Utility routines for orienting the globe and basic geographical mappings. More...

Data Types
interface	ctoc_schm

interface	ctog

interface	ctogr

interface	frametwist

interface	grtoc

interface	gtoc

interface	gtoframe

interface	ininmap

interface	inivmap

interface	paraframe

interface	plctoc

interface	plrot

interface	plroti

Functions/Subroutines
subroutine	dctoc (s, xc1, xc2)
	Evaluate Schmidt transformation, xc1 –> xc2, with scaling parameter s. More...

subroutine	dctocd (s, xc1, xc2, dxc2)
	Evaluate Schmidt transformation, xc1 –> xc2, with scaling parameter s, and its jacobian, dxc2. More...

subroutine	dctocdd (s, xc1, xc2, dxc2, ddxc2)
	Evaluate Schmidt transformation, xc1 –> xc2, with scaling parameter s, its jacobian, dxc2, and its 2nd derivative, ddxc2. More...

subroutine	dctog (xe, dlat, dlon)
	Transform "Cartesian" to "Geographical" coordinates, where the geographical coordinates refer to latitude and longitude (degrees) and cartesian coordinates are standard earth-centered cartesian coordinates: xe(3) pointing north, xe(1) pointing to the 0-meridian. More...

subroutine	dctogr (xe, rlat, rlon)
	Transform "Cartesian" to "Geographical" coordinates, where the geographical coordinates refer to latitude and longitude (radians) and cartesian coordinates are standard earth-centered cartesian coordinates: xe(3) pointing north, xe(1) pointing to the 0-meridian. More...

subroutine	dgrtoc (rlat, rlon, xe)
	Transform "Geographical" to "Cartesian" coordinates. More...

subroutine	dgrtocd (rlat, rlon, xe, dxedlat, dxedlon)
	Transform "Geographical" to "Cartesian" coordinates, together with the partial derivatives of cartesians wrt latitude and longitude. More...

subroutine	dgrtocdd (rlat, rlon, xe, dxedlat, dxedlon, ddxedlatdlat, ddxedlatdlon, ddxedlondlon)
	Transform "Geographical" to "Cartesian" coordinates, together with the 1st and 2nd partial derivatives of cartesians wrt latitude and longitude. More...

subroutine	dgtoc (dlat, dlon, xe)
	Transform "Geographical" to "Cartesian" coordinates, where the geographical coordinates refer to latitude and longitude (degrees) and cartesian coordinates are standard earth-centered cartesian coordinates: xe(3) pointing north, xe(1) pointing to the 0-meridian. More...

subroutine	dgtocd (dlat, dlon, xe, dxedlat, dxedlon)
	Transform "Geographical" to "Cartesian" coordinates, where the geographical coordinates refer to latitude and longitude (degrees) and cartesian coordinates are standard earth-centered cartesian coordinates: xe(3) pointing north, xe(1) pointing to the 0-meridian. More...

subroutine	dgtocdd (dlat, dlon, xe, dxedlat, dxedlon, ddxedlatdlat, ddxedlatdlon, ddxedlondlon)
	Transform "Geographical" to "Cartesian" coordinates, where the geographical coordinates refer to latitude and longitude (degrees) and cartesian coordinates are standard earth-centered cartesian coordinates: xe(3) pointing north, xe(1) pointing to the 0-meridian. More...

subroutine	dininmap (alon0, alat0, rot3)
	Initialize the rotation matrix ROT3 needed to transform standard earth-centered cartesian components to the alternative cartesian frame oriented so as to put geographical point (ALAT0,ALON0) on the projection axis. More...

subroutine	dinivmap (alon0, alat0, rot3)
	Initialize the rotation matrix ROT3 needed to transform standard earth-centered cartesian components to the alternative cartesian frame oriented so as to put geographical point (ALAT0,ALON0) at the viewing nadir. More...

subroutine	dplrot (rot3, n, x, y, z)
	Apply a constant rotation to a three dimensional polyline. More...

subroutine	dplroti (rot3, n, x, y, z)
	Invert the rotation of a three-dimensional polyline. More...

subroutine, public	frametwist (xp, yp, zp, xv, yv, zv, twist)
	Given a principal cartesian orthonormal frame, {xp,yp,zp} (i.e., at P with Earth-centered cartesians, zp), and another similar frame {xv,yv,zv} at V with Earth-centered cartesians zv, find the relative rotation angle, "twist" by which the frame at V is rotated in the counterclockwise sense relative to the parallel-transportation of P's frame to V. More...

subroutine	gtoframem (plat, plon, orth)
	From the degree lat and lon (plat and plon) return the standard orthogonal 3D frame at this location as an orthonormal matrix, orth. More...

subroutine	gtoframev (plat, plon, xp, yp, zp)
	Given a geographical point by its degrees lat and lon, plat and plon, return its standard orthogonal cartesian frame, {xp,yp,zp} in earth-centered coordinates. More...

subroutine, public	paraframe (xp, yp, zp, xv, yv, zv)
	Take a principal reference orthonormal frame, {xp,yp,zp} and a dependent point defined by unit vector, zv, and complete the V-frame cartesian components, {xv,yv}, that are the result of parallel-transport of {xp,yp} along the geodesic between P and V. More...

subroutine, public	plctoc (s, n, x, y, z)
	Perform Schmidt transformation with scaling parameter s to a polyline. More...

subroutine, public	plrot (rot3, n, x, y, z)
	Apply a constant rotation to a three dimensional polyline. More...

subroutine, public	plroti (rot3, n, x, y, z)
	Invert the rotation of a three-dimensional polyline. More...

subroutine	sctoc (s, xc1, xc2)
	Evaluate Schmidt transformation, xc1 –> xc2, with scaling parameter s. More...

subroutine	sctocd (s, xc1, xc2, dxc2)
	Evaluate Schmidt transformation, xc1 –> xc2, with scaling parameter s, and its jacobian, dxc2. More...

subroutine	sctocdd (s, xc1, xc2, dxc2, ddxc2)
	Evaluate Schmidt transformation, xc1 –> xc2, with scaling parameter s, its jacobian, dxc2, and its 2nd derivative, ddxc2. More...

subroutine	sctog (xe, dlat, dlon)
	Transform "Cartesian" to "Geographical" coordinates, where the geographical coordinates refer to latitude and longitude (degrees) and cartesian coordinates are standard earth-centered cartesian coordinates: xe(3) pointing north, xe(1) pointing to the 0-meridian. More...

subroutine	sctogr (xe, rlat, rlon)
	Transform "Cartesian" to "Geographical" coordinates, where the geographical coordinates refer to latitude and longitude (radians) and cartesian coordinates are standard earth-centered cartesian coordinates: xe(3) pointing north, xe(1) pointing to the 0-meridian. More...

subroutine	sframetwist (sxp, syp, szp, sxv, syv, szv, stwist)
	Given a principal cartesian orthonormal frame, {xp,yp,zp} (i.e., at P with Earth-centered cartesians, zp), and another similar frame {xv,yv,zv} at V with Earth-centered cartesians zv, find the relative rotation angle, "twist" by which the frame at V is rotated in the counterclockwise sense relative to the parallel-transportation of P's frame to V. More...

subroutine	sgrtoc (rlat, rlon, xe)
	Transform "Geographical" to "Cartesian" coordinates. More...

subroutine	sgrtocd (rlat, rlon, xe, dxedlat, dxedlon)
	Transform "Geographical" to "Cartesian" coordinates, together with the partial derivatives of cartesians wrt latitude and longitude. More...

subroutine	sgrtocdd (rlat, rlon, xe, dxedlat, dxedlon, ddxedlatdlat, ddxedlatdlon, ddxedlondlon)
	Transform "Geographical" to "Cartesian" coordinates, together with the 1st and 2nd partial derivatives of cartesians wrt latitude and longitude. More...

subroutine	sgtoc (dlat, dlon, xe)
	Transform "Geographical" to "Cartesian" coordinates, where the geographical coordinates refer to latitude and longitude (degrees) and cartesian coordinates are standard earth-centered cartesian coordinates: xe(3) pointing north, xe(1) pointing to the 0-meridian. More...

subroutine	sgtocd (dlat, dlon, xe, dxedlat, dxedlon)
	Transform "Geographical" to "Cartesian" coordinates, where the geographical coordinates refer to latitude and longitude (degrees) and cartesian coordinates are standard earth-centered cartesian coordinates: xe(3) pointing north, xe(1) pointing to the 0-meridian. More...

subroutine	sgtocdd (dlat, dlon, xe, dxedlat, dxedlon, ddxedlatdlat, ddxedlatdlon, ddxedlondlon)
	Transform "Geographical" to "Cartesian" coordinates, where the geographical coordinates refer to latitude and longitude (degrees) and cartesian coordinates are standard earth-centered cartesian coordinates: xe(3) pointing north, xe(1) pointing to the 0-meridian. More...

subroutine	sgtoframem (splat, splon, sorth)
	From the degree lat and lon (plat and plon) return the standard orthogonal 3D frame at this location as an orthonormal matrix, orth. More...

subroutine	sgtoframev (splat, splon, sxp, syp, szp)
	Given a geographical point by its degrees lat and lon, plat and plon, return its standard orthogonal cartesian frame, {xp,yp,zp} in earth-centered coordinates. More...

subroutine	sininmap (alon0, alat0, rot3)
	Initialize the rotation matrix ROT3 needed to transform standard earth-centered cartesian components to the alternative cartesian frame oriented so as to put geographical point (ALAT0,ALON0) on the projection axis. More...

subroutine	sinivmap (alon0, alat0, rot3)
	Initialize the rotation matrix ROT3 needed to transform standard earth-centered cartesian components to the alternative cartesian frame oriented so as to put geographical point (ALAT0,ALON0) at the viewing nadir. More...

subroutine	sparaframe (sxp, syp, szp, sxv, syv, szv)
	Take a principal reference orthonormal frame, {xp,yp,zp} and a dependent point defined by unit vector, zv, and complete the V-frame cartesian components, {xv,yv}, that are the result of parallel-transport of {xp,yp} along the geodesic between P and V. More...

Detailed Description

Utility routines for orienting the globe and basic geographical mappings.

Author: R. J. Purser

Function/Subroutine Documentation

◆ dctoc()

subroutine pmat5::dctoc	(	real(dp), intent(in)	s,
		real(dp), dimension(3), intent(inout)	xc1,
		real(dp), dimension(3), intent(inout)	xc2
	)

Evaluate Schmidt transformation, xc1 –> xc2, with scaling parameter s.

Parameters

[in]	s	Schmidt scaling parameter.
[in,out]	xc1	input cartesian 3-vector.
[in,out]	xc2	output cartesian unit 3-vector.

Author: R. J. Purser

Definition at line 916 of file pmat5.f90.

References pietc::u1, and pietc::u2.

◆ dctocd()

subroutine pmat5::dctocd	(	real(dp), intent(in)	s,
		real(dp), dimension(3), intent(inout)	xc1,
		real(dp), dimension(3), intent(inout)	xc2,
		real(dp), dimension(3,3), intent(out)	dxc2
	)

Evaluate Schmidt transformation, xc1 –> xc2, with scaling parameter s, and its jacobian, dxc2.

Parameters

[in]	s	Schmidt scaling parameter.
[in,out]	xc1	input cartesian 3-vector.
[in,out]	xc2	output cartesian unit 3-vector.
[out]	dxc2	jacobian 1st derivative, d(xc2)/d(xc1).

Author: R. J. Purser

Definition at line 947 of file pmat5.f90.

References pietc::u0, pietc::u1, and pietc::u2.

◆ dctocdd()

subroutine pmat5::dctocdd	(	real(dp), intent(in)	s,
		real(dp), dimension(3), intent(inout)	xc1,
		real(dp), dimension(3), intent(inout)	xc2,
		real(dp), dimension(3,3), intent(out)	dxc2,
		real(dp), dimension(3,3,3), intent(out)	ddxc2
	)

Evaluate Schmidt transformation, xc1 –> xc2, with scaling parameter s, its jacobian, dxc2, and its 2nd derivative, ddxc2.

Parameters

[in]	s	Schmidt scaling parameter.
[in,out]	xc1	input cartesian 3-vector.
[in,out]	xc2	output cartesian unit 3-vector.
[out]	dxc2	jacobian 1st derivative, d(xc2)/d(xc1).
[out]	ddxc2	2nd derivative, d^2(xc2)/(d(xc1)d(xc1)).

Author: R. J. Purser

Definition at line 988 of file pmat5.f90.

References pietc::u0, pietc::u1, and pietc::u2.

◆ dctog()

subroutine pmat5::dctog	(	real(dp), dimension(3), intent(in)	xe,
		real(dp), intent(out)	dlat,
		real(dp), intent(out)	dlon
	)

Transform "Cartesian" to "Geographical" coordinates, where the geographical coordinates refer to latitude and longitude (degrees) and cartesian coordinates are standard earth-centered cartesian coordinates: xe(3) pointing north, xe(1) pointing to the 0-meridian.

Double precision version.

Parameters

[in]	xe	Earth-centered cartesian unit 3-vector.
[out]	dlat	degrees latitude.
[out]	dlon	degrees longitude.

Author: R. J. Purser

Definition at line 398 of file pmat5.f90.

References pietc::rtod, and pietc::u0.

◆ dctogr()

subroutine pmat5::dctogr	(	real(dp), dimension(3), intent(in)	xe,
		real(dp), intent(out)	rlat,
		real(dp), intent(out)	rlon
	)

Transform "Cartesian" to "Geographical" coordinates, where the geographical coordinates refer to latitude and longitude (radians) and cartesian coordinates are standard earth-centered cartesian coordinates: xe(3) pointing north, xe(1) pointing to the 0-meridian.

Double precision version.

Parameters

[in]	xe	Earth-centered cartesian unit 3-vector.
[out]	rlat	radians latitude.
[out]	rlon	radians longitude.

Author: R. J. Purser

Definition at line 198 of file pmat5.f90.

References pietc::u0.

◆ dgrtoc()

subroutine pmat5::dgrtoc	(	real(dp), intent(in)	rlat,
		real(dp), intent(in)	rlon,
		real(dp), dimension(3), intent(out)	xe
	)

private

Transform "Geographical" to "Cartesian" coordinates.

Double proecision version.

Parameters

[in]	rlat	Latitude (radians) of point.
[in]	rlon	Longitude (radians) of point.
[out]	xe	Earth-centered cartesian unit 3-vector of point.

Author: R. J. Purser

Definition at line 237 of file pmat5.f90.

◆ dgrtocd()

subroutine pmat5::dgrtocd	(	real(dp), intent(in)	rlat,
		real(dp), intent(in)	rlon,
		real(dp), dimension(3), intent(out)	xe,
		real(dp), dimension(3), intent(out)	dxedlat,
		real(dp), dimension(3), intent(out)	dxedlon
	)

private

Transform "Geographical" to "Cartesian" coordinates, together with the partial derivatives of cartesians wrt latitude and longitude.

Double precision version.

Parameters

[in]	rlat	Latitude (radians) of point.
[in]	rlon	Longitude (radians) of point.
[out]	xe	Earth-centered cartesian unit 3-vector of point.
[out]	dxedlat	Derivative, d(xe)/d(rlat).
[out]	dxedlon	Derivative, d(xe)/d(rlon).

Author: R. J. Purser

Definition at line 280 of file pmat5.f90.

References pietc::u0.

Referenced by sgrtocd().

◆ dgrtocdd()

subroutine pmat5::dgrtocdd	(	real(dp), intent(in)	rlat,
		real(dp), intent(in)	rlon,
		real(dp), dimension(3), intent(out)	xe,
		real(dp), dimension(3), intent(out)	dxedlat,
		real(dp), dimension(3), intent(out)	dxedlon,
		real(dp), dimension(3), intent(out)	ddxedlatdlat,
		real(dp), dimension(3), intent(out)	ddxedlatdlon,
		real(dp), dimension(3), intent(out)	ddxedlondlon
	)

private

Transform "Geographical" to "Cartesian" coordinates, together with the 1st and 2nd partial derivatives of cartesians wrt latitude and longitude.

Double precision version.

Parameters

[in]	rlat	Latitude (radians) of point.
[in]	rlon	Longitude (radians) of point.
[out]	xe	Earth-centered cartesian unit 3-vector of point.
[out]	dxedlat	Derivative, d(xe)/d(rlat).
[out]	dxedlon	Derivative, d(xe)/d(rlon).
[out]	ddxedlatdlat	Derivative, d^2(xe)/(d(rlat)d(rlat)).
[out]	ddxedlatdlon	Derivative, d^2(xe)/(d(rlat)d(rlon)).
[out]	ddxedlondlon	Derivative, d^2(xe)/(d(rlon)d(rlon)).

Author: R. J. Purser

Definition at line 340 of file pmat5.f90.

References pietc::u0.

◆ dgtoc()

subroutine pmat5::dgtoc	(	real(dp), intent(in)	dlat,
		real(dp), intent(in)	dlon,
		real(dp), dimension(3), intent(out)	xe
	)

Transform "Geographical" to "Cartesian" coordinates, where the geographical coordinates refer to latitude and longitude (degrees) and cartesian coordinates are standard earth-centered cartesian coordinates: xe(3) pointing north, xe(1) pointing to the 0-meridian.

Double precision version.

Parameters

[in]	dlat	degrees latitude.
[in]	dlon	degrees longitude.
[out]	xe	cartesian unit 3-vector.

Author: R. J. Purser

Definition at line 445 of file pmat5.f90.

References pietc::dtor.

◆ dgtocd()

subroutine pmat5::dgtocd	(	real(dp), intent(in)	dlat,
		real(dp), intent(in)	dlon,
		real(dp), dimension(3), intent(out)	xe,
		real(dp), dimension(3), intent(out)	dxedlat,
		real(dp), dimension(3), intent(out)	dxedlon
	)

private

Transform "Geographical" to "Cartesian" coordinates, where the geographical coordinates refer to latitude and longitude (degrees) and cartesian coordinates are standard earth-centered cartesian coordinates: xe(3) pointing north, xe(1) pointing to the 0-meridian.

Also, return the partial derivatives of xe wrt latitude and longitude. Double precision version.

Parameters

[in]	dlat	degrees latitude.
[in]	dlon	degrees longitude.
[out]	xe	cartesian unit 3-vector.
[out]	dxedlat	derivative, d(xe)/d(dlat).
[out]	dxedlon	derivative, d(xe)/d(dlon).

Author: R. J. Purser

Definition at line 496 of file pmat5.f90.

References pietc::dtor, and pietc::u0.

Referenced by sgtocd().

◆ dgtocdd()

subroutine pmat5::dgtocdd	(	real(dp), intent(in)	dlat,
		real(dp), intent(in)	dlon,
		real(dp), dimension(3), intent(out)	xe,
		real(dp), dimension(3), intent(out)	dxedlat,
		real(dp), dimension(3), intent(out)	dxedlon,
		real(dp), dimension(3), intent(out)	ddxedlatdlat,
		real(dp), dimension(3), intent(out)	ddxedlatdlon,
		real(dp), dimension(3), intent(out)	ddxedlondlon
	)

private

Transform "Geographical" to "Cartesian" coordinates, where the geographical coordinates refer to latitude and longitude (degrees) and cartesian coordinates are standard earth-centered cartesian coordinates: xe(3) pointing north, xe(1) pointing to the 0-meridian.

Also, return the 1st and 2nd partial derivatives of xe wrt latitude and longitude. Double precision version.

Parameters

[in]	dlat	degrees latitude.
[in]	dlon	degrees longitude.
[out]	xe	cartesian unit 3-vector.
[out]	dxedlat	d(xe)/d(dlat).
[out]	dxedlon	d(xe)/d(dlon).
[out]	ddxedlatdlat	derivative, d^2(xe)/(d(dlat)d(dlat)).
[out]	ddxedlatdlon	derivative, d^2(xe)/(d(dlat)d(dlon)).
[out]	ddxedlondlon	derivative, d^2(xe)/(d(dlon)d(dlon)).

Author: R. J. Purser

Definition at line 565 of file pmat5.f90.

References pietc::dtor, and pietc::u0.

Referenced by sgrtocdd(), and sgtocdd().

◆ dininmap()

subroutine pmat5::dininmap	(	real(dp), intent(in)	alon0,
		real(dp), intent(in)	alat0,
		real(dp), dimension(3,3), intent(out)	rot3
	)

Initialize the rotation matrix ROT3 needed to transform standard earth-centered cartesian components to the alternative cartesian frame oriented so as to put geographical point (ALAT0,ALON0) on the projection axis.

Double precision version.

Parameters

[in]	alon0	geographical longitude (degrees) of projection center.
[in]	alat0	geographical latitude (degrees) of projection center.
[out]	rot3	rotation matrix.

Author: R. J. Purser

Definition at line 86 of file pmat5.f90.

References pietc::dtor, and pietc::u0.

◆ dinivmap()

subroutine pmat5::dinivmap	(	real(dp), intent(in)	alon0,
		real(dp), intent(in)	alat0,
		real(dp), dimension(3,3), intent(out)	rot3
	)

Initialize the rotation matrix ROT3 needed to transform standard earth-centered cartesian components to the alternative cartesian frame oriented so as to put geographical point (ALAT0,ALON0) at the viewing nadir.

Double precision version.

Parameters

[in]	alon0	geographical longitude (degrees) of viewing nadir.
[in]	alat0	geographical latitude (degrees) of viewing nadir.
[out]	rot3	rotation matrix.

Author: R. J. Purser

Definition at line 140 of file pmat5.f90.

References pietc::dtor, and pietc::u0.

◆ dplrot()

subroutine pmat5::dplrot	(	real(dp), dimension(3,3), intent(in)	rot3,
		integer, intent(in)	n,
		real(dp), dimension(n), intent(inout)	x,
		real(dp), dimension(n), intent(inout)	y,
		real(dp), dimension(n), intent(inout)	z
	)

private

Apply a constant rotation to a three dimensional polyline.

Parameters

[in]	rot3	rotation matrix.
[in]	n	number of points in the polyline.
[in,out]	x	cartesian components of the three dimensional polyline.
[in,out]	y	cartesian components of the three dimensional polyline.
[in,out]	z	cartesian components of the three dimensional polyline.

Author: R. J. Purser

Definition at line 1084 of file pmat5.f90.

◆ dplroti()

subroutine pmat5::dplroti	(	real(dp), dimension(3,3), intent(in)	rot3,
		integer, intent(in)	n,
		real(dp), dimension(n), intent(inout)	x,
		real(dp), dimension(n), intent(inout)	y,
		real(dp), dimension(n), intent(inout)	z
	)

private

Invert the rotation of a three-dimensional polyline.

Parameters

[in]	rot3	rotation to be inverted.
[in]	n	number of points in the polyline.
[in,out]	x	cartesian components of the three dimensional polyline.
[in,out]	y	cartesian components of the three dimensional polyline.
[in,out]	z	cartesian components of the three dimensional polyline.

Author: R. J. Purser

Definition at line 1106 of file pmat5.f90.

◆ frametwist()

subroutine, public pmat5::frametwist	(	real(dp), dimension(3), intent(in)	xp,
		real(dp), dimension(3), intent(in)	yp,
		real(dp), dimension(3), intent(in)	zp,
		real(dp), dimension(3), intent(in)	xv,
		real(dp), dimension(3), intent(in)	yv,
		real(dp), dimension(3), intent(in)	zv,
		real(dp), intent(out)	twist
	)

Given a principal cartesian orthonormal frame, {xp,yp,zp} (i.e., at P with Earth-centered cartesians, zp), and another similar frame {xv,yv,zv} at V with Earth-centered cartesians zv, find the relative rotation angle, "twist" by which the frame at V is rotated in the counterclockwise sense relative to the parallel-transportation of P's frame to V.

Note that, by symmetry, transposing P and V leads to the opposite twist. Double precision version.

Parameters

[in]	xp	P-frame cartesian X-vector.
[in]	yp	P-frame cartesian Y-vector.
[in]	zp	P-frame cartesian Z-vector.
[in]	xv	V-frame cartesian X-vector.
[in]	yv	V-frame cartesian Y-vector.
[in]	zv	V-frame cartesian Z-vector.
[out]	twist	relative rotation angle (radians) of frames.

Author: R. J. Purser

Definition at line 778 of file pmat5.f90.

◆ gtoframem()

subroutine pmat5::gtoframem	(	real(dp), intent(in)	plat,
		real(dp), intent(in)	plon,
		real(dp), dimension(3,3), intent(out)	orth
	)

private

From the degree lat and lon (plat and plon) return the standard orthogonal 3D frame at this location as an orthonormal matrix, orth.

Double precision version.

Parameters

[in]	plat	latitude (degrees) of point.
[in]	plon	longitude (degrees) of point.
[out]	orth	orthonormal matrix.

Author: R. J. Purser

Definition at line 617 of file pmat5.f90.

References gtoframev().

Referenced by sgtoframem().

◆ gtoframev()

subroutine pmat5::gtoframev	(	real(dp), intent(in)	plat,
		real(dp), intent(in)	plon,
		real(dp), dimension(3), intent(out)	xp,
		real(dp), dimension(3), intent(out)	yp,
		real(dp), dimension(3), intent(out)	zp
	)

private

Given a geographical point by its degrees lat and lon, plat and plon, return its standard orthogonal cartesian frame, {xp,yp,zp} in earth-centered coordinates.

Double precision version.

Parameters

[in]	plat	latitude (degrees) of point.
[in]	plon	longitude (degrees) of point.
[out]	xp	unit X-basis vector of cartesian frame.
[out]	yp	unit Y-basis vector of cartesian frame.
[out]	zp	unit Z-basis vector of cartesian frame.

Author: R. J. Purser

Definition at line 662 of file pmat5.f90.

References pietc::u0, and pietc::u1.

Referenced by gtoframem(), and sgtoframev().

◆ paraframe()

subroutine, public pmat5::paraframe	(	real(dp), dimension(3), intent(in)	xp,
		real(dp), dimension(3), intent(in)	yp,
		real(dp), dimension(3), intent(in)	zp,
		real(dp), dimension(3), intent(out)	xv,
		real(dp), dimension(3), intent(out)	yv,
		real(dp), dimension(3), intent(in)	zv
	)

Take a principal reference orthonormal frame, {xp,yp,zp} and a dependent point defined by unit vector, zv, and complete the V-frame cartesian components, {xv,yv}, that are the result of parallel-transport of {xp,yp} along the geodesic between P and V.

Double precision version.

Parameters

[in]	xp	reference orthonormal P-frame cartesian X-vector.
[in]	yp	reference orthonormal P-frame cartesian Y-vector.
[in]	zp	reference orthonormal P-frame cartesian Z-vector.
[out]	xv	V-frame cartesian X-vector.
[out]	yv	V-frame cartesian Y-vector.
[in]	zv	dependent point zenith, V-frame cartesian Z-vector.

Author: R. J. Purser

Definition at line 719 of file pmat5.f90.

◆ plctoc()

subroutine, public pmat5::plctoc	(	real(sp), intent(in)	s,
		integer, intent(in)	n,
		real(sp), dimension(n), intent(inout)	x,
		real(sp), dimension(n), intent(inout)	y,
		real(sp), dimension(n), intent(inout)	z
	)

Perform Schmidt transformation with scaling parameter s to a polyline.

Parameters

[in]	s	Schmidt scaling parameter.
[in]	n	number of points in the polyline.
[in,out]	x	cartesian components of the three dimensional polyline.
[in,out]	y	cartesian components of the three dimensional polyline.
[in,out]	z	cartesian components of the three dimensional polyline.

Author: R. J. Purser

Definition at line 1128 of file pmat5.f90.

◆ plrot()

subroutine, public pmat5::plrot	(	real(sp), dimension(3,3), intent(in)	rot3,
		integer, intent(in)	n,
		real(sp), dimension(n), intent(inout)	x,
		real(sp), dimension(n), intent(inout)	y,
		real(sp), dimension(n), intent(inout)	z
	)

Apply a constant rotation to a three dimensional polyline.

Parameters

[in]	rot3	rotation matrix.
[in]	n	number of points in the polyline.
[in,out]	x	cartesian components of the three dimensional polyline.
[in,out]	y	cartesian components of the three dimensional polyline.
[in,out]	z	cartesian components of the three dimensional polyline.

Author: R. J. Purser

Definition at line 1040 of file pmat5.f90.

References pietc::t.

◆ plroti()

subroutine, public pmat5::plroti	(	real(sp), dimension(3,3), intent(in)	rot3,
		integer, intent(in)	n,
		real(sp), dimension(n), intent(inout)	x,
		real(sp), dimension(n), intent(inout)	y,
		real(sp), dimension(n), intent(inout)	z
	)

Invert the rotation of a three-dimensional polyline.

Parameters

[in]	rot3	rotation to be inverted.
[in]	n	number of points in the polyline.
[in,out]	x	cartesian components of the three dimensional polyline.
[in,out]	y	cartesian components of the three dimensional polyline.
[in,out]	z	cartesian components of the three dimensional polyline.

Author: R. J. Purser

Definition at line 1062 of file pmat5.f90.

References pietc::t.

◆ sctoc()

subroutine pmat5::sctoc	(	real(sp), intent(in)	s,
		real(sp), dimension(3), intent(inout)	xc1,
		real(sp), dimension(3), intent(inout)	xc2
	)

private

Evaluate Schmidt transformation, xc1 –> xc2, with scaling parameter s.

Parameters

[in]	s	Schmidt scaling parameter
[in,out]	xc1	input cartesian 3-vector
[in,out]	xc2	output cartesian unit 3-vector

Author: R. J. Purser

Definition at line 795 of file pmat5.f90.

◆ sctocd()

subroutine pmat5::sctocd	(	real(sp), intent(in)	s,
		real(sp), dimension(3), intent(inout)	xc1,
		real(sp), dimension(3), intent(inout)	xc2,
		real(sp), dimension(3,3), intent(out)	dxc2
	)

Evaluate Schmidt transformation, xc1 –> xc2, with scaling parameter s, and its jacobian, dxc2.

Parameters

[in]	s	Schmidt scaling parameter.
[in,out]	xc1	input cartesian 3-vector.
[in,out]	xc2	output cartesian unit 3-vector.
[out]	dxc2	jacobian 1st derivative, d(xc2)/d(xc1).

Author: R. J. Purser

Definition at line 825 of file pmat5.f90.

◆ sctocdd()

subroutine pmat5::sctocdd	(	real(sp), intent(in)	s,
		real(sp), dimension(3), intent(inout)	xc1,
		real(sp), dimension(3), intent(inout)	xc2,
		real(sp), dimension(3,3), intent(out)	dxc2,
		real(sp), dimension(3,3,3), intent(out)	ddxc2
	)

Evaluate Schmidt transformation, xc1 –> xc2, with scaling parameter s, its jacobian, dxc2, and its 2nd derivative, ddxc2.

Parameters

[in]	s	Schmidt scaling parameter.
[in]	xc1	input cartesian 3-vector.
[in]	xc2	output cartesian unit 3-vector.
[out]	dxc2	jacobian 1st derivative, d(xc2)/d(xc1).
[out]	ddxc2	2nd derivative, d^2(xc2)/(d(xc1)d(xc1)).

Author: R. J. Purser

Definition at line 866 of file pmat5.f90.

◆ sctog()

subroutine pmat5::sctog	(	real(sp), dimension(3), intent(in)	xe,
		real(sp), intent(out)	dlat,
		real(sp), intent(out)	dlon
	)

Transform "Cartesian" to "Geographical" coordinates, where the geographical coordinates refer to latitude and longitude (degrees) and cartesian coordinates are standard earth-centered cartesian coordinates: xe(3) pointing north, xe(1) pointing to the 0-meridian.

Single precision version.

Parameters

[in]	xe	Earth-centered cartesian unit 3-vector.
[out]	dlat	degrees latitude.
[out]	dlon	degrees longitude.

Author: R. J. Purser

Date: 1994

Definition at line 373 of file pmat5.f90.

◆ sctogr()

subroutine pmat5::sctogr	(	real(sp), dimension(3), intent(in)	xe,
		real(sp), intent(out)	rlat,
		real(sp), intent(out)	rlon
	)

Transform "Cartesian" to "Geographical" coordinates, where the geographical coordinates refer to latitude and longitude (radians) and cartesian coordinates are standard earth-centered cartesian coordinates: xe(3) pointing north, xe(1) pointing to the 0-meridian.

Single precision version.

Parameters

[in]	xe	Earth-centered cartesian unit 3-vector.
[out]	rlat	radians latitude.
[out]	rlon	radians longitude.

Author: R. J. Purser

Definition at line 173 of file pmat5.f90.

◆ sframetwist()

subroutine pmat5::sframetwist	(	real(sp), dimension(3), intent(in)	sxp,
		real(sp), dimension(3), intent(in)	syp,
		real(sp), dimension(3), intent(in)	szp,
		real(sp), dimension(3), intent(in)	sxv,
		real(sp), dimension(3), intent(in)	syv,
		real(sp), dimension(3), intent(in)	szv,
		real(sp), intent(out)	stwist
	)

Given a principal cartesian orthonormal frame, {xp,yp,zp} (i.e., at P with Earth-centered cartesians, zp), and another similar frame {xv,yv,zv} at V with Earth-centered cartesians zv, find the relative rotation angle, "twist" by which the frame at V is rotated in the counterclockwise sense relative to the parallel-transportation of P's frame to V.

Note that, by symmetry, transposing P and V leads to the opposite twist. Single precision version.

Parameters

[in]	sxp	P-frame cartesian X-vector.
[in]	syp	P-frame cartesian Y-vector.
[in]	szp	P-frame cartesian Z-vector.
[in]	sxv	V-frame cartesian X-vector.
[in]	syv	V-frame cartesian Y-vector.
[in]	szv	V-frame cartesian Z-vector.
[out]	stwist	relative rotation angle (radians) of frames.

Author: R. J. Purser

Definition at line 751 of file pmat5.f90.

◆ sgrtoc()

subroutine pmat5::sgrtoc	(	real(sp), intent(in)	rlat,
		real(sp), intent(in)	rlon,
		real(sp), dimension(3), intent(out)	xe
	)

Transform "Geographical" to "Cartesian" coordinates.

Single proecision version.

Parameters

[in]	rlat	Latitude (radians) of point.
[in]	rlon	Longitude (radians) of point.
[out]	xe	Earth-centered cartesian unit 3-vector of point.

Author: R. J. Purser

Definition at line 220 of file pmat5.f90.

◆ sgrtocd()

subroutine pmat5::sgrtocd	(	real(sp), intent(in)	rlat,
		real(sp), intent(in)	rlon,
		real(sp), dimension(3), intent(out)	xe,
		real(sp), dimension(3), intent(out)	dxedlat,
		real(sp), dimension(3), intent(out)	dxedlon
	)

private

Transform "Geographical" to "Cartesian" coordinates, together with the partial derivatives of cartesians wrt latitude and longitude.

Single precision version.

Parameters

[in]	rlat	Latitude (radians) of point.
[in]	rlon	Longitude (radians) of point.
[out]	xe	Earth-centered cartesian unit 3-vector of point.
[out]	dxedlat	Derivative, d(xe)/d(rlat).
[out]	dxedlon	Derivative, d(xe)/d(rlon).

Author: R. J. Purser

Definition at line 257 of file pmat5.f90.

References dgrtocd().

◆ sgrtocdd()

subroutine pmat5::sgrtocdd	(	real(sp), intent(in)	rlat,
		real(sp), intent(in)	rlon,
		real(sp), dimension(3), intent(out)	xe,
		real(sp), dimension(3), intent(out)	dxedlat,
		real(sp), dimension(3), intent(out)	dxedlon,
		real(sp), dimension(3), intent(out)	ddxedlatdlat,
		real(sp), dimension(3), intent(out)	ddxedlatdlon,
		real(sp), dimension(3), intent(out)	ddxedlondlon
	)

Transform "Geographical" to "Cartesian" coordinates, together with the 1st and 2nd partial derivatives of cartesians wrt latitude and longitude.

Single precision version.

Parameters

[in]	rlat	Latitude (radians) of point.
[in]	rlon	Longitude (radians) of point.
[out]	xe	Earth-centered cartesian unit 3-vector of point.
[out]	dxedlat	Derivative, d(xe)/d(rlat).
[out]	dxedlon	Derivative, d(xe)/d(rlon).
[out]	ddxedlatdlat	Derivative, d^2(xe)/(d(rlat)d(rlat)).
[out]	ddxedlatdlon	Derivative, d^2(xe)/(d(rlat)d(rlon)).
[out]	ddxedlondlon	Derivative, d^2(xe)/(d(rlon)d(rlon)).

Author: R. J. Purser

Definition at line 307 of file pmat5.f90.

References dgtocdd().

◆ sgtoc()

subroutine pmat5::sgtoc	(	real(sp), intent(in)	dlat,
		real(sp), intent(in)	dlon,
		real(sp), dimension(3), intent(out)	xe
	)

Transform "Geographical" to "Cartesian" coordinates, where the geographical coordinates refer to latitude and longitude (degrees) and cartesian coordinates are standard earth-centered cartesian coordinates: xe(3) pointing north, xe(1) pointing to the 0-meridian.

Single precision version.

Parameters

[in]	dlat	degrees latitude.
[in]	dlon	degrees longitude.
[out]	xe	Earth-centered cartesian unit 3-vector.

Author: R. J. Purser

Date: 1994

Definition at line 423 of file pmat5.f90.

◆ sgtocd()

subroutine pmat5::sgtocd	(	real(sp), intent(in)	dlat,
		real(sp), intent(in)	dlon,
		real(sp), dimension(3), intent(out)	xe,
		real(sp), dimension(3), intent(out)	dxedlat,
		real(sp), dimension(3), intent(out)	dxedlon
	)

Transform "Geographical" to "Cartesian" coordinates, where the geographical coordinates refer to latitude and longitude (degrees) and cartesian coordinates are standard earth-centered cartesian coordinates: xe(3) pointing north, xe(1) pointing to the 0-meridian.

Also, return the partial derivatives of xe wrt latitude and longitude. Single precision version.

Parameters

[in]	dlat	degrees latitude.
[in]	dlon	degrees longitude.
[out]	xe	cartesian unit 3-vector.
[out]	dxedlat	derivative, d(xe)/d(dlat).
[out]	dxedlon	derivative, d(xe)/d(dlon).

Author: R. J. Purser

Definition at line 470 of file pmat5.f90.

References dgtocd().

◆ sgtocdd()

subroutine pmat5::sgtocdd	(	real(sp), intent(in)	dlat,
		real(sp), intent(in)	dlon,
		real(sp), dimension(3), intent(out)	xe,
		real(sp), dimension(3), intent(out)	dxedlat,
		real(sp), dimension(3), intent(out)	dxedlon,
		real(sp), dimension(3), intent(out)	ddxedlatdlat,
		real(sp), dimension(3), intent(out)	ddxedlatdlon,
		real(sp), dimension(3), intent(out)	ddxedlondlon
	)

Transform "Geographical" to "Cartesian" coordinates, where the geographical coordinates refer to latitude and longitude (degrees) and cartesian coordinates are standard earth-centered cartesian coordinates: xe(3) pointing north, xe(1) pointing to the 0-meridian.

Also, return the 1st and 2nd partial derivatives of xe wrt latitude and longitude. Single precision version.

Parameters

[in]	dlat	degrees latitude.
[in]	dlon	degrees longitude.
[out]	xe	cartesian unit 3-vector.
[out]	dxedlat	derivative, d(xe)/d(dlat).
[out]	dxedlon	derivative, d(xe)/d(dlon).
[out]	ddxedlatdlat	derivative, d^2(xe)/(d(dlat)d(dlat)).
[out]	ddxedlatdlon	derivative, d^2(xe)/(d(dlat)d(dlon)).
[out]	ddxedlondlon	derivative, d^2(xe)/(d(dlon)d(dlon)).

Author: R. J. Purser

Definition at line 528 of file pmat5.f90.

References dgtocdd().

◆ sgtoframem()

subroutine pmat5::sgtoframem	(	real(sp), intent(in)	splat,
		real(sp), intent(in)	splon,
		real(sp), dimension(3,3), intent(out)	sorth
	)

From the degree lat and lon (plat and plon) return the standard orthogonal 3D frame at this location as an orthonormal matrix, orth.

Single precision version.

Parameters

[in]	splat	latitude (degrees) of point.
[in]	splon	longitude (degrees) of point.
[out]	sorth	orthonormal matrix.

Author: R. J. Purser

Definition at line 600 of file pmat5.f90.

References gtoframem().

◆ sgtoframev()

subroutine pmat5::sgtoframev	(	real(sp), intent(in)	splat,
		real(sp), intent(in)	splon,
		real(sp), dimension(3), intent(out)	sxp,
		real(sp), dimension(3), intent(out)	syp,
		real(sp), dimension(3), intent(out)	szp
	)

private

Given a geographical point by its degrees lat and lon, plat and plon, return its standard orthogonal cartesian frame, {xp,yp,zp} in earth-centered coordinates.

Single precision version.

Parameters

[in]	splat	latitude (degrees) of point.
[in]	splon	longitude (degrees) of point.
[out]	sxp	xp unit X-basis vector of cartesian frame.
[out]	syp	yp unit Y-basis vector of cartesian frame.
[out]	szp	zp unit Z-basis vector of cartesian frame.

Author: R. J. Purser

Definition at line 637 of file pmat5.f90.

References gtoframev().

◆ sininmap()

subroutine pmat5::sininmap	(	real(sp), intent(in)	alon0,
		real(sp), intent(in)	alat0,
		real(sp), dimension(3,3), intent(out)	rot3
	)

private

Initialize the rotation matrix ROT3 needed to transform standard earth-centered cartesian components to the alternative cartesian frame oriented so as to put geographical point (ALAT0,ALON0) on the projection axis.

Single precision version.

Parameters

[in]	alon0	geographical longitude (degrees) of projection center.
[in]	alat0	geographical latitude (degrees) of projection center.
[out]	rot3	rotation matrix.

Author: R. J. Purser

Date: 1995

Definition at line 64 of file pmat5.f90.

◆ sinivmap()

subroutine pmat5::sinivmap	(	real(sp), intent(in)	alon0,
		real(sp), intent(in)	alat0,
		real(sp), dimension(3,3), intent(out)	rot3
	)

Initialize the rotation matrix ROT3 needed to transform standard earth-centered cartesian components to the alternative cartesian frame oriented so as to put geographical point (ALAT0,ALON0) at the viewing nadir.

Single precision version.

Parameters

[in]	alon0	geographical longitude (degrees) of viewing nadir.
[in]	alat0	geographical latitude (degrees) of viewing nadir.
[out]	rot3	rotation matrix.

Author: R. J. Purser

Date: 1995

Definition at line 108 of file pmat5.f90.

◆ sparaframe()

subroutine pmat5::sparaframe	(	real(sp), dimension(3), intent(in)	sxp,
		real(sp), dimension(3), intent(in)	syp,
		real(sp), dimension(3), intent(in)	szp,
		real(sp), dimension(3), intent(out)	sxv,
		real(sp), dimension(3), intent(out)	syv,
		real(sp), dimension(3), intent(in)	szv
	)

Take a principal reference orthonormal frame, {xp,yp,zp} and a dependent point defined by unit vector, zv, and complete the V-frame cartesian components, {xv,yv}, that are the result of parallel-transport of {xp,yp} along the geodesic between P and V.

Single precision version.

Parameters

[in]	sxp	reference orthonormal P-frame cartesian X-vector.
[in]	syp	reference orthonormal P-frame cartesian Y-vector.
[in]	szp	reference orthonormal P-frame cartesian Z-vector.
[out]	sxv	V-frame cartesian X-vector.
[out]	syv	V-frame cartesian Y-vector.
[in]	szv	dependent point zenith, V-frame cartesian Z-vector.

Author: R. J. Purser

Definition at line 696 of file pmat5.f90.

Data Types

Functions/Subroutines

Detailed Description

Function/Subroutine Documentation

◆ dctoc()

◆ dctocd()

◆ dctocdd()

◆ dctog()

◆ dctogr()

◆ dgrtoc()

◆ dgrtocd()

◆ dgrtocdd()

◆ dgtoc()

◆ dgtocd()

◆ dgtocdd()

◆ dininmap()

◆ dinivmap()

◆ dplrot()

◆ dplroti()

◆ frametwist()

◆ gtoframem()

◆ gtoframev()

◆ paraframe()

◆ plctoc()

◆ plrot()

◆ plroti()

◆ sctoc()

◆ sctocd()

◆ sctocdd()

◆ sctog()

◆ sctogr()

◆ sframetwist()

◆ sgrtoc()

◆ sgrtocd()

◆ sgrtocdd()

◆ sgtoc()

◆ sgtocd()

◆ sgtocdd()

◆ sgtoframem()

◆ sgtoframev()

◆ sininmap()

◆ sinivmap()

◆ sparaframe()