L_MAGNITUDE

=L_MAGNITUDE(vector)

Required: L_COLSUM

Download the Template

In the template file, navigate to the Matrices worksheet to see the L_MAGNITUDE function in action.

Description

The MAGNITUDE of a vector is the square root of the sum of the squares of the elements. There are a number of different ways to calculate this in Excel when a is a vector:

=L_MAGNITUDE(a)
=SQRT(SUM(a*a))
=SQRT(SUM(a^2))
=SQRT(SUMPRODUCT(a,a))
=SQRT(L_DOT(a,a))
=SQRT(SUMSQ(a))

If the matrix A contains multiple columns, then L_MAGNITUDE(A) returns a row vector containing the magnitudes of the individual columns. This is similar in behavior to the vecnorm function in Matlab.

=SQRT(L_COLSUM(A^2))

Lambda Formula

This code for using L_MAGNITUDE in Excel is provided under the License as part of the LAMBDA Library, but to use just this function, you may copy the following code directly into your spreadsheet.

Name: L_MAGNITUDE
Comment: Calculates the magnitude of a vector as SQRT(SUM(x^2))
Refers To:

=LAMBDA(vector,
LET(doc,"https://www.vertex42.com/lambda/magnitude.html",
    vec,IF(AND(ROWS(vector)=1,COLUMNS(vector)>1),TRANSPOSE(vector),vector),
    IF(COLUMNS(vec)>1,
        SQRT(L_COLSUM(vec*vec)),
        SQRT(SUM(vec*vec))
    )
))

/**
* Returns the magnitude (2-norm) of a vector or the magnitude of each column of a matrix
*/
L_MAGNITUDE = LAMBDA(vector,
LET(doc,"https://www.vertex42.com/lambda/magnitude.html",
    vec,IF(AND(ROWS(vector)=1,COLUMNS(vector)>1),TRANSPOSE(vector),vector),
    IF(COLUMNS(vec)>1,
        SQRT(L_COLSUM(vec*vec)),
        SQRT(SUM(vec*vec))
    )
));

Name: L_MAGNITUDE
Description: Calculates the magnitude of a vector as SQRT(SUM(x^2))
Arguments: vector
Function:

LET(doc,"https://www.vertex42.com/lambda/magnitude.html",
    vec,IF(AND(ROWS(vector)=1,COLUMNS(vector)>1),TRANSPOSE(vector),vector),
    IF(COLUMNS(vec)>1,
        ARRAYFORMULA(SQRT(L_COLSUM(vec*vec))),
        ARRAYFORMULA(SQRT(SUM(vec*vec)))
    )
)

L_MAGNITUDE Examples

Test: Copy and Paste this LET function into a cell
=LET(
    a, {4;-4;2},
    b, {0;-3;4},
    c, {1;1;1},
    matrix, HSTACK(a,b,c),
    L_MAGNITUDE(matrix)
)

Result: {6, 5, 1.732}

=LET(
    vector, {0.4934;-0.8654;-0.0873},
    L_MAGNITUDE(vector)
)

Result: 0.999991

=LET(
    vector, {-3; 0; 4},
    vector/L_MAGNITUDE(vector)
)

Result: {-0.6; 0; 0.8}