Annotation of rpl/lapack/lapack/dgeqpf.f, revision 1.3
1.1 bertrand 1: SUBROUTINE DGEQPF( M, N, A, LDA, JPVT, TAU, WORK, INFO )
2: *
3: * -- LAPACK deprecated driver routine (version 3.2) --
4: * -- LAPACK is a software package provided by Univ. of Tennessee, --
5: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
6: * November 2006
7: *
8: * .. Scalar Arguments ..
9: INTEGER INFO, LDA, M, N
10: * ..
11: * .. Array Arguments ..
12: INTEGER JPVT( * )
13: DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * )
14: * ..
15: *
16: * Purpose
17: * =======
18: *
19: * This routine is deprecated and has been replaced by routine DGEQP3.
20: *
21: * DGEQPF computes a QR factorization with column pivoting of a
22: * real M-by-N matrix A: A*P = Q*R.
23: *
24: * Arguments
25: * =========
26: *
27: * M (input) INTEGER
28: * The number of rows of the matrix A. M >= 0.
29: *
30: * N (input) INTEGER
31: * The number of columns of the matrix A. N >= 0
32: *
33: * A (input/output) DOUBLE PRECISION array, dimension (LDA,N)
34: * On entry, the M-by-N matrix A.
35: * On exit, the upper triangle of the array contains the
36: * min(M,N)-by-N upper triangular matrix R; the elements
37: * below the diagonal, together with the array TAU,
38: * represent the orthogonal matrix Q as a product of
39: * min(m,n) elementary reflectors.
40: *
41: * LDA (input) INTEGER
42: * The leading dimension of the array A. LDA >= max(1,M).
43: *
44: * JPVT (input/output) INTEGER array, dimension (N)
45: * On entry, if JPVT(i) .ne. 0, the i-th column of A is permuted
46: * to the front of A*P (a leading column); if JPVT(i) = 0,
47: * the i-th column of A is a free column.
48: * On exit, if JPVT(i) = k, then the i-th column of A*P
49: * was the k-th column of A.
50: *
51: * TAU (output) DOUBLE PRECISION array, dimension (min(M,N))
52: * The scalar factors of the elementary reflectors.
53: *
54: * WORK (workspace) DOUBLE PRECISION array, dimension (3*N)
55: *
56: * INFO (output) INTEGER
57: * = 0: successful exit
58: * < 0: if INFO = -i, the i-th argument had an illegal value
59: *
60: * Further Details
61: * ===============
62: *
63: * The matrix Q is represented as a product of elementary reflectors
64: *
65: * Q = H(1) H(2) . . . H(n)
66: *
67: * Each H(i) has the form
68: *
69: * H = I - tau * v * v'
70: *
71: * where tau is a real scalar, and v is a real vector with
72: * v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i).
73: *
74: * The matrix P is represented in jpvt as follows: If
75: * jpvt(j) = i
76: * then the jth column of P is the ith canonical unit vector.
77: *
78: * Partial column norm updating strategy modified by
79: * Z. Drmac and Z. Bujanovic, Dept. of Mathematics,
80: * University of Zagreb, Croatia.
81: * June 2006.
82: * For more details see LAPACK Working Note 176.
83: *
84: * =====================================================================
85: *
86: * .. Parameters ..
87: DOUBLE PRECISION ZERO, ONE
88: PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
89: * ..
90: * .. Local Scalars ..
91: INTEGER I, ITEMP, J, MA, MN, PVT
92: DOUBLE PRECISION AII, TEMP, TEMP2, TOL3Z
93: * ..
94: * .. External Subroutines ..
95: EXTERNAL DGEQR2, DLARF, DLARFP, DORM2R, DSWAP, XERBLA
96: * ..
97: * .. Intrinsic Functions ..
98: INTRINSIC ABS, MAX, MIN, SQRT
99: * ..
100: * .. External Functions ..
101: INTEGER IDAMAX
102: DOUBLE PRECISION DLAMCH, DNRM2
103: EXTERNAL IDAMAX, DLAMCH, DNRM2
104: * ..
105: * .. Executable Statements ..
106: *
107: * Test the input arguments
108: *
109: INFO = 0
110: IF( M.LT.0 ) THEN
111: INFO = -1
112: ELSE IF( N.LT.0 ) THEN
113: INFO = -2
114: ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
115: INFO = -4
116: END IF
117: IF( INFO.NE.0 ) THEN
118: CALL XERBLA( 'DGEQPF', -INFO )
119: RETURN
120: END IF
121: *
122: MN = MIN( M, N )
123: TOL3Z = SQRT(DLAMCH('Epsilon'))
124: *
125: * Move initial columns up front
126: *
127: ITEMP = 1
128: DO 10 I = 1, N
129: IF( JPVT( I ).NE.0 ) THEN
130: IF( I.NE.ITEMP ) THEN
131: CALL DSWAP( M, A( 1, I ), 1, A( 1, ITEMP ), 1 )
132: JPVT( I ) = JPVT( ITEMP )
133: JPVT( ITEMP ) = I
134: ELSE
135: JPVT( I ) = I
136: END IF
137: ITEMP = ITEMP + 1
138: ELSE
139: JPVT( I ) = I
140: END IF
141: 10 CONTINUE
142: ITEMP = ITEMP - 1
143: *
144: * Compute the QR factorization and update remaining columns
145: *
146: IF( ITEMP.GT.0 ) THEN
147: MA = MIN( ITEMP, M )
148: CALL DGEQR2( M, MA, A, LDA, TAU, WORK, INFO )
149: IF( MA.LT.N ) THEN
150: CALL DORM2R( 'Left', 'Transpose', M, N-MA, MA, A, LDA, TAU,
151: $ A( 1, MA+1 ), LDA, WORK, INFO )
152: END IF
153: END IF
154: *
155: IF( ITEMP.LT.MN ) THEN
156: *
157: * Initialize partial column norms. The first n elements of
158: * work store the exact column norms.
159: *
160: DO 20 I = ITEMP + 1, N
161: WORK( I ) = DNRM2( M-ITEMP, A( ITEMP+1, I ), 1 )
162: WORK( N+I ) = WORK( I )
163: 20 CONTINUE
164: *
165: * Compute factorization
166: *
167: DO 40 I = ITEMP + 1, MN
168: *
169: * Determine ith pivot column and swap if necessary
170: *
171: PVT = ( I-1 ) + IDAMAX( N-I+1, WORK( I ), 1 )
172: *
173: IF( PVT.NE.I ) THEN
174: CALL DSWAP( M, A( 1, PVT ), 1, A( 1, I ), 1 )
175: ITEMP = JPVT( PVT )
176: JPVT( PVT ) = JPVT( I )
177: JPVT( I ) = ITEMP
178: WORK( PVT ) = WORK( I )
179: WORK( N+PVT ) = WORK( N+I )
180: END IF
181: *
182: * Generate elementary reflector H(i)
183: *
184: IF( I.LT.M ) THEN
185: CALL DLARFP( M-I+1, A( I, I ), A( I+1, I ), 1, TAU( I ) )
186: ELSE
187: CALL DLARFP( 1, A( M, M ), A( M, M ), 1, TAU( M ) )
188: END IF
189: *
190: IF( I.LT.N ) THEN
191: *
192: * Apply H(i) to A(i:m,i+1:n) from the left
193: *
194: AII = A( I, I )
195: A( I, I ) = ONE
196: CALL DLARF( 'LEFT', M-I+1, N-I, A( I, I ), 1, TAU( I ),
197: $ A( I, I+1 ), LDA, WORK( 2*N+1 ) )
198: A( I, I ) = AII
199: END IF
200: *
201: * Update partial column norms
202: *
203: DO 30 J = I + 1, N
204: IF( WORK( J ).NE.ZERO ) THEN
205: *
206: * NOTE: The following 4 lines follow from the analysis in
207: * Lapack Working Note 176.
208: *
209: TEMP = ABS( A( I, J ) ) / WORK( J )
210: TEMP = MAX( ZERO, ( ONE+TEMP )*( ONE-TEMP ) )
211: TEMP2 = TEMP*( WORK( J ) / WORK( N+J ) )**2
212: IF( TEMP2 .LE. TOL3Z ) THEN
213: IF( M-I.GT.0 ) THEN
214: WORK( J ) = DNRM2( M-I, A( I+1, J ), 1 )
215: WORK( N+J ) = WORK( J )
216: ELSE
217: WORK( J ) = ZERO
218: WORK( N+J ) = ZERO
219: END IF
220: ELSE
221: WORK( J ) = WORK( J )*SQRT( TEMP )
222: END IF
223: END IF
224: 30 CONTINUE
225: *
226: 40 CONTINUE
227: END IF
228: RETURN
229: *
230: * End of DGEQPF
231: *
232: END
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