Annotation of rpl/lapack/lapack/zgeqpf.f, revision 1.10
1.10 ! bertrand 1: *> \brief \b ZGEQPF
! 2: *
! 3: * =========== DOCUMENTATION ===========
! 4: *
! 5: * Online html documentation available at
! 6: * http://www.netlib.org/lapack/explore-html/
! 7: *
! 8: *> \htmlonly
! 9: *> Download ZGEQPF + dependencies
! 10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zgeqpf.f">
! 11: *> [TGZ]</a>
! 12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zgeqpf.f">
! 13: *> [ZIP]</a>
! 14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zgeqpf.f">
! 15: *> [TXT]</a>
! 16: *> \endhtmlonly
! 17: *
! 18: * Definition:
! 19: * ===========
! 20: *
! 21: * SUBROUTINE ZGEQPF( M, N, A, LDA, JPVT, TAU, WORK, RWORK, INFO )
! 22: *
! 23: * .. Scalar Arguments ..
! 24: * INTEGER INFO, LDA, M, N
! 25: * ..
! 26: * .. Array Arguments ..
! 27: * INTEGER JPVT( * )
! 28: * DOUBLE PRECISION RWORK( * )
! 29: * COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * )
! 30: * ..
! 31: *
! 32: *
! 33: *> \par Purpose:
! 34: * =============
! 35: *>
! 36: *> \verbatim
! 37: *>
! 38: *> This routine is deprecated and has been replaced by routine ZGEQP3.
! 39: *>
! 40: *> ZGEQPF computes a QR factorization with column pivoting of a
! 41: *> complex M-by-N matrix A: A*P = Q*R.
! 42: *> \endverbatim
! 43: *
! 44: * Arguments:
! 45: * ==========
! 46: *
! 47: *> \param[in] M
! 48: *> \verbatim
! 49: *> M is INTEGER
! 50: *> The number of rows of the matrix A. M >= 0.
! 51: *> \endverbatim
! 52: *>
! 53: *> \param[in] N
! 54: *> \verbatim
! 55: *> N is INTEGER
! 56: *> The number of columns of the matrix A. N >= 0
! 57: *> \endverbatim
! 58: *>
! 59: *> \param[in,out] A
! 60: *> \verbatim
! 61: *> A is COMPLEX*16 array, dimension (LDA,N)
! 62: *> On entry, the M-by-N matrix A.
! 63: *> On exit, the upper triangle of the array contains the
! 64: *> min(M,N)-by-N upper triangular matrix R; the elements
! 65: *> below the diagonal, together with the array TAU,
! 66: *> represent the unitary matrix Q as a product of
! 67: *> min(m,n) elementary reflectors.
! 68: *> \endverbatim
! 69: *>
! 70: *> \param[in] LDA
! 71: *> \verbatim
! 72: *> LDA is INTEGER
! 73: *> The leading dimension of the array A. LDA >= max(1,M).
! 74: *> \endverbatim
! 75: *>
! 76: *> \param[in,out] JPVT
! 77: *> \verbatim
! 78: *> JPVT is INTEGER array, dimension (N)
! 79: *> On entry, if JPVT(i) .ne. 0, the i-th column of A is permuted
! 80: *> to the front of A*P (a leading column); if JPVT(i) = 0,
! 81: *> the i-th column of A is a free column.
! 82: *> On exit, if JPVT(i) = k, then the i-th column of A*P
! 83: *> was the k-th column of A.
! 84: *> \endverbatim
! 85: *>
! 86: *> \param[out] TAU
! 87: *> \verbatim
! 88: *> TAU is COMPLEX*16 array, dimension (min(M,N))
! 89: *> The scalar factors of the elementary reflectors.
! 90: *> \endverbatim
! 91: *>
! 92: *> \param[out] WORK
! 93: *> \verbatim
! 94: *> WORK is COMPLEX*16 array, dimension (N)
! 95: *> \endverbatim
! 96: *>
! 97: *> \param[out] RWORK
! 98: *> \verbatim
! 99: *> RWORK is DOUBLE PRECISION array, dimension (2*N)
! 100: *> \endverbatim
! 101: *>
! 102: *> \param[out] INFO
! 103: *> \verbatim
! 104: *> INFO is INTEGER
! 105: *> = 0: successful exit
! 106: *> < 0: if INFO = -i, the i-th argument had an illegal value
! 107: *> \endverbatim
! 108: *
! 109: * Authors:
! 110: * ========
! 111: *
! 112: *> \author Univ. of Tennessee
! 113: *> \author Univ. of California Berkeley
! 114: *> \author Univ. of Colorado Denver
! 115: *> \author NAG Ltd.
! 116: *
! 117: *> \date November 2011
! 118: *
! 119: *> \ingroup complex16GEcomputational
! 120: *
! 121: *> \par Further Details:
! 122: * =====================
! 123: *>
! 124: *> \verbatim
! 125: *>
! 126: *> The matrix Q is represented as a product of elementary reflectors
! 127: *>
! 128: *> Q = H(1) H(2) . . . H(n)
! 129: *>
! 130: *> Each H(i) has the form
! 131: *>
! 132: *> H = I - tau * v * v**H
! 133: *>
! 134: *> where tau is a complex scalar, and v is a complex vector with
! 135: *> v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i).
! 136: *>
! 137: *> The matrix P is represented in jpvt as follows: If
! 138: *> jpvt(j) = i
! 139: *> then the jth column of P is the ith canonical unit vector.
! 140: *>
! 141: *> Partial column norm updating strategy modified by
! 142: *> Z. Drmac and Z. Bujanovic, Dept. of Mathematics,
! 143: *> University of Zagreb, Croatia.
! 144: *> -- April 2011 --
! 145: *> For more details see LAPACK Working Note 176.
! 146: *> \endverbatim
! 147: *>
! 148: * =====================================================================
1.1 bertrand 149: SUBROUTINE ZGEQPF( M, N, A, LDA, JPVT, TAU, WORK, RWORK, INFO )
150: *
1.10 ! bertrand 151: * -- LAPACK computational routine (version 3.4.0) --
1.1 bertrand 152: * -- LAPACK is a software package provided by Univ. of Tennessee, --
153: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.10 ! bertrand 154: * November 2011
1.1 bertrand 155: *
156: * .. Scalar Arguments ..
157: INTEGER INFO, LDA, M, N
158: * ..
159: * .. Array Arguments ..
160: INTEGER JPVT( * )
161: DOUBLE PRECISION RWORK( * )
162: COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * )
163: * ..
164: *
165: * =====================================================================
166: *
167: * .. Parameters ..
168: DOUBLE PRECISION ZERO, ONE
169: PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
170: * ..
171: * .. Local Scalars ..
172: INTEGER I, ITEMP, J, MA, MN, PVT
173: DOUBLE PRECISION TEMP, TEMP2, TOL3Z
174: COMPLEX*16 AII
175: * ..
176: * .. External Subroutines ..
1.5 bertrand 177: EXTERNAL XERBLA, ZGEQR2, ZLARF, ZLARFG, ZSWAP, ZUNM2R
1.1 bertrand 178: * ..
179: * .. Intrinsic Functions ..
180: INTRINSIC ABS, DCMPLX, DCONJG, MAX, MIN, SQRT
181: * ..
182: * .. External Functions ..
183: INTEGER IDAMAX
184: DOUBLE PRECISION DLAMCH, DZNRM2
185: EXTERNAL IDAMAX, DLAMCH, DZNRM2
186: * ..
187: * .. Executable Statements ..
188: *
189: * Test the input arguments
190: *
191: INFO = 0
192: IF( M.LT.0 ) THEN
193: INFO = -1
194: ELSE IF( N.LT.0 ) THEN
195: INFO = -2
196: ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
197: INFO = -4
198: END IF
199: IF( INFO.NE.0 ) THEN
200: CALL XERBLA( 'ZGEQPF', -INFO )
201: RETURN
202: END IF
203: *
204: MN = MIN( M, N )
205: TOL3Z = SQRT(DLAMCH('Epsilon'))
206: *
207: * Move initial columns up front
208: *
209: ITEMP = 1
210: DO 10 I = 1, N
211: IF( JPVT( I ).NE.0 ) THEN
212: IF( I.NE.ITEMP ) THEN
213: CALL ZSWAP( M, A( 1, I ), 1, A( 1, ITEMP ), 1 )
214: JPVT( I ) = JPVT( ITEMP )
215: JPVT( ITEMP ) = I
216: ELSE
217: JPVT( I ) = I
218: END IF
219: ITEMP = ITEMP + 1
220: ELSE
221: JPVT( I ) = I
222: END IF
223: 10 CONTINUE
224: ITEMP = ITEMP - 1
225: *
226: * Compute the QR factorization and update remaining columns
227: *
228: IF( ITEMP.GT.0 ) THEN
229: MA = MIN( ITEMP, M )
230: CALL ZGEQR2( M, MA, A, LDA, TAU, WORK, INFO )
231: IF( MA.LT.N ) THEN
232: CALL ZUNM2R( 'Left', 'Conjugate transpose', M, N-MA, MA, A,
233: $ LDA, TAU, A( 1, MA+1 ), LDA, WORK, INFO )
234: END IF
235: END IF
236: *
237: IF( ITEMP.LT.MN ) THEN
238: *
239: * Initialize partial column norms. The first n elements of
240: * work store the exact column norms.
241: *
242: DO 20 I = ITEMP + 1, N
243: RWORK( I ) = DZNRM2( M-ITEMP, A( ITEMP+1, I ), 1 )
244: RWORK( N+I ) = RWORK( I )
245: 20 CONTINUE
246: *
247: * Compute factorization
248: *
249: DO 40 I = ITEMP + 1, MN
250: *
251: * Determine ith pivot column and swap if necessary
252: *
253: PVT = ( I-1 ) + IDAMAX( N-I+1, RWORK( I ), 1 )
254: *
255: IF( PVT.NE.I ) THEN
256: CALL ZSWAP( M, A( 1, PVT ), 1, A( 1, I ), 1 )
257: ITEMP = JPVT( PVT )
258: JPVT( PVT ) = JPVT( I )
259: JPVT( I ) = ITEMP
260: RWORK( PVT ) = RWORK( I )
261: RWORK( N+PVT ) = RWORK( N+I )
262: END IF
263: *
264: * Generate elementary reflector H(i)
265: *
266: AII = A( I, I )
1.5 bertrand 267: CALL ZLARFG( M-I+1, AII, A( MIN( I+1, M ), I ), 1,
1.1 bertrand 268: $ TAU( I ) )
269: A( I, I ) = AII
270: *
271: IF( I.LT.N ) THEN
272: *
273: * Apply H(i) to A(i:m,i+1:n) from the left
274: *
275: AII = A( I, I )
276: A( I, I ) = DCMPLX( ONE )
277: CALL ZLARF( 'Left', M-I+1, N-I, A( I, I ), 1,
278: $ DCONJG( TAU( I ) ), A( I, I+1 ), LDA, WORK )
279: A( I, I ) = AII
280: END IF
281: *
282: * Update partial column norms
283: *
284: DO 30 J = I + 1, N
285: IF( RWORK( J ).NE.ZERO ) THEN
286: *
287: * NOTE: The following 4 lines follow from the analysis in
288: * Lapack Working Note 176.
289: *
290: TEMP = ABS( A( I, J ) ) / RWORK( J )
291: TEMP = MAX( ZERO, ( ONE+TEMP )*( ONE-TEMP ) )
292: TEMP2 = TEMP*( RWORK( J ) / RWORK( N+J ) )**2
293: IF( TEMP2 .LE. TOL3Z ) THEN
294: IF( M-I.GT.0 ) THEN
295: RWORK( J ) = DZNRM2( M-I, A( I+1, J ), 1 )
296: RWORK( N+J ) = RWORK( J )
297: ELSE
298: RWORK( J ) = ZERO
299: RWORK( N+J ) = ZERO
300: END IF
301: ELSE
302: RWORK( J ) = RWORK( J )*SQRT( TEMP )
303: END IF
304: END IF
305: 30 CONTINUE
306: *
307: 40 CONTINUE
308: END IF
309: RETURN
310: *
311: * End of ZGEQPF
312: *
313: END
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