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

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.
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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