Annotation of rpl/lapack/lapack/dpftrs.f, revision 1.4
1.1 bertrand 1: SUBROUTINE DPFTRS( TRANSR, UPLO, N, NRHS, A, B, LDB, INFO )
2: *
1.4 ! bertrand 3: * -- LAPACK routine (version 3.3.0) --
1.1 bertrand 4: *
5: * -- Contributed by Fred Gustavson of the IBM Watson Research Center --
1.4 ! bertrand 6: * November 2010
1.1 bertrand 7: *
8: * -- LAPACK is a software package provided by Univ. of Tennessee, --
9: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
10: *
11: * .. Scalar Arguments ..
12: CHARACTER TRANSR, UPLO
13: INTEGER INFO, LDB, N, NRHS
14: * ..
15: * .. Array Arguments ..
16: DOUBLE PRECISION A( 0: * ), B( LDB, * )
17: * ..
18: *
19: * Purpose
20: * =======
21: *
22: * DPFTRS solves a system of linear equations A*X = B with a symmetric
23: * positive definite matrix A using the Cholesky factorization
24: * A = U**T*U or A = L*L**T computed by DPFTRF.
25: *
26: * Arguments
27: * =========
28: *
1.4 ! bertrand 29: * TRANSR (input) CHARACTER*1
1.1 bertrand 30: * = 'N': The Normal TRANSR of RFP A is stored;
31: * = 'T': The Transpose TRANSR of RFP A is stored.
32: *
1.4 ! bertrand 33: * UPLO (input) CHARACTER*1
1.1 bertrand 34: * = 'U': Upper triangle of RFP A is stored;
35: * = 'L': Lower triangle of RFP A is stored.
36: *
37: * N (input) INTEGER
38: * The order of the matrix A. N >= 0.
39: *
40: * NRHS (input) INTEGER
41: * The number of right hand sides, i.e., the number of columns
42: * of the matrix B. NRHS >= 0.
43: *
44: * A (input) DOUBLE PRECISION array, dimension ( N*(N+1)/2 ).
45: * The triangular factor U or L from the Cholesky factorization
46: * of RFP A = U**T*U or RFP A = L*L**T, as computed by DPFTRF.
47: * See note below for more details about RFP A.
48: *
49: * B (input/output) DOUBLE PRECISION array, dimension (LDB,NRHS)
50: * On entry, the right hand side matrix B.
51: * On exit, the solution matrix X.
52: *
53: * LDB (input) INTEGER
54: * The leading dimension of the array B. LDB >= max(1,N).
55: *
56: * INFO (output) INTEGER
57: * = 0: successful exit
58: * < 0: if INFO = -i, the i-th argument had an illegal value
59: *
60: * Further Details
61: * ===============
62: *
63: * We first consider Rectangular Full Packed (RFP) Format when N is
64: * even. We give an example where N = 6.
65: *
66: * AP is Upper AP is Lower
67: *
68: * 00 01 02 03 04 05 00
69: * 11 12 13 14 15 10 11
70: * 22 23 24 25 20 21 22
71: * 33 34 35 30 31 32 33
72: * 44 45 40 41 42 43 44
73: * 55 50 51 52 53 54 55
74: *
75: *
76: * Let TRANSR = 'N'. RFP holds AP as follows:
77: * For UPLO = 'U' the upper trapezoid A(0:5,0:2) consists of the last
78: * three columns of AP upper. The lower triangle A(4:6,0:2) consists of
79: * the transpose of the first three columns of AP upper.
80: * For UPLO = 'L' the lower trapezoid A(1:6,0:2) consists of the first
81: * three columns of AP lower. The upper triangle A(0:2,0:2) consists of
82: * the transpose of the last three columns of AP lower.
83: * This covers the case N even and TRANSR = 'N'.
84: *
85: * RFP A RFP A
86: *
87: * 03 04 05 33 43 53
88: * 13 14 15 00 44 54
89: * 23 24 25 10 11 55
90: * 33 34 35 20 21 22
91: * 00 44 45 30 31 32
92: * 01 11 55 40 41 42
93: * 02 12 22 50 51 52
94: *
95: * Now let TRANSR = 'T'. RFP A in both UPLO cases is just the
96: * transpose of RFP A above. One therefore gets:
97: *
98: *
99: * RFP A RFP A
100: *
101: * 03 13 23 33 00 01 02 33 00 10 20 30 40 50
102: * 04 14 24 34 44 11 12 43 44 11 21 31 41 51
103: * 05 15 25 35 45 55 22 53 54 55 22 32 42 52
104: *
105: *
106: * We then consider Rectangular Full Packed (RFP) Format when N is
107: * odd. We give an example where N = 5.
108: *
109: * AP is Upper AP is Lower
110: *
111: * 00 01 02 03 04 00
112: * 11 12 13 14 10 11
113: * 22 23 24 20 21 22
114: * 33 34 30 31 32 33
115: * 44 40 41 42 43 44
116: *
117: *
118: * Let TRANSR = 'N'. RFP holds AP as follows:
119: * For UPLO = 'U' the upper trapezoid A(0:4,0:2) consists of the last
120: * three columns of AP upper. The lower triangle A(3:4,0:1) consists of
121: * the transpose of the first two columns of AP upper.
122: * For UPLO = 'L' the lower trapezoid A(0:4,0:2) consists of the first
123: * three columns of AP lower. The upper triangle A(0:1,1:2) consists of
124: * the transpose of the last two columns of AP lower.
125: * This covers the case N odd and TRANSR = 'N'.
126: *
127: * RFP A RFP A
128: *
129: * 02 03 04 00 33 43
130: * 12 13 14 10 11 44
131: * 22 23 24 20 21 22
132: * 00 33 34 30 31 32
133: * 01 11 44 40 41 42
134: *
135: * Now let TRANSR = 'T'. RFP A in both UPLO cases is just the
136: * transpose of RFP A above. One therefore gets:
137: *
138: * RFP A RFP A
139: *
140: * 02 12 22 00 01 00 10 20 30 40 50
141: * 03 13 23 33 11 33 11 21 31 41 51
142: * 04 14 24 34 44 43 44 22 32 42 52
143: *
144: * =====================================================================
145: *
146: * .. Parameters ..
147: DOUBLE PRECISION ONE
148: PARAMETER ( ONE = 1.0D+0 )
149: * ..
150: * .. Local Scalars ..
151: LOGICAL LOWER, NORMALTRANSR
152: * ..
153: * .. External Functions ..
154: LOGICAL LSAME
155: EXTERNAL LSAME
156: * ..
157: * .. External Subroutines ..
158: EXTERNAL XERBLA, DTFSM
159: * ..
160: * .. Intrinsic Functions ..
161: INTRINSIC MAX
162: * ..
163: * .. Executable Statements ..
164: *
165: * Test the input parameters.
166: *
167: INFO = 0
168: NORMALTRANSR = LSAME( TRANSR, 'N' )
169: LOWER = LSAME( UPLO, 'L' )
170: IF( .NOT.NORMALTRANSR .AND. .NOT.LSAME( TRANSR, 'T' ) ) THEN
171: INFO = -1
172: ELSE IF( .NOT.LOWER .AND. .NOT.LSAME( UPLO, 'U' ) ) THEN
173: INFO = -2
174: ELSE IF( N.LT.0 ) THEN
175: INFO = -3
176: ELSE IF( NRHS.LT.0 ) THEN
177: INFO = -4
178: ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
179: INFO = -7
180: END IF
181: IF( INFO.NE.0 ) THEN
182: CALL XERBLA( 'DPFTRS', -INFO )
183: RETURN
184: END IF
185: *
186: * Quick return if possible
187: *
188: IF( N.EQ.0 .OR. NRHS.EQ.0 )
189: + RETURN
190: *
191: * start execution: there are two triangular solves
192: *
193: IF( LOWER ) THEN
194: CALL DTFSM( TRANSR, 'L', UPLO, 'N', 'N', N, NRHS, ONE, A, B,
195: + LDB )
196: CALL DTFSM( TRANSR, 'L', UPLO, 'T', 'N', N, NRHS, ONE, A, B,
197: + LDB )
198: ELSE
199: CALL DTFSM( TRANSR, 'L', UPLO, 'T', 'N', N, NRHS, ONE, A, B,
200: + LDB )
201: CALL DTFSM( TRANSR, 'L', UPLO, 'N', 'N', N, NRHS, ONE, A, B,
202: + LDB )
203: END IF
204: *
205: RETURN
206: *
207: * End of DPFTRS
208: *
209: END
CVSweb interface <joel.bertrand@systella.fr>
![[BACK]](/cvsweb/icons/back.gif){kind=icon}
Return to dpftrs.f CVS log ![[TXT]](/cvsweb/icons/text.gif){kind=icon}
![[DIR]](/cvsweb/icons/dir.gif){kind=icon}
Up to [local] / rpl / lapack / lapack