zpftrs.f(3)

NAME
zpftrs.f -

SYNOPSIS

  Functions/Subroutines

subroutine zpftrs (TRANSR, UPLO, N, NRHS, A, B, LDB, INFO)
ZPFTRS

Function/Subroutine Documentation

  subroutine zpftrs (characterTRANSR, characterUPLO, integerN, integerNRHS, complex*16, dimension( 0: * )A, complex*16, dimension( ldb, * )B, integerLDB, integerINFO)

ZPFTRS

Purpose:

     ZPFTRS 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 ZPFTRF.

Parameters:
    TRANSR

              TRANSR is CHARACTER*1
              = 'N':  The Normal TRANSR of RFP A is stored;
              = 'C':  The Conjugate-transpose TRANSR of RFP A is stored.

    UPLO

              UPLO is CHARACTER*1
              = 'U':  Upper triangle of RFP A is stored;
              = 'L':  Lower triangle of RFP A is stored.

    N

              N is INTEGER
              The order of the matrix A.  N >= 0.

    NRHS

              NRHS is INTEGER
              The number of right hand sides, i.e., the number of columns
              of the matrix B.  NRHS >= 0.

    A

              A is COMPLEX*16 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 ZPFTRF.
              See note below for more details about RFP A.

    B

              B is COMPLEX*16 array, dimension (LDB,NRHS)
              On entry, the right hand side matrix B.
              On exit, the solution matrix X.

    LDB

              LDB is INTEGER
              The leading dimension of the array B.  LDB >= max(1,N).

    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:
    November 2011

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 221 of file zpftrs.f.

Author

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