Note

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# Plotting vectors

Plotting vectors is handled by `pygmt.Figure.plot`

.

```
import numpy as np
import pygmt
```

## Plot Cartesian Vectors

Create a simple Cartesian vector using a start point through
`x`

, `y`

, and `direction`

parameters.
On the shown figure, the plot is projected on a 10cm X 10cm region,
which is specified by the `projection`

parameter.
The direction is specified
by a list of two 1-D arrays structured as `[[angle_in_degrees], [length]]`

.
The angle is measured in degrees and moves counter-clockwise from the
horizontal.
The length of the vector uses centimeters by default but
could be changed using `pygmt.config`

(Check the next examples for unit changes).

Notice that the `v`

in the `style`

parameter stands for
vector; it distinguishes it from regular lines and allows for
different customization. `0c`

is used to specify the size
of the arrow head which explains why there is no arrow on either
side of the vector.

In this example, we apply the same concept shown previously to plot multiple
vectors. Notice that instead of passing int/float to `x`

and `y`

, a list
of all x and y coordinates will be passed. Similarly, the length of direction
list will increase accordingly.

Additionally, we change the style of the vector to include a red
arrow head at the end (**+e**) of the vector and increase the
thickness (`pen="2p"`

) of the vector stem. A list of different
styling attributes can be found in
Vector heads and tails.

The default unit of vector length is centimeters, however, this can be changed to inches or points. Note that, in PyGMT, one point is defined as 1/72 inch.

In this example, the graphed region is 5in X 5in, but
the length of the first vector is still graphed in centimeters.
Using `pygmt.config(PROJ_LENGTH_UNIT="i")`

, the default unit
can be changed to inches in the second plotted vector.

```
fig = pygmt.Figure()
# Vector 1 with default unit as cm
fig.plot(
region=[0, 10, 0, 10],
projection="X5i/5i",
frame="ag",
x=2,
y=8,
style="v1c+e",
direction=[[0], [3]],
pen="2p",
fill="red3",
)
# Vector 2 after changing default unit to inches
with pygmt.config(PROJ_LENGTH_UNIT="i"):
fig.plot(
x=2,
y=7,
direction=[[0], [3]],
style="v1c+e",
pen="2p",
fill="red3",
)
fig.show()
```

Vectors can also be plotted by including all the information
about a vector in a single list. However, this requires creating
a 2-D list or numpy array containing all vectors.
Each vector list contains the information structured as:
`[x_start, y_start, direction_degrees, length]`

.

If this approach is chosen, the `data`

parameter must be
used instead of `x`

, `y`

, and `direction`

.

Using the functionality mentioned in the previous example,
multiple vectors can be plotted at the same time. Another
vector could be simply added to the 2-D list or numpy
array object and passed using `data`

parameter.

```
# Vector specifications structured as:
# [x_start, y_start, direction_degrees, length]
vector_1 = [2, 3, 45, 4]
vector_2 = [7.5, 8.3, -120.5, 7.2]
# Create a list of lists that include each vector information
vectors = [vector_1, vector_2]
# Vectors structure: [[2, 3, 45, 4], [7.5, 8.3, -120.5, 7.2]]
fig = pygmt.Figure()
fig.plot(
region=[0, 10, 0, 10],
projection="X10c/10c",
frame="ag",
data=vectors,
style="v0.6c+e",
pen="2p",
fill="red3",
)
fig.show()
```

In this example, Cartesian vectors are plotted over a Mercator projection of the continental US. The x values represent the longitude and y values represent the latitude where the vector starts.

This example also shows some of the styles a vector supports.
The beginning point of the vector (**+b**)
should take the shape of a circle (**c**). Similarly, the end
point of the vector (**+e**) should have an arrow shape (**a**)
(to draw a plain arrow, use **A** instead). Lastly, the **+a**
specifies the angle of the vector head apex (30 degrees in
this example).

```
# Create a plot with coast, Mercator projection (M) over the continental US
fig = pygmt.Figure()
fig.coast(
region=[-127, -64, 24, 53],
projection="M10c",
frame="ag",
borders=1,
shorelines="0.25p,black",
area_thresh=4000,
land="grey",
water="lightblue",
)
# Plot a vector using the x, y, direction parameters
style = "v0.4c+bc+ea+a30"
fig.plot(
x=-110,
y=40,
style=style,
direction=[[-25], [3]],
pen="1p",
fill="red3",
)
# vector specifications structured as:
# [x_start, y_start, direction_degrees, length]
vector_2 = [-82, 40.5, 138, 2.5]
vector_3 = [-71.2, 45, -115.7, 4]
# Create a list of lists that include each vector information
vectors = [vector_2, vector_3]
# Plot vectors using the data parameter.
fig.plot(
data=vectors,
style=style,
pen="1p",
fill="yellow",
)
fig.show()
```

Another example of plotting Cartesian vectors over a coast plot. This time a
Transverse Mercator projection is used. Additionally, `numpy.linspace`

is used to create 5 vectors with equal stops.

```
x = np.linspace(36, 42, 5) # x values = [36. 37.5 39. 40.5 42. ]
y = np.linspace(39, 39, 5) # y values = [39. 39. 39. 39.]
direction = np.linspace(-90, -90, 5) # direction values = [-90. -90. -90. -90.]
length = np.linspace(1.5, 1.5, 5) # length values = [1.5 1.5 1.5 1.5]
# Create a plot with coast,
# Transverse Mercator projection (T) over Turkey and Syria
fig = pygmt.Figure()
fig.coast(
region=[20, 50, 30, 45],
projection="T35/10c",
frame=True,
borders=1,
shorelines="0.25p,black",
area_thresh=4000,
land="lightbrown",
water="lightblue",
)
fig.plot(
x=x,
y=y,
style="v0.4c+ea+bc",
direction=[direction, length],
pen="0.6p",
fill="red3",
)
fig.show()
```

## Plot Circular Vectors

When plotting circular vectors, all of the information for a single vector is
to be stored in a list. Each circular vector list is structured as:
`[x_start, y_start, radius, degree_start, degree_stop]`

. The first two
values in the vector list represent the origin of the circle that will be
plotted. The next value is the radius which is represented on the plot in cm.

The last two values in the vector list represent the degree at which the plot
will start and stop. These values are measured counter-clockwise from the
horizontal axis. In this example, the result shown is the left half of a
circle as the plot starts at 90 degrees and goes until 270. Notice that the
`m`

in the `style`

parameter stands for circular vectors.

```
fig = pygmt.Figure()
circular_vector_1 = [0, 0, 2, 90, 270]
data = [circular_vector_1]
fig.plot(
region=[-5, 5, -5, 5],
projection="X10c",
frame="ag",
data=data,
style="m0.5c+ea",
pen="2p",
fill="red3",
)
# Another example using np.array()
circular_vector_2 = [0, 0, 4, -90, 90]
data = np.array([circular_vector_2])
fig.plot(
data=data,
style="m0.5c+ea",
pen="2p",
fill="red3",
)
fig.show()
```

When plotting multiple circular vectors, a two dimensional array or numpy
array object should be passed as the `data`

parameter. In this example,
`numpy.column_stack`

is used to generate this two dimensional array.
Other numpy objects are used to generate linear values for the `radius`

parameter and random values for the `degree_stop`

parameter discussed in
the previous example. This is the reason in which each vector has a different
appearance on the projection.

```
vector_num = 5
radius = 3 - (0.5 * np.arange(0, vector_num))
startdir = np.full(vector_num, 90)
stopdir = 180 + (50 * np.arange(0, vector_num))
data = np.column_stack(
[np.full(vector_num, 0), np.full(vector_num, 0), radius, startdir, stopdir]
)
fig = pygmt.Figure()
fig.plot(
region=[-5, 5, -5, 5],
projection="X10c",
frame="ag",
data=data,
style="m0.5c+ea",
pen="2p",
fill="red3",
)
fig.show()
```

Much like when plotting Cartesian vectors, the default unit used is centimeters. When this is changed to inches, the size of the plot appears larger when the projection units do not change. Below is an example of two circular vectors. One is plotted using the default unit, and the second is plotted using inches. Despite using the same list to plot the vectors, a different measurement unit causes one to be larger than the other.

```
circular_vector = [6, 5, 1, 90, 270]
fig = pygmt.Figure()
fig.plot(
region=[0, 10, 0, 10],
projection="X10c",
frame="ag",
data=[circular_vector],
style="m0.5c+ea",
pen="2p",
fill="red3",
)
with pygmt.config(PROJ_LENGTH_UNIT="i"):
fig.plot(
data=[circular_vector],
style="m0.5c+ea",
pen="2p",
fill="red3",
)
fig.show()
```

## Plot Geographic Vectors

On this map,
`point_1`

and `point_2`

are coordinate pairs used to set the
start and end points of the geographic vector.
The geographical vector is going from Idaho to
Chicago. To style geographic
vectors, use `=`

at the beginning of the `style`

parameter.
Other styling features such as vector stem thickness and head color
can be passed into the `pen`

and `fill`

parameters.

Note that the **+s** is added to use a start point and an end point
to represent the vector instead of input angle and length.

```
point_1 = [-114.7420, 44.0682]
point_2 = [-87.6298, 41.8781]
data = np.array([point_1 + point_2])
fig = pygmt.Figure()
fig.coast(
region=[-127, -64, 24, 53],
projection="M10c",
frame=True,
borders=1,
shorelines="0.25p,black",
area_thresh=4000,
)
fig.plot(
data=data,
style="=0.5c+ea+s",
pen="2p",
fill="red3",
)
fig.show()
```

Using the same technique shown in the previous example,
multiple vectors can be plotted in a chain where the end point
of one is the start point of another. This can be done
by adding the coordinate lists together to create this structure:
`[[start_latitude, start_longitude, end_latitude, end_longitude]]`

.
Each list within the 2-D list contains the start and end information
for each vector.

```
# Coordinate pairs for all the locations used
ME = [-69.4455, 45.2538]
CHI = [-87.6298, 41.8781]
SEA = [-122.3321, 47.6062]
NO = [-90.0715, 29.9511]
KC = [-94.5786, 39.0997]
CA = [-119.4179, 36.7783]
# Add array to piece together the vectors
data = [ME + CHI, CHI + SEA, SEA + KC, KC + NO, NO + CA]
fig = pygmt.Figure()
fig.coast(
region=[-127, -64, 24, 53],
projection="M10c",
frame=True,
borders=1,
shorelines="0.25p,black",
area_thresh=4000,
)
fig.plot(
data=data,
style="=0.5c+ea+s",
pen="2p",
fill="red3",
)
fig.show()
```

This example plots vectors over a Mercator projection. The start points are located at SA which is South Africa and going to four different locations.

```
SA = [22.9375, -30.5595]
EUR = [15.2551, 54.5260]
ME = [-69.4455, 45.2538]
AS = [100.6197, 34.0479]
NM = [-105.8701, 34.5199]
data = np.array([SA + EUR, SA + ME, SA + AS, SA + NM])
fig = pygmt.Figure()
fig.coast(
region=[-180, 180, -80, 80],
projection="M0/0/12c",
frame="afg",
land="lightbrown",
water="lightblue",
)
fig.plot(
data=data,
style="=0.5c+ea+s",
pen="2p",
fill="red3",
)
fig.show()
```

**Total running time of the script:** (0 minutes 2.456 seconds)