PrecisionCalc
xl
Precision
Get Your Numbers Right

 

xlpMMULT

Returns the matrix product of two arrays, with up to 32,767 significant digits of precision. Same as Excel's built-in MMULT function, but with high precision.

A matrix product is in the form of an array, with the same number of rows as the first input array and the same number of columns as the 2nd input array.

xlpMMULT must be array-entered. To array-enter an xlpMMULT formula, follow these steps:

  1. Select the cells in which you want the xlpMMULT formula.
  2. With the cells selected, type the formula in the first (top or left) of the selected cells.
  3. With the cells still selected, press and hold down the CTRL and SHIFT keys.
  4. With the cells still selected, and with the CTRL and SHIFT keys still held down, press Enter.
  5. You should see the xlpMMULT results in the selected cells.

 

Syntax

xlpMMULT(array_rows,array_cols,format_negative,format_thousands,format_currency,exponential_notation,
                  maximum_significant_digits,format_decimal_place)

array_rows Required. The array of rows to be multiplied by the array of columns.

The numbers in the array's cells can be numbers, or text formatted as numbers. Any number of significant digits can be accepted.

array_cols Required. The array of columns to be multiplied by the array of rows.

The numbers in the array's cells can be numbers, or text formatted as numbers. Any number of significant digits can be accepted.

format_negative Optional. Determines whether negatives are formatted with a leading hyphen ("-"), or parentheses ("()"). Set to 1 to format negatives with a leading hyphen. Set to 2 for parentheses. 1 by default.

You can also format negatives with a red font.

format_thousands Optional. Determines whether thousands separators are included. Set to TRUE to include thousands separators. FALSE by default.
format_currency Optional. Determines whether currency symbol is included. Set to TRUE to include currency symbol. The currency symbol will be added either to the beginning or to the end of the result, whichever is appropriate for the locale. FALSE by default.
exponential_notation Optional. Determines whether result is formatted in exponential notation. Set to TRUE to format in exponential notation. FALSE by default.
maximum_significant_digits Optional. Determines the maximum number of significant digits to be returned. Default is 100, or the user's custom maximum set in the About box, or the maximum number allowed by the edition of xlPrecision, whichever is less.
format_decimal_place Optional. Determines whether to add or remove decimal places as required to return the exact specified number of decimal places.

When format_decimal_place causes decimal places to be removed, the remaining decimals are rounded, exactly as Excel's number formatting does.

Set format_decimal_place to the number of decimal places desired. For example, set to 3 to specify that the result should have exactly 3 decimal places, so that:

  • "123.4" is formatted as "123.400"
  • "12.3456" is formatted as "12.346"
  • "9.9999" is formatted as "10.000"


Use the Insert Function Dialog to easily enter these arguments:
(available on most editions of xlPrecision, but not recommended with the Free Edition as it causes the Free Edition dialog to appear multiple times)

   

  


Examples

Formula Description Result
=xlpMMULT(A1:C2,A4:B6)
(array-entered in A8:B9)
 
  A B C
1 1 2 3
2 4 5 6
3      
4 7 10  
5 8 11  
6 9 12  
Matrix product of arrays of rows in cells A1:B2 and columns in cells A4:B6:

Cell A8:  (1 x 7) + (2 x 8) + (3 x 9)

Cell B8:  (1 x 10) + (2 x 11) + (3 x 12)

Cell A9:  (4 x 7) + (5 x 8) + (6 x 9)

Cell B9:  (4 x 10) + (5 x 11) + (6 x 12)

Return area has:
  • 2 rows because array_rows has 2 rows, and:
  • 2 columns because array_cols has 2 columns.
  A B
8 50 68
9 122 167
=xlpMMULT(A1:C2,A4:D6)
(array-entered in A8:D9)
 
  A B C D
1 1 2 3  
2 4 5 6  
3        
4 7 10 13 16
5 8 11 14 17
6 9 12 15 18
Matrix product of arrays of rows in cells A1:C2 and columns in cells A4:D6:

Cell A8:  (1 x 7) + (2 x 8) + (3 x 9)

Cell B8:  (1 x 10) + (2 x 11) + (3 x 12)

Cell C8:  (1 x 13) + (2 x 14) + (3 x 15)

Cell D8:  (1 x 16) + (2 x 17) + (3 x 18)

Cell A9:  (4 x 7) + (5 x 8) + (6 x 9)

Cell B9:  (4 x 10) + (5 x 11) + (6 x 12)

Cell C9:  (4 x 13) + (5 x 14) + (6 x 15)

Cell D9:  (4 x 16) + (5 x 17) + (6 x 18)

Return area has:
  • 2 rows because array_rows has 2 rows, and:
  • 4 columns because array_cols has 4 columns.
  A B C D
8 50 68 86 104
9 122 167 212 257
=xlpMMULT(A1:C4,A6:B9)
(array-entered in A11:B14)
 
  A B C
1 1 2 3
2 4 5 6
3 7 8 9
4 10 11 12
5      
6 13 16  
7 14 17  
9 15 18  
Matrix product of arrays of rows in cells A1:C4 and columns in cells A6:B9:

Cell A11:  (1 x 13) + (2 x 14) + (3 x 15)

Cell B11:  (1 x 16) + (2 x 17) + (3 x 18)

Cell A12:  (4 x 13) + (5 x 14) + (6 x 15)

Cell B12:  (4 x 16) + (5 x 17) + (6 x 18)

Cell A13:  (7 x 13) + (8 x 14) + (9 x 15)

Cell B13:  (7 x 16) + (8 x 17) + (9 x 18)

Cell A14:  (10 x 13) + (11 x 14) + (12 x 15)

Cell B14:  (10 x 16) + (11 x 17) + (12 x 18)

Return area has:
  • 4 rows because array_rows has 4 rows, and:
  • 2 columns because array_cols has 2 columns.
  A B
11 86 104
12 212 257
13 338 410
14 464 563
=xlpMMULT(A1:C2,A4:B6)
(array-entered in A8:B9)
 
  A B C
1 111111111.1 2 3
2 4 5 6
3      
4 777777777.7 10  
5 8 11  
6 9 12  
Matrix product of arrays of rows in cells A1:B2 and columns in cells A4:B6:

Cell A8:
(111111111.1 x 777777777.7)
+ (2 x 8) + (3 x 9)

Cell B8:
(111111111.1 x 10) + (2 x 11) + (3 x 12)

Cell A9:
(4 x 777777777.7) + (5 x 8) + (6 x 9)

Cell B9:
(4 x 10) + (5 x 11) + (6 x 12)

Cell A8 has 19 significant digits. Excel's built-in MMULT function returns 86419753069135900 (not even rounded correctly).
 
  A B
8 8641975306
9135845.47
11111
11169
9 311111
1204.8
167
=xlpMMULT(A1:C2,A4:B6,2)
(array-entered in A8:B9)
 
  A B C
1 -1 -2 -3
2 -4 -5 -6
3      
4 7 10  
5 8 11  
6 9 12  
Negative numbers formatted with parentheses.
 

 

  A B
8 (50) (68)
9 (122) (167)
=xlpMMULT(A1:C2,A4:B6,,TRUE)
(array-entered in A8:B9)
 
  A B C
1 111111111.1 2 3
2 4 5 6
3      
4 777777777.7 10  
5 8 11  
6 9 12  
Formatted with localized thousands separators.

Decimal separators are also localized.

In the USA:
 
  A B
8 86,419,
753,069,
135,845.47
1,111,
111,169
9 3,111,
111,204.8
167

In Germany:

  A B
8 86.419.
753.069.
135.845,47
1.111.
111.169
9 3.111.
111.204,8
167

In France:

  A B
8 86 419
753 069,
135 845,47
1 111
111 169
9 3 111
111 204,8
167
=xlpMMULT(A1:C2,A4:B6,,,TRUE)
(array-entered in A8:B9)
 
  A B C
1 1 2 3
2 4 5 6
3      
4 7 10  
5 8 11  
6 9 12  
Formatted with the local currency symbol.

 

In the USA:

  A B
8 $50 $68
9 $122 $167

In Germany:

  A B
8 50 68
9 122 167

In Estonia:

  A B
8 50 kr 68 kr
9 122 kr 167 kr

In Albania:

  A B
8 50Lek 68Lek
9 122Lek 167Lek
=xlpMMULT(A1:C2,A4:B6,,,,TRUE)
(array-entered in A8:B9)
 
  A B C
1 11 22 33
2 44 55 66
3      
4 7 10  
5 8 11  
6 9 12  
Formatted in exponential notation.
 

 

 

  A B
8 5.5E+2 7.48E+2
9 1.342E+3 1.837E+3
=xlpMMULT(A1:C2,A4:B6,,,,,500)
=xlpMMULT(A1:C2,A4:B6,,,,,500000)
=xlpMMULT(A1:C2,A4:B6,,,,,A3)
Each number in the array is returned with up to 500 (or up to 500,000, or up to the number in A3) significant digits of precision.
=xlpMMULT(A1:C2,A4:B6,,,,,,2)
(array-entered in A8:B9)
 
  A B C
1 1.234 2.345 3.456
2 4 5 6
3      
4 7 10  
5 8 11  
6 9 12  
Formatted to 2 decimal places.

In cell A8, 58.50 is rounded (to the nearest) from 58.502.

In cell B8, 79.61 is rounded (to the nearest) from 79.607.

In cells A9 & B9, 122.00 & 167.00 are padded with zeros to two decimal places.

 
  A B
8 58.50_ 79.61_
9 122.00_ 167.00_


Remarks

 

See Also

xlpMDETERM
 

 

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