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# min

minimum

### Syntax

```m = min(A)
Col = min(A, 'c')
Row = min(A, 'r'|'m')
M = min(A1, A2,..., An)
M = min(list(A1, A2,..., An))
[.., K] = min(..)```

### Arguments

A, A1, ..., An

scalars, vectors, matrices or hypermatrices of encoded integers or of real numbers, in dense or sparse format. They must have the same sizes, or be mixed with scalars (scalars are then implicitly expanded to the arrays sizes). Sparse arrays can't be mixed with dense ones, except with dense scalars.

m

single number = minimum of all values of `A` elements. Always in dense format, even when `A` is sparse encoded.

Col

column vector if `A` is a 2D matrix, or hypermatrix of size(A) with size(A,2) set to 1: Minima over columns (for each row). If `A` is sparse, then `Col` is sparse as well.

Row

row vector if `A` is a 2D matrix, or hypermatrix of size(A) with size(A,1) set to 1: Minima over rows (for each column). If `A` is sparse, then `Row` is sparse as well.

M

Array of size = `size(A1)`, such that for any q `M(q) = min(A1(q),A2(q),..An(q))` If `A`,..,`An` are sparse, then `M` is sparse as well.

K

Indices in `A`.. of the (first) minimum found. When `[m,K]=min(A)` is used,

• If `A` is a vector, K is a scalar.
• Otherwise, `K` is a row vector [i,j,..] of subscripts.

For other syntaxes, `K` has the shape and sizes of `Col`, `Row`, and `M`.

With the `[M,K] = min(A1,A2,..,An)` syntax, we have, for any linear index q: `[M(q),K(q)] = min([A1(q) A2(q) .. An(q)])`.

 `K` is always in dense format, even when `A, A1,..,An` are sparse-encoded. Hence, when the `[M,K]=min(A1,A2,..)` syntax is used with huge but sparse matrices, this may lead to a huge dense `K` matrix. The user must check that enough memory is available for it.

### Description

For `A`, a real vector or matrix, `min(A)` is the least element of `A`.

`[m,K]=min(A)` gives in addition the indices of the first minimum.

A second argument of type string `'r'` or `'c'` can be used : `'r'` is used to get a row vector `Row` such that `Row(j)` contains the minimum of the `j`th column `A(:,j)`, `K(j)` gives the index of the row which contains the minimum, for the column #`j`.

`'c'` is used for the dual operation on the rows of `A`. `'m'` is used for compatibility with Matlab.

`[M,K]=min(list(A1,...,An))` is an equivalent syntax of `[M,K]=min(A1,A2,...,An)`.

 min() ignores NaN values (unless there are only NaN values). `min([])` returns `[]` for values and `K`.
 If `min(A1, A2,..., An)` is used with a huge input sparse matrix of low density, together with a strictly negative scalar input, the sparse result will no longer have any 0 value: It will be a sparse array with density=1, that may lead to a memory failure.

### Examples

```[m, k] = min([])
[m, k] = min([5 3 ; 2 %nan])
[m, n] = min([5 3 ; 2 %nan], 4)
[m, k] = min([5 -1 2], [1 5 1], [0 1 3])
[m, k] = min(list([5 -1 2], [1 5 1], [0 1 3]))```
```--> [m, k] = min([])
m  =
[]
k  =
[]

--> [m, k] = min([5 3 ; 2 %nan])
m  =
2.

k  =
2.   1.

--> [m, k] = min([5 3 ; 2 %nan], 4)
m  =
4.   3.
2.   4.

k  =
2.   1.
1.   2.

--> [m, k] = min([5 -1 2], [1 5 1], [0 1 3])
m  =
0.  -1.   1.

k  =
3.   1.   2.
```

With the "r" or "c" options:

```A = grand(4,6,"uin",0,30); A(3,4) = %nan
[Row, K] = min(A, "r")
[Col, K] = min(A, "c")```
```--> A = grand(4,6,"uin",0,30); A(3,4) = %nan
A  =
24.   14.   24.   4.    6.    11.
23.   25.   29.   6.    19.   5.
30.   2.    20.   Nan    6.   6.
20.   8.    13.   14.   16.   3.

--> [Row, K] = min(A, "r")
Row  =
20.   2.   13.   4.   6.   3.

K  =
4.   3.   4.   1.   1.   4.

--> [Col, K] = min(A, "c")
Col  =
4.
5.
2.
3.

K  =
4.
6.
2.
6.
```

With sparse inputs:

```s = sprand(5,4,0.5); k = s~=0; s(k) = round((s(k)-0.5)*10), full(s)
[Row, K] = min(s, "r")
[Col, K] = min(s, "c")
[M, K] = min(s,1);   [full(s)  ones(s(:,1))*%nan  full(M)]
issparse(M)
K```
```--> s = sprand(5,4,0.5); k = s~=0; s(k) = round((s(k)-0.5)*10), full(s)
s  =
(  5,  4) sparse matrix
(  1,  3)     5.
(  1,  4)    -2.
(  2,  1)    -3.
(  2,  3)    -5.
(  3,  1)     3.
(  3,  2)    -1.
(  3,  3)     3.
(  3,  4)     4.
(  5,  3)     4.
(  5,  4)    -5.

ans  =
0.   0.   5.  -2.
-3.   0.  -5.   0.
3.  -1.   3.   4.
0.   0.   0.   0.
0.   0.   4.  -5.

--> [Row, K] = min(s, "r")
Row  =
(  1,  4) sparse matrix
(  1,  1)    -3.
(  1,  2)    -1.
(  1,  3)    -5.
(  1,  4)    -5.

K  =
2.   3.   2.   5.

--> [Col, K] = min(s, "c")
Col  =
(  5,  1) sparse matrix
(  1,  1)    -2.
(  2,  1)    -5.
(  3,  1)    -1.
(  5,  1)    -5.

K  =
4.
3.
2.
1.
4.

--> [M, K] = min(s,1);   [full(s)  ones(s(:,1))*%nan  full(M)]
ans  =
0.   0.   5.  -2.   Nan   0.   0.   1.  -2.
-3.   0.  -5.   0.   Nan  -3.   0.  -5.   0.
3.  -1.   3.   4.   Nan   1.  -1.   1.   1.
0.   0.   0.   0.   Nan   0.   0.   0.   0.
0.   0.   4.  -5.   Nan   0.   0.   1.  -5.

--> issparse(M)
ans  =
1.

--> K
K  =
1.   1.   2.   1.
1.   1.   1.   1.
2.   1.   2.   2.
1.   1.   1.   1.
1.   1.   2.   1.
```

• max — maximum
• strange — レンジ
• mean — mean of all values, or means along a given dimension
• gsort — sorts boolean, numerical and string arrays
• find — 論理値ベクトルまたは行列のtrue要素の添え字を見つける
• full — 疎行列を通常の行列に変換する

### History

 バージョン 記述 6.0.2 min() now actually works with sparse matrices