Data Structures
struct	SPIbaseflow

struct	SPIgrid1D
	Class to contain various grid parameters. More...

struct	SPIgrid2D

struct	SPIMat

struct	SPIparams

struct	SPIVec

Typedefs
template<class T >
using	Block2D = std::vector< std::vector< T > >

Enumerations
enum	gridtype { FD, FDperiodic, Fourier, Chebyshev, UltraS }
	enumeration of grid types More...

Functions
SPIbaseflow	blasius (SPIparams &params, SPIgrid1D &grid)

int	_bblf (const PetscScalar input[3], PetscScalar output[3])

SPIbaseflow	channel (SPIparams &params, SPIgrid1D &grid)

PetscInt	factorial (PetscInt n)
	compute the factorial of n. This is needed for get_D_Coeffs function More...

SPIVec	get_D_Coeffs (SPIVec &s, PetscInt d)
	get the coefficients of the given stencil. More...

SPIMat	map_D (SPIMat D, SPIVec y, PetscInt d, PetscInt order)
	map the derivative operator to the proper y grid More...

SPIMat	set_D (SPIVec &y, PetscInt d, PetscInt order, PetscBool uniform)
	set the derivative operator for the proper y grid if uniform=false. Uses map_D function More...

SPIMat	set_D_periodic (SPIVec &y, PetscInt d, PetscInt order)
	set the derivative operator for the proper periodic grid assuming uniform discretization. More...

SPIVec	set_FD_stretched_y (PetscScalar y_max, PetscInt ny, PetscScalar delta)
	set stretched grid from [0,y_max] using tanh stretching for use with finite difference operators More...

SPIMat	set_D_Chebyshev (SPIVec &x, PetscInt d, PetscBool need_map)
	set a Chebyshev collocated operator acting with respect to the collocated grid More...

SPIMat	map_D_Chebyshev (SPIVec &x, PetscInt d)
	map a Chebyshev collocated operator acting with respect to the stretched collocated grid More...

SPIVec	set_Cheby_stretched_y (PetscScalar y_max, PetscInt ny, PetscScalar yi)
	create a stretched Chebyshev grid from [0,y_max] with yi being the midpoint location for the number of points More...

SPIVec	set_Cheby_mapped_y (PetscScalar a, PetscScalar b, PetscInt ny)
	create a stretched Chebyshev grid from [a,b] using default Chebfun like mapping More...

SPIVec	set_Cheby_y (PetscInt ny)
	create a Chebyshev grid from [-1,1] More...

SPIVec	set_Fourier_t (PetscScalar T, PetscInt nt)
	create a Fourier grid from [0,T] More...

SPIMat	set_D_Fourier (SPIVec t, PetscInt d)
	create a Fourier derivative operator acting on grid t More...

std::tuple< SPIMat, SPIMat >	set_D_UltraS (SPIVec &x, PetscInt d)
	set a UltraSpherical operator acting with respect to the collocated grid (keeps everything in UltraSpherical space), take in Chebyshev coefficients and outputs coefficients in C(d) coefficient space More...

std::tuple< SPIMat, SPIMat >	set_T_That (PetscInt n)
	set a T and That operators acting with respect to the Chebyshev collocated grid, That: physical -> Chebyshev coefficient, T: Chebyshev coefficient -> physical More...

SPIVec	SPIVec1Dto2D (SPIgrid2D &grid2D, SPIVec &u)
	expand a 1D vector to a 2D vector copying data along time dimension More...

PetscScalar	integrate (const SPIVec &a, SPIgrid1D &grid)
	integrate a vector of chebyshev Coefficients on a physical grid More...

PetscScalar	integrate (const SPIVec &a, SPIgrid2D &grid)
	integrate a vector of chebyshev Coefficients on a physical grid More...

SPIVec	proj (SPIVec &u, SPIVec &v, SPIgrid1D &grid)

SPIVec	proj (SPIVec &u, SPIVec &v, SPIgrid2D &grid)

std::vector< SPIVec >	orthogonalize (std::vector< SPIVec > &x, SPIgrid1D &grid)

std::vector< SPIVec >	orthogonalize (std::vector< SPIVec > &x, SPIgrid2D &grid)

SPIMat	interp1D_Mat (SPIgrid1D &grid1, SPIgrid1D &grid2)

SPIMat	interp1D_Mat (SPIVec &y1, SPIVec &y2)

SPIMat	dft (PetscInt nt)

std::tuple< SPIMat, SPIMat, SPIMat, SPIMat >	dft_dftinv_Ihalf_Ihalfn (PetscInt nt)

std::tuple< PetscScalar, SPIVec >	LST_temporal (SPIparams &params, SPIgrid1D &grid, SPIbaseflow &baseflow, SPIVec q)
	solve the local stability theory problem for the linearized Navier-Stokes equations using parallel baseflow with alpha being pure real, and omega the eigenvalue More...

std::tuple< PetscScalar, SPIVec >	LST_spatial (SPIparams &params, SPIgrid1D &grid, SPIbaseflow &baseflow, SPIVec q)
	solve the local stability theory problem for the linearized Navier-Stokes equations using parallel baseflow with omega being pure real, and alpha the eigenvalue More...

std::tuple< PetscScalar, PetscScalar, SPIVec, SPIVec >	LST_spatial_cg (SPIparams &params, SPIgrid1D &grid, SPIbaseflow &baseflow)
	solve the local stability theory problem for the linearized Navier-Stokes equations using parallel baseflow with omega being pure real, and alpha the eigenvalue More...

std::tuple< PetscScalar, PetscScalar, SPIVec, SPIVec >	LSTNP_spatial (SPIparams &params, SPIgrid1D &grid, SPIbaseflow &baseflow, SPIVec ql, SPIVec qr)
	solve the local stability theory problem for the linearized Navier-Stokes equations using parallel baseflow with omega being pure real, and alpha the eigenvalue More...

std::tuple< PetscScalar, SPIVec >	LSTNP_spatial_right (SPIparams &params, SPIgrid1D &grid, SPIbaseflow &baseflow, SPIVec qr)
	solve the local stability theory problem for the linearized Navier-Stokes equations using parallel baseflow with omega being pure real, and alpha the eigenvalue More...

std::tuple< PetscScalar, SPIVec >	LSTNP_spatial_right2 (SPIparams &params, SPIgrid1D &grid, SPIbaseflow &baseflow, SPIVec qr)
	solve the local stability theory problem for the linearized Navier-Stokes equations using parallel baseflow with omega being pure real, and alpha the eigenvalue More...

std::tuple< std::vector< PetscScalar >, std::vector< SPIVec > >	LSTNP_spatials_right (SPIparams &params, SPIgrid1D &grid, SPIbaseflow &baseflow, std::vector< PetscScalar > &alphas, std::vector< SPIVec > &qrs)
	solve the local stability theory problem for the linearized Navier-Stokes equations using non-parallel baseflow with omega being pure real, and alpha the eigenvalue More...

SPIMat	operator* (const PetscScalar a, const SPIMat A)
	aA operation to be equivalent to Aa More...

SPIMat	operator* (const SPIMat A, const PetscScalar a)
	Aa operation to be equivalent to Aa. More...

SPIVec	operator/ (const SPIVec &b, const SPIMat &A)
	Solve linear system, Ax=b using b/A notation. More...

SPIMat	operator^ (const PetscScalar a, const SPIMat &A)
	Y=a^A operation. More...

SPIVec	solve (const SPIMat &A, const SPIVec &b)
	Solve linear system, Ax=b using solve(A,b) notation. More...

SPIMat	eye (const PetscInt n)
	create, form, and return identity matrix of size n More...

SPIMat	inv (const SPIMat &A)
	Solve linear system A*Ainv=B using MatMatSolve. More...

SPIMat	zeros (const PetscInt m, const PetscInt n)
	create, form, and return zeros matrix of size mxn More...

SPIMat	diag (const SPIVec &d, const PetscInt k)
	set diagonal of matrix More...

SPIMat	kron (const SPIMat &A, const SPIMat &B)
	set kronecker inner product of two matrices More...

std::tuple< std::vector< PetscReal >, std::vector< SPIVec >, std::vector< SPIVec > >	svd (const SPIMat &A)
	solve SVD problem of A=UEV^H for skinny A matrix More...

SPIVec	lstsq (const SPIMat &A, SPIVec &y)
	solve least squares problem of A*x=y for skinny A matrix using SVD More...

SPIVec	lstsq (const std::vector< SPIVec > &A, SPIVec &y)
	solve least squares problem of A*x=y for skinny A matrix (or vectors of columns vectors) using SVD More...

std::tuple< PetscScalar, SPIVec, SPIVec >	eig (const SPIMat &A, const SPIMat &B, const PetscScalar target, const PetscReal tol, const PetscInt max_iter)
	solve general eigenvalue problem of Ax = kBx and return a tuple of tie(PetscScalar alpha, SPIVec eig_vector) More...

std::tuple< PetscScalar, SPIVec >	eig_right (const SPIMat &A, const SPIMat &B, const PetscScalar target, const PetscReal tol, const PetscInt max_iter)
	solve general eigenvalue problem of Ax = kBx and return a tuple of tie(PetscScalar alpha, SPIVec eig_vector) More...

std::tuple< PetscScalar, SPIVec, SPIVec >	eig_init (const SPIMat &A, const SPIMat &B, const PetscScalar target, const SPIVec &ql, const SPIVec &qr, PetscReal tol, const PetscInt max_iter)
	solve general eigenvalue problem of Ax = kBx and return a tuple of tie(PetscScalar alpha, SPIVec eig_vector) More...

std::tuple< PetscScalar, SPIVec >	eig_init_right (const SPIMat &A, const SPIMat &B, const PetscScalar target, const SPIVec &qr, PetscReal tol, const PetscInt max_iter)
	solve general eigenvalue problem of Ax = kBx and return a tuple of tie(PetscScalar alpha, SPIVec eig_vector) More...

std::tuple< std::vector< PetscScalar >, std::vector< SPIVec > >	eig_init_rights (const SPIMat &A, const SPIMat &B, const std::vector< PetscScalar > targets, const std::vector< SPIVec > &qrs, PetscReal tol, const PetscInt max_iter)
	solve general eigenvalue problem of Ax = kBx and return a tuple of tie(PetscScalar alpha, SPIVec eig_vector) More...

std::tuple< PetscScalar, SPIVec >	polyeig (const std::vector< SPIMat > &As, const PetscScalar target, const PetscReal tol, const PetscInt max_iter)
	solve general polynomial eigenvalue problem of (A0 + A1alpha + A2alpha^2 + ...)*x = 0 and return a tuple of tie(PetscScalar alpha, SPIVec eig_vector) More...

std::tuple< PetscScalar, SPIVec >	polyeig_init (const std::vector< SPIMat > &As, const PetscScalar target, const SPIVec &qr, const PetscReal tol, const PetscInt max_iter)
	solve general polynomial eigenvalue problem of (A0 + A1alpha + A2alpha^2 + ...)*x = 0 and return a tuple of tie(PetscScalar alpha, SPIVec eig_vector) using initial subspace vector More...

SPIMat	block ( const Block2D< SPIMat > Blocks)
	set block matrices using an input array of size rows*cols. Fills rows first More...

std::tuple< SPIMat, SPIMat >	meshgrid (SPIVec &x, SPIVec &y)

PetscInt	save (const SPIMat &A, const std::string filename)
	save matrix to filename in binary format (see Petsc documentation for format ) Format is (from Petsc documentation): int MAT_FILE_CLASSID int number of rows int number of columns int total number of nonzeros int number nonzeros in each row int column indices of all nonzeros (starting index is zero) PetscScalar *values of all nonzeros More...

PetscInt	save (const std::vector< SPIMat > &As, const std::string filename)
	save matrices to filename in binary format (see Petsc documentation for format More...

PetscInt	load (SPIMat &A, const std::string filename)
	load matrix from filename from binary format (works with save(SPIMat,std::string) function More...

PetscInt	load (std::vector< SPIMat > &As, const std::string filename)
	load matrix from filename from binary format (works with save(SPIMat,std::string) function More...

PetscInt	draw (const SPIMat &A)
	draw nonzero structure of matrix More...

template<class T >
SPIMat	_Function_on_each_element (T(*f)(T const &), const SPIMat &A)
	take the function of each element in a matrix, e.g. (*f)(A(i,j)) for each i,j More...

SPIMat	sin (const SPIMat &A)
	take the sin of each element in a matrix More...

SPIMat	cos (const SPIMat &A)
	take the cos of each element in a matrix More...

SPIMat	acos (const SPIMat &A)
	take the arccos of each element in a matrix More...

SPIMat	tan (const SPIMat &A)
	take the tan of each element in a matrix More...

SPIMat	abs (const SPIMat &A)
	take the abs of each element in a matrix More...

SPIMat	operator% (const SPIMat &A, const SPIMat &B)
	take the elementwise multiplication of each element in a matrix More...

SPIMat	orthogonalize (const std::vector< SPIVec > &x)

PetscInt	printf (std::string msg,...)

PetscInt	printfc (std::string msg, const PetscScalar val)

SPIVec	operator/ (const PetscScalar a, const SPIVec &A)

SPIVec	operator* (const PetscScalar a, const SPIVec &A)

SPIVec	operator+ (const PetscScalar a, const SPIVec &A)

SPIVec	operator- (const PetscScalar a, const SPIVec &A)

PetscInt	save (const SPIVec &A, std::string filename)

PetscInt	save (std::vector< PetscScalar > A, std::string variablename, std::string filename)

PetscInt	save (std::vector< SPIVec > A, std::string variablename, std::string filename)

PetscInt	load (SPIVec &A, const std::string filename)

SPIVec	ones (const PetscInt rows)

SPIVec	zeros (const PetscInt rows)

SPIVec	conj (const SPIVec &A)

SPIVec	real (const SPIVec &A)
	return the real part of the vector More...

SPIVec	imag (const SPIVec &A)
	return the imaginary part of the vector More...

SPIVec	linspace (const PetscScalar begin, const PetscScalar end, const PetscInt _rows)
	return linspace of number of rows equally spaced points between begin and end More...

SPIVec	arange (const PetscScalar begin, const PetscScalar end, const PetscScalar stepsize)
	return a range of number of equally spaced points between begin and end by step size step More...

SPIVec	arange (const PetscScalar end)

template<class T >
SPIVec	_Function_on_each_element (T(*f)(T const &), const SPIVec &A)
	take the function of each element in a vector, e.g. (*f)(A(i)) for each i More...

SPIVec	sin (const SPIVec &A)
	take the sin of each element in a vector More...

SPIVec	cos (const SPIVec &A)
	take the cos of each element in a vector More...

SPIVec	tan (const SPIVec &A)
	take the tan of each element in a vector More...

SPIVec	exp (const SPIVec &A)
	take the exp of each element in a vector More...

SPIVec	log (const SPIVec &A)
	take the log (natural log) of each element in a vector More...

SPIVec	log10 (const SPIVec &A)
	take the log10 of each element in a vector More...

SPIVec	sinh (const SPIVec &A)
	take the sinh of each element in a vector More...

SPIVec	cosh (const SPIVec &A)
	take the cosh of each element in a vector More...

SPIVec	tanh (const SPIVec &A)
	take the tanh of each element in a vector More...

SPIVec	asin (const SPIVec &A)
	take the asin of each element in a vector More...

SPIVec	acos (const SPIVec &A)
	take the acos of each element in a vector More...

SPIVec	atan (const SPIVec &A)
	take the atan of each element in a vector More...

SPIVec	asinh (const SPIVec &A)
	take the asinh of each element in a vector More...

SPIVec	acosh (const SPIVec &A)
	take the acosh of each element in a vector More...

SPIVec	atanh (const SPIVec &A)
	take the atanh of each element in a vector More...

SPIVec	sqrt (const SPIVec &A)
	take the atanh of each element in a vector More...

SPIVec	erf (const SPIVec &A)
	take the erf of each element in a vector More...

SPIVec	erfc (const SPIVec &A)
	take the erfc(z) = 1-erf(z) of each element in a vector More...

template<class T >
SPIVec	_Function_on_each_element (T(*f)(T const &, T const &), const SPIVec &A, SPIVec &B)
	function to take element by element of two vectors e.g. (*f)(A(i),B(i)) for all i More...

SPIVec	pow (const SPIVec &A, SPIVec &B)
	take the pow of each element in the vectors More...

SPIVec	pow (const SPIVec &A, PetscScalar b)
	take the pow of each element in the vector (A^b) More...

SPIVec	abs (const SPIVec &A)
	take the absolute value of a vector More...

PetscScalar	sum (SPIVec x1)
	take the sum of a vector More...

PetscScalar	integrate_coeffs (const SPIVec &a)
	integrate a vector of chebyshev Coefficients on a grid More...

PetscScalar	integrate_coeffs (const SPIVec &a, const SPIVec &y)
	integrate a vector of chebyshev Coefficients on a stretched grid More...

PetscScalar	dot (SPIVec x, SPIVec y)
	take the inner product of the two vectors (i.e. y^H x) where ^H is the complex conjugate transpose More...

PetscReal	L2 (SPIVec x1, const SPIVec x2, NormType type)
	calculate the \( L_2 \) norm of the difference between \(x_1\) and \(x_2\) vectors. More...

PetscReal	L2 (const SPIVec x1, NormType type)
	calculate the \( L_2 \) norm of the vector More...

SPIVec	diff (SPIVec x)
	diff of the vector (see numpy.diff) More...

PetscScalar	trapz (SPIVec y)
	trapezoidal integration of y with unity coordinate spacing, \(\int y dx \) More...

PetscScalar	trapz (SPIVec y, SPIVec x)
	trapezoidal integration of y with x coordinates, \(\int y dx \) More...

PetscInt	draw (const SPIVec &x)
	draw nonzero structure and wait at command line input More...

Typedef Documentation

◆ Block2D

template<class T >

using SPI::Block2D = typedef std::vector<std::vector<T> >

Definition at line 15 of file SPIMat.hpp.

Enumeration Type Documentation

◆ gridtype

enum SPI::gridtype

enumeration of grid types

Enumerator
FD	finite difference grid
FDperiodic	finite difference grid on periodic grid
Fourier	Fourier transform collocated grid.
Chebyshev	Chebyshev collocated grid.
UltraS	UltraSpherical grid and derivatives.

Definition at line 25 of file SPIgrid.hpp.

Function Documentation

◆ _bblf()

int SPI::_bblf	(	const PetscScalar	input[3],
		PetscScalar	output[3]
	)

Definition at line 243 of file SPIbaseflow.cpp.

◆ _Function_on_each_element() [1/3]

template<class T >

SPIMat SPI::_Function_on_each_element	(	T(*)(T const &)	f,
		const SPIMat &	A
	)

take the function of each element in a matrix, e.g. (*f)(A(i,j)) for each i,j

Parameters

[in]	f	[in] function handle to pass in e.g. std::sin<PetscReal>
[in]	A	[in] matrix to perform function on each element

Definition at line 2011 of file SPIMat.cpp.

◆ _Function_on_each_element() [2/3]

template<class T >

SPIVec SPI::_Function_on_each_element	(	T(*)(T const &)	f,
		const SPIVec &	A
	)

take the function of each element in a vector, e.g. (*f)(A(i)) for each i

Parameters

[in]	f	[in] function handle to pass in e.g. std::sin<PetscReal>
[in]	A	[in] vector to perform function on each element

Definition at line 693 of file SPIVec.cpp.

◆ _Function_on_each_element() [3/3]

template<class T >

SPIVec SPI::_Function_on_each_element	(	T(*)(T const &, T const &)	f,
		const SPIVec &	A,
		SPIVec &	B
	)

function to take element by element of two vectors e.g. (*f)(A(i),B(i)) for all i

Parameters

[in]	f	[in] function handle to pass in e.g. std::pow<PetscReal>
[in]	A	[in] first vector to perform function on each element
[in]	B	[in] second vector

Definition at line 762 of file SPIVec.cpp.

◆ abs() [1/2]

SPIMat SPI::abs ( const SPIMat & A )

take the abs of each element in a matrix

Definition at line 2045 of file SPIMat.cpp.

◆ abs() [2/2]

SPIVec SPI::abs ( const SPIVec & A )

take the absolute value of a vector

Definition at line 798 of file SPIVec.cpp.

◆ acos() [1/2]

SPIMat SPI::acos ( const SPIMat & A )

take the arccos of each element in a matrix

Definition at line 2029 of file SPIMat.cpp.

◆ acos() [2/2]

SPIVec SPI::acos ( const SPIVec & A )

take the acos of each element in a vector

Definition at line 731 of file SPIVec.cpp.

◆ acosh()

SPIVec SPI::acosh ( const SPIVec & A )

take the acosh of each element in a vector

Definition at line 737 of file SPIVec.cpp.

◆ arange() [1/2]

SPIVec SPI::arange	(	const PetscScalar	begin,
		const PetscScalar	end,
		const PetscScalar	stepsize = `1`
	)

return a range of number of equally spaced points between begin and end by step size step

Parameters

[in]	begin	[in] beginning scalar of equally spaced points
[in]	end	[in] end scalar of equally spaced points
[in]	stepsize	[in] step size for equally spaced points

Definition at line 667 of file SPIVec.cpp.

◆ arange() [2/2]

SPIVec SPI::arange ( const PetscScalar end )

Parameters

[in] end [in] end scalar of equally spaced points

Definition at line 684 of file SPIVec.cpp.

◆ asin()

SPIVec SPI::asin ( const SPIVec & A )

take the asin of each element in a vector

Definition at line 729 of file SPIVec.cpp.

◆ asinh()

SPIVec SPI::asinh ( const SPIVec & A )

take the asinh of each element in a vector

Definition at line 735 of file SPIVec.cpp.

◆ atan()

SPIVec SPI::atan ( const SPIVec & A )

take the atan of each element in a vector

Definition at line 733 of file SPIVec.cpp.

◆ atanh()

SPIVec SPI::atanh ( const SPIVec & A )

take the atanh of each element in a vector

Definition at line 739 of file SPIVec.cpp.

◆ blasius()

SPIbaseflow SPI::blasius	(	SPIparams &	params,
		SPIgrid1D &	grid
	)

Parameters

[in]	params	[in] parameters such as x and nu (freestream Uinf=1)
[in]	grid	[in] grid containing wall-normal points

Definition at line 90 of file SPIbaseflow.cpp.

◆ block()

SPIMat SPI::block ( const Block2D< SPIMat > Blocks )

set block matrices using an input array of size rows*cols. Fills rows first

Returns: new matrix with inserted blocks

Parameters

[in] Blocks [in] array of matrices to set into larger matrix e.g. [ A, B, C, D ]

Definition at line 1857 of file SPIMat.cpp.

◆ channel()

SPIbaseflow SPI::channel	(	SPIparams &	params,
		SPIgrid1D &	grid
	)

Parameters

[in]	params	[in] parameters such as x and nu (freestream Uinf=1)
[in]	grid	[in] grid containing wall-normal points

Definition at line 253 of file SPIbaseflow.cpp.

◆ conj()

SPIVec SPI::conj ( const SPIVec & A )

return the conjugate of the vector

Returns: conjugate of A

See also: SPIVec::conj()

Parameters

[in] A [in] vector to conjugate

Definition at line 622 of file SPIVec.cpp.

◆ cos() [1/2]

SPIMat SPI::cos ( const SPIMat & A )

take the cos of each element in a matrix

Definition at line 2027 of file SPIMat.cpp.

◆ cos() [2/2]

SPIVec SPI::cos ( const SPIVec & A )

take the cos of each element in a vector

Definition at line 708 of file SPIVec.cpp.

◆ cosh()

SPIVec SPI::cosh ( const SPIVec & A )

take the cosh of each element in a vector

Definition at line 725 of file SPIVec.cpp.

◆ dft()

SPIMat SPI::dft ( PetscInt nt )

Parameters

[in] nt [in] size of matrix to create

Definition at line 1573 of file SPIgrid.cpp.

◆ dft_dftinv_Ihalf_Ihalfn()

std::tuple< SPIMat, SPIMat, SPIMat, SPIMat > SPI::dft_dftinv_Ihalf_Ihalfn ( PetscInt nt )

Parameters

[in] nt [in] size of matrix to create

Definition at line 1589 of file SPIgrid.cpp.

◆ diag()

SPIMat SPI::diag	(	const SPIVec &	d,
		const PetscInt	k
	)

set diagonal of matrix

Returns: new matrix with a diagonal vector set as the main diagonal

Parameters

[in]	d	[in] diagonal vector to set along main diagonal
[in]	k	[in] diagonal to set, k=0 is main diagonal, k=1 is offset one in positive direction

Definition at line 728 of file SPIMat.cpp.

◆ diff()

SPIVec SPI::diff ( SPIVec x )

diff of the vector (see numpy.diff)

Returns: y[i] = x[i+1]-x[i] for i=0,1,...,x.rows-2

Parameters

[in] x [in] vector to diff (x[i+1]-x[i])

Definition at line 881 of file SPIVec.cpp.

◆ dot()

PetscScalar SPI::dot	(	SPIVec	x,
		SPIVec	y
	)

take the inner product of the two vectors (i.e. y^H x) where ^H is the complex conjugate transpose

Parameters

[in]	x	[in] first vector in inner product
[in]	y	[in] second vector in inner product (this one gets the complex conjugate transpose)

Definition at line 788 of file SPIVec.cpp.

◆ draw() [1/2]

PetscInt SPI::draw ( const SPIMat & A )

draw nonzero structure of matrix

Returns: 0 if successful

Parameters

[in] A [in] A to draw nonzero structure

Definition at line 1994 of file SPIMat.cpp.

◆ draw() [2/2]

PetscInt SPI::draw ( const SPIVec & x )

draw nonzero structure and wait at command line input

Parameters

[in] x [in] vector to draw

Definition at line 932 of file SPIVec.cpp.

◆ eig()

std::tuple< PetscScalar, SPIVec, SPIVec > SPI::eig	(	const SPIMat &	A,
		const SPIMat &	B,
		const PetscScalar	target,
		const PetscReal	tol,
		const PetscInt	max_iter
	)

solve general eigenvalue problem of Ax = kBx and return a tuple of tie(PetscScalar alpha, SPIVec eig_vector)

Returns: tuple of eigenvalue and eigenvector closest to the target value e.g. std::tie(alpha, eig_vector) = eig(A,B,0.1+0.4*PETSC_i)

Parameters

[in]	A	[in] A in Ax=kBx generalized eigenvalue problem
[in]	B	[in] B in Ax=kBx generalized eigenvalue problem
[in]	target	[in] target eigenvalue to solve for
[in]	tol	[in] tolerance of eigenvalue solver
[in]	max_iter	[in] maximum number of iterations

Definition at line 928 of file SPIMat.cpp.

◆ eig_init()

std::tuple< PetscScalar, SPIVec, SPIVec > SPI::eig_init	(	const SPIMat &	A,
		const SPIMat &	B,
		const PetscScalar	target,
		const SPIVec &	ql,
		const SPIVec &	qr,
		PetscReal	tol,
		const PetscInt	max_iter
	)

solve general eigenvalue problem of Ax = kBx and return a tuple of tie(PetscScalar alpha, SPIVec eig_vector)

Returns: tuple of eigenvalue and eigenvector closest to the target value e.g. std::tie(alpha, eig_vector) = eig(A,B,0.1+0.4*PETSC_i) using initial subspace defined by a vector

Parameters

[in]	A	[in] A in Ax=kBx generalized eigenvalue problem
[in]	B	[in] B in Ax=kBx generalized eigenvalue problem
[in]	target	[in] target eigenvalue to solve for
[in]	ql	[in] initial subspace vector for EPS solver (left eigenvector)
[in]	qr	[in] initial subspace vector for EPS solver (right eigenvector)
[in]	tol	[in] tolerance of eigenvalue solver
[in]	max_iter	[in] maximum number of iterations

Definition at line 1217 of file SPIMat.cpp.

◆ eig_init_right()

std::tuple< PetscScalar, SPIVec > SPI::eig_init_right	(	const SPIMat &	A,
		const SPIMat &	B,
		const PetscScalar	target,
		const SPIVec &	qr,
		PetscReal	tol,
		const PetscInt	max_iter
	)

solve general eigenvalue problem of Ax = kBx and return a tuple of tie(PetscScalar alpha, SPIVec eig_vector)

Returns: tuple of eigenvalue and eigenvector closest to the target value e.g. std::tie(alpha, eig_vector) = eig(A,B,0.1+0.4*PETSC_i) using initial subspace defined by a vector

Parameters

[in]	A	[in] A in Ax=kBx generalized eigenvalue problem
[in]	B	[in] B in Ax=kBx generalized eigenvalue problem
[in]	target	[in] target eigenvalue to solve for
[in]	qr	[in] initial subspace vector for EPS solver (right eigenvector)
[in]	tol	[in] tolerance of eigenvalue solver
[in]	max_iter	[in] maximum number of iterations

Definition at line 1368 of file SPIMat.cpp.

◆ eig_init_rights()

std::tuple< std::vector< PetscScalar >, std::vector< SPIVec > > SPI::eig_init_rights	(	const SPIMat &	A,
		const SPIMat &	B,
		const std::vector< PetscScalar >	targets,
		const std::vector< SPIVec > &	qrs,
		PetscReal	tol,
		const PetscInt	max_iter
	)

solve general eigenvalue problem of Ax = kBx and return a tuple of tie(PetscScalar alpha, SPIVec eig_vector)

Returns: tuple of eigenvalue and eigenvector closest to the target value e.g. std::tie(alpha, eig_vector) = eig(A,B,0.1+0.4*PETSC_i) using initial subspace defined by a vector

Parameters

[in]	A	[in] A in Ax=kBx generalized eigenvalue problem
[in]	B	[in] B in Ax=kBx generalized eigenvalue problem
[in]	targets	[in] target eigenvalue to solve for
[in]	qrs	[in] initial subspace vector for EPS solver (right eigenvector)
[in]	tol	[in] tolerance of eigenvalue solver
[in]	max_iter	[in] maximum number of iterations

Definition at line 1521 of file SPIMat.cpp.

◆ eig_right()

std::tuple< PetscScalar, SPIVec > SPI::eig_right	(	const SPIMat &	A,
		const SPIMat &	B,
		const PetscScalar	target,
		const PetscReal	tol,
		const PetscInt	max_iter
	)

solve general eigenvalue problem of Ax = kBx and return a tuple of tie(PetscScalar alpha, SPIVec eig_vector)

Returns: tuple of eigenvalue and eigenvector closest to the target value e.g. std::tie(alpha, eig_vector) = eig(A,B,0.1+0.4*PETSC_i)

Parameters

[in]	A	[in] A in Ax=kBx generalized eigenvalue problem
[in]	B	[in] B in Ax=kBx generalized eigenvalue problem
[in]	target	[in] target eigenvalue to solve for
[in]	tol	[in] tolerance of eigenvalue solver
[in]	max_iter	[in] maximum number of iterations

Definition at line 1072 of file SPIMat.cpp.

◆ erf()

SPIVec SPI::erf ( const SPIVec & A )

take the erf of each element in a vector

Definition at line 743 of file SPIVec.cpp.

◆ erfc()

SPIVec SPI::erfc ( const SPIVec & A )

take the erfc(z) = 1-erf(z) of each element in a vector

Definition at line 752 of file SPIVec.cpp.

◆ exp()

SPIVec SPI::exp ( const SPIVec & A )

take the exp of each element in a vector

Definition at line 712 of file SPIVec.cpp.

◆ eye()

SPIMat SPI::eye ( const PetscInt n )

create, form, and return identity matrix of size n

Returns: identity matrix of size nxn

Parameters

[in] n [in] n size of square identity matrix

Definition at line 697 of file SPIMat.cpp.

◆ factorial()

PetscInt SPI::factorial ( PetscInt n )

compute the factorial of n. This is needed for get_D_Coeffs function

Returns: factorial of n

Parameters

[in] n [in] integer to compute factorial of

Definition at line 6 of file SPIgrid.cpp.

◆ get_D_Coeffs()

SPIVec SPI::get_D_Coeffs	(	SPIVec &	s,
		PetscInt	d
	)

get the coefficients of the given stencil.

Returns: coefficients of stencil for derivative at 0 in s n

Parameters

[in]	s	[in] vector of stencil points e.g. [-3,-2,-1,0,1]
[in]	d	[in] order of desired derivative e.g. 1 or 2

Definition at line 15 of file SPIgrid.cpp.

◆ imag()

SPIVec SPI::imag ( const SPIVec & A )

return the imaginary part of the vector

Parameters

[in] A [in] vector to take imaginary part of

Definition at line 638 of file SPIVec.cpp.

◆ integrate() [1/2]

PetscScalar SPI::integrate	(	const SPIVec &	a,
		SPIgrid1D &	grid
	)

integrate a vector of chebyshev Coefficients on a physical grid

Parameters

[in]	a	[in] vector to integrate over grid (Chebyshev coefficients or physical values)
[in]	grid	[in] respective grid

Definition at line 873 of file SPIgrid.cpp.

◆ integrate() [2/2]

PetscScalar SPI::integrate	(	const SPIVec &	a,
		SPIgrid2D &	grid
	)

integrate a vector of chebyshev Coefficients on a physical grid

Parameters

[in]	a	[in] vector to integrate over grid (Chebyshev coefficients or physical values)
[in]	grid	[in] respective grid

Definition at line 927 of file SPIgrid.cpp.

◆ integrate_coeffs() [1/2]

PetscScalar SPI::integrate_coeffs ( const SPIVec & a )

integrate a vector of chebyshev Coefficients on a grid

Parameters

[in] a [in] chebyshev coefficients to integrate

Definition at line 813 of file SPIVec.cpp.

◆ integrate_coeffs() [2/2]

PetscScalar SPI::integrate_coeffs	(	const SPIVec &	a,
		const SPIVec &	y
	)

integrate a vector of chebyshev Coefficients on a stretched grid

Parameters

[in]	a	[in] chebyshev coefficients
[in]	y	[in] Cheby_mapped_y grid

Definition at line 846 of file SPIVec.cpp.

◆ interp1D_Mat() [1/2]

SPIMat SPI::interp1D_Mat	(	SPIgrid1D &	grid1,
		SPIgrid1D &	grid2
	)

Parameters

[in]	grid1	[in] grid to interpolate values from
[in]	grid2	[in] grid to interpolate values to

Definition at line 1506 of file SPIgrid.cpp.

◆ interp1D_Mat() [2/2]

SPIMat SPI::interp1D_Mat	(	SPIVec &	y1,
		SPIVec &	y2
	)

Parameters

[in]	y1	[in] grid to interpolate values from
[in]	y2	[in] grid to interpolate values to

Definition at line 1538 of file SPIgrid.cpp.

◆ inv()

SPIMat SPI::inv ( const SPIMat & A )

Solve linear system A*Ainv=B using MatMatSolve.

Returns: Ainv matrix

Parameters

[in] A [in] A in A A^-1 = B

Definition at line 603 of file SPIMat.cpp.

◆ kron()

SPIMat SPI::kron	(	const SPIMat &	A,
		const SPIMat &	B
	)

set kronecker inner product of two matrices

Returns: kronecker inner product of the two matrices

Parameters

[in]	A	[in] A in A kron B operation
[in]	B	[in] B in A kron B operation

Definition at line 780 of file SPIMat.cpp.

◆ L2() [1/2]

PetscReal SPI::L2	(	const SPIVec	x1,
		NormType	type
	)

calculate the \( L_2 \) norm of the vector

Returns: \(L_2\) norm of the vector

Parameters

[in]	x1	[in] \(x_1\) l
[in]	type	[in] type of norm (default NORM_2 \(\sqrt{\sum x_1^2}\))

Definition at line 871 of file SPIVec.cpp.

◆ L2() [2/2]

PetscReal SPI::L2	(	SPIVec	x1,
		const SPIVec	x2,
		NormType	type
	)

calculate the \( L_2 \) norm of the difference between \(x_1\) and \(x_2\) vectors.

Returns: \(L_2\) norm of the difference

Parameters

[in]	x1	[in] \(x_1\)
[in]	x2	[in] \(x_2\)
[in]	type	[in] type of norm (default NORM_2 \(\sqrt{\sum \|x_1 - x_2\|^2}\)) (NORM_1 denotes sum_i \|x_i\|), (NORM_2 denotes sqrt(sum_i \|x_i\|^2)), (NORM_INFINITY denotes max_i \|x_i\|)

Definition at line 859 of file SPIVec.cpp.

◆ linspace()

SPIVec SPI::linspace	(	const PetscScalar	begin,
		const PetscScalar	end,
		const PetscInt	_rows
	)

return linspace of number of rows equally spaced points between begin and end

Parameters

[in]	begin	[in] beginning scalar of equally spaced points
[in]	end	[in] end scalar of equally spaced points
[in]	_rows	[in] how many points in array

Definition at line 645 of file SPIVec.cpp.

◆ load() [1/3]

PetscInt SPI::load	(	SPIMat &	A,
		const std::string	filename
	)

load matrix from filename from binary format (works with save(SPIMat,std::string) function

Returns: 0 if successful

Parameters

[in,out]	A	[inout] A to load data into (must be initialized to the right size)
[in]	filename	[in] filename to read

Definition at line 1966 of file SPIMat.cpp.

◆ load() [2/3]

PetscInt SPI::load	(	SPIVec &	A,
		const std::string	filename
	)

load A from hdf5 filename using variable A.name, be sure it has the right size first before loading

Returns: 0 if successful

Parameters

[in,out]	A	[inout] vector to load data into (must be initialized to the right size)
[in]	filename	[in] filename to read

Definition at line 591 of file SPIVec.cpp.

◆ load() [3/3]

PetscInt SPI::load	(	std::vector< SPIMat > &	As,
		const std::string	filename
	)

load matrix from filename from binary format (works with save(SPIMat,std::string) function

Returns: 0 if successful

Parameters

[in,out]	As	[inout] matrices to load data into (must be initialized to the right size)
[in]	filename	[in] filename to read

Definition at line 1978 of file SPIMat.cpp.

◆ log()

SPIVec SPI::log ( const SPIVec & A )

take the log (natural log) of each element in a vector

Definition at line 719 of file SPIVec.cpp.

◆ log10()

SPIVec SPI::log10 ( const SPIVec & A )

take the log10 of each element in a vector

Definition at line 721 of file SPIVec.cpp.

◆ LST_spatial()

std::tuple< PetscScalar, SPIVec > SPI::LST_spatial	(	SPIparams &	params,
		SPIgrid1D &	grid,
		SPIbaseflow &	baseflow,
		SPIVec	q
	)

solve the local stability theory problem for the linearized Navier-Stokes equations using parallel baseflow with omega being pure real, and alpha the eigenvalue

Returns: tuple of eigenvalue and eigenvector closest to the target value e.g. std::tie(omega,eig_vector) = LST_spatial(params,grid,baseflow). Will solve for closest eigenvalue to params.omega

Parameters

[in,out]	params	[inout] contains parameters including Re, alpha, and omega. Will overwrite omega with true omega value once solved
[in]	grid	[in] grid class containing the grid location and respective derivatives
[in]	baseflow	[in] baseflow for parallel flow
[in]	q	[in] initial guess for temporal problem

Definition at line 147 of file SPILST.cpp.

◆ LST_spatial_cg()

std::tuple< PetscScalar, PetscScalar, SPIVec, SPIVec > SPI::LST_spatial_cg	(	SPIparams &	params,
		SPIgrid1D &	grid,
		SPIbaseflow &	baseflow
	)

solve the local stability theory problem for the linearized Navier-Stokes equations using parallel baseflow with omega being pure real, and alpha the eigenvalue

Returns: tuple of eigenvalue and eigenvector closest to the target value e.g. std::tie(omega,eig_vector) = LST_spatial(params,grid,baseflow). Will solve for closest eigenvalue to params.omega

Parameters

[in,out]	params	[inout] contains parameters including Re, alpha, and omega. Will overwrite omega with true omega value once solved
[in]	grid	[in] grid class containing the grid location and respective derivatives
[in]	baseflow	[in] baseflow for parallel flow

Definition at line 349 of file SPILST.cpp.

◆ LST_temporal()

std::tuple< PetscScalar, SPIVec > SPI::LST_temporal	(	SPIparams &	params,
		SPIgrid1D &	grid,
		SPIbaseflow &	baseflow,
		SPIVec	q
	)

solve the local stability theory problem for the linearized Navier-Stokes equations using parallel baseflow with alpha being pure real, and omega the eigenvalue

Returns: tuple of eigenvalue and eigenvector closest to the target value e.g. std::tie(omega,eig_vector) = LST_temporal(params,grid,baseflow). Will solve for closest eigenvalue to params.omega

Parameters

[in,out]	params	[inout] contains parameters including Re, alpha, and omega. Will overwrite omega with true omega value once solved
[in]	grid	[in] grid class containing the grid location and respective derivatives
[in]	baseflow	[in] baseflow for parallel flow
[in]	q	[in] initial guess for temporal problem

Definition at line 5 of file SPILST.cpp.

◆ LSTNP_spatial()

std::tuple< PetscScalar, PetscScalar, SPIVec, SPIVec > SPI::LSTNP_spatial	(	SPIparams &	params,
		SPIgrid1D &	grid,
		SPIbaseflow &	baseflow,
		SPIVec	ql,
		SPIVec	qr
	)

solve the local stability theory problem for the linearized Navier-Stokes equations using parallel baseflow with omega being pure real, and alpha the eigenvalue

Returns: tuple of eigenvalue and eigenvector closest to the target value e.g. std::tie(alpha,group_velocity,left_eig_vector,right_eig_vector) = LSTNP_spatial(params,grid,baseflow). Will solve for closest eigenvalue to params.alpha

Parameters

[in,out]	params	[inout] contains parameters including Re, alpha, and omega. Will overwrite omega with true omega value once solved
[in]	grid	[in] grid class containing the grid location and respective derivatives
[in]	baseflow	[in] baseflow for parallel flow
[in]	ql	[in] initial guess for spatial problem (adjoint) for left eigenfunction
[in]	qr	[in] initial guess for spatial problem

Definition at line 715 of file SPILST.cpp.

◆ LSTNP_spatial_right()

std::tuple< PetscScalar, SPIVec > SPI::LSTNP_spatial_right	(	SPIparams &	params,
		SPIgrid1D &	grid,
		SPIbaseflow &	baseflow,
		SPIVec	qr
	)

solve the local stability theory problem for the linearized Navier-Stokes equations using parallel baseflow with omega being pure real, and alpha the eigenvalue

Returns: tuple of eigenvalue and eigenvector closest to the target value e.g. std::tie(alpha,right_eig_vector) = LSTNP_spatial(params,grid,baseflow). Will solve for closest eigenvalue to params.alpha

Parameters

[in,out]	params	[inout] contains parameters including Re, alpha, and omega. Will overwrite omega with true omega value once solved
[in]	grid	[in] grid class containing the grid location and respective derivatives
[in]	baseflow	[in] baseflow for parallel flow
[in]	qr	[in] initial guess for spatial problem

Definition at line 1046 of file SPILST.cpp.

◆ LSTNP_spatial_right2()

std::tuple< PetscScalar, SPIVec > SPI::LSTNP_spatial_right2	(	SPIparams &	params,
		SPIgrid1D &	grid,
		SPIbaseflow &	baseflow,
		SPIVec	qr
	)

solve the local stability theory problem for the linearized Navier-Stokes equations using parallel baseflow with omega being pure real, and alpha the eigenvalue

Returns: tuple of eigenvalue and eigenvector closest to the target value e.g. std::tie(alpha,right_eig_vector) = LSTNP_spatial(params,grid,baseflow). Will solve for closest eigenvalue to params.alpha

Parameters

[in,out]	params	[inout] contains parameters including Re, alpha, and omega. Will overwrite omega with true omega value once solved
[in]	grid	[in] grid class containing the grid location and respective derivatives
[in]	baseflow	[in] baseflow for parallel flow
[in]	qr	[in] initial guess for spatial problem

Definition at line 1276 of file SPILST.cpp.

◆ LSTNP_spatials_right()

std::tuple< std::vector< PetscScalar >, std::vector< SPIVec > > SPI::LSTNP_spatials_right	(	SPIparams &	params,
		SPIgrid1D &	grid,
		SPIbaseflow &	baseflow,
		std::vector< PetscScalar > &	alphas,
		std::vector< SPIVec > &	qrs
	)

solve the local stability theory problem for the linearized Navier-Stokes equations using non-parallel baseflow with omega being pure real, and alpha the eigenvalue

Returns: tuple of eigenvalue and eigenvector closest to the target value e.g. std::tie(alphas,right_eig_vectors) = LSTNP_spatials_right(params,grid,baseflow). Will solve for closest eigenvalue to params.alpha

Parameters

[in,out]	params	[inout] contains parameters including Re and omega.
[in]	grid	[in] grid class containing the grid location and respective derivatives
[in]	baseflow	[in] baseflow for parallel flow
[in]	alphas	[in] vector of alpha guesses
[in]	qrs	[in] initial guesses for spatial problem

Definition at line 1482 of file SPILST.cpp.

◆ lstsq() [1/2]

SPIVec SPI::lstsq	(	const SPIMat &	A,
		SPIVec &	y
	)

solve least squares problem of A*x=y for skinny A matrix using SVD

Returns: x

Parameters

[in]	A	[in] A matrix in A*x=y least squares problem
[in]	y	[in] y in A*x=y least squares problem

Definition at line 905 of file SPIMat.cpp.

◆ lstsq() [2/2]

SPIVec SPI::lstsq	(	const std::vector< SPIVec > &	A,
		SPIVec &	y
	)

solve least squares problem of A*x=y for skinny A matrix (or vectors of columns vectors) using SVD

Returns: x

Parameters

[in]	A	[in] vectors of columns vectors making up A matrix
[in]	y	[in] y in A*x=y least squares problem

Definition at line 920 of file SPIMat.cpp.

◆ map_D()

SPIMat SPI::map_D	(	SPIMat	D,
		SPIVec	y,
		PetscInt	d,
		PetscInt	order
	)

map the derivative operator to the proper y grid

Returns: mapped derivative to streched grid

Parameters

[in]	D	[in] derivative operator on uniform grid from 0 to 1 (xi grid)
[in]	y	[in] potentially non-uniform grid from 0 to y_max
[in]	d	[in] order of derivative
[in]	order	[in] order of accuracy for finite difference stencil (default 4)

Definition at line 52 of file SPIgrid.cpp.

◆ map_D_Chebyshev()

SPIMat SPI::map_D_Chebyshev	(	SPIVec &	x,
		PetscInt	d
	)

map a Chebyshev collocated operator acting with respect to the stretched collocated grid

Returns: Chebyshev collocated derivative operator

Parameters

[in]	x	[in] grid (created from set_Cheby_stretched_y or set_Cheby_y or similar example)
[in]	d	[in] order of the derivative (default 1)

Definition at line 278 of file SPIgrid.cpp.

◆ meshgrid()

std::tuple< SPIMat, SPIMat > SPI::meshgrid	(	SPIVec &	x,
		SPIVec &	y
	)

Parameters

[in]	x	[in] x input array
[in]	y	[in] y input array

Definition at line 1894 of file SPIMat.cpp.

◆ ones()

SPIVec SPI::ones ( const PetscInt rows )

create a vector of size rows full of ones

Returns: vector of size rows

Parameters

[in] rows [in] number of rows for vector size

Definition at line 605 of file SPIVec.cpp.

◆ operator%()

SPIMat SPI::operator%	(	const SPIMat &	A,
		const SPIMat &	B
	)

take the elementwise multiplication of each element in a matrix

Definition at line 2033 of file SPIMat.cpp.

◆ operator*() [1/3]

SPIMat SPI::operator*	(	const PetscScalar	a,
		const SPIMat	A
	)

a*A operation to be equivalent to A*a

Returns: new matrix of a*A

Parameters

[in]	a	[in] scalar a in a*A
[in]	A	[in] matrix A in a*A

Definition at line 517 of file SPIMat.cpp.

◆ operator*() [2/3]

SPIVec SPI::operator*	(	const PetscScalar	a,
		const SPIVec &	Y
	)

Z=a*Y operation to be equivalent to Y*a

Returns: Z in Z=a*Y operation

Parameters

[in]	a	[in] scalar a in a*Y operation
[in]	Y	[in] Y in Z=a*Y

Definition at line 510 of file SPIVec.cpp.

◆ operator*() [3/3]

SPIMat SPI::operator*	(	const SPIMat	A,
		const PetscScalar	a
	)

A*a operation to be equivalent to A*a.

Returns: new matrix of A*a operation

Definition at line 527 of file SPIMat.cpp.

◆ operator+()

SPIVec SPI::operator+	(	const PetscScalar	a,
		const SPIVec &	Y
	)

Z=a+Y operation to be equivalent to Y+a

Returns: Z in Z=a+Y operation

Parameters

[in]	a	[in] scalar a in a+Y operation
[in]	Y	[in] Y in a+Y operation

Definition at line 521 of file SPIVec.cpp.

◆ operator-()

SPIVec SPI::operator-	(	const PetscScalar	a,
		const SPIVec &	Y
	)

Z=a-Y operation to be equivalent to Y-a

Returns: Z in Z=a-Y operation

Parameters

[in]	a	[in] scalar a in a-Y operation
[in]	Y	[in] Y in a-Y operation

Definition at line 532 of file SPIVec.cpp.

◆ operator/() [1/2]

SPIVec SPI::operator/	(	const PetscScalar	a,
		const SPIVec &	Y
	)

Z=a/Y operation

Returns: Z in Z=a/Y operation

Parameters

[in]	a	[in] scalar a in a/Y operation
[in]	Y	[in] Y in Z=a/Y

Definition at line 497 of file SPIVec.cpp.

◆ operator/() [2/2]

SPIVec SPI::operator/	(	const SPIVec &	b,
		const SPIMat &	A
	)

Solve linear system, Ax=b using b/A notation.

Returns: x vector in Ax=b solved linear system

Parameters

[in]	b	[in] b in Ax=b
[in]	A	[in] A in Ax=b

Definition at line 535 of file SPIMat.cpp.

◆ operator^()

SPIMat SPI::operator^	(	const PetscScalar	a,
		const SPIMat &	A
	)

Y=a^A operation.

Returns: Y matrix in Y=a^A

Parameters

[in]	a	[in] a in Y=a^A
[in]	A	[in] A in Y=a^A

Definition at line 578 of file SPIMat.cpp.

◆ orthogonalize() [1/3]

SPIMat SPI::orthogonalize ( const std::vector< SPIVec > & x )

Parameters

[in] x [in] array of vectors to orthogonalize

Definition at line 2057 of file SPIMat.cpp.

◆ orthogonalize() [2/3]

std::vector< SPIVec > SPI::orthogonalize	(	std::vector< SPIVec > &	x,
		SPIgrid1D &	grid
	)

Parameters

[in]	x	[in] array of vectors to orthogonalize
[in]	grid	[in] respective grid for integration using Gram-Schmidt

Definition at line 1323 of file SPIgrid.cpp.

◆ orthogonalize() [3/3]

std::vector< SPIVec > SPI::orthogonalize	(	std::vector< SPIVec > &	x,
		SPIgrid2D &	grid
	)

Parameters

[in]	x	[in] array of vectors to orthogonalize
[in]	grid	[in] respective grid for integration using Gram-Schmidt

Definition at line 1406 of file SPIgrid.cpp.

◆ polyeig()

std::tuple< PetscScalar, SPIVec > SPI::polyeig	(	const std::vector< SPIMat > &	As,
		const PetscScalar	target,
		const PetscReal	tol,
		const PetscInt	max_iter
	)

solve general polynomial eigenvalue problem of (A0 + A1*alpha + A2*alpha^2 + ...)*x = 0 and return a tuple of tie(PetscScalar alpha, SPIVec eig_vector)

Returns: tuple of eigenvalue and eigenvector closest to the target value e.g. std::tie(alpha, eig_vector) = eig([A0,A1,A2...],0.1+0.4*PETSC_i)

Parameters

[in]	As	[in] [A0,A1,A2...] in generalized polynomial eigenvalue problem
[in]	target	[in] target eigenvalue to solve for
[in]	tol	[in] tolerance of eigenvalue solver
[in]	max_iter	[in] maximum number of iterations

Definition at line 1686 of file SPIMat.cpp.

◆ polyeig_init()

std::tuple< PetscScalar, SPIVec > SPI::polyeig_init	(	const std::vector< SPIMat > &	As,
		const PetscScalar	target,
		const SPIVec &	qr,
		const PetscReal	tol,
		const PetscInt	max_iter
	)

solve general polynomial eigenvalue problem of (A0 + A1*alpha + A2*alpha^2 + ...)*x = 0 and return a tuple of tie(PetscScalar alpha, SPIVec eig_vector) using initial subspace vector

Returns: tuple of eigenvalue and eigenvector closest to the target value e.g. std::tie(alpha, eig_vector) = eig([A0,A1,A2...],0.1+0.4*PETSC_i)

Parameters

[in]	As	[in] [A0,A1,A2...] in generalized polynomial eigenvalue problem
[in]	target	[in] target eigenvalue to solve for
[in]	qr	[in] initial subspace vector for right eigenvalue problem
[in]	tol	[in] tolerance of eigenvalue solver
[in]	max_iter	[in] maximum number of iterations

Definition at line 1754 of file SPIMat.cpp.

◆ pow() [1/2]

SPIVec SPI::pow	(	const SPIVec &	A,
		PetscScalar	b
	)

take the pow of each element in the vector (A^b)

Returns: A^b

Parameters

[in]	A	[in] vector to raise to the power
[in]	b	[in] the exponenet

Definition at line 777 of file SPIVec.cpp.

◆ pow() [2/2]

SPIVec SPI::pow	(	const SPIVec &	A,
		SPIVec &	B
	)

take the pow of each element in the vectors

Definition at line 775 of file SPIVec.cpp.

◆ printf()

PetscInt SPI::printf	(	std::string	msg,
			...
	)

print a message to string using PetscPrintf (also adds a newline at end) (note: only prints on rank 0 processor)

Returns: 0 if successful

Parameters

[in]	msg	[in] message to print with formatting such as %g
[in]	...	[in] scalar or double or int to match formatting string to be output on processor with rank 0

Definition at line 5 of file SPIprint.cpp.

◆ printfc()

PetscInt SPI::printfc	(	std::string	msg,
		PetscScalar	val
	)

print a message to string using PetscPrintf (also adds a newline at end) (note: only prints on rank 0 processor) with PetscScalars as input and two formats per argument

Returns: 0 if successful

Parameters

[in]	msg	[in] message to print with formatting such as %g
[in]	val	[in] scalar or double or int to match formatting string to be output on processor with rank 0

Definition at line 29 of file SPIprint.cpp.

◆ proj() [1/2]

SPIVec SPI::proj	(	SPIVec &	u,
		SPIVec &	v,
		SPIgrid1D &	grid
	)

Parameters

[in]	u	[in] first vector to project
[in]	v	[in] second vector to project
[in]	grid	[in] respective grid

Definition at line 1220 of file SPIgrid.cpp.

◆ proj() [2/2]

SPIVec SPI::proj	(	SPIVec &	u,
		SPIVec &	v,
		SPIgrid2D &	grid
	)

Parameters

[in]	u	[in] first vector to project
[in]	v	[in] second vector to project
[in]	grid	[in] respective grid

Definition at line 1267 of file SPIgrid.cpp.

◆ real()

SPIVec SPI::real ( const SPIVec & A )

return the real part of the vector

Parameters

[in] A [in] vector to take real part of

Definition at line 631 of file SPIVec.cpp.

◆ save() [1/5]

PetscInt SPI::save	(	const SPIMat &	A,
		const std::string	filename
	)

save matrix to filename in binary format (see Petsc documentation for format ) Format is (from Petsc documentation): int MAT_FILE_CLASSID int number of rows int number of columns int total number of nonzeros int *number nonzeros in each row int *column indices of all nonzeros (starting index is zero) PetscScalar *values of all nonzeros

Returns: 0 if successful

Parameters

[in]	A	[in] A to save in
[in]	filename	[in] filename to save data to

Definition at line 1924 of file SPIMat.cpp.

◆ save() [2/5]

PetscInt SPI::save	(	const SPIVec &	A,
		const std::string	filename
	)

save A to hdf5 to filename as variable A.name (note: this will append if filename already exists)

Returns: 0 if successful

Parameters

[in]	A	[in] A to save in hdf5 format under A.name variable
[in]	filename	[in] filename to save

Definition at line 543 of file SPIVec.cpp.

◆ save() [3/5]

PetscInt SPI::save	(	const std::vector< SPIMat > &	As,
		const std::string	filename
	)

save matrices to filename in binary format (see Petsc documentation for format

Returns: 0 if successful

Parameters

[in]	As	[in] A to save in
[in]	filename	[in] filename to save data to

Definition at line 1944 of file SPIMat.cpp.

◆ save() [4/5]

PetscInt SPI::save	(	std::vector< PetscScalar >	A,
		std::string	variablename,
		std::string	filename
	)

save A to hdf5 to filename as variable A.name (note: this will append if filename already exists)

Returns: 0 if successful

Parameters

[in]	A	[in] variable to save to hdf5 file
[in]	variablename	[in] the name of the variable to save in the file
[in]	filename	[in] hdf5 filename

Definition at line 562 of file SPIVec.cpp.

◆ save() [5/5]

PetscInt SPI::save	(	std::vector< SPIVec >	A,
		std::string	variablename,
		std::string	filename
	)

save A to hdf5 to filename as variable A.name (note: this will append if filename already exists)

Returns: 0 if successful

Parameters

[in]	A	[in] variable to save to hdf5 file
[in]	variablename	[in] the name of the variable to save in the file
[in]	filename	[in] hdf5 filename

Definition at line 576 of file SPIVec.cpp.

◆ set_Cheby_mapped_y()

SPIVec SPI::set_Cheby_mapped_y	(	PetscScalar	a,
		PetscScalar	b,
		PetscInt	ny
	)

create a stretched Chebyshev grid from [a,b] using default Chebfun like mapping

Returns: grid in [a,b] using Chebyshev collocated points

Parameters

[in]	a	[in] lower bound of grid domain [a,b]
[in]	b	[in] upper bound of grid domain [a,b]
[in]	ny	[in] number of points on grid

Definition at line 318 of file SPIgrid.cpp.

◆ set_Cheby_stretched_y()

SPIVec SPI::set_Cheby_stretched_y	(	PetscScalar	y_max,
		PetscInt	ny,
		PetscScalar	yi
	)

create a stretched Chebyshev grid from [0,y_max] with yi being the midpoint location for the number of points

Returns: stretched grid using Chebyshev collocated points

Parameters

[in]	y_max	[in] maximum range for [0, y_max] stretching
[in]	ny	[in] number of points
[in]	yi	[in] midpoint location for the number of points (i.e. ny/2 are above and below this point)

Definition at line 305 of file SPIgrid.cpp.

◆ set_Cheby_y()

SPIVec SPI::set_Cheby_y ( PetscInt ny )

create a Chebyshev grid from [-1,1]

Returns: grid using Chebyshev collocated points

Parameters

[in] ny [in] number of points

Definition at line 329 of file SPIgrid.cpp.

◆ set_D()

SPIMat SPI::set_D	(	SPIVec &	y,
		PetscInt	d,
		PetscInt	order,
		PetscBool	uniform
	)

set the derivative operator for the proper y grid if uniform=false. Uses map_D function

Returns: mapped derivative to streched grid

Parameters

[in]	y	[in] grid points
[in]	d	[in] order of derivative
[in]	order	[in] order of accuracy of derivative (default 4)
[in]	uniform	[in] is this for a uniform grid? (default false)

Definition at line 82 of file SPIgrid.cpp.

◆ set_D_Chebyshev()

SPIMat SPI::set_D_Chebyshev	(	SPIVec &	x,
		PetscInt	d,
		PetscBool	need_map
	)

set a Chebyshev collocated operator acting with respect to the collocated grid

Returns: Chebyshev collocated derivative operator

Parameters

[in]	x	[in] grid (created from set_Cheby_stretched_y or set_Cheby_y or similar example)
[in]	d	[in] order of the derivative (default 1)
[in]	need_map	[in] need mapping? (default false)

Definition at line 225 of file SPIgrid.cpp.

◆ set_D_Fourier()

SPIMat SPI::set_D_Fourier	(	SPIVec	t,
		PetscInt	d
	)

create a Fourier derivative operator acting on grid t

Returns: derivative operator using Fourier collocated points

Parameters

[in]	t	[in] grid point created from set_Fourier_t
[in]	d	[in] order of derivatives

Definition at line 407 of file SPIgrid.cpp.

◆ set_D_periodic()

SPIMat SPI::set_D_periodic	(	SPIVec &	y,
		PetscInt	d,
		PetscInt	order
	)

set the derivative operator for the proper periodic grid assuming uniform discretization.

Returns: derivative operator for uniform periodic grid

Parameters

[in]	y	[in] grid points
[in]	d	[in] order of derivative
[in]	order	[in] order of accuracy of derivative (default 4)

Definition at line 172 of file SPIgrid.cpp.

◆ set_D_UltraS()

std::tuple< SPIMat, SPIMat > SPI::set_D_UltraS	(	SPIVec &	x,
		PetscInt	d
	)

set a UltraSpherical operator acting with respect to the collocated grid (keeps everything in UltraSpherical space), take in Chebyshev coefficients and outputs coefficients in C(d) coefficient space

Returns: UltraSpherical derivative operator

Parameters

[in]	x	[in] grid (must be created from set_Cheby_y or set_Cheby_mapped_y)
[in]	d	[in] order of the derivative (default 1)

Definition at line 338 of file SPIgrid.cpp.

◆ set_FD_stretched_y()

SPIVec SPI::set_FD_stretched_y	(	PetscScalar	y_max,
		PetscInt	ny,
		PetscScalar	delta
	)

set stretched grid from [0,y_max] using tanh stretching for use with finite difference operators

Returns: y stretched grid

Parameters

[in]	y_max	[in] upper bound of y in [0,y_max]
[in]	ny	[in] number of points to use in the domain
[in]	delta	[in] stretching parameter, near zero is no stretching, (default 2.0001)

Definition at line 214 of file SPIgrid.cpp.

◆ set_Fourier_t()

SPIVec SPI::set_Fourier_t	(	PetscScalar	T,
		PetscInt	nt
	)

create a Fourier grid from [0,T]

Returns: grid using Fourier collocated points without the last point of linspace(0,T,n+1)[:-1]

Parameters

[in]	T	[in] period or end point for [0,T] domain
[in]	nt	[in] number of points

Definition at line 392 of file SPIgrid.cpp.

◆ set_T_That()

std::tuple< SPIMat, SPIMat > SPI::set_T_That ( PetscInt n )

set a T and That operators acting with respect to the Chebyshev collocated grid, That: physical -> Chebyshev coefficient, T: Chebyshev coefficient -> physical

Returns: UltraSpherical derivative operator

Parameters

[in] n [in] number of discretized points in Chebyshev grid

Definition at line 367 of file SPIgrid.cpp.

◆ sin() [1/2]

SPIMat SPI::sin ( const SPIMat & A )

take the sin of each element in a matrix

Definition at line 2025 of file SPIMat.cpp.

◆ sin() [2/2]

SPIVec SPI::sin ( const SPIVec & A )

take the sin of each element in a vector

Definition at line 706 of file SPIVec.cpp.

◆ sinh()

SPIVec SPI::sinh ( const SPIVec & A )

take the sinh of each element in a vector

Definition at line 723 of file SPIVec.cpp.

◆ solve()

SPIVec SPI::solve	(	const SPIMat &	A,
		const SPIVec &	b
	)

Solve linear system, Ax=b using solve(A,b) notation.

Returns: x vector in Ax=b solved linear system

Parameters

[in]	A	[in] A in Ax=b
[in]	b	[in] b in Ax=b

Definition at line 596 of file SPIMat.cpp.

◆ SPIVec1Dto2D()

SPIVec SPI::SPIVec1Dto2D	(	SPIgrid2D &	grid2D,
		SPIVec &	u
	)

expand a 1D vector to a 2D vector copying data along time dimension

Parameters

[in]	grid2D	[in] 3D grid containing wall-normal and time dimensions
[in]	u	[in] vector to inflate to match the 3D operator

Definition at line 850 of file SPIgrid.cpp.

◆ sqrt()

SPIVec SPI::sqrt ( const SPIVec & A )

take the atanh of each element in a vector

Definition at line 741 of file SPIVec.cpp.

◆ sum()

PetscScalar SPI::sum ( SPIVec x1 )

take the sum of a vector

Parameters

[in] x1 [in] vector to sum

Definition at line 805 of file SPIVec.cpp.

◆ svd()

std::tuple< std::vector< PetscReal >, std::vector< SPIVec >, std::vector< SPIVec > > SPI::svd ( const SPIMat & A )

solve SVD problem of A=U*E*V^H for skinny A matrix

Returns: tuple of sigma,u,v std::tie(sigma, u, v) = svd(A)

Parameters

[in] A [in] A to perform SVD decomposition A=U*E*V^H problem

Definition at line 851 of file SPIMat.cpp.

◆ tan() [1/2]

SPIMat SPI::tan ( const SPIMat & A )

take the tan of each element in a matrix

Definition at line 2031 of file SPIMat.cpp.

◆ tan() [2/2]

SPIVec SPI::tan ( const SPIVec & A )

take the tan of each element in a vector

Definition at line 710 of file SPIVec.cpp.

◆ tanh()

SPIVec SPI::tanh ( const SPIVec & A )

take the tanh of each element in a vector

Definition at line 727 of file SPIVec.cpp.

◆ trapz() [1/2]

PetscScalar SPI::trapz ( SPIVec y )

trapezoidal integration of y with unity coordinate spacing, \(\int y dx \)

Returns: integrated value

Parameters

[in] y [in] vector to integrate, assuming default spacing of one

Definition at line 898 of file SPIVec.cpp.

◆ trapz() [2/2]

PetscScalar SPI::trapz	(	SPIVec	y,
		SPIVec	x
	)

trapezoidal integration of y with x coordinates, \(\int y dx \)

Returns: integrated value

Parameters

[in]	y	[in] vector to integrate
[in]	x	[in] optional, coordinates to integrate over, must be same size as y, and defaults to spacing of one if not given

Definition at line 915 of file SPIVec.cpp.

◆ zeros() [1/2]

SPIMat SPI::zeros	(	const PetscInt	m,
		const PetscInt	n
	)

create, form, and return zeros matrix of size mxn

Returns: zero matrix of size mxn

Parameters

[in]	m	[in] m size of zero matrix
[in]	n	[in] n size of zero matrix

Definition at line 708 of file SPIMat.cpp.

◆ zeros() [2/2]

SPIVec SPI::zeros ( const PetscInt rows )

create and return a vector of size rows full of zeros

Returns: vector of size zeros

Parameters

[in] rows [in] size of vector to create

Definition at line 614 of file SPIVec.cpp.

Data Structures

Typedefs

Enumerations

Functions

Typedef Documentation

◆ Block2D

Enumeration Type Documentation

◆ gridtype

Function Documentation

◆ _bblf()

◆ _Function_on_each_element() [1/3]

◆ _Function_on_each_element() [2/3]

◆ _Function_on_each_element() [3/3]

◆ abs() [1/2]

◆ abs() [2/2]

◆ acos() [1/2]

◆ acos() [2/2]

◆ acosh()

◆ arange() [1/2]

◆ arange() [2/2]

◆ asin()

◆ asinh()

◆ atan()

◆ atanh()

◆ blasius()

◆ block()

◆ channel()

◆ conj()

◆ cos() [1/2]

◆ cos() [2/2]

◆ cosh()

◆ dft()

◆ dft_dftinv_Ihalf_Ihalfn()

◆ diag()

◆ diff()

◆ dot()

◆ draw() [1/2]

◆ draw() [2/2]

◆ eig()

◆ eig_init()

◆ eig_init_right()

◆ eig_init_rights()

◆ eig_right()

◆ erf()

◆ erfc()

◆ exp()

◆ eye()

◆ factorial()

◆ get_D_Coeffs()

◆ imag()

◆ integrate() [1/2]

◆ integrate() [2/2]

◆ integrate_coeffs() [1/2]

◆ integrate_coeffs() [2/2]

◆ interp1D_Mat() [1/2]

◆ interp1D_Mat() [2/2]

◆ inv()

◆ kron()

◆ L2() [1/2]

◆ L2() [2/2]

◆ linspace()

◆ load() [1/3]

◆ load() [2/3]

◆ load() [3/3]

◆ log()

◆ log10()

◆ LST_spatial()

◆ LST_spatial_cg()

◆ LST_temporal()

◆ LSTNP_spatial()

◆ LSTNP_spatial_right()

◆ LSTNP_spatial_right2()

◆ LSTNP_spatials_right()

◆ lstsq() [1/2]

◆ lstsq() [2/2]

◆ map_D()

◆ map_D_Chebyshev()

◆ meshgrid()

◆ ones()

◆ operator%()