Provided by: liblapack-doc-man_3.6.0-2ubuntu2_all bug

NAME

       zpftrs.f -

SYNOPSIS

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

Function/Subroutine Documentation

   subroutine zpftrs (character TRANSR, character UPLO, integer N, integer NRHS, complex*16,
       dimension( 0: * ) A, complex*16, dimension( ldb, * ) B, integer LDB, integer INFO)
       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

Author

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