Changing the shape of a matrix and/or the order of coefficients

Sorting a whole matrix

mat.Sorted(SortOrder=0, SortCriterion=1)

Returns a sorted version of the matrix, sorted according to SortOrder and SortCriterion.

>>> 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

mat.SortedRowsByCol(ColumnToSortBy=0, SortOrder=0, SortCriterion=1)

Returns a sorted version of the matrix, sorted by column ColumnToSortBy, according to SortOrder and SortCriterion.

>>> 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

mat.SortInplace(SortOrder=0, SortCriterion=1)

Sorts the matrix inplace, sorting according to SortOrder and SortCriterion.

>>> 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

mat.SortRowsByCol(ColumnToSortBy=0, SortOrder=0, SortCriterion=1)

Sorts the matrix inplace, sorting according to sortmode.

>>> 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

mat.Resize(r, c)

Resizes the matrix inplace, setting values of coefficients to zero.

>>> 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

mat.ConservativeResize(r, c)

Resizes the matrix inplace, retaining values of existing coefficients.

>>> 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

mat.AsDiagonal()

Returns the first column vector of a matrix as a diagonal matrix.

>>> 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

mat.Adjoint()

Returns the adjoint matrix of the matrix

>>> 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

mat.Conjugate()

Returns the conjugate matrix of matrix ?matA.

>>> 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

mat.Transpose()

Returns the transposed matrix of matrix ?matA.

>>> 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

mat.ReverseFull()

Returns the full reverse of matrix ?matA.

>>> 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

mat.ReverseRowwise()

Returns the row-wise reverse of matrix ?matA.

>>> 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

mat.ReverseColwise()

Returns the column-wise reverse of matrix ?matA.

>>> 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

mat.ReplicateFull(Vertical, Horizontal)

Returns a full replication of matrix ?matA.

>>> 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

mat.ReplicateRowwise(Horizontal)

Returns a row-wise replication of matrix ?matA.

>>> 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

mat.ReplicateColwise(Vertical)

Returns a column-wise replication of matrix ?matA.

>>> 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

mat.ConcatHorizontal(matB)

Returns the horizontal concatenation of matrix ?matA with matrix matB.

>>> 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

mat.ConcatVertical(matB)

Returns the vertical concatenation of matrix ?matA with matrix matB.

>>> 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,