Annotation of rpl/lapack/lapack/zgbtf2.f, revision 1.2
1.1 bertrand 1: SUBROUTINE ZGBTF2( M, N, KL, KU, AB, LDAB, 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, KL, KU, LDAB, M, N
10: * ..
11: * .. Array Arguments ..
12: INTEGER IPIV( * )
13: COMPLEX*16 AB( LDAB, * )
14: * ..
15: *
16: * Purpose
17: * =======
18: *
19: * ZGBTF2 computes an LU factorization of a complex m-by-n band matrix
20: * A using partial pivoting with row interchanges.
21: *
22: * This is the unblocked version of the algorithm, calling Level 2 BLAS.
23: *
24: * Arguments
25: * =========
26: *
27: * M (input) INTEGER
28: * The number of rows of the matrix A. M >= 0.
29: *
30: * N (input) INTEGER
31: * The number of columns of the matrix A. N >= 0.
32: *
33: * KL (input) INTEGER
34: * The number of subdiagonals within the band of A. KL >= 0.
35: *
36: * KU (input) INTEGER
37: * The number of superdiagonals within the band of A. KU >= 0.
38: *
39: * AB (input/output) COMPLEX*16 array, dimension (LDAB,N)
40: * On entry, the matrix A in band storage, in rows KL+1 to
41: * 2*KL+KU+1; rows 1 to KL of the array need not be set.
42: * The j-th column of A is stored in the j-th column of the
43: * array AB as follows:
44: * AB(kl+ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(m,j+kl)
45: *
46: * On exit, details of the factorization: U is stored as an
47: * upper triangular band matrix with KL+KU superdiagonals in
48: * rows 1 to KL+KU+1, and the multipliers used during the
49: * factorization are stored in rows KL+KU+2 to 2*KL+KU+1.
50: * See below for further details.
51: *
52: * LDAB (input) INTEGER
53: * The leading dimension of the array AB. LDAB >= 2*KL+KU+1.
54: *
55: * IPIV (output) INTEGER array, dimension (min(M,N))
56: * The pivot indices; for 1 <= i <= min(M,N), row i of the
57: * matrix was interchanged with row IPIV(i).
58: *
59: * INFO (output) INTEGER
60: * = 0: successful exit
61: * < 0: if INFO = -i, the i-th argument had an illegal value
62: * > 0: if INFO = +i, U(i,i) is exactly zero. The factorization
63: * has been completed, but the factor U is exactly
64: * singular, and division by zero will occur if it is used
65: * to solve a system of equations.
66: *
67: * Further Details
68: * ===============
69: *
70: * The band storage scheme is illustrated by the following example, when
71: * M = N = 6, KL = 2, KU = 1:
72: *
73: * On entry: On exit:
74: *
75: * * * * + + + * * * u14 u25 u36
76: * * * + + + + * * u13 u24 u35 u46
77: * * a12 a23 a34 a45 a56 * u12 u23 u34 u45 u56
78: * a11 a22 a33 a44 a55 a66 u11 u22 u33 u44 u55 u66
79: * a21 a32 a43 a54 a65 * m21 m32 m43 m54 m65 *
80: * a31 a42 a53 a64 * * m31 m42 m53 m64 * *
81: *
82: * Array elements marked * are not used by the routine; elements marked
83: * + need not be set on entry, but are required by the routine to store
84: * elements of U, because of fill-in resulting from the row
85: * interchanges.
86: *
87: * =====================================================================
88: *
89: * .. Parameters ..
90: COMPLEX*16 ONE, ZERO
91: PARAMETER ( ONE = ( 1.0D+0, 0.0D+0 ),
92: $ ZERO = ( 0.0D+0, 0.0D+0 ) )
93: * ..
94: * .. Local Scalars ..
95: INTEGER I, J, JP, JU, KM, KV
96: * ..
97: * .. External Functions ..
98: INTEGER IZAMAX
99: EXTERNAL IZAMAX
100: * ..
101: * .. External Subroutines ..
102: EXTERNAL XERBLA, ZGERU, ZSCAL, ZSWAP
103: * ..
104: * .. Intrinsic Functions ..
105: INTRINSIC MAX, MIN
106: * ..
107: * .. Executable Statements ..
108: *
109: * KV is the number of superdiagonals in the factor U, allowing for
110: * fill-in.
111: *
112: KV = KU + KL
113: *
114: * Test the input parameters.
115: *
116: INFO = 0
117: IF( M.LT.0 ) THEN
118: INFO = -1
119: ELSE IF( N.LT.0 ) THEN
120: INFO = -2
121: ELSE IF( KL.LT.0 ) THEN
122: INFO = -3
123: ELSE IF( KU.LT.0 ) THEN
124: INFO = -4
125: ELSE IF( LDAB.LT.KL+KV+1 ) THEN
126: INFO = -6
127: END IF
128: IF( INFO.NE.0 ) THEN
129: CALL XERBLA( 'ZGBTF2', -INFO )
130: RETURN
131: END IF
132: *
133: * Quick return if possible
134: *
135: IF( M.EQ.0 .OR. N.EQ.0 )
136: $ RETURN
137: *
138: * Gaussian elimination with partial pivoting
139: *
140: * Set fill-in elements in columns KU+2 to KV to zero.
141: *
142: DO 20 J = KU + 2, MIN( KV, N )
143: DO 10 I = KV - J + 2, KL
144: AB( I, J ) = ZERO
145: 10 CONTINUE
146: 20 CONTINUE
147: *
148: * JU is the index of the last column affected by the current stage
149: * of the factorization.
150: *
151: JU = 1
152: *
153: DO 40 J = 1, MIN( M, N )
154: *
155: * Set fill-in elements in column J+KV to zero.
156: *
157: IF( J+KV.LE.N ) THEN
158: DO 30 I = 1, KL
159: AB( I, J+KV ) = ZERO
160: 30 CONTINUE
161: END IF
162: *
163: * Find pivot and test for singularity. KM is the number of
164: * subdiagonal elements in the current column.
165: *
166: KM = MIN( KL, M-J )
167: JP = IZAMAX( KM+1, AB( KV+1, J ), 1 )
168: IPIV( J ) = JP + J - 1
169: IF( AB( KV+JP, J ).NE.ZERO ) THEN
170: JU = MAX( JU, MIN( J+KU+JP-1, N ) )
171: *
172: * Apply interchange to columns J to JU.
173: *
174: IF( JP.NE.1 )
175: $ CALL ZSWAP( JU-J+1, AB( KV+JP, J ), LDAB-1,
176: $ AB( KV+1, J ), LDAB-1 )
177: IF( KM.GT.0 ) THEN
178: *
179: * Compute multipliers.
180: *
181: CALL ZSCAL( KM, ONE / AB( KV+1, J ), AB( KV+2, J ), 1 )
182: *
183: * Update trailing submatrix within the band.
184: *
185: IF( JU.GT.J )
186: $ CALL ZGERU( KM, JU-J, -ONE, AB( KV+2, J ), 1,
187: $ AB( KV, J+1 ), LDAB-1, AB( KV+1, J+1 ),
188: $ LDAB-1 )
189: END IF
190: ELSE
191: *
192: * If pivot is zero, set INFO to the index of the pivot
193: * unless a zero pivot has already been found.
194: *
195: IF( INFO.EQ.0 )
196: $ INFO = J
197: END IF
198: 40 CONTINUE
199: RETURN
200: *
201: * End of ZGBTF2
202: *
203: END
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