Annotation of rpl/lapack/lapack/zlaqp2.f, revision 1.9
1.1 bertrand 1: SUBROUTINE ZLAQP2( M, N, OFFSET, A, LDA, JPVT, TAU, VN1, VN2,
2: $ WORK )
3: *
1.9 ! bertrand 4: * -- LAPACK auxiliary routine (version 3.3.1) --
1.1 bertrand 5: * -- LAPACK is a software package provided by Univ. of Tennessee, --
6: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.9 ! bertrand 7: * -- April 2011 --
1.1 bertrand 8: *
9: * .. Scalar Arguments ..
10: INTEGER LDA, M, N, OFFSET
11: * ..
12: * .. Array Arguments ..
13: INTEGER JPVT( * )
14: DOUBLE PRECISION VN1( * ), VN2( * )
15: COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * )
16: * ..
17: *
18: * Purpose
19: * =======
20: *
21: * ZLAQP2 computes a QR factorization with column pivoting of
22: * the block A(OFFSET+1:M,1:N).
23: * The block A(1:OFFSET,1:N) is accordingly pivoted, but not factorized.
24: *
25: * Arguments
26: * =========
27: *
28: * M (input) INTEGER
29: * The number of rows of the matrix A. M >= 0.
30: *
31: * N (input) INTEGER
32: * The number of columns of the matrix A. N >= 0.
33: *
34: * OFFSET (input) INTEGER
35: * The number of rows of the matrix A that must be pivoted
36: * but no factorized. OFFSET >= 0.
37: *
38: * A (input/output) COMPLEX*16 array, dimension (LDA,N)
39: * On entry, the M-by-N matrix A.
40: * On exit, the upper triangle of block A(OFFSET+1:M,1:N) is
41: * the triangular factor obtained; the elements in block
42: * A(OFFSET+1:M,1:N) below the diagonal, together with the
43: * array TAU, represent the orthogonal matrix Q as a product of
44: * elementary reflectors. Block A(1:OFFSET,1:N) has been
45: * accordingly pivoted, but no factorized.
46: *
47: * LDA (input) INTEGER
48: * The leading dimension of the array A. LDA >= max(1,M).
49: *
50: * JPVT (input/output) INTEGER array, dimension (N)
51: * On entry, if JPVT(i) .ne. 0, the i-th column of A is permuted
52: * to the front of A*P (a leading column); if JPVT(i) = 0,
53: * the i-th column of A is a free column.
54: * On exit, if JPVT(i) = k, then the i-th column of A*P
55: * was the k-th column of A.
56: *
57: * TAU (output) COMPLEX*16 array, dimension (min(M,N))
58: * The scalar factors of the elementary reflectors.
59: *
60: * VN1 (input/output) DOUBLE PRECISION array, dimension (N)
61: * The vector with the partial column norms.
62: *
63: * VN2 (input/output) DOUBLE PRECISION array, dimension (N)
64: * The vector with the exact column norms.
65: *
66: * WORK (workspace) COMPLEX*16 array, dimension (N)
67: *
68: * Further Details
69: * ===============
70: *
71: * Based on contributions by
72: * G. Quintana-Orti, Depto. de Informatica, Universidad Jaime I, Spain
73: * X. Sun, Computer Science Dept., Duke University, USA
74: *
75: * Partial column norm updating strategy modified by
76: * Z. Drmac and Z. Bujanovic, Dept. of Mathematics,
77: * University of Zagreb, Croatia.
1.9 ! bertrand 78: * -- April 2011 --
1.1 bertrand 79: * For more details see LAPACK Working Note 176.
80: * =====================================================================
81: *
82: * .. Parameters ..
83: DOUBLE PRECISION ZERO, ONE
84: COMPLEX*16 CONE
85: PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0,
86: $ CONE = ( 1.0D+0, 0.0D+0 ) )
87: * ..
88: * .. Local Scalars ..
89: INTEGER I, ITEMP, J, MN, OFFPI, PVT
90: DOUBLE PRECISION TEMP, TEMP2, TOL3Z
91: COMPLEX*16 AII
92: * ..
93: * .. External Subroutines ..
1.5 bertrand 94: EXTERNAL ZLARF, ZLARFG, ZSWAP
1.1 bertrand 95: * ..
96: * .. Intrinsic Functions ..
97: INTRINSIC ABS, DCONJG, MAX, MIN, SQRT
98: * ..
99: * .. External Functions ..
100: INTEGER IDAMAX
101: DOUBLE PRECISION DLAMCH, DZNRM2
102: EXTERNAL IDAMAX, DLAMCH, DZNRM2
103: * ..
104: * .. Executable Statements ..
105: *
106: MN = MIN( M-OFFSET, N )
107: TOL3Z = SQRT(DLAMCH('Epsilon'))
108: *
109: * Compute factorization.
110: *
111: DO 20 I = 1, MN
112: *
113: OFFPI = OFFSET + I
114: *
115: * Determine ith pivot column and swap if necessary.
116: *
117: PVT = ( I-1 ) + IDAMAX( N-I+1, VN1( I ), 1 )
118: *
119: IF( PVT.NE.I ) THEN
120: CALL ZSWAP( M, A( 1, PVT ), 1, A( 1, I ), 1 )
121: ITEMP = JPVT( PVT )
122: JPVT( PVT ) = JPVT( I )
123: JPVT( I ) = ITEMP
124: VN1( PVT ) = VN1( I )
125: VN2( PVT ) = VN2( I )
126: END IF
127: *
128: * Generate elementary reflector H(i).
129: *
130: IF( OFFPI.LT.M ) THEN
1.5 bertrand 131: CALL ZLARFG( M-OFFPI+1, A( OFFPI, I ), A( OFFPI+1, I ), 1,
1.1 bertrand 132: $ TAU( I ) )
133: ELSE
1.5 bertrand 134: CALL ZLARFG( 1, A( M, I ), A( M, I ), 1, TAU( I ) )
1.1 bertrand 135: END IF
136: *
137: IF( I.LT.N ) THEN
138: *
1.9 ! bertrand 139: * Apply H(i)**H to A(offset+i:m,i+1:n) from the left.
1.1 bertrand 140: *
141: AII = A( OFFPI, I )
142: A( OFFPI, I ) = CONE
143: CALL ZLARF( 'Left', M-OFFPI+1, N-I, A( OFFPI, I ), 1,
144: $ DCONJG( TAU( I ) ), A( OFFPI, I+1 ), LDA,
145: $ WORK( 1 ) )
146: A( OFFPI, I ) = AII
147: END IF
148: *
149: * Update partial column norms.
150: *
151: DO 10 J = I + 1, N
152: IF( VN1( J ).NE.ZERO ) THEN
153: *
154: * NOTE: The following 4 lines follow from the analysis in
155: * Lapack Working Note 176.
156: *
157: TEMP = ONE - ( ABS( A( OFFPI, J ) ) / VN1( J ) )**2
158: TEMP = MAX( TEMP, ZERO )
159: TEMP2 = TEMP*( VN1( J ) / VN2( J ) )**2
160: IF( TEMP2 .LE. TOL3Z ) THEN
161: IF( OFFPI.LT.M ) THEN
162: VN1( J ) = DZNRM2( M-OFFPI, A( OFFPI+1, J ), 1 )
163: VN2( J ) = VN1( J )
164: ELSE
165: VN1( J ) = ZERO
166: VN2( J ) = ZERO
167: END IF
168: ELSE
169: VN1( J ) = VN1( J )*SQRT( TEMP )
170: END IF
171: END IF
172: 10 CONTINUE
173: *
174: 20 CONTINUE
175: *
176: RETURN
177: *
178: * End of ZLAQP2
179: *
180: END
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