Annotation of rpl/lapack/lapack/dgetf2.f, revision 1.6
1.1 bertrand 1: SUBROUTINE DGETF2( M, N, A, LDA, IPIV, INFO )
2: *
3: * -- LAPACK 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 IPIV( * )
13: DOUBLE PRECISION A( LDA, * )
14: * ..
15: *
16: * Purpose
17: * =======
18: *
19: * DGETF2 computes an LU factorization of a general m-by-n matrix A
20: * using partial pivoting with row interchanges.
21: *
22: * The factorization has the form
23: * A = P * L * U
24: * where P is a permutation matrix, L is lower triangular with unit
25: * diagonal elements (lower trapezoidal if m > n), and U is upper
26: * triangular (upper trapezoidal if m < n).
27: *
28: * This is the right-looking Level 2 BLAS version of the algorithm.
29: *
30: * Arguments
31: * =========
32: *
33: * M (input) INTEGER
34: * The number of rows of the matrix A. M >= 0.
35: *
36: * N (input) INTEGER
37: * The number of columns of the matrix A. N >= 0.
38: *
39: * A (input/output) DOUBLE PRECISION array, dimension (LDA,N)
40: * On entry, the m by n matrix to be factored.
41: * On exit, the factors L and U from the factorization
42: * A = P*L*U; the unit diagonal elements of L are not stored.
43: *
44: * LDA (input) INTEGER
45: * The leading dimension of the array A. LDA >= max(1,M).
46: *
47: * IPIV (output) INTEGER array, dimension (min(M,N))
48: * The pivot indices; for 1 <= i <= min(M,N), row i of the
49: * matrix was interchanged with row IPIV(i).
50: *
51: * INFO (output) INTEGER
52: * = 0: successful exit
53: * < 0: if INFO = -k, the k-th argument had an illegal value
54: * > 0: if INFO = k, U(k,k) is exactly zero. The factorization
55: * has been completed, but the factor U is exactly
56: * singular, and division by zero will occur if it is used
57: * to solve a system of equations.
58: *
59: * =====================================================================
60: *
61: * .. Parameters ..
62: DOUBLE PRECISION ONE, ZERO
63: PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
64: * ..
65: * .. Local Scalars ..
66: DOUBLE PRECISION SFMIN
67: INTEGER I, J, JP
68: * ..
69: * .. External Functions ..
70: DOUBLE PRECISION DLAMCH
71: INTEGER IDAMAX
72: EXTERNAL DLAMCH, IDAMAX
73: * ..
74: * .. External Subroutines ..
75: EXTERNAL DGER, DSCAL, DSWAP, XERBLA
76: * ..
77: * .. Intrinsic Functions ..
78: INTRINSIC MAX, MIN
79: * ..
80: * .. Executable Statements ..
81: *
82: * Test the input parameters.
83: *
84: INFO = 0
85: IF( M.LT.0 ) THEN
86: INFO = -1
87: ELSE IF( N.LT.0 ) THEN
88: INFO = -2
89: ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
90: INFO = -4
91: END IF
92: IF( INFO.NE.0 ) THEN
93: CALL XERBLA( 'DGETF2', -INFO )
94: RETURN
95: END IF
96: *
97: * Quick return if possible
98: *
99: IF( M.EQ.0 .OR. N.EQ.0 )
100: $ RETURN
101: *
102: * Compute machine safe minimum
103: *
104: SFMIN = DLAMCH('S')
105: *
106: DO 10 J = 1, MIN( M, N )
107: *
108: * Find pivot and test for singularity.
109: *
110: JP = J - 1 + IDAMAX( M-J+1, A( J, J ), 1 )
111: IPIV( J ) = JP
112: IF( A( JP, J ).NE.ZERO ) THEN
113: *
114: * Apply the interchange to columns 1:N.
115: *
116: IF( JP.NE.J )
117: $ CALL DSWAP( N, A( J, 1 ), LDA, A( JP, 1 ), LDA )
118: *
119: * Compute elements J+1:M of J-th column.
120: *
121: IF( J.LT.M ) THEN
122: IF( ABS(A( J, J )) .GE. SFMIN ) THEN
123: CALL DSCAL( M-J, ONE / A( J, J ), A( J+1, J ), 1 )
124: ELSE
125: DO 20 I = 1, M-J
126: A( J+I, J ) = A( J+I, J ) / A( J, J )
127: 20 CONTINUE
128: END IF
129: END IF
130: *
131: ELSE IF( INFO.EQ.0 ) THEN
132: *
133: INFO = J
134: END IF
135: *
136: IF( J.LT.MIN( M, N ) ) THEN
137: *
138: * Update trailing submatrix.
139: *
140: CALL DGER( M-J, N-J, -ONE, A( J+1, J ), 1, A( J, J+1 ), LDA,
141: $ A( J+1, J+1 ), LDA )
142: END IF
143: 10 CONTINUE
144: RETURN
145: *
146: * End of DGETF2
147: *
148: END
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