Annotation of rpl/lapack/lapack/dgeqpf.f, revision 1.10
1.10 ! bertrand 1: *> \brief \b DGEQPF
! 2: *
! 3: * =========== DOCUMENTATION ===========
! 4: *
! 5: * Online html documentation available at
! 6: * http://www.netlib.org/lapack/explore-html/
! 7: *
! 8: *> \htmlonly
! 9: *> Download DGEQPF + dependencies
! 10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dgeqpf.f">
! 11: *> [TGZ]</a>
! 12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dgeqpf.f">
! 13: *> [ZIP]</a>
! 14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dgeqpf.f">
! 15: *> [TXT]</a>
! 16: *> \endhtmlonly
! 17: *
! 18: * Definition:
! 19: * ===========
! 20: *
! 21: * SUBROUTINE DGEQPF( M, N, A, LDA, JPVT, TAU, WORK, INFO )
! 22: *
! 23: * .. Scalar Arguments ..
! 24: * INTEGER INFO, LDA, M, N
! 25: * ..
! 26: * .. Array Arguments ..
! 27: * INTEGER JPVT( * )
! 28: * DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * )
! 29: * ..
! 30: *
! 31: *
! 32: *> \par Purpose:
! 33: * =============
! 34: *>
! 35: *> \verbatim
! 36: *>
! 37: *> This routine is deprecated and has been replaced by routine DGEQP3.
! 38: *>
! 39: *> DGEQPF computes a QR factorization with column pivoting of a
! 40: *> real M-by-N matrix A: A*P = Q*R.
! 41: *> \endverbatim
! 42: *
! 43: * Arguments:
! 44: * ==========
! 45: *
! 46: *> \param[in] M
! 47: *> \verbatim
! 48: *> M is INTEGER
! 49: *> The number of rows of the matrix A. M >= 0.
! 50: *> \endverbatim
! 51: *>
! 52: *> \param[in] N
! 53: *> \verbatim
! 54: *> N is INTEGER
! 55: *> The number of columns of the matrix A. N >= 0
! 56: *> \endverbatim
! 57: *>
! 58: *> \param[in,out] A
! 59: *> \verbatim
! 60: *> A is DOUBLE PRECISION array, dimension (LDA,N)
! 61: *> On entry, the M-by-N matrix A.
! 62: *> On exit, the upper triangle of the array contains the
! 63: *> min(M,N)-by-N upper triangular matrix R; the elements
! 64: *> below the diagonal, together with the array TAU,
! 65: *> represent the orthogonal matrix Q as a product of
! 66: *> min(m,n) elementary reflectors.
! 67: *> \endverbatim
! 68: *>
! 69: *> \param[in] LDA
! 70: *> \verbatim
! 71: *> LDA is INTEGER
! 72: *> The leading dimension of the array A. LDA >= max(1,M).
! 73: *> \endverbatim
! 74: *>
! 75: *> \param[in,out] JPVT
! 76: *> \verbatim
! 77: *> JPVT is INTEGER array, dimension (N)
! 78: *> On entry, if JPVT(i) .ne. 0, the i-th column of A is permuted
! 79: *> to the front of A*P (a leading column); if JPVT(i) = 0,
! 80: *> the i-th column of A is a free column.
! 81: *> On exit, if JPVT(i) = k, then the i-th column of A*P
! 82: *> was the k-th column of A.
! 83: *> \endverbatim
! 84: *>
! 85: *> \param[out] TAU
! 86: *> \verbatim
! 87: *> TAU is DOUBLE PRECISION array, dimension (min(M,N))
! 88: *> The scalar factors of the elementary reflectors.
! 89: *> \endverbatim
! 90: *>
! 91: *> \param[out] WORK
! 92: *> \verbatim
! 93: *> WORK is DOUBLE PRECISION array, dimension (3*N)
! 94: *> \endverbatim
! 95: *>
! 96: *> \param[out] INFO
! 97: *> \verbatim
! 98: *> INFO is INTEGER
! 99: *> = 0: successful exit
! 100: *> < 0: if INFO = -i, the i-th argument had an illegal value
! 101: *> \endverbatim
! 102: *
! 103: * Authors:
! 104: * ========
! 105: *
! 106: *> \author Univ. of Tennessee
! 107: *> \author Univ. of California Berkeley
! 108: *> \author Univ. of Colorado Denver
! 109: *> \author NAG Ltd.
! 110: *
! 111: *> \date November 2011
! 112: *
! 113: *> \ingroup doubleGEcomputational
! 114: *
! 115: *> \par Further Details:
! 116: * =====================
! 117: *>
! 118: *> \verbatim
! 119: *>
! 120: *> The matrix Q is represented as a product of elementary reflectors
! 121: *>
! 122: *> Q = H(1) H(2) . . . H(n)
! 123: *>
! 124: *> Each H(i) has the form
! 125: *>
! 126: *> H = I - tau * v * v**T
! 127: *>
! 128: *> where tau is a real scalar, and v is a real vector with
! 129: *> v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i).
! 130: *>
! 131: *> The matrix P is represented in jpvt as follows: If
! 132: *> jpvt(j) = i
! 133: *> then the jth column of P is the ith canonical unit vector.
! 134: *>
! 135: *> Partial column norm updating strategy modified by
! 136: *> Z. Drmac and Z. Bujanovic, Dept. of Mathematics,
! 137: *> University of Zagreb, Croatia.
! 138: *> -- April 2011 --
! 139: *> For more details see LAPACK Working Note 176.
! 140: *> \endverbatim
! 141: *>
! 142: * =====================================================================
1.1 bertrand 143: SUBROUTINE DGEQPF( M, N, A, LDA, JPVT, TAU, WORK, INFO )
144: *
1.10 ! bertrand 145: * -- LAPACK computational routine (version 3.4.0) --
1.1 bertrand 146: * -- LAPACK is a software package provided by Univ. of Tennessee, --
147: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.10 ! bertrand 148: * November 2011
1.1 bertrand 149: *
150: * .. Scalar Arguments ..
151: INTEGER INFO, LDA, M, N
152: * ..
153: * .. Array Arguments ..
154: INTEGER JPVT( * )
155: DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * )
156: * ..
157: *
158: * =====================================================================
159: *
160: * .. Parameters ..
161: DOUBLE PRECISION ZERO, ONE
162: PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
163: * ..
164: * .. Local Scalars ..
165: INTEGER I, ITEMP, J, MA, MN, PVT
166: DOUBLE PRECISION AII, TEMP, TEMP2, TOL3Z
167: * ..
168: * .. External Subroutines ..
1.5 bertrand 169: EXTERNAL DGEQR2, DLARF, DLARFG, DORM2R, DSWAP, XERBLA
1.1 bertrand 170: * ..
171: * .. Intrinsic Functions ..
172: INTRINSIC ABS, MAX, MIN, SQRT
173: * ..
174: * .. External Functions ..
175: INTEGER IDAMAX
176: DOUBLE PRECISION DLAMCH, DNRM2
177: EXTERNAL IDAMAX, DLAMCH, DNRM2
178: * ..
179: * .. Executable Statements ..
180: *
181: * Test the input arguments
182: *
183: INFO = 0
184: IF( M.LT.0 ) THEN
185: INFO = -1
186: ELSE IF( N.LT.0 ) THEN
187: INFO = -2
188: ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
189: INFO = -4
190: END IF
191: IF( INFO.NE.0 ) THEN
192: CALL XERBLA( 'DGEQPF', -INFO )
193: RETURN
194: END IF
195: *
196: MN = MIN( M, N )
197: TOL3Z = SQRT(DLAMCH('Epsilon'))
198: *
199: * Move initial columns up front
200: *
201: ITEMP = 1
202: DO 10 I = 1, N
203: IF( JPVT( I ).NE.0 ) THEN
204: IF( I.NE.ITEMP ) THEN
205: CALL DSWAP( M, A( 1, I ), 1, A( 1, ITEMP ), 1 )
206: JPVT( I ) = JPVT( ITEMP )
207: JPVT( ITEMP ) = I
208: ELSE
209: JPVT( I ) = I
210: END IF
211: ITEMP = ITEMP + 1
212: ELSE
213: JPVT( I ) = I
214: END IF
215: 10 CONTINUE
216: ITEMP = ITEMP - 1
217: *
218: * Compute the QR factorization and update remaining columns
219: *
220: IF( ITEMP.GT.0 ) THEN
221: MA = MIN( ITEMP, M )
222: CALL DGEQR2( M, MA, A, LDA, TAU, WORK, INFO )
223: IF( MA.LT.N ) THEN
224: CALL DORM2R( 'Left', 'Transpose', M, N-MA, MA, A, LDA, TAU,
225: $ A( 1, MA+1 ), LDA, WORK, INFO )
226: END IF
227: END IF
228: *
229: IF( ITEMP.LT.MN ) THEN
230: *
231: * Initialize partial column norms. The first n elements of
232: * work store the exact column norms.
233: *
234: DO 20 I = ITEMP + 1, N
235: WORK( I ) = DNRM2( M-ITEMP, A( ITEMP+1, I ), 1 )
236: WORK( N+I ) = WORK( I )
237: 20 CONTINUE
238: *
239: * Compute factorization
240: *
241: DO 40 I = ITEMP + 1, MN
242: *
243: * Determine ith pivot column and swap if necessary
244: *
245: PVT = ( I-1 ) + IDAMAX( N-I+1, WORK( I ), 1 )
246: *
247: IF( PVT.NE.I ) THEN
248: CALL DSWAP( M, A( 1, PVT ), 1, A( 1, I ), 1 )
249: ITEMP = JPVT( PVT )
250: JPVT( PVT ) = JPVT( I )
251: JPVT( I ) = ITEMP
252: WORK( PVT ) = WORK( I )
253: WORK( N+PVT ) = WORK( N+I )
254: END IF
255: *
256: * Generate elementary reflector H(i)
257: *
258: IF( I.LT.M ) THEN
1.5 bertrand 259: CALL DLARFG( M-I+1, A( I, I ), A( I+1, I ), 1, TAU( I ) )
1.1 bertrand 260: ELSE
1.5 bertrand 261: CALL DLARFG( 1, A( M, M ), A( M, M ), 1, TAU( M ) )
1.1 bertrand 262: END IF
263: *
264: IF( I.LT.N ) THEN
265: *
266: * Apply H(i) to A(i:m,i+1:n) from the left
267: *
268: AII = A( I, I )
269: A( I, I ) = ONE
270: CALL DLARF( 'LEFT', M-I+1, N-I, A( I, I ), 1, TAU( I ),
271: $ A( I, I+1 ), LDA, WORK( 2*N+1 ) )
272: A( I, I ) = AII
273: END IF
274: *
275: * Update partial column norms
276: *
277: DO 30 J = I + 1, N
278: IF( WORK( J ).NE.ZERO ) THEN
279: *
280: * NOTE: The following 4 lines follow from the analysis in
281: * Lapack Working Note 176.
282: *
283: TEMP = ABS( A( I, J ) ) / WORK( J )
284: TEMP = MAX( ZERO, ( ONE+TEMP )*( ONE-TEMP ) )
285: TEMP2 = TEMP*( WORK( J ) / WORK( N+J ) )**2
286: IF( TEMP2 .LE. TOL3Z ) THEN
287: IF( M-I.GT.0 ) THEN
288: WORK( J ) = DNRM2( M-I, A( I+1, J ), 1 )
289: WORK( N+J ) = WORK( J )
290: ELSE
291: WORK( J ) = ZERO
292: WORK( N+J ) = ZERO
293: END IF
294: ELSE
295: WORK( J ) = WORK( J )*SQRT( TEMP )
296: END IF
297: END IF
298: 30 CONTINUE
299: *
300: 40 CONTINUE
301: END IF
302: RETURN
303: *
304: * End of DGEQPF
305: *
306: END
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