LAPACK  3.8.0
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.
Date
December 2016
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 222 of file cpftrs.f.

222 *
223 * -- LAPACK computational routine (version 3.7.0) --
224 * -- LAPACK is a software package provided by Univ. of Tennessee, --
225 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
226 * December 2016
227 *
228 * .. Scalar Arguments ..
229  CHARACTER transr, uplo
230  INTEGER info, ldb, n, nrhs
231 * ..
232 * .. Array Arguments ..
233  COMPLEX a( 0: * ), b( ldb, * )
234 * ..
235 *
236 * =====================================================================
237 *
238 * .. Parameters ..
239  COMPLEX cone
240  parameter( cone = ( 1.0e+0, 0.0e+0 ) )
241 * ..
242 * .. Local Scalars ..
243  LOGICAL lower, normaltransr
244 * ..
245 * .. External Functions ..
246  LOGICAL lsame
247  EXTERNAL lsame
248 * ..
249 * .. External Subroutines ..
250  EXTERNAL xerbla, ctfsm
251 * ..
252 * .. Intrinsic Functions ..
253  INTRINSIC max
254 * ..
255 * .. Executable Statements ..
256 *
257 * Test the input parameters.
258 *
259  info = 0
260  normaltransr = lsame( transr, 'N' )
261  lower = lsame( uplo, 'L' )
262  IF( .NOT.normaltransr .AND. .NOT.lsame( transr, 'C' ) ) THEN
263  info = -1
264  ELSE IF( .NOT.lower .AND. .NOT.lsame( uplo, 'U' ) ) THEN
265  info = -2
266  ELSE IF( n.LT.0 ) THEN
267  info = -3
268  ELSE IF( nrhs.LT.0 ) THEN
269  info = -4
270  ELSE IF( ldb.LT.max( 1, n ) ) THEN
271  info = -7
272  END IF
273  IF( info.NE.0 ) THEN
274  CALL xerbla( 'CPFTRS', -info )
275  RETURN
276  END IF
277 *
278 * Quick return if possible
279 *
280  IF( n.EQ.0 .OR. nrhs.EQ.0 )
281  $ RETURN
282 *
283 * start execution: there are two triangular solves
284 *
285  IF( lower ) THEN
286  CALL ctfsm( transr, 'L', uplo, 'N', 'N', n, nrhs, cone, a, b,
287  $ ldb )
288  CALL ctfsm( transr, 'L', uplo, 'C', 'N', n, nrhs, cone, a, b,
289  $ ldb )
290  ELSE
291  CALL ctfsm( transr, 'L', uplo, 'C', 'N', n, nrhs, cone, a, b,
292  $ ldb )
293  CALL ctfsm( transr, 'L', uplo, 'N', 'N', n, nrhs, cone, a, b,
294  $ ldb )
295  END IF
296 *
297  RETURN
298 *
299 * End of CPFTRS
300 *
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:300
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55
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