Annotation of rpl/lapack/lapack/zla_porpvgrw.f, revision 1.2
1.1 bertrand 1: DOUBLE PRECISION FUNCTION ZLA_PORPVGRW( UPLO, NCOLS, A, LDA, AF,
2: $ LDAF, WORK )
3: *
4: * -- LAPACK routine (version 3.2.2) --
5: * -- Contributed by James Demmel, Deaglan Halligan, Yozo Hida and --
6: * -- Jason Riedy of Univ. of California Berkeley. --
7: * -- June 2010 --
8: *
9: * -- LAPACK is a software package provided by Univ. of Tennessee, --
10: * -- Univ. of California Berkeley and NAG Ltd. --
11: *
12: IMPLICIT NONE
13: * ..
14: * .. Scalar Arguments ..
15: CHARACTER*1 UPLO
16: INTEGER NCOLS, LDA, LDAF
17: * ..
18: * .. Array Arguments ..
19: COMPLEX*16 A( LDA, * ), AF( LDAF, * )
20: DOUBLE PRECISION WORK( * )
21: * ..
22: *
23: * Purpose
24: * =======
25: *
26: * ZLA_PORPVGRW computes the reciprocal pivot growth factor
27: * norm(A)/norm(U). The "max absolute element" norm is used. If this is
28: * much less than 1, the stability of the LU factorization of the
29: * (equilibrated) matrix A could be poor. This also means that the
30: * solution X, estimated condition numbers, and error bounds could be
31: * unreliable.
32: *
33: * Arguments
34: * =========
35: *
36: * UPLO (input) CHARACTER*1
37: * = 'U': Upper triangle of A is stored;
38: * = 'L': Lower triangle of A is stored.
39: *
40: * NCOLS (input) INTEGER
41: * The number of columns of the matrix A. NCOLS >= 0.
42: *
43: * A (input) COMPLEX*16 array, dimension (LDA,N)
44: * On entry, the N-by-N matrix A.
45: *
46: * LDA (input) INTEGER
47: * The leading dimension of the array A. LDA >= max(1,N).
48: *
49: * AF (input) COMPLEX*16 array, dimension (LDAF,N)
50: * The triangular factor U or L from the Cholesky factorization
51: * A = U**T*U or A = L*L**T, as computed by ZPOTRF.
52: *
53: * LDAF (input) INTEGER
54: * The leading dimension of the array AF. LDAF >= max(1,N).
55: *
56: * WORK (input) COMPLEX*16 array, dimension (2*N)
57: *
58: * =====================================================================
59: *
60: * .. Local Scalars ..
61: INTEGER I, J
62: DOUBLE PRECISION AMAX, UMAX, RPVGRW
63: LOGICAL UPPER
64: COMPLEX*16 ZDUM
65: * ..
66: * .. External Functions ..
67: EXTERNAL LSAME, ZLASET
68: LOGICAL LSAME
69: * ..
70: * .. Intrinsic Functions ..
71: INTRINSIC ABS, MAX, MIN, REAL, DIMAG
72: * ..
73: * .. Statement Functions ..
74: DOUBLE PRECISION CABS1
75: * ..
76: * .. Statement Function Definitions ..
77: CABS1( ZDUM ) = ABS( DBLE( ZDUM ) ) + ABS( DIMAG( ZDUM ) )
78: * ..
79: * .. Executable Statements ..
80: UPPER = LSAME( 'Upper', UPLO )
81: *
82: * DPOTRF will have factored only the NCOLSxNCOLS leading minor, so
83: * we restrict the growth search to that minor and use only the first
84: * 2*NCOLS workspace entries.
85: *
86: RPVGRW = 1.0D+0
87: DO I = 1, 2*NCOLS
88: WORK( I ) = 0.0D+0
89: END DO
90: *
91: * Find the max magnitude entry of each column.
92: *
93: IF ( UPPER ) THEN
94: DO J = 1, NCOLS
95: DO I = 1, J
96: WORK( NCOLS+J ) =
97: $ MAX( CABS1( A( I, J ) ), WORK( NCOLS+J ) )
98: END DO
99: END DO
100: ELSE
101: DO J = 1, NCOLS
102: DO I = J, NCOLS
103: WORK( NCOLS+J ) =
104: $ MAX( CABS1( A( I, J ) ), WORK( NCOLS+J ) )
105: END DO
106: END DO
107: END IF
108: *
109: * Now find the max magnitude entry of each column of the factor in
110: * AF. No pivoting, so no permutations.
111: *
112: IF ( LSAME( 'Upper', UPLO ) ) THEN
113: DO J = 1, NCOLS
114: DO I = 1, J
115: WORK( J ) = MAX( CABS1( AF( I, J ) ), WORK( J ) )
116: END DO
117: END DO
118: ELSE
119: DO J = 1, NCOLS
120: DO I = J, NCOLS
121: WORK( J ) = MAX( CABS1( AF( I, J ) ), WORK( J ) )
122: END DO
123: END DO
124: END IF
125: *
126: * Compute the *inverse* of the max element growth factor. Dividing
127: * by zero would imply the largest entry of the factor's column is
128: * zero. Than can happen when either the column of A is zero or
129: * massive pivots made the factor underflow to zero. Neither counts
130: * as growth in itself, so simply ignore terms with zero
131: * denominators.
132: *
133: IF ( LSAME( 'Upper', UPLO ) ) THEN
134: DO I = 1, NCOLS
135: UMAX = WORK( I )
136: AMAX = WORK( NCOLS+I )
137: IF ( UMAX /= 0.0D+0 ) THEN
138: RPVGRW = MIN( AMAX / UMAX, RPVGRW )
139: END IF
140: END DO
141: ELSE
142: DO I = 1, NCOLS
143: UMAX = WORK( I )
144: AMAX = WORK( NCOLS+I )
145: IF ( UMAX /= 0.0D+0 ) THEN
146: RPVGRW = MIN( AMAX / UMAX, RPVGRW )
147: END IF
148: END DO
149: END IF
150:
151: ZLA_PORPVGRW = RPVGRW
152: END
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