LAPACK  3.10.0
LAPACK: Linear Algebra PACKage

◆ cpftrs()

subroutine cpftrs ( character  TRANSR,
character  UPLO,
integer  N,
integer  NRHS,
complex, dimension( 0: * )  A,
complex, dimension( ldb, * )  B,
integer  LDB,
integer  INFO 
)

CPFTRS

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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)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
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
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