The Annotated M[UMPS] Standards

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$%MTXADD^MATH

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Matrices, Rows and Columns

In a language like "C", and array can be initialized as {0, 1, 2, 3, 4, 5, 6, ..., 119}, and then passed to a procedure, where its dimensions could be defined to be any one of:

one_dimensional [120];
two_dimensional_1 [10] [12];
two_dimensional_2 [12] [10];
three_dimensional_1 [5] [4] [6];
three_dimensional_2 [6] [5] [4];
three_dimensional_3 [4] [5] [6];
five_dimensional [2] [2] [2] [3] [5];

and many other possibilities.

In its rendition as "two_dimensional_1", the array would look like:

a [0,0] =0	a [0,1] =1	a [0,2] =2	a [0,3] =3	a [0,4] =4	a [0,5] =5	a [0,6] =6	a [0,7] =7	a [0,8] =8	a [0,9] =9	a [0,10] =10	a [0,11] =11
a [1,0] =12	a [1,1] =13	a [1,2] =14	a [1,3] =15	a [1,4] =16	a [1,5] =17	a [1,6] =18	a [1,7] =19	a [1,8] =20	a [1,9] =21	a [1,10] =22	a [1,11] =23
a [2,0] =24	a [2,1] =25	a [2,2] =26	a [2,3] =27	a [2,4] =28	a [2,5] =29	a [2,6] =30	a [2,7] =31	a [2,8] =32	a [2,9] =33	a [2,10] =34	a [2,11] =35
a [3,0] =36	a [3,1] =37	a [3,2] =38	a [3,3] =39	a [3,4] =40	a [3,5] =41	a [3,6] =42	a [3,7] =43	a [3,8] =44	a [3,9] =45	a [3,10] =46	a [3,11] =47
a [4,0] =48	a [4,1] =49	a [4,2] =50	a [4,3] =51	a [4,4] =52	a [4,5] =53	a [4,6] =54	a [4,7] =55	a [4,8] =56	a [4,9] =57	a [4,10] =58	a [4,11] =59
a [5,0] =60	a [5,1] =61	a [5,2] =62	a [5,3] =63	a [5,4] =64	a [5,5] =65	a [5,6] =66	a [5,7] =67	a [5,8] =68	a [5,9] =69	a [5,10] =70	a [5,11] =71
a [6,0] =72	a [6,1] =73	a [6,2] =74	a [6,3] =75	a [6,4] =76	a [6,5] =77	a [6,6] =78	a [6,7] =79	a [6,8] =80	a [6,9] =81	a [6,10] =82	a [6,11] =83
a [7,0] =84	a [7,1] =85	a [7,2] =86	a [7,3] =87	a [7,4] =88	a [7,5] =89	a [7,6] =90	a [7,7] =91	a [7,8] =92	a [7,9] =93	a [7,10] =94	a [7,11] =95
a [8,0] =96	a [8,1] =97	a [8,2] =98	a [8,3] =99	a [8,4] =100	a [8,5] =101	a [8,6] =102	a [8,7] =103	a [8,8] =104	a [8,9] =105	a [8,10] =106	a [8,11] =107
a [9,0] =108	a [9,1] =109	a [9,2] =110	a [9,3] =111	a [9,4] =112	a [9,5] =113	a [9,6] =114	a [9,7] =115	a [9,8] =116	a [9,9] =117	a [9,10] =118	a [9,11] =119

In its rendition as "two_dimensional_1", the array would look like:

a [0,0] =0	a [0,1] =1	a [0,2] =2	a [0,3] =3	a [0,4] =4	a [0,5] =5	a [0,6] =6	a [0,7] =7	a [0,8] =8	a [0,9] =9
a [1,0] =10	a [1,1] =11	a [1,2] =12	a [1,3] =13	a [1,4] =14	a [1,5] =15	a [1,6] =16	a [1,7] =17	a [1,8] =18	a [1,9] =19
a [2,0] =20	a [2,1] =21	a [2,2] =22	a [2,3] =23	a [2,4] =24	a [2,5] =25	a [2,6] =26	a [2,7] =27	a [2,8] =28	a [2,9] =29
a [3,0] =30	a [3,1] =31	a [3,2] =32	a [3,3] =33	a [3,4] =34	a [3,5] =35	a [3,6] =36	a [3,7] =37	a [3,8] =38	a [3,9] =39
a [4,0] =40	a [4,1] =41	a [4,2] =42	a [4,3] =43	a [4,4] =44	a [4,5] =45	a [4,6] =46	a [4,7] =47	a [4,8] =48	a [4,9] =49
a [5,0] =50	a [5,1] =51	a [5,2] =52	a [5,3] =53	a [5,4] =54	a [5,5] =55	a [5,6] =56	a [5,7] =57	a [5,8] =58	a [5,9] =59
a [6,0] =60	a [6,1] =61	a [6,2] =62	a [6,3] =63	a [6,4] =64	a [6,5] =65	a [6,6] =66	a [6,7] =67	a [6,8] =68	a [6,9] =69
a [7,0] =70	a [7,1] =71	a [7,2] =72	a [7,3] =73	a [7,4] =74	a [7,5] =75	a [7,6] =76	a [7,7] =77	a [7,8] =78	a [7,9] =79
a [8,0] =80	a [8,1] =81	a [8,2] =82	a [8,3] =83	a [8,4] =84	a [8,5] =85	a [8,6] =86	a [8,7] =87	a [8,8] =88	a [8,9] =89
a [9,0] =90	a [9,1] =91	a [9,2] =92	a [9,3] =93	a [9,4] =94	a [9,5] =95	a [9,6] =96	a [9,7] =97	a [9,8] =98	a [9,9] =99
a [10,0] =100	a [10,1] =101	a [10,2] =102	a [10,3] =103	a [10,4] =104	a [10,5] =105	a [10,6] =106	a [10,7] =107	a [10,8] =108	a [10,9] =109
a [11,0] =110	a [11,1] =111	a [11,2] =112	a [11,3] =113	a [11,4] =114	a [11,5] =115	a [11,6] =116	a [11,7] =117	a [11,8] =118	a [11,9] =119

In a language like M[UMPS] arrays are not pre-allocated, nor is there a predefined notion that makes a specific subscript correspond to "rows" or "columns". Since it is attractive to write code like:
Set one="" For Set one=$Order(array(one)) Quit:one="" Do . Write ! . Set two="" For Set two=$Order(array(two)) Quit:two="" Do . . ; etcetera
many people will consider the first subscript in a two-dimensional array to be the "row" subscript and the second one the "column" subscript.

However, there is nothing that prohibits a programmer from creating an array with elements like:
Set A(1,1)=11,A(1,2)=12,A(1,3)=13 Set A(2,1)=21,A(2,2)=22,A(2,3)=23
and then using the data in this array in either of the following ways:
For y=1:1:2 Write ! For x=1:1:3 Write $Justify(A(y,x),6)
which would lead to:
11 12 13 21 22 23
which looks like two rows of three columns, whereas:
For x=1:1:3 Write ! For y=1:1:2 Write $Justify(A(x,y),6)
which would lead to:
11 21 12 22 13 23
which looks like three rows of two columns.

In M[UMPS] the assignment of subscripts to notions like rows and columns is up to the author of the application. However, for the purpose of the standardized functions for matrix manipulation, a choice has been pre-made to use the first subscript for rows and the second one for columns.

Be aware, though, that it is possible to define an array like:

a [0,0] =0			a [0,3] =3	a [0,4] =4		a [0,6] =6			a [0,9] =9
a [1,0] =10		a [1,2] =12	a [1,3] =13		a [1,5] =15				a [1,9] =19
a [2,0] =20	a [2,1] =21	a [2,2] =22	a [2,3] =23	a [2,4] =24	a [2,5] =25		a [2,7] =27	a [2,8] =28	a [2,9] =29
a [3,0] =30	a [3,1] =31		a [3,3] =33	a [3,4] =34	a [3,5] =35	a [3,6] =36		a [3,8] =38	a [3,9] =39
a [4,0] =40	a [4,1] =41	a [4,2] =42	a [4,3] =43	a [4,4] =44	a [4,5] =45	a [4,6] =46	a [4,7] =47	a [4,8] =48
a [5,0] =50	a [5,1] =51		a [5,3] =53	a [5,4] =54	a [5,5] =55		a [5,7] =57	a [5,8] =58	a [5,9] =59
	a [6,1] =61	a [6,2] =62	a [6,3] =63	a [6,4] =64		a [6,6] =66		a [6,8] =68	a [6,9] =69
a [7,0] =70	a [7,1] =71	a [7,2] =72	a [7,3] =73	a [7,4] =74	a [7,5] =75	a [7,6] =76	a [7,7] =77		a [7,9] =79
a [8,0] =80		a [8,2] =82	a [8,3] =83			a [8,6] =86		a [8,8] =88	a [8,9] =89
a [9,0] =90	a [9,1] =91	a [9,2] =92	a [9,3] =93		a [9,5] =95		a [9,7] =97	a [9,8] =98	a [9,9] =99

When used in a function call like:
Set X=$%MTXADD^MATH(.a,.SECOND,.RESULT,3,3)
only the part of the matrix that is highlighted below would be used.

a [0,0] =0			a [0,3] =3	a [0,4] =4		a [0,6] =6			a [0,9] =9
a [1,0] =10		a [1,2] =12	a [1,3] =13		a [1,5] =15				a [1,9] =19
a [2,0] =20	a [2,1] =21	a [2,2] =22	a [2,3] =23	a [2,4] =24	a [2,5] =25		a [2,7] =27	a [2,8] =28	a [2,9] =29
a [3,0] =30	a [3,1] =31		a [3,3] =33	a [3,4] =34	a [3,5] =35	a [3,6] =36		a [3,8] =38	a [3,9] =39
a [4,0] =40	a [4,1] =41	a [4,2] =42	a [4,3] =43	a [4,4] =44	a [4,5] =45	a [4,6] =46	a [4,7] =47	a [4,8] =48
a [5,0] =50	a [5,1] =51		a [5,3] =53	a [5,4] =54	a [5,5] =55		a [5,7] =57	a [5,8] =58	a [5,9] =59
	a [6,1] =61	a [6,2] =62	a [6,3] =63	a [6,4] =64		a [6,6] =66		a [6,8] =68	a [6,9] =69
a [7,0] =70	a [7,1] =71	a [7,2] =72	a [7,3] =73	a [7,4] =74	a [7,5] =75	a [7,6] =76	a [7,7] =77		a [7,9] =79
a [8,0] =80		a [8,2] =82	a [8,3] =83			a [8,6] =86		a [8,8] =88	a [8,9] =89
a [9,0] =90	a [9,1] =91	a [9,2] =92	a [9,3] =93		a [9,5] =95		a [9,7] =97	a [9,8] =98	a [9,9] =99

When used in a function call like:
Set X=$%MTXADD^MATH(.a,.SECOND,.RESULT,8,5)
only the part of the matrix that is highlighted below would be used.

a [0,0] =0			a [0,3] =3	a [0,4] =4		a [0,6] =6			a [0,9] =9
a [1,0] =10		a [1,2] =12	a [1,3] =13		a [1,5] =15				a [1,9] =19
a [2,0] =20	a [2,1] =21	a [2,2] =22	a [2,3] =23	a [2,4] =24	a [2,5] =25		a [2,7] =27	a [2,8] =28	a [2,9] =29
a [3,0] =30	a [3,1] =31		a [3,3] =33	a [3,4] =34	a [3,5] =35	a [3,6] =36		a [3,8] =38	a [3,9] =39
a [4,0] =40	a [4,1] =41	a [4,2] =42	a [4,3] =43	a [4,4] =44	a [4,5] =45	a [4,6] =46	a [4,7] =47	a [4,8] =48
a [5,0] =50	a [5,1] =51		a [5,3] =53	a [5,4] =54	a [5,5] =55		a [5,7] =57	a [5,8] =58	a [5,9] =59
	a [6,1] =61	a [6,2] =62	a [6,3] =63	a [6,4] =64		a [6,6] =66		a [6,8] =68	a [6,9] =69
a [7,0] =70	a [7,1] =71	a [7,2] =72	a [7,3] =73	a [7,4] =74	a [7,5] =75	a [7,6] =76	a [7,7] =77		a [7,9] =79
a [8,0] =80		a [8,2] =82	a [8,3] =83			a [8,6] =86		a [8,8] =88	a [8,9] =89
a [9,0] =90	a [9,1] =91	a [9,2] =92	a [9,3] =93		a [9,5] =95		a [9,7] =97	a [9,8] =98	a [9,9] =99

Copyright © Standard Documents; 1977-2024 MUMPS Development Committee;
Copyright © Examples: 1995-2024 Ed de Moel;
Copyright © Annotations: 2003-2008 Jacquard Systems Research
Copyright © Annotations: 2008-2024 Ed de Moel.

Some specifications are "approved for inclusion in a future standard". Note that the MUMPS Development Committee cannot guarantee that such future standards will indeed be published.

This page most recently updated on 13-Sep-2014, 17:04:44.

For comments, contact Ed de Moel (demoel@jacquardsystems.com)