Annotation of rpl/lapack/lapack/dgeqrfp.f, revision 1.6
1.6 ! bertrand 1: *> \brief \b DGEQRFP
! 2: *
! 3: * =========== DOCUMENTATION ===========
! 4: *
! 5: * Online html documentation available at
! 6: * http://www.netlib.org/lapack/explore-html/
! 7: *
! 8: *> \htmlonly
! 9: *> Download DGEQRFP + dependencies
! 10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dgeqrfp.f">
! 11: *> [TGZ]</a>
! 12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dgeqrfp.f">
! 13: *> [ZIP]</a>
! 14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dgeqrfp.f">
! 15: *> [TXT]</a>
! 16: *> \endhtmlonly
! 17: *
! 18: * Definition:
! 19: * ===========
! 20: *
! 21: * SUBROUTINE DGEQRFP( M, N, A, LDA, TAU, WORK, LWORK, INFO )
! 22: *
! 23: * .. Scalar Arguments ..
! 24: * INTEGER INFO, LDA, LWORK, M, N
! 25: * ..
! 26: * .. Array Arguments ..
! 27: * DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * )
! 28: * ..
! 29: *
! 30: *
! 31: *> \par Purpose:
! 32: * =============
! 33: *>
! 34: *> \verbatim
! 35: *>
! 36: *> DGEQRFP computes a QR factorization of a real M-by-N matrix A:
! 37: *> A = Q * R.
! 38: *> \endverbatim
! 39: *
! 40: * Arguments:
! 41: * ==========
! 42: *
! 43: *> \param[in] M
! 44: *> \verbatim
! 45: *> M is INTEGER
! 46: *> The number of rows of the matrix A. M >= 0.
! 47: *> \endverbatim
! 48: *>
! 49: *> \param[in] N
! 50: *> \verbatim
! 51: *> N is INTEGER
! 52: *> The number of columns of the matrix A. N >= 0.
! 53: *> \endverbatim
! 54: *>
! 55: *> \param[in,out] A
! 56: *> \verbatim
! 57: *> A is DOUBLE PRECISION array, dimension (LDA,N)
! 58: *> On entry, the M-by-N matrix A.
! 59: *> On exit, the elements on and above the diagonal of the array
! 60: *> contain the min(M,N)-by-N upper trapezoidal matrix R (R is
! 61: *> upper triangular if m >= n); the elements below the diagonal,
! 62: *> with the array TAU, represent the orthogonal matrix Q as a
! 63: *> product of min(m,n) elementary reflectors (see Further
! 64: *> Details).
! 65: *> \endverbatim
! 66: *>
! 67: *> \param[in] LDA
! 68: *> \verbatim
! 69: *> LDA is INTEGER
! 70: *> The leading dimension of the array A. LDA >= max(1,M).
! 71: *> \endverbatim
! 72: *>
! 73: *> \param[out] TAU
! 74: *> \verbatim
! 75: *> TAU is DOUBLE PRECISION array, dimension (min(M,N))
! 76: *> The scalar factors of the elementary reflectors (see Further
! 77: *> Details).
! 78: *> \endverbatim
! 79: *>
! 80: *> \param[out] WORK
! 81: *> \verbatim
! 82: *> WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK))
! 83: *> On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
! 84: *> \endverbatim
! 85: *>
! 86: *> \param[in] LWORK
! 87: *> \verbatim
! 88: *> LWORK is INTEGER
! 89: *> The dimension of the array WORK. LWORK >= max(1,N).
! 90: *> For optimum performance LWORK >= N*NB, where NB is
! 91: *> the optimal blocksize.
! 92: *>
! 93: *> If LWORK = -1, then a workspace query is assumed; the routine
! 94: *> only calculates the optimal size of the WORK array, returns
! 95: *> this value as the first entry of the WORK array, and no error
! 96: *> message related to LWORK is issued by XERBLA.
! 97: *> \endverbatim
! 98: *>
! 99: *> \param[out] INFO
! 100: *> \verbatim
! 101: *> INFO is INTEGER
! 102: *> = 0: successful exit
! 103: *> < 0: if INFO = -i, the i-th argument had an illegal value
! 104: *> \endverbatim
! 105: *
! 106: * Authors:
! 107: * ========
! 108: *
! 109: *> \author Univ. of Tennessee
! 110: *> \author Univ. of California Berkeley
! 111: *> \author Univ. of Colorado Denver
! 112: *> \author NAG Ltd.
! 113: *
! 114: *> \date November 2011
! 115: *
! 116: *> \ingroup doubleGEcomputational
! 117: *
! 118: *> \par Further Details:
! 119: * =====================
! 120: *>
! 121: *> \verbatim
! 122: *>
! 123: *> The matrix Q is represented as a product of elementary reflectors
! 124: *>
! 125: *> Q = H(1) H(2) . . . H(k), where k = min(m,n).
! 126: *>
! 127: *> Each H(i) has the form
! 128: *>
! 129: *> H(i) = I - tau * v * v**T
! 130: *>
! 131: *> where tau is a real scalar, and v is a real vector with
! 132: *> v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i),
! 133: *> and tau in TAU(i).
! 134: *> \endverbatim
! 135: *>
! 136: * =====================================================================
1.1 bertrand 137: SUBROUTINE DGEQRFP( M, N, A, LDA, TAU, WORK, LWORK, INFO )
138: *
1.6 ! bertrand 139: * -- LAPACK computational routine (version 3.4.0) --
1.1 bertrand 140: * -- LAPACK is a software package provided by Univ. of Tennessee, --
141: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.6 ! bertrand 142: * November 2011
1.1 bertrand 143: *
144: * .. Scalar Arguments ..
145: INTEGER INFO, LDA, LWORK, M, N
146: * ..
147: * .. Array Arguments ..
148: DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * )
149: * ..
150: *
151: * =====================================================================
152: *
153: * .. Local Scalars ..
154: LOGICAL LQUERY
155: INTEGER I, IB, IINFO, IWS, K, LDWORK, LWKOPT, NB,
156: $ NBMIN, NX
157: * ..
158: * .. External Subroutines ..
159: EXTERNAL DGEQR2P, DLARFB, DLARFT, XERBLA
160: * ..
161: * .. Intrinsic Functions ..
162: INTRINSIC MAX, MIN
163: * ..
164: * .. External Functions ..
165: INTEGER ILAENV
166: EXTERNAL ILAENV
167: * ..
168: * .. Executable Statements ..
169: *
170: * Test the input arguments
171: *
172: INFO = 0
173: NB = ILAENV( 1, 'DGEQRF', ' ', M, N, -1, -1 )
174: LWKOPT = N*NB
175: WORK( 1 ) = LWKOPT
176: LQUERY = ( LWORK.EQ.-1 )
177: IF( M.LT.0 ) THEN
178: INFO = -1
179: ELSE IF( N.LT.0 ) THEN
180: INFO = -2
181: ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
182: INFO = -4
183: ELSE IF( LWORK.LT.MAX( 1, N ) .AND. .NOT.LQUERY ) THEN
184: INFO = -7
185: END IF
186: IF( INFO.NE.0 ) THEN
187: CALL XERBLA( 'DGEQRFP', -INFO )
188: RETURN
189: ELSE IF( LQUERY ) THEN
190: RETURN
191: END IF
192: *
193: * Quick return if possible
194: *
195: K = MIN( M, N )
196: IF( K.EQ.0 ) THEN
197: WORK( 1 ) = 1
198: RETURN
199: END IF
200: *
201: NBMIN = 2
202: NX = 0
203: IWS = N
204: IF( NB.GT.1 .AND. NB.LT.K ) THEN
205: *
206: * Determine when to cross over from blocked to unblocked code.
207: *
208: NX = MAX( 0, ILAENV( 3, 'DGEQRF', ' ', M, N, -1, -1 ) )
209: IF( NX.LT.K ) THEN
210: *
211: * Determine if workspace is large enough for blocked code.
212: *
213: LDWORK = N
214: IWS = LDWORK*NB
215: IF( LWORK.LT.IWS ) THEN
216: *
217: * Not enough workspace to use optimal NB: reduce NB and
218: * determine the minimum value of NB.
219: *
220: NB = LWORK / LDWORK
221: NBMIN = MAX( 2, ILAENV( 2, 'DGEQRF', ' ', M, N, -1,
222: $ -1 ) )
223: END IF
224: END IF
225: END IF
226: *
227: IF( NB.GE.NBMIN .AND. NB.LT.K .AND. NX.LT.K ) THEN
228: *
229: * Use blocked code initially
230: *
231: DO 10 I = 1, K - NX, NB
232: IB = MIN( K-I+1, NB )
233: *
234: * Compute the QR factorization of the current block
235: * A(i:m,i:i+ib-1)
236: *
237: CALL DGEQR2P( M-I+1, IB, A( I, I ), LDA, TAU( I ), WORK,
238: $ IINFO )
239: IF( I+IB.LE.N ) THEN
240: *
241: * Form the triangular factor of the block reflector
242: * H = H(i) H(i+1) . . . H(i+ib-1)
243: *
244: CALL DLARFT( 'Forward', 'Columnwise', M-I+1, IB,
245: $ A( I, I ), LDA, TAU( I ), WORK, LDWORK )
246: *
1.5 bertrand 247: * Apply H**T to A(i:m,i+ib:n) from the left
1.1 bertrand 248: *
249: CALL DLARFB( 'Left', 'Transpose', 'Forward',
250: $ 'Columnwise', M-I+1, N-I-IB+1, IB,
251: $ A( I, I ), LDA, WORK, LDWORK, A( I, I+IB ),
252: $ LDA, WORK( IB+1 ), LDWORK )
253: END IF
254: 10 CONTINUE
255: ELSE
256: I = 1
257: END IF
258: *
259: * Use unblocked code to factor the last or only block.
260: *
261: IF( I.LE.K )
262: $ CALL DGEQR2P( M-I+1, N-I+1, A( I, I ), LDA, TAU( I ), WORK,
263: $ IINFO )
264: *
265: WORK( 1 ) = IWS
266: RETURN
267: *
268: * End of DGEQRFP
269: *
270: END
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