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|newpage| Changing the shape of a matrix and/or the order of coefficients =============================================================================== Sorting a whole matrix ------------------------------------------------------------------------------- .. method:: mat.Sorted(SortOrder=0, SortCriterion=1) Returns a sorted version of the matrix, sorted according to SortOrder and SortCriterion. .. code-block:: pycon >>> from xlcalcnet import * >>> ctx = mp14.drf() >>> A = ctx.read_from_sqlite(mp14.dbpath(), "DecTableA6x4", ""); A.show("A") A: 11, 12, 13, 14, 21, 22, 23, 24, 31, 32, 33, 34, 41, 42, 43, 44, 51, 52, 53, 54, 61, 62, 63, 64, >>> # returns a copy of the whole matrix in ascending order (SortOrder=0) >>> B = A.sorted(SortOrder=0); B.show("B") B: 11, 23, 41, 53, 12, 24, 42, 54, 13, 31, 43, 61, 14, 32, 44, 62, 21, 33, 51, 63, 22, 34, 52, 64, >>> # sorts the whole matrix in descending order (SortOrder=1) >>> C = A.sorted(SortOrder=1); C.show("C") C: 64, 52, 34, 22, 63, 51, 33, 21, 62, 44, 32, 14, 61, 43, 31, 13, 54, 42, 24, 12, 53, 41, 23, 11, Sorting the rows of a matrix by a given column ------------------------------------------------------------------------------- .. method:: mat.SortedRowsByCol(ColumnToSortBy=0, SortOrder=0, SortCriterion=1) Returns a sorted version of the matrix, sorted by column ColumnToSortBy, according to SortOrder and SortCriterion. .. code-block:: pycon >>> from xlcalcnet import * >>> ctx = mp14.drf() >>> A = ctx.read_from_sqlite(mp14.dbpath(), "DecTableA6x4", ""); A.show("A") A: 11, 12, 13, 14, 21, 22, 23, 24, 31, 32, 33, 34, 41, 42, 43, 44, 51, 52, 53, 54, 61, 62, 63, 64, >>> # sorts the whole matrix by column 0 in descending order (SortOrder=1) >>> B = A.sorted_rows_by_col(ColumnToSortBy=0, SortOrder=1); B.show("B") B: 61, 62, 63, 64, 51, 52, 53, 54, 41, 42, 43, 44, 31, 32, 33, 34, 21, 22, 23, 24, 11, 12, 13, 14, >>> # sorts the whole matrix in descending order (SortOrder=0) >>> C = A.sorted_rows_by_col(ColumnToSortBy=0, SortOrder=0); C.show("C") C: 11, 12, 13, 14, 21, 22, 23, 24, 31, 32, 33, 34, 41, 42, 43, 44, 51, 52, 53, 54, 61, 62, 63, 64, Sorting a whole matrix in place ------------------------------------------------------------------------------- .. method:: mat.SortInplace(SortOrder=0, SortCriterion=1) Sorts the matrix inplace, sorting according to SortOrder and SortCriterion. .. code-block:: pycon >>> from xlcalcnet import * >>> ctx = mp14.drf() >>> A = ctx.read_from_sqlite(mp14.dbpath(), "DecTableA6x4", ""); A.show("A") A: 11, 12, 13, 14, 21, 22, 23, 24, 31, 32, 33, 34, 41, 42, 43, 44, 51, 52, 53, 54, 61, 62, 63, 64, >>> # sorts the whole matrix in ascending order (SortOrder=0) >>> A.sort(SortOrder=0); A.show("A") A: 11, 23, 41, 53, 12, 24, 42, 54, 13, 31, 43, 61, 14, 32, 44, 62, 21, 33, 51, 63, 22, 34, 52, 64, >>> # sorts the whole matrix in descending order (SortOrder=1) >>> A.sort(SortOrder=1); A.show("A") A: 64, 52, 34, 22, 63, 51, 33, 21, 62, 44, 32, 14, 61, 43, 31, 13, 54, 42, 24, 12, 53, 41, 23, 11, Sorting the rows of a matrix by a given column, in place ------------------------------------------------------------------------------- .. method:: mat.SortRowsByCol(ColumnToSortBy=0, SortOrder=0, SortCriterion=1) Sorts the matrix inplace, sorting according to sortmode. .. code-block:: pycon >>> from xlcalcnet import * >>> ctx = mp14.drf() >>> A = ctx.read_from_sqlite(mp14.dbpath(), "DecTableA6x4", ""); A.show("A") A: 11, 12, 13, 14, 21, 22, 23, 24, 31, 32, 33, 34, 41, 42, 43, 44, 51, 52, 53, 54, 61, 62, 63, 64, >>> # sorts the whole matrix by column 0 in descending order (SortOrder=1) >>> A.sort_rows_by_col(ColumnToSortBy=0, SortOrder=1); A.show("A") A: 61, 62, 63, 64, 51, 52, 53, 54, 41, 42, 43, 44, 31, 32, 33, 34, 21, 22, 23, 24, 11, 12, 13, 14, >>> # sorts the whole matrix in descending order (SortOrder=0) >>> A.sort(SortOrder=0); A.show("A") A: 11, 12, 13, 14, 21, 22, 23, 24, 31, 32, 33, 34, 41, 42, 43, 44, 51, 52, 53, 54, 61, 62, 63, 64, Resize a matrix ------------------------------------------------------------------------------- .. method:: mat.Resize(r, c) Resizes the matrix inplace, setting values of coefficients to zero. .. code-block:: pycon >>> from xlcalcnet import * >>> ctx = mp14.drf() >>> A = ctx.read_from_sqlite(mp14.dbpath(), "DecTableA6x4", ""); A.show("A") A: 11, 12, 13, 14, 21, 22, 23, 24, 31, 32, 33, 34, 41, 42, 43, 44, 51, 52, 53, 54, 61, 62, 63, 64, >>> # resizes the matrix to 3 rows and 2 columns, setting values of coefficients to zero. >>> A.resize(3,2); A.show("A") A: 0, 0, 0, 0, 0, 0, Conservatively resize a matrix ------------------------------------------------------------------------------- .. method:: mat.ConservativeResize(r, c) Resizes the matrix inplace, retaining values of existing coefficients. .. code-block:: pycon >>> from xlcalcnet import * >>> ctx = mp14.drf() >>> A = ctx.read_from_sqlite(mp14.dbpath(), "DecTableA6x4", ""); A.show("A") A: 11, 12, 13, 14, 21, 22, 23, 24, 31, 32, 33, 34, 41, 42, 43, 44, 51, 52, 53, 54, 61, 62, 63, 64, >>> # resizes the matrix to 3 rows and 6 columns, retaining values of existing coefficients. >>> A.conservative_resize(3,6); A.show("A") A: 11, 12, 13, 14, 0, 0, 21, 22, 23, 24, 0, 0, 31, 32, 33, 34, 0, 0, Convert vector to diagonal matrix ------------------------------------------------------------------------------- .. method:: mat.AsDiagonal() Returns the first column vector of a matrix as a diagonal matrix. .. code-block:: pycon >>> from xlcalcnet import * >>> ctx = mp14.drf() >>> # read the first column from the matrix >>> A = ctx.read_from_sqlite(mp14.dbpath(), "DecTableA6x4", "").col(0); A.show("A") A: 11, 21, 31, 41, 51, 61, >>> # resizes the matrix to 3 rows and 6 columns, retaining values of existing coefficients. >>> B = A.as_diagonal(); B.show("B") B: 11, 0, 0, 0, 0, 0, 0, 21, 0, 0, 0, 0, 0, 0, 31, 0, 0, 0, 0, 0, 0, 41, 0, 0, 0, 0, 0, 0, 51, 0, 0, 0, 0, 0, 0, 61, Adjoint of a matrix ------------------------------------------------------------------------------- .. method:: mat.Adjoint() Returns the adjoint matrix of the matrix .. code-block:: pycon >>> from xlcalcnet import * >>> # example with a real matrix >>> ctx = mp14.drf() >>> A = ctx.read_from_sqlite(mp14.dbpath(), "DecTableA6x6", ""); A.show("A") A: 11, 12, 13, 14, 15, 16, 21, 22, 23, 24, 25, 26, 31, 32, 33, 34, 35, 36, 41, 42, 43, 44, 45, 46, 51, 52, 53, 54, 55, 56, 61, 62, 63, 64, 65, 66, >>> # returns the adjoint matrix of a real matrix, i.e. the transpose >>> B = A.adjoint(); B.show("B") B: 11, 21, 31, 41, 51, 61, 12, 22, 32, 42, 52, 62, 13, 23, 33, 43, 53, 63, 14, 24, 34, 44, 54, 64, 15, 25, 35, 45, 55, 65, 16, 26, 36, 46, 56, 66, >>> # example with a complex matrix >>> ctx = mp14.dcf() >>> A = ctx.read_from_sqlite(mp14.dbpath(), "DecCplxTableA6x6", ""); A.show("A") A: 11 + 31j, 12 + 32j, 13 + 33j, 14 + 34j, 15 + 35j, 16 + 36j, 21 + 41j, 22 + 42j, 23 + 43j, 24 + 44j, 25 + 45j, 26 + 46j, 31 + 51j, 32 + 52j, 33 + 53j, 34 + 54j, 35 + 55j, 36 + 56j, 41 + 61j, 42 + 62j, 43 + 63j, 44 + 64j, 45 + 65j, 46 + 66j, 51 + 71j, 52 + 72j, 53 + 73j, 54 + 74j, 55 + 75j, 56 + 76j, 61 + 81j, 62 + 82j, 63 + 83j, 64 + 84j, 65 + 85j, 66 + 86j, >>> # returns the adjoint matrix of a complex matrix, i.e. the conjugate of the transpose >>> B = A.adjoint(); B.show("B") B: 11 + -31j, 21 + -41j, 31 + -51j, 41 + -61j, 51 + -71j, 61 + -81j, 12 + -32j, 22 + -42j, 32 + -52j, 42 + -62j, 52 + -72j, 62 + -82j, 13 + -33j, 23 + -43j, 33 + -53j, 43 + -63j, 53 + -73j, 63 + -83j, 14 + -34j, 24 + -44j, 34 + -54j, 44 + -64j, 54 + -74j, 64 + -84j, 15 + -35j, 25 + -45j, 35 + -55j, 45 + -65j, 55 + -75j, 65 + -85j, 16 + -36j, 26 + -46j, 36 + -56j, 46 + -66j, 56 + -76j, 66 + -86j, Conjugate of a matrix ------------------------------------------------------------------------------- .. method:: mat.Conjugate() Returns the conjugate matrix of matrix ?matA. .. code-block:: pycon >>> from xlcalcnet import * >>> # example with a real matrix >>> ctx = mp14.drf() >>> A = ctx.read_from_sqlite(mp14.dbpath(), "DecTableA6x6", ""); A.show("A") A: 11, 12, 13, 14, 15, 16, 21, 22, 23, 24, 25, 26, 31, 32, 33, 34, 35, 36, 41, 42, 43, 44, 45, 46, 51, 52, 53, 54, 55, 56, 61, 62, 63, 64, 65, 66, >>> # returns the conjugate matrix of a real matrix, i.e. the matrix itself >>> B = A.conjugate(); B.show("B") B: 11, 12, 13, 14, 15, 16, 21, 22, 23, 24, 25, 26, 31, 32, 33, 34, 35, 36, 41, 42, 43, 44, 45, 46, 51, 52, 53, 54, 55, 56, 61, 62, 63, 64, 65, 66, >>> # example with a complex matrix >>> ctx = mp14.dcf() >>> A = ctx.read_from_sqlite(mp14.dbpath(), "DecCplxTableA6x6", ""); A.show("A") A: 11 + 31j, 12 + 32j, 13 + 33j, 14 + 34j, 15 + 35j, 16 + 36j, 21 + 41j, 22 + 42j, 23 + 43j, 24 + 44j, 25 + 45j, 26 + 46j, 31 + 51j, 32 + 52j, 33 + 53j, 34 + 54j, 35 + 55j, 36 + 56j, 41 + 61j, 42 + 62j, 43 + 63j, 44 + 64j, 45 + 65j, 46 + 66j, 51 + 71j, 52 + 72j, 53 + 73j, 54 + 74j, 55 + 75j, 56 + 76j, 61 + 81j, 62 + 82j, 63 + 83j, 64 + 84j, 65 + 85j, 66 + 86j, >>> # returns the conjugate matrix of a complex matrix >>> B = A.conjugate(); B.show("B") B: 11 + -31j, 12 + -32j, 13 + -33j, 14 + -34j, 15 + -35j, 16 + -36j, 21 + -41j, 22 + -42j, 23 + -43j, 24 + -44j, 25 + -45j, 26 + -46j, 31 + -51j, 32 + -52j, 33 + -53j, 34 + -54j, 35 + -55j, 36 + -56j, 41 + -61j, 42 + -62j, 43 + -63j, 44 + -64j, 45 + -65j, 46 + -66j, 51 + -71j, 52 + -72j, 53 + -73j, 54 + -74j, 55 + -75j, 56 + -76j, 61 + -81j, 62 + -82j, 63 + -83j, 64 + -84j, 65 + -85j, 66 + -86j, Transpose of a matrix ------------------------------------------------------------------------------- .. method:: mat.Transpose() Returns the transposed matrix of matrix ?matA. .. code-block:: pycon >>> from xlcalcnet import * >>> ctx = mp14.drf() >>> A = ctx.read_from_sqlite(mp14.dbpath(), "DecTableA6x4", ""); A.show("A") A: 11, 12, 13, 14, 21, 22, 23, 24, 31, 32, 33, 34, 41, 42, 43, 44, 51, 52, 53, 54, 61, 62, 63, 64, >>> # returns the transpose matrix of a real matrix >>> B = A.transpose(); B.show("B") B: 11, 21, 31, 41, 51, 61, 12, 22, 32, 42, 52, 62, 13, 23, 33, 43, 53, 63, 14, 24, 34, 44, 54, 64, Full Reverse of a matrix ------------------------------------------------------------------------------- .. method:: mat.ReverseFull() Returns the full reverse of matrix ?matA. .. code-block:: pycon >>> from xlcalcnet import * >>> ctx = mp14.drf() >>> A = ctx.read_from_sqlite(mp14.dbpath(), "DecTableA6x4", ""); A.show("A") A: 11, 12, 13, 14, 21, 22, 23, 24, 31, 32, 33, 34, 41, 42, 43, 44, 51, 52, 53, 54, 61, 62, 63, 64, >>> # returns the full reverse of the matrix >>> B = A.reverse_full(); B.show("B") B: 64, 63, 62, 61, 54, 53, 52, 51, 44, 43, 42, 41, 34, 33, 32, 31, 24, 23, 22, 21, 14, 13, 12, 11, Row-wise Reverse of a matrix ------------------------------------------------------------------------------- .. method:: mat.ReverseRowwise() Returns the row-wise reverse of matrix ?matA. .. code-block:: pycon >>> from xlcalcnet import * >>> ctx = mp14.drf() >>> A = ctx.read_from_sqlite(mp14.dbpath(), "DecTableA6x4", ""); A.show("A") A: 11, 12, 13, 14, 21, 22, 23, 24, 31, 32, 33, 34, 41, 42, 43, 44, 51, 52, 53, 54, 61, 62, 63, 64, >>> # returns the row-wise reverse of the matrix >>> B = A.reverse_rowwise(); B.show("B") 14, 13, 12, 11, 24, 23, 22, 21, 34, 33, 32, 31, 44, 43, 42, 41, 54, 53, 52, 51, 64, 63, 62, 61, Column-wise Reverse of a matrix ------------------------------------------------------------------------------- .. method:: mat.ReverseColwise() Returns the column-wise reverse of matrix ?matA. .. code-block:: pycon >>> from xlcalcnet import * >>> ctx = mp14.drf() >>> A = ctx.read_from_sqlite(mp14.dbpath(), "DecTableA6x4", ""); A.show("A") A: 11, 12, 13, 14, 21, 22, 23, 24, 31, 32, 33, 34, 41, 42, 43, 44, 51, 52, 53, 54, 61, 62, 63, 64, >>> # returns the column-wise reverse of the matrix >>> B = A.reverse_colwise(); B.show("B") B: 61, 62, 63, 64, 51, 52, 53, 54, 41, 42, 43, 44, 31, 32, 33, 34, 21, 22, 23, 24, 11, 12, 13, 14, Full Replication of a matrix ------------------------------------------------------------------------------- .. method:: mat.ReplicateFull(Vertical, Horizontal) Returns a full replication of matrix ?matA. .. code-block:: pycon >>> from xlcalcnet import * >>> ctx = mp14.drf() >>> A = ctx.read_from_sqlite(mp14.dbpath(), "DecTableA6x4", ""); A.show("A") A: 11, 12, 13, 14, 21, 22, 23, 24, 31, 32, 33, 34, 41, 42, 43, 44, 51, 52, 53, 54, 61, 62, 63, 64, >>> # returns a full replication (Vertical=2, Horizontal=3) of the matrix >>> B = A.replicate_full(2, 3); B.show("B") B: 11, 12, 13, 14, 11, 12, 13, 14, 11, 12, 13, 14, 21, 22, 23, 24, 21, 22, 23, 24, 21, 22, 23, 24, 31, 32, 33, 34, 31, 32, 33, 34, 31, 32, 33, 34, 41, 42, 43, 44, 41, 42, 43, 44, 41, 42, 43, 44, 51, 52, 53, 54, 51, 52, 53, 54, 51, 52, 53, 54, 61, 62, 63, 64, 61, 62, 63, 64, 61, 62, 63, 64, 11, 12, 13, 14, 11, 12, 13, 14, 11, 12, 13, 14, 21, 22, 23, 24, 21, 22, 23, 24, 21, 22, 23, 24, 31, 32, 33, 34, 31, 32, 33, 34, 31, 32, 33, 34, 41, 42, 43, 44, 41, 42, 43, 44, 41, 42, 43, 44, 51, 52, 53, 54, 51, 52, 53, 54, 51, 52, 53, 54, 61, 62, 63, 64, 61, 62, 63, 64, 61, 62, 63, 64, Row-wise Replication of a matrix ------------------------------------------------------------------------------- .. method:: mat.ReplicateRowwise(Horizontal) Returns a row-wise replication of matrix ?matA. .. code-block:: pycon >>> from xlcalcnet import * >>> ctx = mp14.drf() >>> A = ctx.read_from_sqlite(mp14.dbpath(), "DecTableA6x4", ""); A.show("A") A: 11, 12, 13, 14, 21, 22, 23, 24, 31, 32, 33, 34, 41, 42, 43, 44, 51, 52, 53, 54, 61, 62, 63, 64, >>> # returns a row-wise replication (Horizontal=4) of the matrix >>> B = A.replicate_rowwise(4); B.show("B") B: 11, 12, 13, 14, 11, 12, 13, 14, 11, 12, 13, 14, 11, 12, 13, 14, 21, 22, 23, 24, 21, 22, 23, 24, 21, 22, 23, 24, 21, 22, 23, 24, 31, 32, 33, 34, 31, 32, 33, 34, 31, 32, 33, 34, 31, 32, 33, 34, 41, 42, 43, 44, 41, 42, 43, 44, 41, 42, 43, 44, 41, 42, 43, 44, 51, 52, 53, 54, 51, 52, 53, 54, 51, 52, 53, 54, 51, 52, 53, 54, 61, 62, 63, 64, 61, 62, 63, 64, 61, 62, 63, 64, 61, 62, 63, 64, Column-wise Replication of a matrix ------------------------------------------------------------------------------- .. method:: mat.ReplicateColwise(Vertical) Returns a column-wise replication of matrix ?matA. .. code-block:: pycon >>> from xlcalcnet import * >>> ctx = mp14.drf() >>> A = ctx.read_from_sqlite(mp14.dbpath(), "DecTableA6x4", ""); A.show("A") A: 11, 12, 13, 14, 21, 22, 23, 24, 31, 32, 33, 34, 41, 42, 43, 44, 51, 52, 53, 54, 61, 62, 63, 64, >>> # returns a column-wise replication (Vertical=2) of the matrix >>> B = A.replicate_colwise(2); B.show("B") B: 11, 12, 13, 14, 21, 22, 23, 24, 31, 32, 33, 34, 41, 42, 43, 44, 51, 52, 53, 54, 61, 62, 63, 64, 11, 12, 13, 14, 21, 22, 23, 24, 31, 32, 33, 34, 41, 42, 43, 44, 51, 52, 53, 54, 61, 62, 63, 64, Horizontal concatenation of two matrices ------------------------------------------------------------------------------- .. method:: mat.ConcatHorizontal(matB) Returns the horizontal concatenation of matrix ?matA with matrix matB. .. code-block:: pycon >>> from xlcalcnet import * >>> ctx = mp14.drf() >>> A = ctx.read_from_sqlite(mp14.dbpath(), "DecTableA6x6", ""); A.show("A") A: 11, 12, 13, 14, 15, 16, 21, 22, 23, 24, 25, 26, 31, 32, 33, 34, 35, 36, 41, 42, 43, 44, 45, 46, 51, 52, 53, 54, 55, 56, 61, 62, 63, 64, 65, 66, >>> B = ctx.read_from_sqlite(mp14.dbpath(), "DecTableB6x6", ""); B.show("B") B: 911, 912, 913, 914, 915, 916, 921, 922, 923, 924, 925, 926, 931, 932, 933, 934, 935, 936, 941, 942, 943, 944, 945, 946, 951, 952, 953, 954, 955, 956, 961, 962, 963, 964, 965, 966, >>> # returns a column-wise replication (Vertical=2) of the matrix >>> C = A.concat_horizontal(B); C.show("C") C: 11, 12, 13, 14, 15, 16, 911, 912, 913, 914, 915, 916, 21, 22, 23, 24, 25, 26, 921, 922, 923, 924, 925, 926, 31, 32, 33, 34, 35, 36, 931, 932, 933, 934, 935, 936, 41, 42, 43, 44, 45, 46, 941, 942, 943, 944, 945, 946, 51, 52, 53, 54, 55, 56, 951, 952, 953, 954, 955, 956, 61, 62, 63, 64, 65, 66, 961, 962, 963, 964, 965, 966, Vertical concatenation of two matrices ------------------------------------------------------------------------------- .. method:: mat.ConcatVertical(matB) Returns the vertical concatenation of matrix ?matA with matrix matB. .. code-block:: pycon >>> from xlcalcnet import * >>> ctx = mp14.drf() >>> A = ctx.read_from_sqlite(mp14.dbpath(), "DecTableA6x6", ""); A.show("A") A: 11, 12, 13, 14, 15, 16, 21, 22, 23, 24, 25, 26, 31, 32, 33, 34, 35, 36, 41, 42, 43, 44, 45, 46, 51, 52, 53, 54, 55, 56, 61, 62, 63, 64, 65, 66, >>> B = ctx.read_from_sqlite(mp14.dbpath(), "DecTableB6x6", ""); B.show("B") B: 911, 912, 913, 914, 915, 916, 921, 922, 923, 924, 925, 926, 931, 932, 933, 934, 935, 936, 941, 942, 943, 944, 945, 946, 951, 952, 953, 954, 955, 956, 961, 962, 963, 964, 965, 966, >>> # returns a column-wise replication (Vertical=2) of the matrix >>> C = A.concat_vertical(B); C.show("C") C: 11, 12, 13, 14, 15, 16, 21, 22, 23, 24, 25, 26, 31, 32, 33, 34, 35, 36, 41, 42, 43, 44, 45, 46, 51, 52, 53, 54, 55, 56, 61, 62, 63, 64, 65, 66, 911, 912, 913, 914, 915, 916, 921, 922, 923, 924, 925, 926, 931, 932, 933, 934, 935, 936, 941, 942, 943, 944, 945, 946, 951, 952, 953, 954, 955, 956, 961, 962, 963, 964, 965, 966,