def intersect(
vdf: vDataFrame, index: str, gid: str, g: str = "", x: str = "", y: str = "",
):
"""
---------------------------------------------------------------------------
Spatially intersects a point or points with a set of polygons.
Parameters
----------
vdf: vDataFrame
vDataFrame to use to compute the spatial join.
index: str
Name of the index.
gid: str
An integer column or integer that uniquely identifies the spatial object(s)
of g or x and y.
g: str, optional
A geometry or geography (WGS84) column that contains points.
The g column can contain only point geometries or geographies.
x: str, optional
x-coordinate or longitude.
y: str, optional
y-coordinate or latitude.
Returns
-------
vDataFrame
object containing the result of the intersection.
"""
check_types(
[
("vdf", vdf, [vDataFrame],),
("gid", gid, [str],),
("g", g, [str],),
("x", x, [str],),
("y", y, [str],),
("index", index, [str],),
]
)
table = vdf.__genSQL__()
columns_check([gid], vdf)
if g:
columns_check([g], vdf)
g = vdf_columns_names([g], vdf)[0]
query = f"(SELECT STV_Intersect({gid}, {g} USING PARAMETERS index='{index}') OVER (PARTITION BEST) AS (point_id, polygon_gid) FROM {table}) x"
elif x and y:
columns_check([x, y], vdf)
x, y = vdf_columns_names([x, y], vdf)
query = f"(SELECT STV_Intersect({gid}, {x}, {y} USING PARAMETERS index='{index}') OVER (PARTITION BEST) AS (point_id, polygon_gid) FROM {table}) x"
else:
raise ParameterError("Either 'x' and 'y' or 'g' must not be empty.")
return vdf_from_relation(query, cursor=vdf._VERTICAPY_VARIABLES_["cursor"])
def durbin_watson(
vdf: vDataFrame, eps: str, ts: str, by: list = [],
):
"""
---------------------------------------------------------------------------
Durbin Watson test (residuals autocorrelation).
Parameters
----------
vdf: vDataFrame
Input vDataFrame.
eps: str
Input residual vcolumn.
ts: str
vcolumn used as timeline. It will be to use to order the data. It can be
a numerical or type date like (date, datetime, timestamp...) vcolumn.
by: list, optional
vcolumns used in the partition.
Returns
-------
float
Durbin Watson statistic
"""
check_types(
[
("ts", ts, [str],),
("eps", eps, [str],),
("by", by, [list],),
("vdf", vdf, [vDataFrame, str,],),
],
)
columns_check([eps] + [ts] + by, vdf)
eps = vdf_columns_names([eps], vdf)[0]
ts = vdf_columns_names([ts], vdf)[0]
by = vdf_columns_names(by, vdf)
query = "(SELECT et, LAG(et) OVER({}ORDER BY {}) AS lag_et FROM (SELECT {} AS et, {}{} FROM {}) VERTICAPY_SUBTABLE) VERTICAPY_SUBTABLE".format(
"PARTITION BY {} ".format(", ".join(by)) if (by) else "",
ts,
eps,
ts,
(", " + ", ".join(by)) if (by) else "",
vdf.__genSQL__(),
)
vdf.__executeSQL__(
"SELECT SUM(POWER(et - lag_et, 2)) / SUM(POWER(et, 2)) FROM {}".format(query),
title="Computes the Durbin Watson d.",
)
d = vdf._VERTICAPY_VARIABLES_["cursor"].fetchone()[0]
return d
def create_index(
vdf: vDataFrame,
gid: str,
g: str,
index: str,
overwrite: bool = False,
max_mem_mb: int = 256,
skip_nonindexable_polygons: bool = False,
):
"""
---------------------------------------------------------------------------
Creates a spatial index on a set of polygons to speed up spatial intersection
with a set of points.
Parameters
----------
vdf: vDataFrame
vDataFrame to use to compute the spatial join.
gid: str
Name of an integer column that uniquely identifies the polygon. The gid
cannot be NULL.
g: str
Name of a geometry or geography (WGS84) column or expression that contains
polygons and multipolygons. Only polygon and multipolygon can be indexed.
Other shape types are excluded from the index.
index: str
Name of the index.
overwrite: bool, optional
BOOLEAN value that specifies whether to overwrite the index, if an index exists.
max_mem_mb: int, optional
A positive integer that assigns a limit to the amount of memory in megabytes
that create_index can allocate during index construction.
skip_nonindexable_polygons: bool, optional
In rare cases, intricate polygons (for instance, with too high resolution or
anomalous spikes) cannot be indexed. These polygons are considered non-indexable.
When set to False, non-indexable polygons cause the index creation to fail.
When set to True, index creation can succeed by excluding non-indexable polygons
from the index.
Returns
-------
vDataFrame
object result of the join.
"""
check_types([
(
"vdf",
vdf,
[vDataFrame],
),
(
"gid",
gid,
[str],
),
(
"index",
index,
[str],
),
(
"g",
g,
[str],
),
(
"overwrite",
overwrite,
[bool],
),
(
"max_mem_mb",
max_mem_mb,
[int],
),
(
"skip_nonindexable_polygons",
skip_nonindexable_polygons,
[bool],
),
])
columns_check([gid, g], vdf)
gid, g = vdf_columns_names([gid, g], vdf)
query = "SELECT STV_Create_Index({}, {} USING PARAMETERS index='{}', overwrite={} , max_mem_mb={}, skip_nonindexable_polygons={}) OVER() FROM {}"
query = query.format(gid, g, index, overwrite, max_mem_mb,
skip_nonindexable_polygons, vdf.__genSQL__())
return to_tablesample(query, vdf._VERTICAPY_VARIABLES_["cursor"])
def het_white(
vdf: vDataFrame, eps: str, X: list,
):
"""
---------------------------------------------------------------------------
White’s Lagrange Multiplier Test for heteroscedasticity.
Parameters
----------
vdf: vDataFrame
Input vDataFrame.
eps: str
Input residual vcolumn.
X: str
Exogenous Variables to test the heteroscedasticity on.
Returns
-------
tablesample
An object containing the result. For more information, see
utilities.tablesample.
"""
check_types(
[("eps", eps, [str],), ("X", X, [list],), ("vdf", vdf, [vDataFrame, str,],),],
)
columns_check([eps] + X, vdf)
eps = vdf_columns_names([eps], vdf)[0]
X = vdf_columns_names(X, vdf)
X_0 = ["1"] + X
variables = []
variables_names = []
for i in range(len(X_0)):
for j in range(i, len(X_0)):
if i != 0 or j != 0:
variables += ["{} * {} AS var_{}_{}".format(X_0[i], X_0[j], i, j)]
variables_names += ["var_{}_{}".format(i, j)]
query = "(SELECT {}, POWER({}, 2) AS VERTICAPY_TEMP_eps2 FROM {}) VERTICAPY_SUBTABLE".format(
", ".join(variables), eps, vdf.__genSQL__()
)
vdf_white = vdf_from_relation(query, cursor=vdf._VERTICAPY_VARIABLES_["cursor"])
from verticapy.learn.linear_model import LinearRegression
schema_writing = vdf._VERTICAPY_VARIABLES_["schema_writing"]
if not (schema_writing):
schema_writing = "public"
name = schema_writing + ".VERTICAPY_TEMP_MODEL_LINEAR_REGRESSION_{}".format(
get_session(vdf._VERTICAPY_VARIABLES_["cursor"])
)
model = LinearRegression(name, cursor=vdf._VERTICAPY_VARIABLES_["cursor"])
try:
model.fit(vdf_white, variables_names, "VERTICAPY_TEMP_eps2")
R2 = model.score("r2")
model.drop()
except:
try:
model.set_params({"solver": "bfgs"})
model.fit(vdf_white, variables_names, "VERTICAPY_TEMP_eps2")
R2 = model.score("r2")
model.drop()
except:
model.drop()
raise
n = vdf.shape()[0]
if len(X) > 1:
k = 2 * len(X) + math.factorial(len(X)) / 2 / (math.factorial(len(X) - 2))
else:
k = 1
LM = n * R2
lm_pvalue = chi2.sf(LM, k)
F = (n - k - 1) * R2 / (1 - R2) / k
f_pvalue = f.sf(F, k, n - k - 1)
result = tablesample(
{
"index": [
"Lagrange Multiplier Statistic",
"lm_p_value",
"F Value",
"f_p_value",
],
"value": [LM, lm_pvalue, F, f_pvalue],
}
)
return result
def adfuller(
vdf: vDataFrame,
column: str,
ts: str,
by: list = [],
p: int = 1,
with_trend: bool = False,
regresults: bool = False,
):
"""
---------------------------------------------------------------------------
Augmented Dickey Fuller test (Time Series stationarity).
Parameters
----------
vdf: vDataFrame
Input vDataFrame.
column: str
Input vcolumn to test.
ts: str
vcolumn used as timeline. It will be to use to order the data. It can be
a numerical or type date like (date, datetime, timestamp...) vcolumn.
by: list, optional
vcolumns used in the partition.
p: int, optional
Number of lags to consider in the test.
with_trend: bool, optional
Adds a trend in the Regression.
regresults: bool, optional
If True, the full regression results are returned.
Returns
-------
tablesample
An object containing the result. For more information, see
utilities.tablesample.
"""
def critical_value(alpha, N, with_trend):
if not (with_trend):
if N <= 25:
if alpha == 0.01:
return -3.75
elif alpha == 0.10:
return -2.62
elif alpha == 0.025:
return -3.33
else:
return -3.00
elif N <= 50:
if alpha == 0.01:
return -3.58
elif alpha == 0.10:
return -2.60
elif alpha == 0.025:
return -3.22
else:
return -2.93
elif N <= 100:
if alpha == 0.01:
return -3.51
elif alpha == 0.10:
return -2.58
elif alpha == 0.025:
return -3.17
else:
return -2.89
elif N <= 250:
if alpha == 0.01:
return -3.46
elif alpha == 0.10:
return -2.57
elif alpha == 0.025:
return -3.14
else:
return -2.88
elif N <= 500:
if alpha == 0.01:
return -3.44
elif alpha == 0.10:
return -2.57
elif alpha == 0.025:
return -3.13
else:
return -2.87
else:
if alpha == 0.01:
return -3.43
elif alpha == 0.10:
return -2.57
elif alpha == 0.025:
return -3.12
else:
return -2.86
else:
if N <= 25:
if alpha == 0.01:
return -4.38
elif alpha == 0.10:
return -3.24
elif alpha == 0.025:
return -3.95
else:
return -3.60
elif N <= 50:
if alpha == 0.01:
return -4.15
elif alpha == 0.10:
return -3.18
elif alpha == 0.025:
return -3.80
else:
return -3.50
elif N <= 100:
if alpha == 0.01:
return -4.04
elif alpha == 0.10:
return -3.15
elif alpha == 0.025:
return -3.73
else:
return -5.45
elif N <= 250:
if alpha == 0.01:
return -3.99
elif alpha == 0.10:
return -3.13
elif alpha == 0.025:
return -3.69
else:
return -3.43
elif N <= 500:
if alpha == 0.01:
return 3.98
elif alpha == 0.10:
return -3.13
elif alpha == 0.025:
return -3.68
else:
return -3.42
else:
if alpha == 0.01:
return -3.96
elif alpha == 0.10:
return -3.12
elif alpha == 0.025:
return -3.66
else:
return -3.41
check_types(
[
("ts", ts, [str],),
("column", column, [str],),
("p", p, [int, float],),
("by", by, [list],),
("with_trend", with_trend, [bool],),
("regresults", regresults, [bool],),
("vdf", vdf, [vDataFrame,],),
],
)
columns_check([ts, column] + by, vdf)
ts = vdf_columns_names([ts], vdf)[0]
column = vdf_columns_names([column], vdf)[0]
by = vdf_columns_names(by, vdf)
schema = vdf._VERTICAPY_VARIABLES_["schema_writing"]
if not (schema):
schema = "public"
name = "{}.VERTICAPY_TEMP_MODEL_LINEAR_REGRESSION_{}".format(
schema, gen_name([column]).upper()
)
relation_name = "{}.VERTICAPY_TEMP_MODEL_LINEAR_REGRESSION_VIEW_{}".format(
schema, gen_name([column]).upper()
)
try:
vdf._VERTICAPY_VARIABLES_["cursor"].execute(
"DROP MODEL IF EXISTS {}".format(name)
)
vdf._VERTICAPY_VARIABLES_["cursor"].execute(
"DROP VIEW IF EXISTS {}".format(relation_name)
)
except:
pass
lag = [
"LAG({}, 1) OVER ({}ORDER BY {}) AS lag1".format(
column, "PARTITION BY {}".format(", ".join(by)) if (by) else "", ts
)
]
lag += [
"LAG({}, {}) OVER ({}ORDER BY {}) - LAG({}, {}) OVER ({}ORDER BY {}) AS delta{}".format(
column,
i,
"PARTITION BY {}".format(", ".join(by)) if (by) else "",
ts,
column,
i + 1,
"PARTITION BY {}".format(", ".join(by)) if (by) else "",
ts,
i,
)
for i in range(1, p + 1)
]
lag += [
"{} - LAG({}, 1) OVER ({}ORDER BY {}) AS delta".format(
column, column, "PARTITION BY {}".format(", ".join(by)) if (by) else "", ts
)
]
query = "CREATE VIEW {} AS SELECT {}, {} AS ts FROM {}".format(
relation_name,
", ".join(lag),
"TIMESTAMPDIFF(SECOND, {}, MIN({}) OVER ())".format(ts, ts)
if vdf[ts].isdate()
else ts,
vdf.__genSQL__(),
)
vdf._VERTICAPY_VARIABLES_["cursor"].execute(query)
model = LinearRegression(
name, vdf._VERTICAPY_VARIABLES_["cursor"], solver="Newton", max_iter=1000
)
predictors = ["lag1"] + ["delta{}".format(i) for i in range(1, p + 1)]
if with_trend:
predictors += ["ts"]
model.fit(
relation_name, predictors, "delta",
)
coef = model.coef_
vdf._VERTICAPY_VARIABLES_["cursor"].execute("DROP MODEL IF EXISTS {}".format(name))
vdf._VERTICAPY_VARIABLES_["cursor"].execute(
"DROP VIEW IF EXISTS {}".format(relation_name)
)
if regresults:
return coef
coef = coef.transpose()
DF = coef.values["lag1"][0] / (max(coef.values["lag1"][1], 1e-99))
p_value = coef.values["lag1"][3]
count = vdf.shape()[0]
result = tablesample(
{
"index": [
"ADF Test Statistic",
"p_value",
"# Lags used",
"# Observations Used",
"Critical Value (1%)",
"Critical Value (2.5%)",
"Critical Value (5%)",
"Critical Value (10%)",
"Stationarity (alpha = 1%)",
],
"value": [
DF,
p_value,
p,
count,
critical_value(0.01, count, with_trend),
critical_value(0.025, count, with_trend),
critical_value(0.05, count, with_trend),
critical_value(0.10, count, with_trend),
DF < critical_value(0.01, count, with_trend) and p_value < 0.01,
],
}
)
return result
def het_arch(
vdf: vDataFrame, eps: str, ts: str, by: list = [], p: int = 1,
):
"""
---------------------------------------------------------------------------
Engle’s Test for Autoregressive Conditional Heteroscedasticity (ARCH).
Parameters
----------
vdf: vDataFrame
Input vDataFrame.
eps: str
Input residual vcolumn.
ts: str
vcolumn used as timeline. It will be to use to order the data. It can be
a numerical or type date like (date, datetime, timestamp...) vcolumn.
by: list, optional
vcolumns used in the partition.
p: int, optional
Number of lags to consider in the test.
Returns
-------
tablesample
An object containing the result. For more information, see
utilities.tablesample.
"""
check_types(
[
("eps", eps, [str],),
("ts", ts, [str],),
("p", p, [int, float],),
("vdf", vdf, [vDataFrame, str,],),
],
)
columns_check([eps, ts] + by, vdf)
eps = vdf_columns_names([eps], vdf)[0]
ts = vdf_columns_names([ts], vdf)[0]
by = vdf_columns_names(by, vdf)
X = []
X_names = []
for i in range(0, p + 1):
X += [
"LAG(POWER({}, 2), {}) OVER({}ORDER BY {}) AS lag_{}".format(
eps, i, ("PARTITION BY " + ", ".join(by)) if (by) else "", ts, i
)
]
X_names += ["lag_{}".format(i)]
query = "(SELECT {} FROM {}) VERTICAPY_SUBTABLE".format(
", ".join(X), vdf.__genSQL__()
)
vdf_lags = vdf_from_relation(query, cursor=vdf._VERTICAPY_VARIABLES_["cursor"])
from verticapy.learn.linear_model import LinearRegression
schema_writing = vdf._VERTICAPY_VARIABLES_["schema_writing"]
if not (schema_writing):
schema_writing = "public"
name = schema_writing + ".VERTICAPY_TEMP_MODEL_LINEAR_REGRESSION_{}".format(
get_session(vdf._VERTICAPY_VARIABLES_["cursor"])
)
model = LinearRegression(name, cursor=vdf._VERTICAPY_VARIABLES_["cursor"])
try:
model.fit(vdf_lags, X_names[1:], X_names[0])
R2 = model.score("r2")
model.drop()
except:
try:
model.set_params({"solver": "bfgs"})
model.fit(vdf_lags, X_names[1:], X_names[0])
R2 = model.score("r2")
model.drop()
except:
model.drop()
raise
n = vdf.shape()[0]
k = len(X)
LM = (n - p) * R2
lm_pvalue = chi2.sf(LM, p)
F = (n - 2 * p - 1) * R2 / (1 - R2) / p
f_pvalue = f.sf(F, p, n - 2 * p - 1)
result = tablesample(
{
"index": [
"Lagrange Multiplier Statistic",
"lm_p_value",
"F Value",
"f_p_value",
],
"value": [LM, lm_pvalue, F, f_pvalue],
}
)
return result
def mkt(vdf: vDataFrame, column: str, ts: str, alpha: float = 0.05):
"""
---------------------------------------------------------------------------
Mann Kendall test (Time Series trend).
\u26A0 Warning : This Test is computationally expensive. It is using a CROSS
JOIN during the computation. The complexity is O(n * k), n
being the total count of the vDataFrame and k the number
of rows to use to do the test.
Parameters
----------
vdf: vDataFrame
Input vDataFrame.
column: str
Input vcolumn to test.
ts: str
vcolumn used as timeline. It will be to use to order the data. It can be
a numerical or type date like (date, datetime, timestamp...) vcolumn.
alpha: float, optional
Significance Level. Probability to accept H0.
Returns
-------
tablesample
An object containing the result. For more information, see
utilities.tablesample.
"""
check_types(
[
("ts", ts, [str],),
("column", column, [str],),
("alpha", alpha, [int, float],),
("vdf", vdf, [vDataFrame,],),
],
)
columns_check([column, ts], vdf)
column = vdf_columns_names([column], vdf)[0]
ts = vdf_columns_names([ts], vdf)[0]
table = "(SELECT {}, {} FROM {})".format(column, ts, vdf.__genSQL__())
query = "SELECT SUM(SIGN(y.{} - x.{})) FROM {} x CROSS JOIN {} y WHERE y.{} > x.{}".format(
column, column, table, table, ts, ts
)
vdf.__executeSQL__(query, title="Computes the Mann Kendall S.")
S = vdf._VERTICAPY_VARIABLES_["cursor"].fetchone()[0]
try:
S = float(S)
except:
S = None
n = vdf[column].count()
query = "SELECT SQRT(({} * ({} - 1) * (2 * {} + 5) - SUM(row * (row - 1) * (2 * row + 5))) / 18) FROM (SELECT row FROM (SELECT ROW_NUMBER() OVER (PARTITION BY {}) AS row FROM {}) VERTICAPY_SUBTABLE GROUP BY row) VERTICAPY_SUBTABLE".format(
n, n, n, column, vdf.__genSQL__()
)
vdf.__executeSQL__(query, title="Computes the Mann Kendall S standard deviation.")
STDS = vdf._VERTICAPY_VARIABLES_["cursor"].fetchone()[0]
try:
STDS = float(STDS)
except:
STDS = None
if STDS in (None, 0) or S == None:
return None
if S > 0:
ZMK = (S - 1) / STDS
trend = "increasing"
elif S < 0:
ZMK = (S + 1) / STDS
trend = "decreasing"
else:
ZMK = 0
trend = "no trend"
pvalue = 2 * norm.sf(abs(ZMK))
result = (
True
if (ZMK <= 0 and pvalue < alpha) or (ZMK >= 0 and pvalue < alpha)
else False
)
if not (result):
trend = "no trend"
result = tablesample(
{
"index": [
"Mann Kendall Test Statistic",
"S",
"STDS",
"p_value",
"Monotonic Trend",
"Trend",
],
"value": [ZMK, S, STDS, pvalue, result, trend],
}
)
return result