Expression of a mathematical vector or matrix as an array object. More...
#include <ArrayWrapper.h>
Inheritance diagram for ArrayWrapper< ExpressionType >:Public Types | |
| typedef internal::traits< ArrayWrapper< ExpressionType > >::Index | Index |
| The type of indices. | |
Public Member Functions | |
| const CwiseUnaryOp< internal::scalar_abs_op< Scalar >, const ArrayWrapper< ExpressionType > > | abs () const |
| const CwiseUnaryOp< internal::scalar_abs2_op< Scalar >, const ArrayWrapper< ExpressionType > > | abs2 () const |
| const CwiseUnaryOp< internal::scalar_acos_op< Scalar >, const ArrayWrapper< ExpressionType > > | acos () const |
| bool | all (void) const |
| bool | any (void) const |
| const CwiseUnaryOp< internal::scalar_asin_op< Scalar >, const ArrayWrapper< ExpressionType > > | asin () const |
| const CwiseBinaryOp< CustomBinaryOp, const ArrayWrapper< ExpressionType >, const OtherDerived > | binaryExpr (const Eigen::ArrayBase< OtherDerived > &other, const CustomBinaryOp &func=CustomBinaryOp()) const |
| Block< ArrayWrapper< ExpressionType >, BlockRows, BlockCols > | block (Index startRow, Index startCol) |
| const Block< const ArrayWrapper< ExpressionType >, BlockRows, BlockCols > | block (Index startRow, Index startCol) const |
| Block< ArrayWrapper< ExpressionType > > | block (Index startRow, Index startCol, Index blockRows, Index blockCols) |
| const Block< const ArrayWrapper< ExpressionType > > | block (Index startRow, Index startCol, Index blockRows, Index blockCols) const |
| Block< ArrayWrapper< ExpressionType >, CRows, CCols > | bottomLeftCorner () |
| const Block< const ArrayWrapper< ExpressionType >, CRows, CCols > | bottomLeftCorner () const |
| Block< ArrayWrapper< ExpressionType > > | bottomLeftCorner (Index cRows, Index cCols) |
| const Block< const ArrayWrapper< ExpressionType > > | bottomLeftCorner (Index cRows, Index cCols) const |
| Block< ArrayWrapper< ExpressionType >, CRows, CCols > | bottomRightCorner () |
| const Block< const ArrayWrapper< ExpressionType >, CRows, CCols > | bottomRightCorner () const |
| Block< ArrayWrapper< ExpressionType > > | bottomRightCorner (Index cRows, Index cCols) |
| const Block< const ArrayWrapper< ExpressionType > > | bottomRightCorner (Index cRows, Index cCols) const |
| NRowsBlockXpr< N >::Type | bottomRows () |
| ConstNRowsBlockXpr< N >::Type | bottomRows () const |
| RowsBlockXpr | bottomRows (Index n) |
| ConstRowsBlockXpr | bottomRows (Index n) const |
| internal::cast_return_type< ArrayWrapper< ExpressionType >, constCwiseUnaryOp< internal::scalar_cast_op< typenameinternal::traits< ArrayWrapper< ExpressionType > >::Scalar, NewType >, constDerived > >::type | cast () const |
| ColXpr | col (Index i) |
| ConstColXpr | col (Index i) const |
| ColwiseReturnType | colwise () |
| ConstColwiseReturnType | colwise () const |
| ConjugateReturnType | conjugate () const |
| const CwiseUnaryOp< internal::scalar_cos_op< Scalar >, const ArrayWrapper< ExpressionType > > | cos () const |
| Index | count () const |
| const CwiseUnaryOp< internal::scalar_cube_op< Scalar >, const ArrayWrapper< ExpressionType > > | cube () const |
| const CwiseUnaryOp< internal::scalar_abs_op< Scalar >, const ArrayWrapper< ExpressionType > > | cwiseAbs () const |
| const CwiseUnaryOp< internal::scalar_abs2_op< Scalar >, const ArrayWrapper< ExpressionType > > | cwiseAbs2 () const |
| const CwiseUnaryOp< std::binder1st< std::equal_to< Scalar > >, const ArrayWrapper< ExpressionType > > | cwiseEqual (const Scalar &s) const |
| const CwiseUnaryOp< internal::scalar_inverse_op< Scalar >, const ArrayWrapper< ExpressionType > > | cwiseInverse () const |
| const CwiseUnaryOp< internal::scalar_sqrt_op< Scalar >, const ArrayWrapper< ExpressionType > > | cwiseSqrt () const |
| const | EIGEN_CWISE_PRODUCT_RETURN_TYPE (ArrayWrapper< ExpressionType >, OtherDerived) cwiseProduct(const Eigen |
| EvalReturnType | eval () const |
| const CwiseUnaryOp< internal::scalar_exp_op< Scalar >, const ArrayWrapper< ExpressionType > > | exp () const |
| void | fill (const Scalar &value) |
| const Flagged< ArrayWrapper< ExpressionType >, Added, Removed > | flagged () const |
| const WithFormat< ArrayWrapper< ExpressionType > > | format (const IOFormat &fmt) const |
| DenseBase< ArrayWrapper< ExpressionType > >::template FixedSegmentReturnType< Size >::Type | head () |
| DenseBase< ArrayWrapper< ExpressionType > >::template ConstFixedSegmentReturnType< Size >::Type | head () const |
| SegmentReturnType | head (Index size) |
| DenseBase::ConstSegmentReturnType | head (Index size) const |
| NonConstImagReturnType | imag () |
| const ImagReturnType | imag () const |
| Index | innerSize () const |
| const CwiseUnaryOp< internal::scalar_inverse_op< Scalar >, const ArrayWrapper< ExpressionType > > | inverse () const |
| bool | isApprox (const DenseBase< OtherDerived > &other, RealScalar prec=NumTraits< Scalar >::dummy_precision()) const |
| bool | isApproxToConstant (const Scalar &value, RealScalar prec=NumTraits< Scalar >::dummy_precision()) const |
| bool | isConstant (const Scalar &value, RealScalar prec=NumTraits< Scalar >::dummy_precision()) const |
| bool | isMuchSmallerThan (const DenseBase< OtherDerived > &other, RealScalar prec=NumTraits< Scalar >::dummy_precision()) const |
| bool | isMuchSmallerThan (const typename NumTraits< Scalar >::Real &other, RealScalar prec) const |
| bool | isOnes (RealScalar prec=NumTraits< Scalar >::dummy_precision()) const |
| bool | isZero (RealScalar prec=NumTraits< Scalar >::dummy_precision()) const |
| NColsBlockXpr< N >::Type | leftCols () |
| ConstNColsBlockXpr< N >::Type | leftCols () const |
| ColsBlockXpr | leftCols (Index n) |
| ConstColsBlockXpr | leftCols (Index n) const |
| const CwiseUnaryOp< internal::scalar_log_op< Scalar >, const ArrayWrapper< ExpressionType > > | log () const |
| MatrixWrapper< ArrayWrapper< ExpressionType > > | matrix () |
| internal::traits< ArrayWrapper< ExpressionType > >::Scalar | maxCoeff () const |
| internal::traits< ArrayWrapper< ExpressionType > >::Scalar | maxCoeff (IndexType *index) const |
| internal::traits< ArrayWrapper< ExpressionType > >::Scalar | maxCoeff (IndexType *row, IndexType *col) const |
| Scalar | mean () const |
| NColsBlockXpr< N >::Type | middleCols (Index startCol) |
| ConstNColsBlockXpr< N >::Type | middleCols (Index startCol) const |
| ColsBlockXpr | middleCols (Index startCol, Index numCols) |
| ConstColsBlockXpr | middleCols (Index startCol, Index numCols) const |
| NRowsBlockXpr< N >::Type | middleRows (Index startRow) |
| ConstNRowsBlockXpr< N >::Type | middleRows (Index startRow) const |
| RowsBlockXpr | middleRows (Index startRow, Index numRows) |
| ConstRowsBlockXpr | middleRows (Index startRow, Index numRows) const |
| internal::traits< ArrayWrapper< ExpressionType > >::Scalar | minCoeff () const |
| internal::traits< ArrayWrapper< ExpressionType > >::Scalar | minCoeff (IndexType *index) const |
| internal::traits< ArrayWrapper< ExpressionType > >::Scalar | minCoeff (IndexType *row, IndexType *col) const |
| const NestByValue< ArrayWrapper< ExpressionType > > | nestByValue () const |
| Index | nonZeros () const |
| const CwiseBinaryOp< internal::scalar_boolean_and_op, const ArrayWrapper< ExpressionType >, const OtherDerived > | operator&& (const Eigen::ArrayBase< OtherDerived > &other) const |
| const ScalarMultipleReturnType | operator* (const Scalar &scalar) const |
| const CwiseUnaryOp< internal::scalar_multiple2_op< Scalar, std::complex< Scalar > >, const ArrayWrapper< ExpressionType > > | operator* (const std::complex< Scalar > &scalar) const |
| ArrayWrapper< ExpressionType > & | operator*= (const ArrayBase< OtherDerived > &other) |
| ArrayWrapper< ExpressionType > & | operator+= (const ArrayBase< OtherDerived > &other) |
| const CwiseUnaryOp< internal::scalar_opposite_op< typename internal::traits< ArrayWrapper< ExpressionType > >::Scalar >, const ArrayWrapper< ExpressionType > > | operator- () const |
| const CwiseUnaryOp< internal::scalar_add_op< Scalar >, const ArrayWrapper< ExpressionType > > | operator- (const Scalar &scalar) const |
| ArrayWrapper< ExpressionType > & | operator-= (const ArrayBase< OtherDerived > &other) |
| const CwiseUnaryOp< internal::scalar_quotient1_op< typename internal::traits< ArrayWrapper< ExpressionType > >::Scalar >, const ArrayWrapper< ExpressionType > > | operator/ (const Scalar &scalar) const |
| ArrayWrapper< ExpressionType > & | operator/= (const ArrayBase< OtherDerived > &other) |
| CommaInitializer< ArrayWrapper< ExpressionType > > | operator<< (const DenseBase< OtherDerived > &other) |
| CommaInitializer< ArrayWrapper< ExpressionType > > | operator<< (const Scalar &s) |
| const CwiseBinaryOp< internal::scalar_boolean_or_op, const ArrayWrapper< ExpressionType >, const OtherDerived > | operator|| (const Eigen::ArrayBase< OtherDerived > &other) const |
| Index | outerSize () const |
| const CwiseUnaryOp< internal::scalar_pow_op< Scalar >, const ArrayWrapper< ExpressionType > > | pow (const Scalar &exponent) const |
| Scalar | prod () const |
| NonConstRealReturnType | real () |
| RealReturnType | real () const |
| internal::result_of< Func(typenameinternal::traits< ArrayWrapper< ExpressionType > >::Scalar)>::type | redux (const Func &func) const |
| const Replicate< ArrayWrapper< ExpressionType >, RowFactor, ColFactor > | replicate () const |
| const Replicate< ArrayWrapper< ExpressionType >, Dynamic, Dynamic > | replicate (Index rowFacor, Index colFactor) const |
| void | resize (Index nbRows, Index nbCols) |
| void | resize (Index newSize) |
| ReverseReturnType | reverse () |
| ConstReverseReturnType | reverse () const |
| void | reverseInPlace () |
| NColsBlockXpr< N >::Type | rightCols () |
| ConstNColsBlockXpr< N >::Type | rightCols () const |
| ColsBlockXpr | rightCols (Index n) |
| ConstColsBlockXpr | rightCols (Index n) const |
| RowXpr | row (Index i) |
| ConstRowXpr | row (Index i) const |
| RowwiseReturnType | rowwise () |
| ConstRowwiseReturnType | rowwise () const |
| DenseBase< ArrayWrapper< ExpressionType > >::template FixedSegmentReturnType< Size >::Type | segment (Index start) |
| DenseBase< ArrayWrapper< ExpressionType > >::template ConstFixedSegmentReturnType< Size >::Type | segment (Index start) const |
| SegmentReturnType | segment (Index start, Index size) |
| DenseBase::ConstSegmentReturnType | segment (Index start, Index size) const |
| const Select< ArrayWrapper< ExpressionType >, ThenDerived, ElseDerived > | select (const DenseBase< ThenDerived > &thenMatrix, const DenseBase< ElseDerived > &elseMatrix) const |
| const Select< ArrayWrapper< ExpressionType >, ThenDerived, typename ThenDerived::ConstantReturnType > | select (const DenseBase< ThenDerived > &thenMatrix, typename ThenDerived::Scalar elseScalar) const |
| const Select< ArrayWrapper< ExpressionType >, typename ElseDerived::ConstantReturnType, ElseDerived > | select (typename ElseDerived::Scalar thenScalar, const DenseBase< ElseDerived > &elseMatrix) const |
| ArrayWrapper< ExpressionType > & | setConstant (const Scalar &value) |
| ArrayWrapper< ExpressionType > & | setLinSpaced (const Scalar &low, const Scalar &high) |
| Sets a linearly space vector. | |
| ArrayWrapper< ExpressionType > & | setLinSpaced (Index size, const Scalar &low, const Scalar &high) |
| Sets a linearly space vector. | |
| ArrayWrapper< ExpressionType > & | setOnes () |
| ArrayWrapper< ExpressionType > & | setRandom () |
| ArrayWrapper< ExpressionType > & | setZero () |
| const CwiseUnaryOp< internal::scalar_sin_op< Scalar >, const ArrayWrapper< ExpressionType > > | sin () const |
| const CwiseUnaryOp< internal::scalar_sqrt_op< Scalar >, const ArrayWrapper< ExpressionType > > | sqrt () const |
| const CwiseUnaryOp< internal::scalar_square_op< Scalar >, const ArrayWrapper< ExpressionType > > | square () const |
| Scalar | sum () const |
| void | swap (const DenseBase< OtherDerived > &other, int=OtherDerived::ThisConstantIsPrivateInPlainObjectBase) |
| void | swap (PlainObjectBase< OtherDerived > &other) |
| DenseBase< ArrayWrapper< ExpressionType > >::template FixedSegmentReturnType< Size >::Type | tail () |
| DenseBase< ArrayWrapper< ExpressionType > >::template ConstFixedSegmentReturnType< Size >::Type | tail () const |
| SegmentReturnType | tail (Index size) |
| DenseBase::ConstSegmentReturnType | tail (Index size) const |
| const CwiseUnaryOp< internal::scalar_tan_op< Scalar >, ArrayWrapper< ExpressionType > > | tan () const |
| Block< ArrayWrapper< ExpressionType >, CRows, CCols > | topLeftCorner () |
| const Block< const ArrayWrapper< ExpressionType >, CRows, CCols > | topLeftCorner () const |
| Block< ArrayWrapper< ExpressionType > > | topLeftCorner (Index cRows, Index cCols) |
| const Block< const ArrayWrapper< ExpressionType > > | topLeftCorner (Index cRows, Index cCols) const |
| Block< ArrayWrapper< ExpressionType >, CRows, CCols > | topRightCorner () |
| const Block< const ArrayWrapper< ExpressionType >, CRows, CCols > | topRightCorner () const |
| Block< ArrayWrapper< ExpressionType > > | topRightCorner (Index cRows, Index cCols) |
| const Block< const ArrayWrapper< ExpressionType > > | topRightCorner (Index cRows, Index cCols) const |
| NRowsBlockXpr< N >::Type | topRows () |
| ConstNRowsBlockXpr< N >::Type | topRows () const |
| RowsBlockXpr | topRows (Index n) |
| ConstRowsBlockXpr | topRows (Index n) const |
| Eigen::Transpose< ArrayWrapper< ExpressionType > > | transpose () |
| ConstTransposeReturnType | transpose () const |
| void | transposeInPlace () |
| const CwiseUnaryOp< CustomUnaryOp, const ArrayWrapper< ExpressionType > > | unaryExpr (const CustomUnaryOp &func=CustomUnaryOp()) const |
| Apply a unary operator coefficient-wise. | |
| const CwiseUnaryView< CustomViewOp, const ArrayWrapper< ExpressionType > > | unaryViewExpr (const CustomViewOp &func=CustomViewOp()) const |
| CoeffReturnType | value () const |
| void | visit (Visitor &func) const |
Static Public Member Functions | |
| static const ConstantReturnType | Constant (const Scalar &value) |
| static const ConstantReturnType | Constant (Index rows, Index cols, const Scalar &value) |
| static const ConstantReturnType | Constant (Index size, const Scalar &value) |
| static const RandomAccessLinSpacedReturnType | LinSpaced (const Scalar &low, const Scalar &high) |
| static const RandomAccessLinSpacedReturnType | LinSpaced (Index size, const Scalar &low, const Scalar &high) |
| Sets a linearly space vector. | |
| static const SequentialLinSpacedReturnType | LinSpaced (Sequential_t, const Scalar &low, const Scalar &high) |
| static const SequentialLinSpacedReturnType | LinSpaced (Sequential_t, Index size, const Scalar &low, const Scalar &high) |
| Sets a linearly space vector. | |
| static const CwiseNullaryOp< CustomNullaryOp, ArrayWrapper< ExpressionType > > | NullaryExpr (const CustomNullaryOp &func) |
| static const CwiseNullaryOp< CustomNullaryOp, ArrayWrapper< ExpressionType > > | NullaryExpr (Index rows, Index cols, const CustomNullaryOp &func) |
| static const CwiseNullaryOp< CustomNullaryOp, ArrayWrapper< ExpressionType > > | NullaryExpr (Index size, const CustomNullaryOp &func) |
| static const ConstantReturnType | Ones () |
| static const ConstantReturnType | Ones (Index rows, Index cols) |
| static const ConstantReturnType | Ones (Index size) |
| static const CwiseNullaryOp< internal::scalar_random_op< Scalar >, ArrayWrapper< ExpressionType > > | Random () |
| static const CwiseNullaryOp< internal::scalar_random_op< Scalar >, ArrayWrapper< ExpressionType > > | Random (Index rows, Index cols) |
| static const CwiseNullaryOp< internal::scalar_random_op< Scalar >, ArrayWrapper< ExpressionType > > | Random (Index size) |
| static const ConstantReturnType | Zero () |
| static const ConstantReturnType | Zero (Index rows, Index cols) |
| static const ConstantReturnType | Zero (Index size) |
Related Symbols | |
(Note that these are not member symbols.) | |
| std::ostream & | operator<< (std::ostream &s, const DenseBase< ArrayWrapper< ExpressionType > > &m) |
Expression of a mathematical vector or matrix as an array object.
This class is the return type of MatrixBase::array(), and most of the time this is the only way it is use.
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inherited |
The type of indices.
To change this, #define the preprocessor symbol EIGEN_DEFAULT_DENSE_INDEX_TYPE.
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inlineinherited |
*this Example:
Output:
1 2 3
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inlineinherited |
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inlineinherited |
Example:
Output:
1.57 0.785 0
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inlineinherited |
Example:
Output:
Is ( 0.68 -0.211 0.566) inside the box: 0 Is (0.597 0.823 0.605) inside the box: 1
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inlineinherited |
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inlineinherited |
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inlineinherited |
*this and other *this and other The template parameter CustomBinaryOp is the type of the functor of the custom operator (see class CwiseBinaryOp for an example)
Here is an example illustrating the use of custom functors:
Output:
(0.68,0.271) (0.823,-0.967) (-0.444,-0.687) (-0.27,0.998) (-0.211,0.435) (-0.605,-0.514) (0.108,-0.198) (0.0268,-0.563) (0.566,-0.717) (-0.33,-0.726) (-0.0452,-0.74) (0.904,0.0259) (0.597,0.214) (0.536,0.608) (0.258,-0.782) (0.832,0.678)
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inlineinherited |
The template parameters BlockRows and BlockCols are the number of rows and columns in the block.
| startRow | the first row in the block |
| startCol | the first column in the block |
Example:
Output:
Here is the matrix m: 7 9 -5 -3 -2 -6 1 0 6 -3 0 9 6 6 3 9 Here is m.block<2,2>(1,1): -6 1 -3 0 Now the matrix m is: 7 9 -5 -3 -2 0 0 0 6 0 0 9 6 6 3 9
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inlineinherited |
This is the const version of block<>(Index, Index).
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inlineinherited |
| startRow | the first row in the block |
| startCol | the first column in the block |
| blockRows | the number of rows in the block |
| blockCols | the number of columns in the block |
Example:
Output:
Here is the matrix m: 7 9 -5 -3 -2 -6 1 0 6 -3 0 9 6 6 3 9 Here is m.block(1, 1, 2, 2): -6 1 -3 0 Now the matrix m is: 7 9 -5 -3 -2 0 0 0 6 0 0 9 6 6 3 9
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inlineinherited |
This is the const version of block(Index,Index,Index,Index).
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inlineinherited |
The template parameters CRows and CCols are the number of rows and columns in the corner.
Example:
Output:
Here is the matrix m: 7 9 -5 -3 -2 -6 1 0 6 -3 0 9 6 6 3 9 Here is m.bottomLeftCorner<2,2>(): 6 -3 6 6 Now the matrix m is: 7 9 -5 -3 -2 -6 1 0 0 0 0 9 0 0 3 9
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inlineinherited |
This is the const version of bottomLeftCorner<int, int>().
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inlineinherited |
| cRows | the number of rows in the corner |
| cCols | the number of columns in the corner |
Example:
Output:
Here is the matrix m: 7 9 -5 -3 -2 -6 1 0 6 -3 0 9 6 6 3 9 Here is m.bottomLeftCorner(2, 2): 6 -3 6 6 Now the matrix m is: 7 9 -5 -3 -2 -6 1 0 0 0 0 9 0 0 3 9
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inlineinherited |
This is the const version of bottomLeftCorner(Index, Index).
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inlineinherited |
The template parameters CRows and CCols are the number of rows and columns in the corner.
Example:
Output:
Here is the matrix m: 7 9 -5 -3 -2 -6 1 0 6 -3 0 9 6 6 3 9 Here is m.bottomRightCorner<2,2>(): 0 9 3 9 Now the matrix m is: 7 9 -5 -3 -2 -6 1 0 6 -3 0 0 6 6 0 0
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inlineinherited |
This is the const version of bottomRightCorner<int, int>().
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inlineinherited |
| cRows | the number of rows in the corner |
| cCols | the number of columns in the corner |
Example:
Output:
Here is the matrix m: 7 9 -5 -3 -2 -6 1 0 6 -3 0 9 6 6 3 9 Here is m.bottomRightCorner(2, 2): 0 9 3 9 Now the matrix m is: 7 9 -5 -3 -2 -6 1 0 6 -3 0 0 6 6 0 0
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inlineinherited |
This is the const version of bottomRightCorner(Index, Index).
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inlineinherited |
| N | the number of rows in the block |
Example:
Output:
Here is the array a: 7 9 -5 -3 -2 -6 1 0 6 -3 0 9 6 6 3 9 Here is a.bottomRows<2>(): 6 -3 0 9 6 6 3 9 Now the array a is: 7 9 -5 -3 -2 -6 1 0 0 0 0 0 0 0 0 0
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inlineinherited |
This is the const version of bottomRows<int>().
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inlineinherited |
| n | the number of rows in the block |
Example:
Output:
Here is the array a: 7 9 -5 -3 -2 -6 1 0 6 -3 0 9 6 6 3 9 Here is a.bottomRows(2): 6 -3 0 9 6 6 3 9 Now the array a is: 7 9 -5 -3 -2 -6 1 0 0 0 0 0 0 0 0 0
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inlineinherited |
This is the const version of bottomRows(Index).
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inlineinherited |
The template parameter NewScalar is the type we are casting the scalars to.
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inlineinherited |
Example:
Output:
1 4 0 0 5 0 0 6 1
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inlineinherited |
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inlineinherited |
Example:
Output:
Here is the matrix m: 0.68 0.597 -0.33 -0.211 0.823 0.536 0.566 -0.605 -0.444 Here is the sum of each column: 1.04 0.815 -0.238 Here is the maximum absolute value of each column: 0.68 0.823 0.536
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inlineinherited |
*this.
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inlinestaticinherited |
This variant is only for fixed-size DenseBase types. For dynamic-size types, you need to use the variants taking size arguments.
The template parameter CustomNullaryOp is the type of the functor.
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inlinestaticinherited |
The parameters rows and cols are the number of rows and of columns of the returned matrix. Must be compatible with this DenseBase type.
This variant is meant to be used for dynamic-size matrix types. For fixed-size types, it is redundant to pass rows and cols as arguments, so Zero() should be used instead.
The template parameter CustomNullaryOp is the type of the functor.
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inlinestaticinherited |
The parameter size is the size of the returned vector. Must be compatible with this DenseBase type.
This is only for vectors (either row-vectors or column-vectors), i.e. matrices which are known at compile-time to have either one row or one column.
This variant is meant to be used for dynamic-size vector types. For fixed-size types, it is redundant to pass size as argument, so Zero() should be used instead.
The template parameter CustomNullaryOp is the type of the functor.
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inlineinherited |
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inlineinherited |
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inlineinherited |
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inlineinherited |
*this Example:
Output:
2 4 6 5 1 0
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inlineinherited |
*this Example:
Output:
4 16 36 25 1 0
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inlineinherited |
*this and a scalar s
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inlineinherited |
Example:
Output:
0.5 2 1 0.333 4 1
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inlineinherited |
Example:
Output:
1 1.41 2
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inlineinherited |
Example:
Output:
a: 7 6 -3 -2 9 6 6 -6 -5 b: 1 -3 9 0 0 3 3 9 5 c: 7 -18 -27 0 0 18 18 -54 -25
Example:
Output:
Comparing m with identity matrix: 1 1 0 1 Number of coefficients that are equal: 3
Example:
Output:
Comparing m with identity matrix: 0 0 1 0 Number of coefficients that are not equal: 1
Example:
Output:
2 2 3
Example:
Output:
4 3 4
Example:
Output:
0.5 1.5 1.33
*this and other *this and other *this and other Example:
Output:
2 2 3
*this and scalar other *this and other Example:
Output:
4 3 4
*this and scalar other Example:
Output:
1 0 0
Example:
Output:
1 1 0
Example:
Output:
0 0 1
Example:
Output:
0 1 1
Example:
Output:
0 1 0
Example:
Output:
1 0 1
*this with each coeff incremented by the constant scalar Example:
Output:
6 7 8
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inlineinherited |
Notice that in the case of a plain matrix or vector (not an expression) this function just returns a const reference, in order to avoid a useless copy.
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inlineinherited |
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inlineinherited |
Alias for setConstant(): sets all coefficients in this expression to value.
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inlineinherited |
This is mostly for internal use.
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inlineinherited |
See class IOFormat for some examples.
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inlineinherited |
This is only for vectors (either row-vectors or column-vectors), i.e. matrices which are known at compile-time to have either one row or one column.
The template parameter Size is the number of coefficients in the block
Example:
Output:
Here is the vector v: 7 -2 6 6 Here is v.head(2): 7 -2 Now the vector v is: 0 0 6 6
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inlineinherited |
This is the const version of head<int>().
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inlineinherited |
This is only for vectors (either row-vectors or column-vectors), i.e. matrices which are known at compile-time to have either one row or one column.
| size | the number of coefficients in the block |
Example:
Output:
Here is the vector v: 7 -2 6 6 Here is v.head(2): 7 -2 Now the vector v is: 0 0 6 6
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inlineinherited |
This is the const version of head(Index).
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inlineinherited |
*this.
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inlineinherited |
*this.
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inlineinherited |
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inlineinherited |
Example:
Output:
0.5 0.333 0.25
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inherited |
true if *this is approximately equal to other, within the precision determined by prec.


![\[ \Vert v - w \Vert \leqslant p\,\min(\Vert v\Vert, \Vert w\Vert). \]](form_15.png)
*this is approximately equal to the zero matrix or vector. Indeed, isApprox(zero) returns false unless *this itself is exactly the zero matrix or vector. If you want to test whether *this is zero, use internal::isMuchSmallerThan(const
RealScalar&, RealScalar) instead.
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inherited |
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inherited |
This is just an alias for isApproxToConstant().
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inherited |
true if the norm of *this is much smaller than the norm of other, within the precision determined by prec.


![\[ \Vert v \Vert \leqslant p\,\Vert w\Vert. \]](form_18.png)
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inherited |
true if the norm of *this is much smaller than other, within the precision determined by prec.


![\[ \Vert v \Vert \leqslant p\,\vert x\vert. \]](form_17.png)
For matrices, the comparison is done using the Hilbert-Schmidt norm. For this reason, the value of the reference scalar other should come from the Hilbert-Schmidt norm of a reference matrix of same dimensions.
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inherited |
Example:
Output:
Here's the matrix m: 1 1 1 1 1 1 1 1 1 m.isOnes() returns: 0 m.isOnes(1e-3) returns: 1
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inherited |
Example:
Output:
Here's the matrix m:
0 0 0.0001
0 0 0
0 0 0
m.isZero() returns: 0
m.isZero(1e-3) returns: 1
|
inlineinherited |
| N | the number of columns in the block |
Example:
Output:
Here is the array a: 7 9 -5 -3 -2 -6 1 0 6 -3 0 9 6 6 3 9 Here is a.leftCols<2>(): 7 9 -2 -6 6 -3 6 6 Now the array a is: 0 0 -5 -3 0 0 1 0 0 0 0 9 0 0 3 9
|
inlineinherited |
This is the const version of leftCols<int>().
|
inlineinherited |
| n | the number of columns in the block |
Example:
Output:
Here is the array a: 7 9 -5 -3 -2 -6 1 0 6 -3 0 9 6 6 3 9 Here is a.leftCols(2): 7 9 -2 -6 6 -3 6 6 Now the array a is: 0 0 -5 -3 0 0 1 0 0 0 0 9 0 0 3 9
|
inlineinherited |
This is the const version of leftCols(Index).
|
inlinestaticinherited |
Special version for fixed size types which does not require the size parameter.
|
inlinestaticinherited |
Sets a linearly space vector.
The function generates 'size' equally spaced values in the closed interval [low,high]. When size is set to 1, a vector of length 1 containing 'high' is returned.
This is only for vectors (either row-vectors or column-vectors), i.e. matrices which are known at compile-time to have either one row or one column.
Example:
Output:
7 8 9 10 0 0.25 0.5 0.75 1
|
inlinestaticinherited |
Special version for fixed size types which does not require the size parameter.
|
inlinestaticinherited |
Sets a linearly space vector.
The function generates 'size' equally spaced values in the closed interval [low,high]. This particular version of LinSpaced() uses sequential access, i.e. vector access is assumed to be a(0), a(1), ..., a(size). This assumption allows for better vectorization and yields faster code than the random access version.
When size is set to 1, a vector of length 1 containing 'high' is returned.
This is only for vectors (either row-vectors or column-vectors), i.e. matrices which are known at compile-time to have either one row or one column.
Example:
Output:
7 8 9 10 0 0.25 0.5 0.75 1
|
inlineinherited |
Example:
Output:
0 0.693 1.1
|
inlineinherited |
|
inlineinherited |
|
inherited |
|
inherited |
|
inlineinherited |
|
inlineinherited |
| N | the number of columns in the block |
| startCol | the index of the first column in the block |
Example:
Output:
A = 7 -6 0 9 -10 -2 -3 3 3 -5 6 6 -3 5 -8 6 -5 0 -8 6 9 1 9 2 -7 A(:,1..3) = -6 0 9 -3 3 3 6 -3 5 -5 0 -8 1 9 2
|
inlineinherited |
This is the const version of middleCols<int>().
| startCol | the index of the first column in the block |
| numCols | the number of columns in the block |
Example:
Output:
A = 7 -6 0 9 -10 -2 -3 3 3 -5 6 6 -3 5 -8 6 -5 0 -8 6 9 1 9 2 -7 A(1..3,:) = -6 0 9 -3 3 3 6 -3 5 -5 0 -8 1 9 2
This is the const version of middleCols(Index,Index).
|
inlineinherited |
| N | the number of rows in the block |
| startRow | the index of the first row in the block |
Example:
Output:
A = 7 -6 0 9 -10 -2 -3 3 3 -5 6 6 -3 5 -8 6 -5 0 -8 6 9 1 9 2 -7 A(1..3,:) = -2 -3 3 3 -5 6 6 -3 5 -8 6 -5 0 -8 6
|
inlineinherited |
This is the const version of middleRows<int>().
| startRow | the index of the first row in the block |
| numRows | the number of rows in the block |
Example:
Output:
A = 7 -6 0 9 -10 -2 -3 3 3 -5 6 6 -3 5 -8 6 -5 0 -8 6 9 1 9 2 -7 A(2..3,:) = 6 6 -3 5 -8 6 -5 0 -8 6
This is the const version of middleRows(Index,Index).
|
inlineinherited |
|
inherited |
|
inherited |
|
inlineinherited |
|
inlineinherited |
|
inlinestaticinherited |
This variant is only for fixed-size DenseBase types. For dynamic-size types, you need to use the variants taking size arguments.
The template parameter CustomNullaryOp is the type of the functor.
|
inlinestaticinherited |
The parameters rows and cols are the number of rows and of columns of the returned matrix. Must be compatible with this MatrixBase type.
This variant is meant to be used for dynamic-size matrix types. For fixed-size types, it is redundant to pass rows and cols as arguments, so Zero() should be used instead.
The template parameter CustomNullaryOp is the type of the functor.
|
inlinestaticinherited |
The parameter size is the size of the returned vector. Must be compatible with this MatrixBase type.
This is only for vectors (either row-vectors or column-vectors), i.e. matrices which are known at compile-time to have either one row or one column.
This variant is meant to be used for dynamic-size vector types. For fixed-size types, it is redundant to pass size as argument, so Zero() should be used instead.
The template parameter CustomNullaryOp is the type of the functor.
|
inlinestaticinherited |
This variant is only for fixed-size MatrixBase types. For dynamic-size types, you need to use the variants taking size arguments.
Example:
Output:
1 1 1 1 6 6 6 6
|
inlinestaticinherited |
The parameters rows and cols are the number of rows and of columns of the returned matrix. Must be compatible with this MatrixBase type.
This variant is meant to be used for dynamic-size matrix types. For fixed-size types, it is redundant to pass rows and cols as arguments, so Ones() should be used instead.
Example:
Output:
1 1 1 1 1 1
|
inlinestaticinherited |
The parameter size is the size of the returned vector. Must be compatible with this MatrixBase type.
This is only for vectors (either row-vectors or column-vectors), i.e. matrices which are known at compile-time to have either one row or one column.
This variant is meant to be used for dynamic-size vector types. For fixed-size types, it is redundant to pass size as argument, so Ones() should be used instead.
Example:
Output:
6 6 6 6 1 1
|
inlineinherited |
Example:
Output:
0 0 0
|
inlineinherited |
*this scaled by the scalar factor scalar
|
inlineinherited |
Overloaded for efficient real matrix times complex scalar value
|
inlineinherited |
replaces *this by *this * other coefficient wise.
*this
|
inlineinherited |
replaces *this by *this + other.
*this
|
inlineinherited |
*this
|
inlineinherited |
*this with each coeff decremented by the constant scalar Example:
Output:
-4 -3 -2
|
inlineinherited |
replaces *this by *this - other.
*this
|
inlineinherited |
*this divided by the scalar value scalar
|
inlineinherited |
replaces *this by *this / other coefficient wise.
*this
|
inlineinherited |
|
inlineinherited |
Convenient operator to set the coefficients of a matrix.
The coefficients must be provided in a row major order and exactly match the size of the matrix. Otherwise an assertion is raised.
Example:
Output:
1 2 3 4 5 6 7 8 9 10 11 0 12 13 0 0 0 1 14 15 16 14 5 6 15 8 9
|
inlineinherited |
Example:
Output:
1 0 1
|
inlineinherited |
|
inlineinherited |
|
inlineinherited |
Example:
Output:
Here is the matrix m: 0.68 0.597 -0.33 -0.211 0.823 0.536 0.566 -0.605 -0.444 Here is the product of all the coefficients: 0.0019
|
inlinestaticinherited |
This variant is only for fixed-size MatrixBase types. For dynamic-size types, you need to use the variants taking size arguments.
Example:
Output:
700 600 -200 600
This expression has the "evaluate before nesting" flag so that it will be evaluated into a temporary matrix whenever it is nested in a larger expression. This prevents unexpected behavior with expressions involving random matrices.
|
inlinestaticinherited |
The parameters rows and cols are the number of rows and of columns of the returned matrix. Must be compatible with this MatrixBase type.
This variant is meant to be used for dynamic-size matrix types. For fixed-size types, it is redundant to pass rows and cols as arguments, so Random() should be used instead.
Example:
Output:
7 6 9 -2 6 -6
This expression has the "evaluate before nesting" flag so that it will be evaluated into a temporary matrix whenever it is nested in a larger expression. This prevents unexpected behavior with expressions involving random matrices.
|
inlinestaticinherited |
The parameter size is the size of the returned vector. Must be compatible with this MatrixBase type.
This is only for vectors (either row-vectors or column-vectors), i.e. matrices which are known at compile-time to have either one row or one column.
This variant is meant to be used for dynamic-size vector types. For fixed-size types, it is redundant to pass size as argument, so Random() should be used instead.
Example:
Output:
7 -2
This expression has the "evaluate before nesting" flag so that it will be evaluated into a temporary vector whenever it is nested in a larger expression. This prevents unexpected behavior with expressions involving random matrices.
|
inlineinherited |
*this.
|
inlineinherited |
*this.
|
inlineinherited |
The template parameter BinaryOp is the type of the functor func which must be an associative operator. Both current STL and TR1 functor styles are handled.
|
inlineinherited |
*this Example:
Output:
Here is the matrix m: 7 6 9 -2 6 -6 m.replicate<3,2>() = ... 7 6 9 7 6 9 -2 6 -6 -2 6 -6 7 6 9 7 6 9 -2 6 -6 -2 6 -6 7 6 9 7 6 9 -2 6 -6 -2 6 -6
|
inlineinherited |
*this Example:
Output:
Here is the vector v: 7 -2 6 v.replicate(2,5) = ... 7 7 7 7 7 -2 -2 -2 -2 -2 6 6 6 6 6 7 7 7 7 7 -2 -2 -2 -2 -2 6 6 6 6 6
Forwards the resizing request to the nested expression
|
inline |
Forwards the resizing request to the nested expression
|
inlineinherited |
Example:
Output:
Here is the matrix m: 7 6 -3 1 -2 9 6 0 6 -6 -5 3 Here is the reverse of m: 3 -5 -6 6 0 6 9 -2 1 -3 6 7 Here is the coefficient (1,0) in the reverse of m: 0 Let us overwrite this coefficient with the value 4. Now the matrix m is: 7 6 -3 1 -2 9 6 4 6 -6 -5 3
|
inlineinherited |
This is the const version of reverse().
|
inlineinherited |
This is the "in place" version of reverse: it reverses *this.
In most cases it is probably better to simply use the reversed expression of a matrix. However, when reversing the matrix data itself is really needed, then this "in-place" version is probably the right choice because it provides the following additional features:
|
inlineinherited |
| N | the number of columns in the block |
Example:
Output:
Here is the array a: 7 9 -5 -3 -2 -6 1 0 6 -3 0 9 6 6 3 9 Here is a.rightCols<2>(): -5 -3 1 0 0 9 3 9 Now the array a is: 7 9 0 0 -2 -6 0 0 6 -3 0 0 6 6 0 0
|
inlineinherited |
This is the const version of rightCols<int>().
|
inlineinherited |
| n | the number of columns in the block |
Example:
Output:
Here is the array a: 7 9 -5 -3 -2 -6 1 0 6 -3 0 9 6 6 3 9 Here is a.rightCols(2): -5 -3 1 0 0 9 3 9 Now the array a is: 7 9 0 0 -2 -6 0 0 6 -3 0 0 6 6 0 0
|
inlineinherited |
This is the const version of rightCols(Index).
|
inlineinherited |
Example:
Output:
1 0 0 4 5 6 0 0 1
|
inlineinherited |
|
inlineinherited |
Example:
Output:
Here is the matrix m: 0.68 0.597 -0.33 -0.211 0.823 0.536 0.566 -0.605 -0.444 Here is the sum of each row: 0.948 1.15 -0.483 Here is the maximum absolute value of each row: 0.68 0.823 0.605
|
inlineinherited |
*this This is only for vectors (either row-vectors or column-vectors), i.e. matrices which are known at compile-time to have either one row or one column.
The template parameter Size is the number of coefficients in the block
| start | the index of the first element of the sub-vector |
Example:
Output:
Here is the vector v: 7 -2 6 6 Here is v.segment<2>(1): -2 6 Now the vector v is: 7 -2 0 0
|
inlineinherited |
This is the const version of segment<int>(Index).
|
inlineinherited |
This is only for vectors (either row-vectors or column-vectors), i.e. matrices which are known at compile-time to have either one row or one column.
| start | the first coefficient in the segment |
| size | the number of coefficients in the segment |
Example:
Output:
Here is the vector v: 7 -2 6 6 Here is v.segment(1, 2): -2 6 Now the vector v is: 7 0 0 6
|
inlineinherited |
This is the const version of segment(Index,Index).
|
inlineinherited |
*this(i,j), and elseMatrix(i,j) otherwise.Example:
Output:
1 2 3 4 -5 -6 -7 -8 -9
|
inlineinherited |
Version of DenseBase::select(const DenseBase&, const DenseBase&) with the else expression being a scalar value.
|
inlineinherited |
Version of DenseBase::select(const DenseBase&, const DenseBase&) with the then expression being a scalar value.
|
inlineinherited |
Sets all coefficients in this expression to value.
|
inlineinherited |
Sets a linearly space vector.
The function fill *this with equally spaced values in the closed interval [low,high]. When size is set to 1, a vector of length 1 containing 'high' is returned.
This is only for vectors (either row-vectors or column-vectors), i.e. matrices which are known at compile-time to have either one row or one column.
|
inlineinherited |
Sets a linearly space vector.
The function generates 'size' equally spaced values in the closed interval [low,high]. When size is set to 1, a vector of length 1 containing 'high' is returned.
This is only for vectors (either row-vectors or column-vectors), i.e. matrices which are known at compile-time to have either one row or one column.
Example:
Output:
0.5 0.75 1 1.25 1.5
|
inlineinherited |
Sets all coefficients in this expression to one.
Example:
Output:
7 9 -5 -3 1 1 1 1 6 -3 0 9 6 6 3 9
|
inlineinherited |
Sets all coefficients in this expression to random values.
Example:
Output:
0 7 0 0 0 -2 0 0 0 6 0 0 0 6 0 0
|
inlineinherited |
Sets all coefficients in this expression to zero.
Example:
Output:
7 9 -5 -3 0 0 0 0 6 -3 0 9 6 6 3 9
|
inlineinherited |
|
inlineinherited |
|
inlineinherited |
Example:
Output:
4 9 16
|
inlineinherited |
|
inlineinherited |
swaps *this with the expression other.
|
inlineinherited |
swaps *this with the matrix or array other.
|
inlineinherited |
This is only for vectors (either row-vectors or column-vectors), i.e. matrices which are known at compile-time to have either one row or one column.
The template parameter Size is the number of coefficients in the block
Example:
Output:
Here is the vector v: 7 -2 6 6 Here is v.tail(2): 6 6 Now the vector v is: 7 -2 0 0
|
inlineinherited |
This is the const version of tail<int>.
|
inlineinherited |
This is only for vectors (either row-vectors or column-vectors), i.e. matrices which are known at compile-time to have either one row or one column.
| size | the number of coefficients in the block |
Example:
Output:
Here is the vector v: 7 -2 6 6 Here is v.tail(2): 6 6 Now the vector v is: 7 -2 0 0
|
inlineinherited |
This is the const version of tail(Index).
|
inlineinherited |
|
inlineinherited |
The template parameters CRows and CCols are the number of rows and columns in the corner.
Example:
Output:
Here is the matrix m: 7 9 -5 -3 -2 -6 1 0 6 -3 0 9 6 6 3 9 Here is m.topLeftCorner<2,2>(): 7 9 -2 -6 Now the matrix m is: 0 0 -5 -3 0 0 1 0 6 -3 0 9 6 6 3 9
|
inlineinherited |
This is the const version of topLeftCorner<int, int>().
|
inlineinherited |
| cRows | the number of rows in the corner |
| cCols | the number of columns in the corner |
Example:
Output:
Here is the matrix m: 7 9 -5 -3 -2 -6 1 0 6 -3 0 9 6 6 3 9 Here is m.topLeftCorner(2, 2): 7 9 -2 -6 Now the matrix m is: 0 0 -5 -3 0 0 1 0 6 -3 0 9 6 6 3 9
|
inlineinherited |
This is the const version of topLeftCorner(Index, Index).
|
inlineinherited |
The template parameters CRows and CCols are the number of rows and columns in the corner.
Example:
Output:
Here is the matrix m: 7 9 -5 -3 -2 -6 1 0 6 -3 0 9 6 6 3 9 Here is m.topRightCorner<2,2>(): -5 -3 1 0 Now the matrix m is: 7 9 0 0 -2 -6 0 0 6 -3 0 9 6 6 3 9
|
inlineinherited |
This is the const version of topRightCorner<int, int>().
|
inlineinherited |
| cRows | the number of rows in the corner |
| cCols | the number of columns in the corner |
Example:
Output:
Here is the matrix m: 7 9 -5 -3 -2 -6 1 0 6 -3 0 9 6 6 3 9 Here is m.topRightCorner(2, 2): -5 -3 1 0 Now the matrix m is: 7 9 0 0 -2 -6 0 0 6 -3 0 9 6 6 3 9
|
inlineinherited |
This is the const version of topRightCorner(Index, Index).
|
inlineinherited |
| N | the number of rows in the block |
Example:
Output:
Here is the array a: 7 9 -5 -3 -2 -6 1 0 6 -3 0 9 6 6 3 9 Here is a.topRows<2>(): 7 9 -5 -3 -2 -6 1 0 Now the array a is: 0 0 0 0 0 0 0 0 6 -3 0 9 6 6 3 9
|
inlineinherited |
This is the const version of topRows<int>().
|
inlineinherited |
| n | the number of rows in the block |
Example:
Output:
Here is the array a: 7 9 -5 -3 -2 -6 1 0 6 -3 0 9 6 6 3 9 Here is a.topRows(2): 7 9 -5 -3 -2 -6 1 0 Now the array a is: 0 0 0 0 0 0 0 0 6 -3 0 9 6 6 3 9
|
inlineinherited |
This is the const version of topRows(Index).
|
inlineinherited |
Example:
Output:
Here is the matrix m: 7 6 -2 6 Here is the transpose of m: 7 -2 6 6 Here is the coefficient (1,0) in the transpose of m: 6 Let us overwrite this coefficient with the value 0. Now the matrix m is: 7 0 -2 6
|
inlineinherited |
This is the const version of transpose().
Make sure you read the warning for transpose() !
|
inlineinherited |
This is the "in place" version of transpose(): it replaces *this by its own transpose. Thus, doing
has the same effect on m as doing
and is faster and also safer because in the latter line of code, forgetting the eval() results in a bug caused by aliasing.
Notice however that this method is only useful if you want to replace a matrix by its own transpose. If you just need the transpose of a matrix, use transpose().
*this must be a resizable matrix.
|
inlineinherited |
Apply a unary operator coefficient-wise.
| [in] | func | Functor implementing the unary operator |
| CustomUnaryOp | Type of func |
The function ptr_fun() from the C++ standard library can be used to make functors out of normal functions.
Example:
Output:
0.68 0.823 -0.444 -0.27
-0.211 -0.605 0.108 0.0268
0.566 -0.33 -0.0452 0.904
0.597 0.536 0.258 0.832
becomes:
0.68 0.823 0 0
0 0 0.108 0.0268
0.566 0 0 0.904
0.597 0.536 0.258 0.832
Genuine functors allow for more possibilities, for instance it may contain a state.
Example:
Output:
0.68 0.823 -0.444 -0.27
-0.211 -0.605 0.108 0.0268
0.566 -0.33 -0.0452 0.904
0.597 0.536 0.258 0.832
becomes:
0.5 0.5 -0.444 -0.27
-0.211 -0.5 0.108 0.0268
0.5 -0.33 -0.0452 0.5
0.5 0.5 0.258 0.5
|
inlineinherited |
The template parameter CustomUnaryOp is the type of the functor of the custom unary operator.
Example:
Output:
0.68 0.823 -0.444 -0.27
-0.211 -0.605 0.108 0.0268
0.566 -0.33 -0.0452 0.904
0.597 0.536 0.258 0.832
becomes:
0.5 0.5 -0.444 -0.27
-0.211 -0.5 0.108 0.0268
0.5 -0.33 -0.0452 0.5
0.5 0.5 0.258 0.5
|
inlineinherited |
|
inherited |
Applies the visitor visitor to the whole coefficients of the matrix or vector.
The template parameter Visitor is the type of the visitor and provides the following interface:
|
inlinestaticinherited |
This variant is only for fixed-size MatrixBase types. For dynamic-size types, you need to use the variants taking size arguments.
Example:
Output:
0 0 0 0 0 0 0 0
|
inlinestaticinherited |
The parameters rows and cols are the number of rows and of columns of the returned matrix. Must be compatible with this MatrixBase type.
This variant is meant to be used for dynamic-size matrix types. For fixed-size types, it is redundant to pass rows and cols as arguments, so Zero() should be used instead.
Example:
Output:
0 0 0 0 0 0
|
inlinestaticinherited |
The parameter size is the size of the returned vector. Must be compatible with this MatrixBase type.
This is only for vectors (either row-vectors or column-vectors), i.e. matrices which are known at compile-time to have either one row or one column.
This variant is meant to be used for dynamic-size vector types. For fixed-size types, it is redundant to pass size as argument, so Zero() should be used instead.
Example:
Output:
0 0 0 0 0 0
|
Outputs the matrix, to the given stream.
If you wish to print the matrix with a format different than the default, use DenseBase::format().
It is also possible to change the default format by defining EIGEN_DEFAULT_IO_FORMAT before including Eigen headers. If not defined, this will automatically be defined to Eigen::IOFormat(), that is the Eigen::IOFormat with default parameters.