LAPACK 3.12.0
LAPACK: Linear Algebra PACKage
Loading...
Searching...
No Matches

◆ cpftrs()

subroutine cpftrs ( character  transr,
character  uplo,
integer  n,
integer  nrhs,
complex, dimension( 0: * )  a,
complex, dimension( ldb, * )  b,
integer  ldb,
integer  info 
)

CPFTRS

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

Purpose:
 CPFTRS solves a system of linear equations A*X = B with a Hermitian
 positive definite matrix A using the Cholesky factorization
 A = U**H*U or A = L*L**H computed by CPFTRF.
Parameters
[in]TRANSR
          TRANSR is CHARACTER*1
          = 'N':  The Normal TRANSR of RFP A is stored;
          = 'C':  The Conjugate-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 COMPLEX array, dimension ( N*(N+1)/2 );
          The triangular factor U or L from the Cholesky factorization
          of RFP A = U**H*U or RFP A = L*L**H, as computed by CPFTRF.
          See note below for more details about RFP A.
[in,out]B
          B is COMPLEX 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 Standard Packed 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
  conjugate-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
  conjugate-transpose of the last three columns of AP lower.
  To denote conjugate we place -- above the element. 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 = 'C'. RFP A in both UPLO cases is just the conjugate-
  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 next  consider Standard Packed 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
  conjugate-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
  conjugate-transpose of the last two   columns of AP lower.
  To denote conjugate we place -- above the element. 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 = 'C'. RFP A in both UPLO cases is just the conjugate-
  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 219 of file cpftrs.f.

220*
221* -- LAPACK computational routine --
222* -- LAPACK is a software package provided by Univ. of Tennessee, --
223* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
224*
225* .. Scalar Arguments ..
226 CHARACTER TRANSR, UPLO
227 INTEGER INFO, LDB, N, NRHS
228* ..
229* .. Array Arguments ..
230 COMPLEX A( 0: * ), B( LDB, * )
231* ..
232*
233* =====================================================================
234*
235* .. Parameters ..
236 COMPLEX CONE
237 parameter( cone = ( 1.0e+0, 0.0e+0 ) )
238* ..
239* .. Local Scalars ..
240 LOGICAL LOWER, NORMALTRANSR
241* ..
242* .. External Functions ..
243 LOGICAL LSAME
244 EXTERNAL lsame
245* ..
246* .. External Subroutines ..
247 EXTERNAL xerbla, ctfsm
248* ..
249* .. Intrinsic Functions ..
250 INTRINSIC max
251* ..
252* .. Executable Statements ..
253*
254* Test the input parameters.
255*
256 info = 0
257 normaltransr = lsame( transr, 'N' )
258 lower = lsame( uplo, 'L' )
259 IF( .NOT.normaltransr .AND. .NOT.lsame( transr, 'C' ) ) THEN
260 info = -1
261 ELSE IF( .NOT.lower .AND. .NOT.lsame( uplo, 'U' ) ) THEN
262 info = -2
263 ELSE IF( n.LT.0 ) THEN
264 info = -3
265 ELSE IF( nrhs.LT.0 ) THEN
266 info = -4
267 ELSE IF( ldb.LT.max( 1, n ) ) THEN
268 info = -7
269 END IF
270 IF( info.NE.0 ) THEN
271 CALL xerbla( 'CPFTRS', -info )
272 RETURN
273 END IF
274*
275* Quick return if possible
276*
277 IF( n.EQ.0 .OR. nrhs.EQ.0 )
278 $ RETURN
279*
280* start execution: there are two triangular solves
281*
282 IF( lower ) THEN
283 CALL ctfsm( transr, 'L', uplo, 'N', 'N', n, nrhs, cone, a, b,
284 $ ldb )
285 CALL ctfsm( transr, 'L', uplo, 'C', 'N', n, nrhs, cone, a, b,
286 $ ldb )
287 ELSE
288 CALL ctfsm( transr, 'L', uplo, 'C', 'N', n, nrhs, cone, a, b,
289 $ ldb )
290 CALL ctfsm( transr, 'L', uplo, 'N', 'N', n, nrhs, cone, a, b,
291 $ ldb )
292 END IF
293*
294 RETURN
295*
296* End of CPFTRS
297*
subroutine xerbla(srname, info)
Definition cblat2.f:3285
logical function lsame(ca, cb)
LSAME
Definition lsame.f:48
subroutine ctfsm(transr, side, uplo, trans, diag, m, n, alpha, a, b, ldb)
CTFSM solves a matrix equation (one operand is a triangular matrix in RFP format).
Definition ctfsm.f:298
Here is the call graph for this function:
Here is the caller graph for this function: