LAPACK 3.12.1
LAPACK: Linear Algebra PACKage
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◆ dpftrs()

subroutine dpftrs ( character transr,
character uplo,
integer n,
integer nrhs,
double precision, dimension( 0: * ) a,
double precision, dimension( ldb, * ) b,
integer ldb,
integer info )

DPFTRS

Download DPFTRS + dependencies [TGZ] [ZIP] [TXT]

Purpose:
!>
!> DPFTRS solves a system of linear equations A*X = B with a symmetric
!> positive definite matrix A using the Cholesky factorization
!> A = U**T*U or A = L*L**T computed by DPFTRF.
!>
Parameters
[in]TRANSR
!>          TRANSR is CHARACTER*1
!>          = 'N':  The Normal TRANSR of RFP A is stored;
!>          = 'T':  The Transpose TRANSR of RFP A is stored.
!>
[in]UPLO
!>          UPLO is CHARACTER*1
!>          = 'U':  Upper triangle of RFP A is stored;
!>          = 'L':  Lower triangle of RFP A is stored.
!>
[in]N
!>          N is INTEGER
!>          The order of the matrix A.  N >= 0.
!>
[in]NRHS
!>          NRHS is INTEGER
!>          The number of right hand sides, i.e., the number of columns
!>          of the matrix B.  NRHS >= 0.
!>
[in]A
!>          A is DOUBLE PRECISION array, dimension ( N*(N+1)/2 ).
!>          The triangular factor U or L from the Cholesky factorization
!>          of RFP A = U**T*U or RFP A = L*L**T, as computed by DPFTRF.
!>          See note below for more details about RFP A.
!>
[in,out]B
!>          B is DOUBLE PRECISION array, dimension (LDB,NRHS)
!>          On entry, the right hand side matrix B.
!>          On exit, the solution matrix X.
!>
[in]LDB
!>          LDB is INTEGER
!>          The leading dimension of the array B.  LDB >= max(1,N).
!>
[out]INFO
!>          INFO is INTEGER
!>          = 0:  successful exit
!>          < 0:  if INFO = -i, the i-th argument had an illegal value
!>
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Further Details:
!>
!>  We first consider Rectangular Full Packed (RFP) Format when N is
!>  even. We give an example where N = 6.
!>
!>      AP is Upper             AP is Lower
!>
!>   00 01 02 03 04 05       00
!>      11 12 13 14 15       10 11
!>         22 23 24 25       20 21 22
!>            33 34 35       30 31 32 33
!>               44 45       40 41 42 43 44
!>                  55       50 51 52 53 54 55
!>
!>
!>  Let TRANSR = 'N'. RFP holds AP as follows:
!>  For UPLO = 'U' the upper trapezoid A(0:5,0:2) consists of the last
!>  three columns of AP upper. The lower triangle A(4:6,0:2) consists of
!>  the transpose of the first three columns of AP upper.
!>  For UPLO = 'L' the lower trapezoid A(1:6,0:2) consists of the first
!>  three columns of AP lower. The upper triangle A(0:2,0:2) consists of
!>  the transpose of the last three columns of AP lower.
!>  This covers the case N even and TRANSR = 'N'.
!>
!>         RFP A                   RFP A
!>
!>        03 04 05                33 43 53
!>        13 14 15                00 44 54
!>        23 24 25                10 11 55
!>        33 34 35                20 21 22
!>        00 44 45                30 31 32
!>        01 11 55                40 41 42
!>        02 12 22                50 51 52
!>
!>  Now let TRANSR = 'T'. RFP A in both UPLO cases is just the
!>  transpose of RFP A above. One therefore gets:
!>
!>
!>           RFP A                   RFP A
!>
!>     03 13 23 33 00 01 02    33 00 10 20 30 40 50
!>     04 14 24 34 44 11 12    43 44 11 21 31 41 51
!>     05 15 25 35 45 55 22    53 54 55 22 32 42 52
!>
!>
!>  We then consider Rectangular Full Packed (RFP) Format when N is
!>  odd. We give an example where N = 5.
!>
!>     AP is Upper                 AP is Lower
!>
!>   00 01 02 03 04              00
!>      11 12 13 14              10 11
!>         22 23 24              20 21 22
!>            33 34              30 31 32 33
!>               44              40 41 42 43 44
!>
!>
!>  Let TRANSR = 'N'. RFP holds AP as follows:
!>  For UPLO = 'U' the upper trapezoid A(0:4,0:2) consists of the last
!>  three columns of AP upper. The lower triangle A(3:4,0:1) consists of
!>  the transpose of the first two columns of AP upper.
!>  For UPLO = 'L' the lower trapezoid A(0:4,0:2) consists of the first
!>  three columns of AP lower. The upper triangle A(0:1,1:2) consists of
!>  the transpose of the last two columns of AP lower.
!>  This covers the case N odd and TRANSR = 'N'.
!>
!>         RFP A                   RFP A
!>
!>        02 03 04                00 33 43
!>        12 13 14                10 11 44
!>        22 23 24                20 21 22
!>        00 33 34                30 31 32
!>        01 11 44                40 41 42
!>
!>  Now let TRANSR = 'T'. RFP A in both UPLO cases is just the
!>  transpose of RFP A above. One therefore gets:
!>
!>           RFP A                   RFP A
!>
!>     02 12 22 00 01             00 10 20 30 40 50
!>     03 13 23 33 11             33 11 21 31 41 51
!>     04 14 24 34 44             43 44 22 32 42 52
!>

Definition at line 196 of file dpftrs.f.

197*
198* -- LAPACK computational routine --
199* -- LAPACK is a software package provided by Univ. of Tennessee, --
200* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
201*
202* .. Scalar Arguments ..
203 CHARACTER TRANSR, UPLO
204 INTEGER INFO, LDB, N, NRHS
205* ..
206* .. Array Arguments ..
207 DOUBLE PRECISION A( 0: * ), B( LDB, * )
208* ..
209*
210* =====================================================================
211*
212* .. Parameters ..
213 DOUBLE PRECISION ONE
214 parameter( one = 1.0d+0 )
215* ..
216* .. Local Scalars ..
217 LOGICAL LOWER, NORMALTRANSR
218* ..
219* .. External Functions ..
220 LOGICAL LSAME
221 EXTERNAL lsame
222* ..
223* .. External Subroutines ..
224 EXTERNAL xerbla, dtfsm
225* ..
226* .. Intrinsic Functions ..
227 INTRINSIC max
228* ..
229* .. Executable Statements ..
230*
231* Test the input parameters.
232*
233 info = 0
234 normaltransr = lsame( transr, 'N' )
235 lower = lsame( uplo, 'L' )
236 IF( .NOT.normaltransr .AND. .NOT.lsame( transr, 'T' ) ) THEN
237 info = -1
238 ELSE IF( .NOT.lower .AND. .NOT.lsame( uplo, 'U' ) ) THEN
239 info = -2
240 ELSE IF( n.LT.0 ) THEN
241 info = -3
242 ELSE IF( nrhs.LT.0 ) THEN
243 info = -4
244 ELSE IF( ldb.LT.max( 1, n ) ) THEN
245 info = -7
246 END IF
247 IF( info.NE.0 ) THEN
248 CALL xerbla( 'DPFTRS', -info )
249 RETURN
250 END IF
251*
252* Quick return if possible
253*
254 IF( n.EQ.0 .OR. nrhs.EQ.0 )
255 $ RETURN
256*
257* start execution: there are two triangular solves
258*
259 IF( lower ) THEN
260 CALL dtfsm( transr, 'L', uplo, 'N', 'N', n, nrhs, one, a, b,
261 $ ldb )
262 CALL dtfsm( transr, 'L', uplo, 'T', 'N', n, nrhs, one, a, b,
263 $ ldb )
264 ELSE
265 CALL dtfsm( transr, 'L', uplo, 'T', 'N', n, nrhs, one, a, b,
266 $ ldb )
267 CALL dtfsm( transr, 'L', uplo, 'N', 'N', n, nrhs, one, a, b,
268 $ ldb )
269 END IF
270*
271 RETURN
272*
273* End of DPFTRS
274*
xerbla
subroutine xerbla(srname, info)
Definition cblat2.f:3285
lsame
logical function lsame(ca, cb)
LSAME
Definition lsame.f:48
dtfsm
subroutine dtfsm(transr, side, uplo, trans, diag, m, n, alpha, a, b, ldb)
DTFSM solves a matrix equation (one operand is a triangular matrix in RFP format).
Definition dtfsm.f:277
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