatim
! 102: *> LDA is INTEGER
! 103: *> The leading dimension of the array A. LDA >= max(1,N).
! 104: *> \endverbatim
! 105: *>
! 106: *> \param[out] TAUA
! 107: *> \verbatim
! 108: *> TAUA is COMPLEX*16 array, dimension (min(N,M))
! 109: *> The scalar factors of the elementary reflectors which
! 110: *> represent the unitary matrix Q (see Further Details).
! 111: *> \endverbatim
! 112: *>
! 113: *> \param[in,out] B
! 114: *> \verbatim
! 115: *> B is COMPLEX*16 array, dimension (LDB,P)
! 116: *> On entry, the N-by-P matrix B.
! 117: *> On exit, if N <= P, the upper triangle of the subarray
! 118: *> B(1:N,P-N+1:P) contains the N-by-N upper triangular matrix T;
! 119: *> if N > P, the elements on and above the (N-P)-th subdiagonal
! 120: *> contain the N-by-P upper trapezoidal matrix T; the remaining
! 121: *> elements, with the array TAUB, represent the unitary
! 122: *> matrix Z as a product of elementary reflectors (see Further
! 123: *> Details).
! 124: *> \endverbatim
! 125: *>
! 126: *> \param[in] LDB
! 127: *> \verbatim
! 128: *> LDB is INTEGER
! 129: *> The leading dimension of the array B. LDB >= max(1,N).
! 130: *> \endverbatim
! 131: *>
! 132: *> \param[out] TAUB
! 133: *> \verbatim
! 134: *> TAUB is COMPLEX*16 array, dimension (min(N,P))
! 135: *> The scalar factors of the elementary reflectors which
! 136: *> represent the unitary matrix Z (see Further Details).
! 137: *> \endverbatim
! 138: *>
! 139: *> \param[out] WORK
! 140: *> \verbatim
! 141: *> WORK is COMPLEX*16 array, dimension (MAX(1,LWORK))
! 142: *> On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
! 143: *> \endverbatim
! 144: *>
! 145: *> \param[in] LWORK
! 146: *> \verbatim
! 147: *> LWORK is INTEGER
! 148: *> The dimension of the array WORK. LWORK >= max(1,N,M,P).
! 149: *> For optimum performance LWORK >= max(N,M,P)*max(NB1,NB2,NB3),
! 150: *> where NB1 is the optimal blocksize for the QR factorization
! 151: *> of an N-by-M matrix, NB2 is the optimal blocksize for the
! 152: *> RQ factorization of an N-by-P matrix, and NB3 is the optimal
! 153: *> blocksize for a call of ZUNMQR.
! 154: *>
! 155: *> If LWORK = -1, then a workspace query is assumed; the routine
! 156: *> only calculates the optimal size of the WORK array, returns
! 157: *> this value as the first entry of the WORK array, and no error
! 158: *> message related to LWORK is issued by XERBLA.
! 159: *> \endverbatim
! 160: *>
! 161: *> \param[out] INFO
! 162: *> \verbatim
! 163: *> INFO is INTEGER
! 164: *> = 0: successful exit
! 165: *> < 0: if INFO = -i, the i-th argument had an illegal value.
! 166: *> \endverbatim
! 167: *
! 168: * Authors:
! 169: * ========
! 170: *
! 171: *> \author Univ. of Tennessee
! 172: *> \author Univ. of California Berkeley
! 173: *> \author Univ. of Colorado Denver
! 174: *> \author NAG Ltd.
! 175: *
! 176: *> \date November 2011
! 177: *
! 178: *> \ingroup complex16OTHERcomputational
! 179: *
! 180: *> \par Further Details:
! 181: * =====================
! 182: *>
! 183: *> \verbatim
! 184: *>
! 185: *> The matrix Q is represented as a product of elementary reflectors
! 186: *>
! 187: *> Q = H(1) H(2) . . . H(k), where k = min(n,m).
! 188: *>
! 189: *> Each H(i) has the form
! 190: *>
! 191: *> H(i) = I - taua * v * v**H
! 192: *>
! 193: *> where taua is a complex scalar, and v is a complex vector with
! 194: *> v(1:i-1) = 0 and v(i) = 1; v(i+1:n) is stored on exit in A(i+1:n,i),
! 195: *> and taua in TAUA(i).
! 196: *> To form Q explicitly, use LAPACK subroutine ZUNGQR.
! 197: *> To use Q to update another matrix, use LAPACK subroutine ZUNMQR.
! 198: *>
! 199: *> The matrix Z is represented as a product of elementary reflectors
! 200: *>
! 201: *> Z = H(1) H(2) . . . H(k), where k = min(n,p).
! 202: *>
! 203: *> Each H(i) has the form
! 204: *>
! 205: *> H(i) = I - taub * v * v**H
! 206: *>
! 207: *> where taub is a complex scalar, and v is a complex vector with
! 208: *> v(p-k+i+1:p) = 0 and v(p-k+i) = 1; v(1:p-k+i-1) is stored on exit in
! 209: *> B(n-k+i,1:p-k+i-1), and taub in TAUB(i).
! 210: *> To form Z explicitly, use LAPACK subroutine ZUNGRQ.
! 211: *> To use Z to update another matrix, use LAPACK subroutine ZUNMRQ.
! 212: *> \endverbatim
! 213: *>
! 214: * =====================================================================
1.1 bertrand 215: SUBROUTINE ZGGQRF( N, M, P, A, LDA, TAUA, B, LDB, TAUB, WORK,
216: $ LWORK, INFO )
217: *
1.9 ! bertrand 218: * -- LAPACK computational routine (version 3.4.0) --
1.1 bertrand 219: * -- LAPACK is a software package provided by Univ. of Tennessee, --
220: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.9 ! bertrand 221: * November 2011
1.1 bertrand 222: *
223: * .. Scalar Arguments ..
224: INTEGER INFO, LDA, LDB, LWORK, M, N, P
225: * ..
226: * .. Array Arguments ..
227: COMPLEX*16 A( LDA, * ), B( LDB, * ), TAUA( * ), TAUB( * ),
228: $ WORK( * )
229: * ..
230: *
231: * =====================================================================
232: *
233: * .. Local Scalars ..
234: LOGICAL LQUERY
235: INTEGER LOPT, LWKOPT, NB, NB1, NB2, NB3
236: * ..
237: * .. External Subroutines ..
238: EXTERNAL XERBLA, ZGEQRF, ZGERQF, ZUNMQR
239: * ..
240: * .. External Functions ..
241: INTEGER ILAENV
242: EXTERNAL ILAENV
243: * ..
244: * .. Intrinsic Functions ..
245: INTRINSIC INT, MAX, MIN
246: * ..
247: * .. Executable Statements ..
248: *
249: * Test the input parameters
250: *
251: INFO = 0
252: NB1 = ILAENV( 1, 'ZGEQRF', ' ', N, M, -1, -1 )
253: NB2 = ILAENV( 1, 'ZGERQF', ' ', N, P, -1, -1 )
254: NB3 = ILAENV( 1, 'ZUNMQR', ' ', N, M, P, -1 )
255: NB = MAX( NB1, NB2, NB3 )
256: LWKOPT = MAX( N, M, P )*NB
257: WORK( 1 ) = LWKOPT
258: LQUERY = ( LWORK.EQ.-1 )
259: IF( N.LT.0 ) THEN
260: INFO = -1
261: ELSE IF( M.LT.0 ) THEN
262: INFO = -2
263: ELSE IF( P.LT.0 ) THEN
264: INFO = -3
265: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
266: INFO = -5
267: ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
268: INFO = -8
269: ELSE IF( LWORK.LT.MAX( 1, N, M, P ) .AND. .NOT.LQUERY ) THEN
270: INFO = -11
271: END IF
272: IF( INFO.NE.0 ) THEN
273: CALL XERBLA( 'ZGGQRF', -INFO )
274: RETURN
275: ELSE IF( LQUERY ) THEN
276: RETURN
277: END IF
278: *
279: * QR factorization of N-by-M matrix A: A = Q*R
280: *
281: CALL ZGEQRF( N, M, A, LDA, TAUA, WORK, LWORK, INFO )
282: LOPT = WORK( 1 )
283: *
1.8 bertrand 284: * Update B := Q**H*B.
1.1 bertrand 285: *
286: CALL ZUNMQR( 'Left', 'Conjugate Transpose', N, P, MIN( N, M ), A,
287: $ LDA, TAUA, B, LDB, WORK, LWORK, INFO )
288: LOPT = MAX( LOPT, INT( WORK( 1 ) ) )
289: *
290: * RQ factorization of N-by-P matrix B: B = T*Z.
291: *
292: CALL ZGERQF( N, P, B, LDB, TAUB, WORK, LWORK, INFO )
293: WORK( 1 ) = MAX( LOPT, INT( WORK( 1 ) ) )
294: *
295: RETURN
296: *
297: * End of ZGGQRF
298: *
299: END
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