1 SUBROUTINE SGETF2( 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 REAL A( LDA, * )
14 * ..
15 *
16 * Purpose
17 * =======
18 *
19 * SGETF2 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) REAL 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 REAL ONE, ZERO
63 PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 )
64 * ..
65 * .. Local Scalars ..
66 REAL SFMIN
67 INTEGER I, J, JP
68 * ..
69 * .. External Functions ..
70 REAL SLAMCH
71 INTEGER ISAMAX
72 EXTERNAL SLAMCH, ISAMAX
73 * ..
74 * .. External Subroutines ..
75 EXTERNAL SGER, SSCAL, SSWAP, 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( 'SGETF2', -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 = SLAMCH('S')
105 *
106 DO 10 J = 1, MIN( M, N )
107 *
108 * Find pivot and test for singularity.
109 *
110 JP = J - 1 + ISAMAX( 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 SSWAP( 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 SSCAL( 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 SGER( 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 SGETF2
147 *
148 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 REAL A( LDA, * )
14 * ..
15 *
16 * Purpose
17 * =======
18 *
19 * SGETF2 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) REAL 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 REAL ONE, ZERO
63 PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 )
64 * ..
65 * .. Local Scalars ..
66 REAL SFMIN
67 INTEGER I, J, JP
68 * ..
69 * .. External Functions ..
70 REAL SLAMCH
71 INTEGER ISAMAX
72 EXTERNAL SLAMCH, ISAMAX
73 * ..
74 * .. External Subroutines ..
75 EXTERNAL SGER, SSCAL, SSWAP, 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( 'SGETF2', -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 = SLAMCH('S')
105 *
106 DO 10 J = 1, MIN( M, N )
107 *
108 * Find pivot and test for singularity.
109 *
110 JP = J - 1 + ISAMAX( 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 SSWAP( 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 SSCAL( 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 SGER( 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 SGETF2
147 *
148 END