LAPACK 3.12.0 LAPACK: Linear Algebra PACKage
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spftrs.f
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1*> \brief \b SPFTRS
2*
3* =========== DOCUMENTATION ===========
4*
5* Online html documentation available at
6* http://www.netlib.org/lapack/explore-html/
7*
8*> \htmlonly
10*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/spftrs.f">
11*> [TGZ]</a>
12*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/spftrs.f">
13*> [ZIP]</a>
14*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/spftrs.f">
15*> [TXT]</a>
16*> \endhtmlonly
17*
18* Definition:
19* ===========
20*
21* SUBROUTINE SPFTRS( TRANSR, UPLO, N, NRHS, A, B, LDB, INFO )
22*
23* .. Scalar Arguments ..
24* CHARACTER TRANSR, UPLO
25* INTEGER INFO, LDB, N, NRHS
26* ..
27* .. Array Arguments ..
28* REAL A( 0: * ), B( LDB, * )
29* ..
30*
31*
32*> \par Purpose:
33* =============
34*>
35*> \verbatim
36*>
37*> SPFTRS solves a system of linear equations A*X = B with a symmetric
38*> positive definite matrix A using the Cholesky factorization
39*> A = U**T*U or A = L*L**T computed by SPFTRF.
40*> \endverbatim
41*
42* Arguments:
43* ==========
44*
45*> \param[in] TRANSR
46*> \verbatim
47*> TRANSR is CHARACTER*1
48*> = 'N': The Normal TRANSR of RFP A is stored;
49*> = 'T': The Transpose TRANSR of RFP A is stored.
50*> \endverbatim
51*>
52*> \param[in] UPLO
53*> \verbatim
54*> UPLO is CHARACTER*1
55*> = 'U': Upper triangle of RFP A is stored;
56*> = 'L': Lower triangle of RFP A is stored.
57*> \endverbatim
58*>
59*> \param[in] N
60*> \verbatim
61*> N is INTEGER
62*> The order of the matrix A. N >= 0.
63*> \endverbatim
64*>
65*> \param[in] NRHS
66*> \verbatim
67*> NRHS is INTEGER
68*> The number of right hand sides, i.e., the number of columns
69*> of the matrix B. NRHS >= 0.
70*> \endverbatim
71*>
72*> \param[in] A
73*> \verbatim
74*> A is REAL array, dimension ( N*(N+1)/2 )
75*> The triangular factor U or L from the Cholesky factorization
76*> of RFP A = U**H*U or RFP A = L*L**T, as computed by SPFTRF.
77*> See note below for more details about RFP A.
78*> \endverbatim
79*>
80*> \param[in,out] B
81*> \verbatim
82*> B is REAL array, dimension (LDB,NRHS)
83*> On entry, the right hand side matrix B.
84*> On exit, the solution matrix X.
85*> \endverbatim
86*>
87*> \param[in] LDB
88*> \verbatim
89*> LDB is INTEGER
90*> The leading dimension of the array B. LDB >= max(1,N).
91*> \endverbatim
92*>
93*> \param[out] INFO
94*> \verbatim
95*> INFO is INTEGER
96*> = 0: successful exit
97*> < 0: if INFO = -i, the i-th argument had an illegal value
98*> \endverbatim
99*
100* Authors:
101* ========
102*
103*> \author Univ. of Tennessee
104*> \author Univ. of California Berkeley
105*> \author Univ. of Colorado Denver
106*> \author NAG Ltd.
107*
108*> \ingroup pftrs
109*
110*> \par Further Details:
111* =====================
112*>
113*> \verbatim
114*>
115*> We first consider Rectangular Full Packed (RFP) Format when N is
116*> even. We give an example where N = 6.
117*>
118*> AP is Upper AP is Lower
119*>
120*> 00 01 02 03 04 05 00
121*> 11 12 13 14 15 10 11
122*> 22 23 24 25 20 21 22
123*> 33 34 35 30 31 32 33
124*> 44 45 40 41 42 43 44
125*> 55 50 51 52 53 54 55
126*>
127*>
128*> Let TRANSR = 'N'. RFP holds AP as follows:
129*> For UPLO = 'U' the upper trapezoid A(0:5,0:2) consists of the last
130*> three columns of AP upper. The lower triangle A(4:6,0:2) consists of
131*> the transpose of the first three columns of AP upper.
132*> For UPLO = 'L' the lower trapezoid A(1:6,0:2) consists of the first
133*> three columns of AP lower. The upper triangle A(0:2,0:2) consists of
134*> the transpose of the last three columns of AP lower.
135*> This covers the case N even and TRANSR = 'N'.
136*>
137*> RFP A RFP A
138*>
139*> 03 04 05 33 43 53
140*> 13 14 15 00 44 54
141*> 23 24 25 10 11 55
142*> 33 34 35 20 21 22
143*> 00 44 45 30 31 32
144*> 01 11 55 40 41 42
145*> 02 12 22 50 51 52
146*>
147*> Now let TRANSR = 'T'. RFP A in both UPLO cases is just the
148*> transpose of RFP A above. One therefore gets:
149*>
150*>
151*> RFP A RFP A
152*>
153*> 03 13 23 33 00 01 02 33 00 10 20 30 40 50
154*> 04 14 24 34 44 11 12 43 44 11 21 31 41 51
155*> 05 15 25 35 45 55 22 53 54 55 22 32 42 52
156*>
157*>
158*> We then consider Rectangular Full Packed (RFP) Format when N is
159*> odd. We give an example where N = 5.
160*>
161*> AP is Upper AP is Lower
162*>
163*> 00 01 02 03 04 00
164*> 11 12 13 14 10 11
165*> 22 23 24 20 21 22
166*> 33 34 30 31 32 33
167*> 44 40 41 42 43 44
168*>
169*>
170*> Let TRANSR = 'N'. RFP holds AP as follows:
171*> For UPLO = 'U' the upper trapezoid A(0:4,0:2) consists of the last
172*> three columns of AP upper. The lower triangle A(3:4,0:1) consists of
173*> the transpose of the first two columns of AP upper.
174*> For UPLO = 'L' the lower trapezoid A(0:4,0:2) consists of the first
175*> three columns of AP lower. The upper triangle A(0:1,1:2) consists of
176*> the transpose of the last two columns of AP lower.
177*> This covers the case N odd and TRANSR = 'N'.
178*>
179*> RFP A RFP A
180*>
181*> 02 03 04 00 33 43
182*> 12 13 14 10 11 44
183*> 22 23 24 20 21 22
184*> 00 33 34 30 31 32
185*> 01 11 44 40 41 42
186*>
187*> Now let TRANSR = 'T'. RFP A in both UPLO cases is just the
188*> transpose of RFP A above. One therefore gets:
189*>
190*> RFP A RFP A
191*>
192*> 02 12 22 00 01 00 10 20 30 40 50
193*> 03 13 23 33 11 33 11 21 31 41 51
194*> 04 14 24 34 44 43 44 22 32 42 52
195*> \endverbatim
196*>
197* =====================================================================
198 SUBROUTINE spftrs( TRANSR, UPLO, N, NRHS, A, B, LDB, INFO )
199*
200* -- LAPACK computational routine --
201* -- LAPACK is a software package provided by Univ. of Tennessee, --
202* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
203*
204* .. Scalar Arguments ..
205 CHARACTER TRANSR, UPLO
206 INTEGER INFO, LDB, N, NRHS
207* ..
208* .. Array Arguments ..
209 REAL A( 0: * ), B( LDB, * )
210* ..
211*
212* =====================================================================
213*
214* .. Parameters ..
215 REAL ONE
216 parameter( one = 1.0e+0 )
217* ..
218* .. Local Scalars ..
219 LOGICAL LOWER, NORMALTRANSR
220* ..
221* .. External Functions ..
222 LOGICAL LSAME
223 EXTERNAL lsame
224* ..
225* .. External Subroutines ..
226 EXTERNAL xerbla, stfsm
227* ..
228* .. Intrinsic Functions ..
229 INTRINSIC max
230* ..
231* .. Executable Statements ..
232*
233* Test the input parameters.
234*
235 info = 0
236 normaltransr = lsame( transr, 'N' )
237 lower = lsame( uplo, 'L' )
238 IF( .NOT.normaltransr .AND. .NOT.lsame( transr, 'T' ) ) THEN
239 info = -1
240 ELSE IF( .NOT.lower .AND. .NOT.lsame( uplo, 'U' ) ) THEN
241 info = -2
242 ELSE IF( n.LT.0 ) THEN
243 info = -3
244 ELSE IF( nrhs.LT.0 ) THEN
245 info = -4
246 ELSE IF( ldb.LT.max( 1, n ) ) THEN
247 info = -7
248 END IF
249 IF( info.NE.0 ) THEN
250 CALL xerbla( 'SPFTRS', -info )
251 RETURN
252 END IF
253*
254* Quick return if possible
255*
256 IF( n.EQ.0 .OR. nrhs.EQ.0 )
257 \$ RETURN
258*
259* start execution: there are two triangular solves
260*
261 IF( lower ) THEN
262 CALL stfsm( transr, 'L', uplo, 'N', 'N', n, nrhs, one, a, b,
263 \$ ldb )
264 CALL stfsm( transr, 'L', uplo, 'T', 'N', n, nrhs, one, a, b,
265 \$ ldb )
266 ELSE
267 CALL stfsm( transr, 'L', uplo, 'T', 'N', n, nrhs, one, a, b,
268 \$ ldb )
269 CALL stfsm( transr, 'L', uplo, 'N', 'N', n, nrhs, one, a, b,
270 \$ ldb )
271 END IF
272*
273 RETURN
274*
275* End of SPFTRS
276*
277 END
subroutine xerbla(srname, info)
Definition cblat2.f:3285
subroutine spftrs(transr, uplo, n, nrhs, a, b, ldb, info)
SPFTRS
Definition spftrs.f:199
subroutine stfsm(transr, side, uplo, trans, diag, m, n, alpha, a, b, ldb)
STFSM solves a matrix equation (one operand is a triangular matrix in RFP format).
Definition stfsm.f:277