Sleipnir Python API
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Classes | Functions
sleipnir.autodiff Namespace Reference

Classes

class  ExpressionType
 
class  Gradient
 
class  Hessian
 
class  Jacobian
 
class  Variable
 
class  VariableBlock
 
class  VariableMatrix
 

Functions

Variable abs (float x)
 
Variable abs (Variable x)
 
VariableMatrix abs (VariableMatrix x)
 
VariableMatrix abs (VariableBlock x)
 
Variable acos (float x)
 
Variable acos (Variable x)
 
VariableMatrix acos (VariableMatrix x)
 
VariableMatrix acos (VariableBlock x)
 
Variable asin (float x)
 
Variable asin (Variable x)
 
VariableMatrix asin (VariableMatrix x)
 
VariableMatrix asin (VariableBlock x)
 
Variable atan (float x)
 
Variable atan (Variable x)
 
VariableMatrix atan (VariableMatrix x)
 
VariableMatrix atan (VariableBlock x)
 
Variable atan2 (float y, float x)
 
Variable atan2 (float y, Variable x)
 
Variable atan2 (Variable y, float x)
 
Variable atan2 (Variable y, Variable x)
 
Variable cbrt (float x)
 
Variable cbrt (Variable x)
 
VariableMatrix cbrt (VariableMatrix x)
 
VariableMatrix cbrt (VariableBlock x)
 
Variable cos (float x)
 
Variable cos (Variable x)
 
VariableMatrix cos (VariableMatrix x)
 
VariableMatrix cos (VariableBlock x)
 
Variable cosh (float x)
 
Variable cosh (Variable x)
 
VariableMatrix cosh (VariableMatrix x)
 
VariableMatrix cosh (VariableBlock x)
 
Variable erf (float x)
 
Variable erf (Variable x)
 
VariableMatrix erf (VariableMatrix x)
 
VariableMatrix erf (VariableBlock x)
 
Variable exp (float x)
 
Variable exp (Variable x)
 
VariableMatrix exp (VariableMatrix x)
 
VariableMatrix exp (VariableBlock x)
 
Variable hypot (float x, float y)
 
Variable hypot (float x, Variable y)
 
Variable hypot (Variable x, float y)
 
Variable hypot (Variable x, Variable y)
 
Variable hypot (float x, float y, float z)
 
Variable hypot (float x, float y, Variable z)
 
Variable hypot (float x, Variable y, float z)
 
Variable hypot (float x, Variable y, Variable z)
 
Variable hypot (Variable x, float y, float z)
 
Variable hypot (Variable x, float y, Variable z)
 
Variable hypot (Variable x, Variable y, float z)
 
Variable hypot (Variable x, Variable y, Variable z)
 
Variable log (float x)
 
Variable log (Variable x)
 
VariableMatrix log (VariableMatrix x)
 
VariableMatrix log (VariableBlock x)
 
Variable log10 (float x)
 
Variable log10 (Variable x)
 
VariableMatrix log10 (VariableMatrix x)
 
VariableMatrix log10 (VariableBlock x)
 
Variable max (float a, float b)
 
Variable max (float a, Variable b)
 
Variable max (Variable a, float b)
 
Variable max (Variable a, Variable b)
 
Variable min (float a, float b)
 
Variable min (float a, Variable b)
 
Variable min (Variable a, float b)
 
Variable min (Variable a, Variable b)
 
Variable pow (float base, float power)
 
Variable pow (float base, Variable power)
 
Variable pow (Variable base, float power)
 
Variable pow (Variable base, Variable power)
 
Variable sign (float x)
 
Variable sign (Variable x)
 
VariableMatrix sign (VariableMatrix x)
 
VariableMatrix sign (VariableBlock x)
 
Variable sin (float x)
 
Variable sin (Variable x)
 
VariableMatrix sin (VariableMatrix x)
 
VariableMatrix sin (VariableBlock x)
 
Variable sinh (float x)
 
Variable sinh (Variable x)
 
VariableMatrix sinh (VariableMatrix x)
 
VariableMatrix sinh (VariableBlock x)
 
Variable sqrt (float x)
 
Variable sqrt (Variable x)
 
VariableMatrix sqrt (VariableMatrix x)
 
VariableMatrix sqrt (VariableBlock x)
 
Variable tan (float x)
 
Variable tan (Variable x)
 
VariableMatrix tan (VariableMatrix x)
 
VariableMatrix tan (VariableBlock x)
 
Variable tanh (float x)
 
Variable tanh (Variable x)
 
VariableMatrix tanh (VariableMatrix x)
 
VariableMatrix tanh (VariableBlock x)
 
VariableMatrix cwise_reduce (VariableMatrix lhs, VariableMatrix rhs, Callable[[Variable, Variable], Variable] func)
 
VariableMatrix block (Sequence[Sequence[VariableMatrix]] list)
 
VariableMatrix solve (VariableMatrix A, VariableMatrix B)
 
 spy (scipy.sparse.csc_matrix mat)
 

Function Documentation

◆ abs() [1/4]

Variable sleipnir.autodiff.abs ( float  x) 
abs() for Variables.

Template parameter ``Scalar``:
    Scalar type.

Parameter ``x``:
    The argument.

◆ abs() [2/4]

Variable sleipnir.autodiff.abs ( Variable  x)

◆ abs() [3/4]

VariableMatrix sleipnir.autodiff.abs ( VariableBlock  x)

◆ abs() [4/4]

VariableMatrix sleipnir.autodiff.abs ( VariableMatrix  x)

◆ acos() [1/4]

Variable sleipnir.autodiff.acos ( float  x) 
acos() for Variables.

Template parameter ``Scalar``:
    Scalar type.

Parameter ``x``:
    The argument.

◆ acos() [2/4]

Variable sleipnir.autodiff.acos ( Variable  x)

◆ acos() [3/4]

VariableMatrix sleipnir.autodiff.acos ( VariableBlock  x)

◆ acos() [4/4]

VariableMatrix sleipnir.autodiff.acos ( VariableMatrix  x)

◆ asin() [1/4]

Variable sleipnir.autodiff.asin ( float  x) 
asin() for Variables.

Template parameter ``Scalar``:
    Scalar type.

Parameter ``x``:
    The argument.

◆ asin() [2/4]

Variable sleipnir.autodiff.asin ( Variable  x)

◆ asin() [3/4]

VariableMatrix sleipnir.autodiff.asin ( VariableBlock  x)

◆ asin() [4/4]

VariableMatrix sleipnir.autodiff.asin ( VariableMatrix  x)

◆ atan() [1/4]

Variable sleipnir.autodiff.atan ( float  x) 
atan() for Variables.

Template parameter ``Scalar``:
    Scalar type.

Parameter ``x``:
    The argument.

◆ atan() [2/4]

Variable sleipnir.autodiff.atan ( Variable  x)

◆ atan() [3/4]

VariableMatrix sleipnir.autodiff.atan ( VariableBlock  x)

◆ atan() [4/4]

VariableMatrix sleipnir.autodiff.atan ( VariableMatrix  x)

◆ atan2() [1/4]

Variable sleipnir.autodiff.atan2 ( float  y,
float  x 
) 
atan2() for Variables.

Template parameter ``Scalar``:
    Scalar type.

Parameter ``y``:
    The y argument.

Parameter ``x``:
    The x argument.

◆ atan2() [2/4]

Variable sleipnir.autodiff.atan2 ( float  y,
Variable  x 
)

◆ atan2() [3/4]

Variable sleipnir.autodiff.atan2 ( Variable  y,
float  x 
)

◆ atan2() [4/4]

Variable sleipnir.autodiff.atan2 ( Variable  y,
Variable  x 
)

◆ block()

VariableMatrix sleipnir.autodiff.block ( Sequence[Sequence[VariableMatrix]]  list) 
Assembles a VariableMatrix from a nested list of blocks.

Each row's blocks must have the same height, and the assembled block
rows must have the same width. For example, for the block matrix [[A,
B], [C]] to be constructible, the number of rows in A and B must
match, and the number of columns in [A, B] and [C] must match.

Template parameter ``Scalar``:
    Scalar type.

Parameter ``list``:
    The nested list of blocks.

◆ cbrt() [1/4]

Variable sleipnir.autodiff.cbrt ( float  x) 
cbrt() for Variables.

Template parameter ``Scalar``:
    Scalar type.

Parameter ``x``:
    The argument.

◆ cbrt() [2/4]

Variable sleipnir.autodiff.cbrt ( Variable  x)

◆ cbrt() [3/4]

VariableMatrix sleipnir.autodiff.cbrt ( VariableBlock  x)

◆ cbrt() [4/4]

VariableMatrix sleipnir.autodiff.cbrt ( VariableMatrix  x)

◆ cos() [1/4]

Variable sleipnir.autodiff.cos ( float  x) 
cos() for Variables.

Template parameter ``Scalar``:
    Scalar type.

Parameter ``x``:
    The argument.

◆ cos() [2/4]

Variable sleipnir.autodiff.cos ( Variable  x)

◆ cos() [3/4]

VariableMatrix sleipnir.autodiff.cos ( VariableBlock  x)

◆ cos() [4/4]

VariableMatrix sleipnir.autodiff.cos ( VariableMatrix  x)

◆ cosh() [1/4]

Variable sleipnir.autodiff.cosh ( float  x) 
cosh() for Variables.

Template parameter ``Scalar``:
    Scalar type.

Parameter ``x``:
    The argument.

◆ cosh() [2/4]

Variable sleipnir.autodiff.cosh ( Variable  x)

◆ cosh() [3/4]

VariableMatrix sleipnir.autodiff.cosh ( VariableBlock  x)

◆ cosh() [4/4]

VariableMatrix sleipnir.autodiff.cosh ( VariableMatrix  x)

◆ cwise_reduce()

VariableMatrix sleipnir.autodiff.cwise_reduce ( VariableMatrix  lhs,
VariableMatrix  rhs,
Callable[[Variable, Variable], Variable]  func 
) 
Applies a coefficient-wise reduce operation to two matrices.

Template parameter ``Scalar``:
    Scalar type.

Parameter ``lhs``:
    The left-hand side of the binary operator.

Parameter ``rhs``:
    The right-hand side of the binary operator.

Parameter ``binary_op``:
    The binary operator to use for the reduce operation.

◆ erf() [1/4]

Variable sleipnir.autodiff.erf ( float  x) 
erf() for Variables.

Template parameter ``Scalar``:
    Scalar type.

Parameter ``x``:
    The argument.

◆ erf() [2/4]

Variable sleipnir.autodiff.erf ( Variable  x)

◆ erf() [3/4]

VariableMatrix sleipnir.autodiff.erf ( VariableBlock  x)

◆ erf() [4/4]

VariableMatrix sleipnir.autodiff.erf ( VariableMatrix  x)

◆ exp() [1/4]

Variable sleipnir.autodiff.exp ( float  x) 
exp() for Variables.

Template parameter ``Scalar``:
    Scalar type.

Parameter ``x``:
    The argument.

◆ exp() [2/4]

Variable sleipnir.autodiff.exp ( Variable  x)

◆ exp() [3/4]

VariableMatrix sleipnir.autodiff.exp ( VariableBlock  x)

◆ exp() [4/4]

VariableMatrix sleipnir.autodiff.exp ( VariableMatrix  x)

◆ hypot() [1/12]

Variable sleipnir.autodiff.hypot ( float  x,
float  y 
) 
hypot() for Variables.

Template parameter ``Scalar``:
    Scalar type.

Parameter ``x``:
    The x argument.

Parameter ``y``:
    The y argument.

◆ hypot() [2/12]

Variable sleipnir.autodiff.hypot ( float  x,
float  y,
float  z 
)

◆ hypot() [3/12]

Variable sleipnir.autodiff.hypot ( float  x,
float  y,
Variable  z 
)

◆ hypot() [4/12]

Variable sleipnir.autodiff.hypot ( float  x,
Variable  y 
)

◆ hypot() [5/12]

Variable sleipnir.autodiff.hypot ( float  x,
Variable  y,
float  z 
)

◆ hypot() [6/12]

Variable sleipnir.autodiff.hypot ( float  x,
Variable  y,
Variable  z 
)

◆ hypot() [7/12]

Variable sleipnir.autodiff.hypot ( Variable  x,
float  y 
)

◆ hypot() [8/12]

Variable sleipnir.autodiff.hypot ( Variable  x,
float  y,
float  z 
)

◆ hypot() [9/12]

Variable sleipnir.autodiff.hypot ( Variable  x,
float  y,
Variable  z 
)

◆ hypot() [10/12]

Variable sleipnir.autodiff.hypot ( Variable  x,
Variable  y 
)

◆ hypot() [11/12]

Variable sleipnir.autodiff.hypot ( Variable  x,
Variable  y,
float  z 
)

◆ hypot() [12/12]

Variable sleipnir.autodiff.hypot ( Variable  x,
Variable  y,
Variable  z 
)

◆ log() [1/4]

Variable sleipnir.autodiff.log ( float  x) 
log() for Variables.

Template parameter ``Scalar``:
    Scalar type.

Parameter ``x``:
    The argument.

◆ log() [2/4]

Variable sleipnir.autodiff.log ( Variable  x)

◆ log() [3/4]

VariableMatrix sleipnir.autodiff.log ( VariableBlock  x)

◆ log() [4/4]

VariableMatrix sleipnir.autodiff.log ( VariableMatrix  x)

◆ log10() [1/4]

Variable sleipnir.autodiff.log10 ( float  x) 
log10() for Variables.

Template parameter ``Scalar``:
    Scalar type.

Parameter ``x``:
    The argument.

◆ log10() [2/4]

Variable sleipnir.autodiff.log10 ( Variable  x)

◆ log10() [3/4]

VariableMatrix sleipnir.autodiff.log10 ( VariableBlock  x)

◆ log10() [4/4]

VariableMatrix sleipnir.autodiff.log10 ( VariableMatrix  x)

◆ max() [1/4]

Variable sleipnir.autodiff.max ( float  a,
float  b 
) 
max() for Variables.

Returns the greater of a and b. If the values are equivalent, returns
a.

Template parameter ``Scalar``:
    Scalar type.

Parameter ``a``:
    The a argument.

Parameter ``b``:
    The b argument.

◆ max() [2/4]

Variable sleipnir.autodiff.max ( float  a,
Variable  b 
)

◆ max() [3/4]

Variable sleipnir.autodiff.max ( Variable  a,
float  b 
)

◆ max() [4/4]

Variable sleipnir.autodiff.max ( Variable  a,
Variable  b 
)

◆ min() [1/4]

Variable sleipnir.autodiff.min ( float  a,
float  b 
) 
min() for Variables.

Returns the lesser of a and b. If the values are equivalent, returns
a.

Template parameter ``Scalar``:
    Scalar type.

Parameter ``a``:
    The a argument.

Parameter ``b``:
    The b argument.

◆ min() [2/4]

Variable sleipnir.autodiff.min ( float  a,
Variable  b 
)

◆ min() [3/4]

Variable sleipnir.autodiff.min ( Variable  a,
float  b 
)

◆ min() [4/4]

Variable sleipnir.autodiff.min ( Variable  a,
Variable  b 
)

◆ pow() [1/4]

Variable sleipnir.autodiff.pow ( float  base,
float  power 
) 
pow() for Variables.

Template parameter ``Scalar``:
    Scalar type.

Parameter ``base``:
    The base.

Parameter ``power``:
    The power.

◆ pow() [2/4]

Variable sleipnir.autodiff.pow ( float  base,
Variable  power 
)

◆ pow() [3/4]

Variable sleipnir.autodiff.pow ( Variable  base,
float  power 
)

◆ pow() [4/4]

Variable sleipnir.autodiff.pow ( Variable  base,
Variable  power 
)

◆ sign() [1/4]

Variable sleipnir.autodiff.sign ( float  x) 
sign() for Variables.

Template parameter ``Scalar``:
    Scalar type.

Parameter ``x``:
    The argument.

◆ sign() [2/4]

Variable sleipnir.autodiff.sign ( Variable  x)

◆ sign() [3/4]

VariableMatrix sleipnir.autodiff.sign ( VariableBlock  x)

◆ sign() [4/4]

VariableMatrix sleipnir.autodiff.sign ( VariableMatrix  x)

◆ sin() [1/4]

Variable sleipnir.autodiff.sin ( float  x) 
sin() for Variables.

Template parameter ``Scalar``:
    Scalar type.

Parameter ``x``:
    The argument.

◆ sin() [2/4]

Variable sleipnir.autodiff.sin ( Variable  x)

◆ sin() [3/4]

VariableMatrix sleipnir.autodiff.sin ( VariableBlock  x)

◆ sin() [4/4]

VariableMatrix sleipnir.autodiff.sin ( VariableMatrix  x)

◆ sinh() [1/4]

Variable sleipnir.autodiff.sinh ( float  x) 
sinh() for Variables.

Template parameter ``Scalar``:
    Scalar type.

Parameter ``x``:
    The argument.

◆ sinh() [2/4]

Variable sleipnir.autodiff.sinh ( Variable  x)

◆ sinh() [3/4]

VariableMatrix sleipnir.autodiff.sinh ( VariableBlock  x)

◆ sinh() [4/4]

VariableMatrix sleipnir.autodiff.sinh ( VariableMatrix  x)

◆ solve()

VariableMatrix sleipnir.autodiff.solve ( VariableMatrix  A,
VariableMatrix  B 
) 
Solves the VariableMatrix equation AX = B for X.

Template parameter ``Scalar``:
    Scalar type.

Parameter ``A``:
    The left-hand side.

Parameter ``B``:
    The right-hand side.

Returns:
    The solution X.

◆ spy()

sleipnir.autodiff.spy ( scipy.sparse.csc_matrix  mat) 
Plot the sparsity pattern of a sparse matrix.

Green points represent positive values and red points represent negative
values.

Parameter ``mat``:
    The sparse matrix.

◆ sqrt() [1/4]

Variable sleipnir.autodiff.sqrt ( float  x) 
sqrt() for Variables.

Template parameter ``Scalar``:
    Scalar type.

Parameter ``x``:
    The argument.

◆ sqrt() [2/4]

Variable sleipnir.autodiff.sqrt ( Variable  x)

◆ sqrt() [3/4]

VariableMatrix sleipnir.autodiff.sqrt ( VariableBlock  x)

◆ sqrt() [4/4]

VariableMatrix sleipnir.autodiff.sqrt ( VariableMatrix  x)

◆ tan() [1/4]

Variable sleipnir.autodiff.tan ( float  x) 
tan() for Variables.

Template parameter ``Scalar``:
    Scalar type.

Parameter ``x``:
    The argument.

◆ tan() [2/4]

Variable sleipnir.autodiff.tan ( Variable  x)

◆ tan() [3/4]

VariableMatrix sleipnir.autodiff.tan ( VariableBlock  x)

◆ tan() [4/4]

VariableMatrix sleipnir.autodiff.tan ( VariableMatrix  x)

◆ tanh() [1/4]

Variable sleipnir.autodiff.tanh ( float  x) 
tanh() for Variables.

Template parameter ``Scalar``:
    Scalar type.

Parameter ``x``:
    The argument.

◆ tanh() [2/4]

Variable sleipnir.autodiff.tanh ( Variable  x)

◆ tanh() [3/4]

VariableMatrix sleipnir.autodiff.tanh ( VariableBlock  x)

◆ tanh() [4/4]

VariableMatrix sleipnir.autodiff.tanh ( VariableMatrix  x)