# Matrix

#### trait Matrix[E] extends MatrixLike[E, Matrix[E]]

Linear Supertypes
MatrixLike[E, Matrix[E]], Tensor[(Int, Int), E], TensorLike[(Int, Int), E, Matrix[E]], NumericOps[Matrix[E]], QuasiTensor[(Int, Int), E], AnyRef, Any
Known Subclasses
Ordering
1. Alphabetic
2. By inheritance
Inherited
1. Matrix
2. MatrixLike
3. Tensor
4. TensorLike
5. NumericOps
6. QuasiTensor
7. AnyRef
8. Any
1. Hide All
2. Show all
Visibility
1. Public
2. All

### Abstract Value Members

1. #### abstract def activeIterator: Iterator[((Int, Int), E)]

Definition Classes
QuasiTensor
2. #### abstract def activeKeysIterator: Iterator[(Int, Int)]

Definition Classes
QuasiTensor
3. #### abstract def activeSize: Int

Definition Classes
TensorLike
4. #### abstract def activeValuesIterator: Iterator[E]

Definition Classes
QuasiTensor

8. #### abstract def repr: Matrix[E]

Definition Classes
NumericOps

### Concrete Value Members

1. #### final def !=(arg0: AnyRef): Boolean

Definition Classes
AnyRef
2. #### final def !=(arg0: Any): Boolean

Definition Classes
Any
3. #### final def ##(): Int

Definition Classes
AnyRef → Any
4. #### final def %[TT >: Matrix[E], B, That](b: B)(implicit op: operators.OpMod.Impl2[TT, B, That]): That

Alias for :%(b) when b is a scalar.

Alias for :%(b) when b is a scalar.

Definition Classes
NumericOps
5. #### final def %=[TT >: Matrix[E], B](b: B)(implicit op: operators.OpMod.InPlaceImpl2[TT, B]): Matrix[E]

Alias for :%=(b) when b is a scalar.

Alias for :%=(b) when b is a scalar.

Definition Classes
NumericOps
6. #### final def &[TT >: Matrix[E], B, That](b: B)(implicit op: operators.OpAnd.Impl2[TT, B, That]): That

Alias for :&&(b) for all b.

Alias for :&&(b) for all b.

Definition Classes
NumericOps
7. #### final def &=[TT >: Matrix[E], B](b: B)(implicit op: operators.OpAnd.InPlaceImpl2[TT, B]): Matrix[E]

Mutates this by element-wise and of this and b.

Mutates this by element-wise and of this and b.

Definition Classes
NumericOps
8. #### final def *[TT >: Matrix[E], B, That](b: B)(implicit op: operators.OpMulMatrix.Impl2[TT, B, That]): That

Matrix multiplication

Matrix multiplication

Definition Classes
NumericOps
9. #### final def *=[TT >: Matrix[E], B](b: B)(implicit op: operators.OpMulScalar.InPlaceImpl2[TT, B]): Matrix[E]

Alias for :*=(b) when b is a scalar.

Alias for :*=(b) when b is a scalar.

Definition Classes
NumericOps
10. #### final def +[TT >: Matrix[E], B, That](b: B)(implicit op: operators.OpAdd.Impl2[TT, B, That]): That

Alias for :+(b) for all b.

Alias for :+(b) for all b.

Definition Classes
NumericOps
11. #### final def +=[TT >: Matrix[E], B](b: B)(implicit op: operators.OpAdd.InPlaceImpl2[TT, B]): Matrix[E]

Alias for :+=(b) for all b.

Alias for :+=(b) for all b.

Definition Classes
NumericOps
12. #### final def -[TT >: Matrix[E], B, That](b: B)(implicit op: operators.OpSub.Impl2[TT, B, That]): That

Alias for :-(b) for all b.

Alias for :-(b) for all b.

Definition Classes
NumericOps
13. #### final def -=[TT >: Matrix[E], B](b: B)(implicit op: operators.OpSub.InPlaceImpl2[TT, B]): Matrix[E]

Alias for :-=(b) for all b.

Alias for :-=(b) for all b.

Definition Classes
NumericOps
14. #### final def /[TT >: Matrix[E], B, That](b: B)(implicit op: operators.OpDiv.Impl2[TT, B, That]): That

Alias for :/(b) when b is a scalar.

Alias for :/(b) when b is a scalar.

Definition Classes
NumericOps
15. #### final def /=[TT >: Matrix[E], B](b: B)(implicit op: operators.OpDiv.InPlaceImpl2[TT, B]): Matrix[E]

Alias for :/=(b) when b is a scalar.

Alias for :/=(b) when b is a scalar.

Definition Classes
NumericOps
16. #### final def :!=[TT >: Matrix[E], B, That](b: B)(implicit op: operators.OpNe.Impl2[TT, B, That]): That

Element-wise inequality comparator of this and b.

Element-wise inequality comparator of this and b.

Definition Classes
NumericOps
17. #### final def :%[TT >: Matrix[E], B, That](b: B)(implicit op: operators.OpMod.Impl2[TT, B, That]): That

Element-wise modulo of this and b.

Element-wise modulo of this and b.

Definition Classes
NumericOps
18. #### final def :%=[TT >: Matrix[E], B](b: B)(implicit op: operators.OpMod.InPlaceImpl2[TT, B]): Matrix[E]

Mutates this by element-wise modulo of b into this.

Mutates this by element-wise modulo of b into this.

Definition Classes
NumericOps
19. #### final def :&[TT >: Matrix[E], B, That](b: B)(implicit op: operators.OpAnd.Impl2[TT, B, That]): That

Element-wise logical "and" operator -- returns true if corresponding elements are non-zero.

Element-wise logical "and" operator -- returns true if corresponding elements are non-zero.

Definition Classes
NumericOps
20. #### final def :&=[TT >: Matrix[E], B](b: B)(implicit op: operators.OpAnd.InPlaceImpl2[TT, B]): Matrix[E]

Mutates this by element-wise and of this and b.

Mutates this by element-wise and of this and b.

Definition Classes
NumericOps
21. #### final def :*[TT >: Matrix[E], B, That](b: B)(implicit op: operators.OpMulScalar.Impl2[TT, B, That]): That

Element-wise product of this and b.

Element-wise product of this and b.

Definition Classes
NumericOps
22. #### final def :*=[TT >: Matrix[E], B](b: B)(implicit op: operators.OpMulScalar.InPlaceImpl2[TT, B]): Matrix[E]

Mutates this by element-wise multiplication of b into this.

Mutates this by element-wise multiplication of b into this.

Definition Classes
NumericOps
23. #### final def :+[TT >: Matrix[E], B, That](b: B)(implicit op: operators.OpAdd.Impl2[TT, B, That]): That

Element-wise sum of this and b.

Element-wise sum of this and b.

Definition Classes
NumericOps
24. #### final def :+=[TT >: Matrix[E], B](b: B)(implicit op: operators.OpAdd.InPlaceImpl2[TT, B]): Matrix[E]

Mutates this by element-wise addition of b into this.

Mutates this by element-wise addition of b into this.

Definition Classes
NumericOps
25. #### final def :-[TT >: Matrix[E], B, That](b: B)(implicit op: operators.OpSub.Impl2[TT, B, That]): That

Element-wise difference of this and b.

Element-wise difference of this and b.

Definition Classes
NumericOps
26. #### final def :-=[TT >: Matrix[E], B](b: B)(implicit op: operators.OpSub.InPlaceImpl2[TT, B]): Matrix[E]

Mutates this by element-wise subtraction of b from this

Mutates this by element-wise subtraction of b from this

Definition Classes
NumericOps
27. #### final def :/[TT >: Matrix[E], B, That](b: B)(implicit op: operators.OpDiv.Impl2[TT, B, That]): That

Element-wise quotient of this and b.

Element-wise quotient of this and b.

Definition Classes
NumericOps
28. #### final def :/=[TT >: Matrix[E], B](b: B)(implicit op: operators.OpDiv.InPlaceImpl2[TT, B]): Matrix[E]

Mutates this by element-wise division of b into this

Mutates this by element-wise division of b into this

Definition Classes
NumericOps
29. #### final def :<[TT >: Matrix[E], B, That](b: B)(implicit op: operators.OpLT.Impl2[TT, B, That]): That

Element-wise less=than comparator of this and b.

Element-wise less=than comparator of this and b.

Definition Classes
NumericOps
30. #### final def :<=[TT >: Matrix[E], B, That](b: B)(implicit op: operators.OpLTE.Impl2[TT, B, That]): That

Element-wise less-than-or-equal-to comparator of this and b.

Element-wise less-than-or-equal-to comparator of this and b.

Definition Classes
NumericOps
31. #### final def :=[TT >: Matrix[E], B](b: B)(implicit op: operators.OpSet.InPlaceImpl2[TT, B]): Matrix[E]

Mutates this by element-wise assignment of b into this.

Mutates this by element-wise assignment of b into this.

Definition Classes
NumericOps
32. #### final def :==[TT >: Matrix[E], B, That](b: B)(implicit op: operators.OpEq.Impl2[TT, B, That]): That

Element-wise equality comparator of this and b.

Element-wise equality comparator of this and b.

Definition Classes
NumericOps
33. #### final def :>[TT >: Matrix[E], B, That](b: B)(implicit op: operators.OpGT.Impl2[TT, B, That]): That

Element-wise greater-than comparator of this and b.

Element-wise greater-than comparator of this and b.

Definition Classes
NumericOps
34. #### final def :>=[TT >: Matrix[E], B, That](b: B)(implicit op: operators.OpGTE.Impl2[TT, B, That]): That

Element-wise greater-than-or-equal-to comparator of this and b.

Element-wise greater-than-or-equal-to comparator of this and b.

Definition Classes
NumericOps
35. #### final def :^[TT >: Matrix[E], B, That](b: B)(implicit op: operators.OpPow.Impl2[TT, B, That]): That

Element-wise exponentiation of this and b.

Element-wise exponentiation of this and b.

Definition Classes
NumericOps
36. #### final def :^=[TT >: Matrix[E], B](b: B)(implicit op: operators.OpPow.InPlaceImpl2[TT, B]): Matrix[E]

Mutates this by element-wise exponentiation of this by b.

Mutates this by element-wise exponentiation of this by b.

Definition Classes
NumericOps
37. #### final def :^^[TT >: Matrix[E], B, That](b: B)(implicit op: operators.OpXor.Impl2[TT, B, That]): That

Element-wise logical "xor" operator -- returns true if only one of the corresponding elements is non-zero.

Element-wise logical "xor" operator -- returns true if only one of the corresponding elements is non-zero.

Definition Classes
NumericOps
38. #### final def :^^=[TT >: Matrix[E], B](b: B)(implicit op: operators.OpXor.InPlaceImpl2[TT, B]): Matrix[E]

Mutates this by element-wise xor of this and b.

Mutates this by element-wise xor of this and b.

Definition Classes
NumericOps
39. #### final def :|[TT >: Matrix[E], B, That](b: B)(implicit op: operators.OpOr.Impl2[TT, B, That]): That

Element-wise logical "or" operator -- returns true if either element is non-zero.

Element-wise logical "or" operator -- returns true if either element is non-zero.

Definition Classes
NumericOps
40. #### final def :|=[TT >: Matrix[E], B](b: B)(implicit op: operators.OpOr.InPlaceImpl2[TT, B]): Matrix[E]

Mutates this by element-wise or of this and b.

Mutates this by element-wise or of this and b.

Definition Classes
NumericOps
41. #### final def ==(arg0: AnyRef): Boolean

Definition Classes
AnyRef
42. #### final def ==(arg0: Any): Boolean

Definition Classes
Any
43. #### def \[TT >: Matrix[E], B, That](b: B)(implicit op: operators.OpSolveMatrixBy.Impl2[TT, B, That]): That

Shaped solve of this by b.

Shaped solve of this by b.

Definition Classes
NumericOps
44. #### final def ^^[TT >: Matrix[E], B, That](b: B)(implicit op: operators.OpXor.Impl2[TT, B, That]): That

Alias for :^^(b) for all b.

Alias for :^^(b) for all b.

Definition Classes
NumericOps
45. #### final def ^^=[TT >: Matrix[E], B](b: B)(implicit op: operators.OpXor.InPlaceImpl2[TT, B]): Matrix[E]

Mutates this by element-wise xor of this and b.

Mutates this by element-wise xor of this and b.

Definition Classes
NumericOps
46. #### def active: TensorActive[(Int, Int), E, Matrix[E]]

Definition Classes
TensorLike
47. #### final def apply(i: (Int, Int)): E

Definition Classes
MatrixTensorLikeQuasiTensor
48. #### def apply[Slice1, Slice2, Result](slice1: Slice1, slice2: Slice2)(implicit canSlice: CanSlice2[Matrix[E], Slice1, Slice2, Result]): Result

Method for slicing that is tuned for Matrices.

Method for slicing that is tuned for Matrices.

returns

Definition Classes
TensorLike
49. #### def apply[Result](a: (Int, Int), slice: (Int, Int)*)(implicit canSlice: CanSlice[Matrix[E], Seq[(Int, Int)], Result]): Result

Slice a sequence of elements.

Slice a sequence of elements. Must be at least 2.

Result
a
slice
canSlice
returns

Definition Classes
TensorLike
50. #### def apply[Slice, Result](slice: Slice)(implicit canSlice: CanSlice[Matrix[E], Slice, Result]): Result

method for slicing a tensor.

method for slicing a tensor. For instance, DenseVectors support efficient slicing by a Range object.

returns

Definition Classes
TensorLike
51. #### def argmax(implicit ord: Ordering[E]): (Int, Int)

Definition Classes
QuasiTensor
52. #### def argmin(implicit ord: Ordering[E]): (Int, Int)

Definition Classes
QuasiTensor
53. #### def argsort(implicit ord: Ordering[E]): IndexedSeq[(Int, Int)]

Definition Classes
QuasiTensor
54. #### def argtopk(k: Int)(implicit ordering: Ordering[E]): IndexedSeq[(Int, Int)]

Returns the k indices with maximum value.

Returns the k indices with maximum value. (NOT absolute value.)

k

how many to return

ordering
returns

Definition Classes
QuasiTensor
55. #### final def asInstanceOf[T0]: T0

Definition Classes
Any
56. #### def clone(): AnyRef

Attributes
protected[java.lang]
Definition Classes
AnyRef
Annotations
@throws( ... )
57. #### final def dot[TT >: Matrix[E], B, BB >: B, That](b: B)(implicit op: operators.OpMulInner.Impl2[TT, BB, That]): That

Inner product of this and b.

Inner product of this and b.

Definition Classes
NumericOps
58. #### final def eq(arg0: AnyRef): Boolean

Definition Classes
AnyRef
59. #### def equals(arg0: Any): Boolean

Definition Classes
AnyRef → Any
60. #### def finalize(): Unit

Attributes
protected[java.lang]
Definition Classes
AnyRef
Annotations
@throws( classOf[java.lang.Throwable] )
61. #### def findAll(f: (E) ⇒ Boolean): IndexedSeq[(Int, Int)]

Returns all indices k whose value satisfies a predicate.

Returns all indices k whose value satisfies a predicate.

Definition Classes
QuasiTensor
62. #### def forall(fn: ((Int, Int), E) ⇒ Boolean): Boolean

Returns true if and only if the given predicate is true for all elements.

Returns true if and only if the given predicate is true for all elements.

Definition Classes
TensorLike
63. #### def forallValues(fn: (E) ⇒ Boolean): Boolean

Returns true if and only if the given predicate is true for all elements.

Returns true if and only if the given predicate is true for all elements.

Definition Classes
TensorLike
64. #### def foreachKey[U](fn: ((Int, Int)) ⇒ U): Unit

Applies the given function to each key in the tensor.

Applies the given function to each key in the tensor.

Definition Classes
TensorLike
65. #### def foreachPair[U](fn: ((Int, Int), E) ⇒ U): Unit

Applies the given function to each key and its corresponding value.

Applies the given function to each key and its corresponding value.

Definition Classes
TensorLike
66. #### def foreachValue[U](fn: (E) ⇒ U): Unit

Applies the given function to each value in the map (one for each element of the domain, including zeros).

Applies the given function to each value in the map (one for each element of the domain, including zeros).

Definition Classes
TensorLike
67. #### final def getClass(): Class[_]

Definition Classes
AnyRef → Any
68. #### def hashCode(): Int

Definition Classes
AnyRef → Any
69. #### final def isInstanceOf[T0]: Boolean

Definition Classes
Any
70. #### def iterator: Iterator[((Int, Int), E)]

Definition Classes
MatrixQuasiTensor
71. #### def keySet: Set[(Int, Int)]

Definition Classes
MatrixQuasiTensor
72. #### def keys: TensorKeys[(Int, Int), E, Matrix[E]]

Definition Classes
TensorLike
73. #### def keysIterator: Iterator[(Int, Int)]

Definition Classes
MatrixQuasiTensor
74. #### def map[E2, That](fn: (E) ⇒ E2)(implicit canMapValues: CanMapValues[Matrix[E], E, E2, That]): That

Definition Classes
MatrixLike
75. #### def mapActivePairs[TT >: Matrix[E], O, That](f: ((Int, Int), E) ⇒ O)(implicit bf: CanMapKeyValuePairs[TT, (Int, Int), E, O, That]): That

Maps all active key-value pairs values.

Maps all active key-value pairs values.

Definition Classes
TensorLike
76. #### def mapActiveValues[TT >: Matrix[E], O, That](f: (E) ⇒ O)(implicit bf: CanMapValues[TT, E, O, That]): That

Maps all non-zero values.

Maps all non-zero values.

Definition Classes
TensorLike
77. #### def mapPairs[TT >: Matrix[E], O, That](f: ((Int, Int), E) ⇒ O)(implicit bf: CanMapKeyValuePairs[TT, (Int, Int), E, O, That]): That

Creates a new map containing a transformed copy of this map.

Creates a new map containing a transformed copy of this map.

Definition Classes
TensorLike
78. #### def mapValues[TT >: Matrix[E], O, That](f: (E) ⇒ O)(implicit bf: CanMapValues[TT, E, O, That]): That

Creates a new map containing a transformed copy of this map.

Creates a new map containing a transformed copy of this map.

Definition Classes
TensorLike
79. #### def max(implicit ord: Ordering[E]): E

Definition Classes
QuasiTensor
80. #### def min(implicit ord: Ordering[E]): E

Definition Classes
QuasiTensor
81. #### final def ne(arg0: AnyRef): Boolean

Definition Classes
AnyRef
82. #### final def norm[TT >: Matrix[E], B, R](b: B)(implicit op: norm.Impl2[TT, B, R]): R

Represents the norm of this vector

Represents the norm of this vector

Definition Classes
NumericOps
83. #### final def norm[TT >: Matrix[E], R]()(implicit op: norm.Impl[TT, R]): R

Represents the "natural" norm of this vector, for types that don't support arbitrary norms

Represents the "natural" norm of this vector, for types that don't support arbitrary norms

Definition Classes
NumericOps
84. #### final def notify(): Unit

Definition Classes
AnyRef
85. #### final def notifyAll(): Unit

Definition Classes
AnyRef
86. #### def pairs: TensorPairs[(Int, Int), E, Matrix[E]]

Definition Classes
TensorLike
87. #### def size: Int

Definition Classes
MatrixTensorLike
88. #### def sum(implicit num: Numeric[E]): E

Definition Classes
QuasiTensor
89. #### final def synchronized[T0](arg0: ⇒ T0): T0

Definition Classes
AnyRef
90. #### final def t[TT >: Matrix[E], That, Slice1, Slice2, Result](a: Slice1, b: Slice2)(implicit op: CanTranspose[TT, That], canSlice: CanSlice2[That, Slice1, Slice2, Result]): Result

A transposed view of this object, followed by a slice.

A transposed view of this object, followed by a slice. Sadly frequently necessary.

Definition Classes
NumericOps
91. #### final def t[TT >: Matrix[E], That](implicit op: CanTranspose[TT, That]): That

A transposed view of this object.

A transposed view of this object.

Definition Classes
NumericOps

93. #### def toString(): String

Definition Classes
Matrix → AnyRef → Any

95. #### final def unary_![TT >: Matrix[E], That](implicit op: operators.OpNot.Impl[TT, That]): That

Definition Classes
NumericOps
96. #### final def unary_-[TT >: Matrix[E], That](implicit op: operators.OpNeg.Impl[TT, That]): That

Definition Classes
NumericOps
97. #### final def update(i: (Int, Int), e: E): Unit

Definition Classes
MatrixTensorLikeQuasiTensor
98. #### def values: TensorValues[(Int, Int), E, Matrix[E]]

Definition Classes
TensorLike
99. #### def valuesIterator: Iterator[E]

Definition Classes
MatrixQuasiTensor
100. #### final def wait(): Unit

Definition Classes
AnyRef
Annotations
@throws( ... )
101. #### final def wait(arg0: Long, arg1: Int): Unit

Definition Classes
AnyRef
Annotations
@throws( ... )
102. #### final def wait(arg0: Long): Unit

Definition Classes
AnyRef
Annotations
@throws( ... )
103. #### final def |[TT >: Matrix[E], B, That](b: B)(implicit op: operators.OpOr.Impl2[TT, B, That]): That

Alias for :||(b) for all b.

Alias for :||(b) for all b.

Definition Classes
NumericOps
104. #### final def |=[TT >: Matrix[E], B](b: B)(implicit op: operators.OpOr.InPlaceImpl2[TT, B]): Matrix[E]

Mutates this by element-wise or of this and b.

Mutates this by element-wise or of this and b.

Definition Classes
NumericOps

### Deprecated Value Members

1. #### def all(implicit semi: Semiring[E]): Boolean

Returns true if all elements are non-zero

Returns true if all elements are non-zero

Definition Classes
QuasiTensor
Annotations
@deprecated
Deprecated

(Since version 0.6) Use breeze.linalg.all instead

2. #### def any(implicit semi: Semiring[E]): Boolean

Returns true if some element is non-zero

Returns true if some element is non-zero

Definition Classes
QuasiTensor
Annotations
@deprecated
Deprecated

(Since version 0.6) Use breeze.linalg.any instead