1 SUBROUTINE CGETF2( 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 COMPLEX A( LDA, * )
14 * ..
15 *
16 * Purpose
17 * =======
18 *
19 * CGETF2 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) COMPLEX 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 COMPLEX ONE, ZERO
63 PARAMETER ( ONE = ( 1.0E+0, 0.0E+0 ),
64 $ ZERO = ( 0.0E+0, 0.0E+0 ) )
65 * ..
66 * .. Local Scalars ..
67 REAL SFMIN
68 INTEGER I, J, JP
69 * ..
70 * .. External Functions ..
71 REAL SLAMCH
72 INTEGER ICAMAX
73 EXTERNAL SLAMCH, ICAMAX
74 * ..
75 * .. External Subroutines ..
76 EXTERNAL CGERU, CSCAL, CSWAP, XERBLA
77 * ..
78 * .. Intrinsic Functions ..
79 INTRINSIC MAX, MIN
80 * ..
81 * .. Executable Statements ..
82 *
83 * Test the input parameters.
84 *
85 INFO = 0
86 IF( M.LT.0 ) THEN
87 INFO = -1
88 ELSE IF( N.LT.0 ) THEN
89 INFO = -2
90 ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
91 INFO = -4
92 END IF
93 IF( INFO.NE.0 ) THEN
94 CALL XERBLA( 'CGETF2', -INFO )
95 RETURN
96 END IF
97 *
98 * Quick return if possible
99 *
100 IF( M.EQ.0 .OR. N.EQ.0 )
101 $ RETURN
102 *
103 * Compute machine safe minimum
104 *
105 SFMIN = SLAMCH('S')
106 *
107 DO 10 J = 1, MIN( M, N )
108 *
109 * Find pivot and test for singularity.
110 *
111 JP = J - 1 + ICAMAX( M-J+1, A( J, J ), 1 )
112 IPIV( J ) = JP
113 IF( A( JP, J ).NE.ZERO ) THEN
114 *
115 * Apply the interchange to columns 1:N.
116 *
117 IF( JP.NE.J )
118 $ CALL CSWAP( N, A( J, 1 ), LDA, A( JP, 1 ), LDA )
119 *
120 * Compute elements J+1:M of J-th column.
121 *
122 IF( J.LT.M ) THEN
123 IF( ABS(A( J, J )) .GE. SFMIN ) THEN
124 CALL CSCAL( M-J, ONE / A( J, J ), A( J+1, J ), 1 )
125 ELSE
126 DO 20 I = 1, M-J
127 A( J+I, J ) = A( J+I, J ) / A( J, J )
128 20 CONTINUE
129 END IF
130 END IF
131 *
132 ELSE IF( INFO.EQ.0 ) THEN
133 *
134 INFO = J
135 END IF
136 *
137 IF( J.LT.MIN( M, N ) ) THEN
138 *
139 * Update trailing submatrix.
140 *
141 CALL CGERU( M-J, N-J, -ONE, A( J+1, J ), 1, A( J, J+1 ),
142 $ LDA, A( J+1, J+1 ), LDA )
143 END IF
144 10 CONTINUE
145 RETURN
146 *
147 * End of CGETF2
148 *
149 END
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 COMPLEX A( LDA, * )
14 * ..
15 *
16 * Purpose
17 * =======
18 *
19 * CGETF2 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) COMPLEX 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 COMPLEX ONE, ZERO
63 PARAMETER ( ONE = ( 1.0E+0, 0.0E+0 ),
64 $ ZERO = ( 0.0E+0, 0.0E+0 ) )
65 * ..
66 * .. Local Scalars ..
67 REAL SFMIN
68 INTEGER I, J, JP
69 * ..
70 * .. External Functions ..
71 REAL SLAMCH
72 INTEGER ICAMAX
73 EXTERNAL SLAMCH, ICAMAX
74 * ..
75 * .. External Subroutines ..
76 EXTERNAL CGERU, CSCAL, CSWAP, XERBLA
77 * ..
78 * .. Intrinsic Functions ..
79 INTRINSIC MAX, MIN
80 * ..
81 * .. Executable Statements ..
82 *
83 * Test the input parameters.
84 *
85 INFO = 0
86 IF( M.LT.0 ) THEN
87 INFO = -1
88 ELSE IF( N.LT.0 ) THEN
89 INFO = -2
90 ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
91 INFO = -4
92 END IF
93 IF( INFO.NE.0 ) THEN
94 CALL XERBLA( 'CGETF2', -INFO )
95 RETURN
96 END IF
97 *
98 * Quick return if possible
99 *
100 IF( M.EQ.0 .OR. N.EQ.0 )
101 $ RETURN
102 *
103 * Compute machine safe minimum
104 *
105 SFMIN = SLAMCH('S')
106 *
107 DO 10 J = 1, MIN( M, N )
108 *
109 * Find pivot and test for singularity.
110 *
111 JP = J - 1 + ICAMAX( M-J+1, A( J, J ), 1 )
112 IPIV( J ) = JP
113 IF( A( JP, J ).NE.ZERO ) THEN
114 *
115 * Apply the interchange to columns 1:N.
116 *
117 IF( JP.NE.J )
118 $ CALL CSWAP( N, A( J, 1 ), LDA, A( JP, 1 ), LDA )
119 *
120 * Compute elements J+1:M of J-th column.
121 *
122 IF( J.LT.M ) THEN
123 IF( ABS(A( J, J )) .GE. SFMIN ) THEN
124 CALL CSCAL( M-J, ONE / A( J, J ), A( J+1, J ), 1 )
125 ELSE
126 DO 20 I = 1, M-J
127 A( J+I, J ) = A( J+I, J ) / A( J, J )
128 20 CONTINUE
129 END IF
130 END IF
131 *
132 ELSE IF( INFO.EQ.0 ) THEN
133 *
134 INFO = J
135 END IF
136 *
137 IF( J.LT.MIN( M, N ) ) THEN
138 *
139 * Update trailing submatrix.
140 *
141 CALL CGERU( M-J, N-J, -ONE, A( J+1, J ), 1, A( J, J+1 ),
142 $ LDA, A( J+1, J+1 ), LDA )
143 END IF
144 10 CONTINUE
145 RETURN
146 *
147 * End of CGETF2
148 *
149 END