Provided by: liblapack-doc_3.12.0-3build1.1_all bug

NAME

       lanhf - lan{hf,sf}: Hermitian/symmetric matrix, RFP

SYNOPSIS

   Functions
       real function clanhf (norm, transr, uplo, n, a, work)
           CLANHF returns the value of the 1-norm, or the Frobenius norm, or the infinity norm,
           or the element of largest absolute value of a Hermitian matrix in RFP format.
       double precision function dlansf (norm, transr, uplo, n, a, work)
           DLANSF returns the value of the 1-norm, or the Frobenius norm, or the infinity norm,
           or the element of largest absolute value of a symmetric matrix in RFP format.
       real function slansf (norm, transr, uplo, n, a, work)
           SLANSF
       double precision function zlanhf (norm, transr, uplo, n, a, work)
           ZLANHF returns the value of the 1-norm, or the Frobenius norm, or the infinity norm,
           or the element of largest absolute value of a Hermitian matrix in RFP format.

Detailed Description

Function Documentation

   real function clanhf (character norm, character transr, character uplo, integer n, complex,
       dimension( 0: * ) a, real, dimension( 0: * ) work)
       CLANHF returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or
       the element of largest absolute value of a Hermitian matrix in RFP format.

       Purpose:

            CLANHF  returns the value of the one norm,  or the Frobenius norm, or
            the  infinity norm,  or the  element of  largest absolute value  of a
            complex Hermitian matrix A in RFP format.

       Returns
           CLANHF

               CLANHF = ( max(abs(A(i,j))), NORM = 'M' or 'm'
                        (
                        ( norm1(A),         NORM = '1', 'O' or 'o'
                        (
                        ( normI(A),         NORM = 'I' or 'i'
                        (
                        ( normF(A),         NORM = 'F', 'f', 'E' or 'e'

            where  norm1  denotes the  one norm of a matrix (maximum column sum),
            normI  denotes the  infinity norm  of a matrix  (maximum row sum) and
            normF  denotes the  Frobenius norm of a matrix (square root of sum of
            squares).  Note that  max(abs(A(i,j)))  is not a  matrix norm.

       Parameters
           NORM

                     NORM is CHARACTER
                       Specifies the value to be returned in CLANHF as described
                       above.

           TRANSR

                     TRANSR is CHARACTER
                       Specifies whether the RFP format of A is normal or
                       conjugate-transposed format.
                       = 'N':  RFP format is Normal
                       = 'C':  RFP format is Conjugate-transposed

           UPLO

                     UPLO is CHARACTER
                       On entry, UPLO specifies whether the RFP matrix A came from
                       an upper or lower triangular matrix as follows:

                       UPLO = 'U' or 'u' RFP A came from an upper triangular
                       matrix

                       UPLO = 'L' or 'l' RFP A came from a  lower triangular
                       matrix

           N

                     N is INTEGER
                       The order of the matrix A.  N >= 0.  When N = 0, CLANHF is
                       set to zero.

           A

                     A is COMPLEX array, dimension ( N*(N+1)/2 );
                       On entry, the matrix A in RFP Format.
                       RFP Format is described by TRANSR, UPLO and N as follows:
                       If TRANSR='N' then RFP A is (0:N,0:K-1) when N is even;
                       K=N/2. RFP A is (0:N-1,0:K) when N is odd; K=N/2. If
                       TRANSR = 'C' then RFP is the Conjugate-transpose of RFP A
                       as defined when TRANSR = 'N'. The contents of RFP A are
                       defined by UPLO as follows: If UPLO = 'U' the RFP A
                       contains the ( N*(N+1)/2 ) elements of upper packed A
                       either in normal or conjugate-transpose Format. If
                       UPLO = 'L' the RFP A contains the ( N*(N+1) /2 ) elements
                       of lower packed A either in normal or conjugate-transpose
                       Format. The LDA of RFP A is (N+1)/2 when TRANSR = 'C'. When
                       TRANSR is 'N' the LDA is N+1 when N is even and is N when
                       is odd. See the Note below for more details.
                       Unchanged on exit.

           WORK

                     WORK is REAL array, dimension (LWORK),
                       where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise,
                       WORK is not referenced.

       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

   double precision function dlansf (character norm, character transr, character uplo, integer n,
       double precision, dimension( 0: * ) a, double precision, dimension( 0: * ) work)
       DLANSF returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or
       the element of largest absolute value of a symmetric matrix in RFP format.

       Purpose:

            DLANSF returns the value of the one norm, or the Frobenius norm, or
            the infinity norm, or the element of largest absolute value of a
            real symmetric matrix A in RFP format.

       Returns
           DLANSF

               DLANSF = ( max(abs(A(i,j))), NORM = 'M' or 'm'
                        (
                        ( norm1(A),         NORM = '1', 'O' or 'o'
                        (
                        ( normI(A),         NORM = 'I' or 'i'
                        (
                        ( normF(A),         NORM = 'F', 'f', 'E' or 'e'

            where  norm1  denotes the  one norm of a matrix (maximum column sum),
            normI  denotes the  infinity norm  of a matrix  (maximum row sum) and
            normF  denotes the  Frobenius norm of a matrix (square root of sum of
            squares).  Note that  max(abs(A(i,j)))  is not a  matrix norm.

       Parameters
           NORM

                     NORM is CHARACTER*1
                     Specifies the value to be returned in DLANSF as described
                     above.

           TRANSR

                     TRANSR is CHARACTER*1
                     Specifies whether the RFP format of A is normal or
                     transposed format.
                     = 'N':  RFP format is Normal;
                     = 'T':  RFP format is Transpose.

           UPLO

                     UPLO is CHARACTER*1
                      On entry, UPLO specifies whether the RFP matrix A came from
                      an upper or lower triangular matrix as follows:
                      = 'U': RFP A came from an upper triangular matrix;
                      = 'L': RFP A came from a lower triangular matrix.

           N

                     N is INTEGER
                     The order of the matrix A. N >= 0. When N = 0, DLANSF is
                     set to zero.

           A

                     A is DOUBLE PRECISION array, dimension ( N*(N+1)/2 );
                     On entry, the upper (if UPLO = 'U') or lower (if UPLO = 'L')
                     part of the symmetric matrix A stored in RFP format. See the
                     'Notes' below for more details.
                     Unchanged on exit.

           WORK

                     WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)),
                     where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise,
                     WORK is not referenced.

       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

   real function slansf (character norm, character transr, character uplo, integer n, real,
       dimension( 0: * ) a, real, dimension( 0: * ) work)
       SLANSF

       Purpose:

            SLANSF returns the value of the one norm, or the Frobenius norm, or
            the infinity norm, or the element of largest absolute value of a
            real symmetric matrix A in RFP format.

       Returns
           SLANSF

               SLANSF = ( max(abs(A(i,j))), NORM = 'M' or 'm'
                        (
                        ( norm1(A),         NORM = '1', 'O' or 'o'
                        (
                        ( normI(A),         NORM = 'I' or 'i'
                        (
                        ( normF(A),         NORM = 'F', 'f', 'E' or 'e'

            where  norm1  denotes the  one norm of a matrix (maximum column sum),
            normI  denotes the  infinity norm  of a matrix  (maximum row sum) and
            normF  denotes the  Frobenius norm of a matrix (square root of sum of
            squares).  Note that  max(abs(A(i,j)))  is not a  matrix norm.

       Parameters
           NORM

                     NORM is CHARACTER*1
                     Specifies the value to be returned in SLANSF as described
                     above.

           TRANSR

                     TRANSR is CHARACTER*1
                     Specifies whether the RFP format of A is normal or
                     transposed format.
                     = 'N':  RFP format is Normal;
                     = 'T':  RFP format is Transpose.

           UPLO

                     UPLO is CHARACTER*1
                      On entry, UPLO specifies whether the RFP matrix A came from
                      an upper or lower triangular matrix as follows:
                      = 'U': RFP A came from an upper triangular matrix;
                      = 'L': RFP A came from a lower triangular matrix.

           N

                     N is INTEGER
                     The order of the matrix A. N >= 0. When N = 0, SLANSF is
                     set to zero.

           A

                     A is REAL array, dimension ( N*(N+1)/2 );
                     On entry, the upper (if UPLO = 'U') or lower (if UPLO = 'L')
                     part of the symmetric matrix A stored in RFP format. See the
                     'Notes' below for more details.
                     Unchanged on exit.

           WORK

                     WORK is REAL array, dimension (MAX(1,LWORK)),
                     where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise,
                     WORK is not referenced.

       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

   double precision function zlanhf (character norm, character transr, character uplo, integer n,
       complex*16, dimension( 0: * ) a, double precision, dimension( 0: * ) work)
       ZLANHF returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or
       the element of largest absolute value of a Hermitian matrix in RFP format.

       Purpose:

            ZLANHF  returns the value of the one norm,  or the Frobenius norm, or
            the  infinity norm,  or the  element of  largest absolute value  of a
            complex Hermitian matrix A in RFP format.

       Returns
           ZLANHF

               ZLANHF = ( max(abs(A(i,j))), NORM = 'M' or 'm'
                        (
                        ( norm1(A),         NORM = '1', 'O' or 'o'
                        (
                        ( normI(A),         NORM = 'I' or 'i'
                        (
                        ( normF(A),         NORM = 'F', 'f', 'E' or 'e'

            where  norm1  denotes the  one norm of a matrix (maximum column sum),
            normI  denotes the  infinity norm  of a matrix  (maximum row sum) and
            normF  denotes the  Frobenius norm of a matrix (square root of sum of
            squares).  Note that  max(abs(A(i,j)))  is not a  matrix norm.

       Parameters
           NORM

                     NORM is CHARACTER
                       Specifies the value to be returned in ZLANHF as described
                       above.

           TRANSR

                     TRANSR is CHARACTER
                       Specifies whether the RFP format of A is normal or
                       conjugate-transposed format.
                       = 'N':  RFP format is Normal
                       = 'C':  RFP format is Conjugate-transposed

           UPLO

                     UPLO is CHARACTER
                       On entry, UPLO specifies whether the RFP matrix A came from
                       an upper or lower triangular matrix as follows:

                       UPLO = 'U' or 'u' RFP A came from an upper triangular
                       matrix

                       UPLO = 'L' or 'l' RFP A came from a  lower triangular
                       matrix

           N

                     N is INTEGER
                       The order of the matrix A.  N >= 0.  When N = 0, ZLANHF is
                       set to zero.

           A

                     A is COMPLEX*16 array, dimension ( N*(N+1)/2 );
                       On entry, the matrix A in RFP Format.
                       RFP Format is described by TRANSR, UPLO and N as follows:
                       If TRANSR='N' then RFP A is (0:N,0:K-1) when N is even;
                       K=N/2. RFP A is (0:N-1,0:K) when N is odd; K=N/2. If
                       TRANSR = 'C' then RFP is the Conjugate-transpose of RFP A
                       as defined when TRANSR = 'N'. The contents of RFP A are
                       defined by UPLO as follows: If UPLO = 'U' the RFP A
                       contains the ( N*(N+1)/2 ) elements of upper packed A
                       either in normal or conjugate-transpose Format. If
                       UPLO = 'L' the RFP A contains the ( N*(N+1) /2 ) elements
                       of lower packed A either in normal or conjugate-transpose
                       Format. The LDA of RFP A is (N+1)/2 when TRANSR = 'C'. When
                       TRANSR is 'N' the LDA is N+1 when N is even and is N when
                       is odd. See the Note below for more details.
                       Unchanged on exit.

           WORK

                     WORK is DOUBLE PRECISION array, dimension (LWORK),
                       where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise,
                       WORK is not referenced.

       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

Author

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