LAPACK  3.10.0
LAPACK: Linear Algebra PACKage

◆ spftrs()

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

SPFTRS

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

Purpose:
 SPFTRS 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 SPFTRF.
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 REAL 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**T, as computed by SPFTRF.
          See note below for more details about RFP A.
[in,out]B
          B is REAL 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 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 198 of file spftrs.f.

199 *
200 * -- LAPACK computational routine --
201 * -- LAPACK is a software package provided by Univ. of Tennessee, --
202 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
203 *
204 * .. Scalar Arguments ..
205  CHARACTER TRANSR, UPLO
206  INTEGER INFO, LDB, N, NRHS
207 * ..
208 * .. Array Arguments ..
209  REAL A( 0: * ), B( LDB, * )
210 * ..
211 *
212 * =====================================================================
213 *
214 * .. Parameters ..
215  REAL ONE
216  parameter( one = 1.0e+0 )
217 * ..
218 * .. Local Scalars ..
219  LOGICAL LOWER, NORMALTRANSR
220 * ..
221 * .. External Functions ..
222  LOGICAL LSAME
223  EXTERNAL lsame
224 * ..
225 * .. External Subroutines ..
226  EXTERNAL xerbla, stfsm
227 * ..
228 * .. Intrinsic Functions ..
229  INTRINSIC max
230 * ..
231 * .. Executable Statements ..
232 *
233 * Test the input parameters.
234 *
235  info = 0
236  normaltransr = lsame( transr, 'N' )
237  lower = lsame( uplo, 'L' )
238  IF( .NOT.normaltransr .AND. .NOT.lsame( transr, 'T' ) ) THEN
239  info = -1
240  ELSE IF( .NOT.lower .AND. .NOT.lsame( uplo, 'U' ) ) THEN
241  info = -2
242  ELSE IF( n.LT.0 ) THEN
243  info = -3
244  ELSE IF( nrhs.LT.0 ) THEN
245  info = -4
246  ELSE IF( ldb.LT.max( 1, n ) ) THEN
247  info = -7
248  END IF
249  IF( info.NE.0 ) THEN
250  CALL xerbla( 'SPFTRS', -info )
251  RETURN
252  END IF
253 *
254 * Quick return if possible
255 *
256  IF( n.EQ.0 .OR. nrhs.EQ.0 )
257  $ RETURN
258 *
259 * start execution: there are two triangular solves
260 *
261  IF( lower ) THEN
262  CALL stfsm( transr, 'L', uplo, 'N', 'N', n, nrhs, one, a, b,
263  $ ldb )
264  CALL stfsm( transr, 'L', uplo, 'T', 'N', n, nrhs, one, a, b,
265  $ ldb )
266  ELSE
267  CALL stfsm( transr, 'L', uplo, 'T', 'N', n, nrhs, one, a, b,
268  $ ldb )
269  CALL stfsm( transr, 'L', uplo, 'N', 'N', n, nrhs, one, a, b,
270  $ ldb )
271  END IF
272 *
273  RETURN
274 *
275 * End of SPFTRS
276 *
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
subroutine stfsm(TRANSR, SIDE, UPLO, TRANS, DIAG, M, N, ALPHA, A, B, LDB)
STFSM solves a matrix equation (one operand is a triangular matrix in RFP format).
Definition: stfsm.f:277
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