LAPACK  3.8.0 LAPACK: Linear Algebra PACKage

## ◆ 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

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```
Date
December 2016
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 201 of file dpftrs.f.

201 *
202 * -- LAPACK computational routine (version 3.7.0) --
203 * -- LAPACK is a software package provided by Univ. of Tennessee, --
204 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
205 * December 2016
206 *
207 * .. Scalar Arguments ..
208  CHARACTER transr, uplo
209  INTEGER info, ldb, n, nrhs
210 * ..
211 * .. Array Arguments ..
212  DOUBLE PRECISION a( 0: * ), b( ldb, * )
213 * ..
214 *
215 * =====================================================================
216 *
217 * .. Parameters ..
218  DOUBLE PRECISION one
219  parameter( one = 1.0d+0 )
220 * ..
221 * .. Local Scalars ..
222  LOGICAL lower, normaltransr
223 * ..
224 * .. External Functions ..
225  LOGICAL lsame
226  EXTERNAL lsame
227 * ..
228 * .. External Subroutines ..
229  EXTERNAL xerbla, dtfsm
230 * ..
231 * .. Intrinsic Functions ..
232  INTRINSIC max
233 * ..
234 * .. Executable Statements ..
235 *
236 * Test the input parameters.
237 *
238  info = 0
239  normaltransr = lsame( transr, 'N' )
240  lower = lsame( uplo, 'L' )
241  IF( .NOT.normaltransr .AND. .NOT.lsame( transr, 'T' ) ) THEN
242  info = -1
243  ELSE IF( .NOT.lower .AND. .NOT.lsame( uplo, 'U' ) ) THEN
244  info = -2
245  ELSE IF( n.LT.0 ) THEN
246  info = -3
247  ELSE IF( nrhs.LT.0 ) THEN
248  info = -4
249  ELSE IF( ldb.LT.max( 1, n ) ) THEN
250  info = -7
251  END IF
252  IF( info.NE.0 ) THEN
253  CALL xerbla( 'DPFTRS', -info )
254  RETURN
255  END IF
256 *
257 * Quick return if possible
258 *
259  IF( n.EQ.0 .OR. nrhs.EQ.0 )
260  \$ RETURN
261 *
262 * start execution: there are two triangular solves
263 *
264  IF( lower ) THEN
265  CALL dtfsm( transr, 'L', uplo, 'N', 'N', n, nrhs, one, a, b,
266  \$ ldb )
267  CALL dtfsm( transr, 'L', uplo, 'T', 'N', n, nrhs, one, a, b,
268  \$ ldb )
269  ELSE
270  CALL dtfsm( transr, 'L', uplo, 'T', 'N', n, nrhs, one, a, b,
271  \$ ldb )
272  CALL dtfsm( transr, 'L', uplo, 'N', 'N', n, nrhs, one, a, b,
273  \$ ldb )
274  END IF
275 *
276  RETURN
277 *
278 * End of DPFTRS
279 *
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55
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:279
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