From cbc72ef9d3c36fba38480709de60ec8ba06f578c Mon Sep 17 00:00:00 2001 From: Niyonika Gaur <83643952+niyonikagaur@users.noreply.github.com> Date: Sun, 2 Jun 2024 11:31:01 +0530 Subject: [PATCH 01/16] Visualizing_nifti_files.md --- .../Visualizing_nifti_files.md | 90 +++++++++++++++++++ 1 file changed, 90 insertions(+) create mode 100644 contrib/plotting-visualization/Visualizing_nifti_files.md diff --git a/contrib/plotting-visualization/Visualizing_nifti_files.md b/contrib/plotting-visualization/Visualizing_nifti_files.md new file mode 100644 index 0000000..4baaca3 --- /dev/null +++ b/contrib/plotting-visualization/Visualizing_nifti_files.md @@ -0,0 +1,90 @@ +## NIfTI Files +Neuroimaging Informatics Technology Initiative is a data format for storage. Functional Magnetic Resonance Imaging (fMRI) and other medical images. +## In this, we'll be using different packages: +1. Matplotlib +2. Nibabel: It gives access to a variety of imaging formats, it provides a common interface for various formats produced by different scanners. + +## Various Methods for viewing a NIfTI file +### 1. Load NIfTI file +``` +brain_vol = nib.load("") #Enter the path to NIfTI file here +type(brain_vol) +``` +### 2. View Metadata +``` +print(brain_vol.header) +``` +### Output +``` + object, endian='<' +sizeof_hdr : 348 +data_type : b'' +db_name : b'' +extents : 0 +session_error : 0 +regular : b'r' +dim_info : 54 +dim : [ 3 192 256 256 1 1 1 1] +intent_p1 : 0.0 +intent_p2 : 0.0 +intent_p3 : 0.0 +intent_code : none +datatype : int16 +bitpix : 16 +slice_start : 0 +pixdim : [1. 1. 1. 1. 2.3 0. 0. 0. ] +vox_offset : 0.0 +scl_slope : nan +scl_inter : nan +slice_end : 0 +slice_code : unknown +xyzt_units : 10 +cal_max : 0.0 +cal_min : 0.0 +slice_duration : 0.0 +toffset : 0.0 +glmax : 0 +glmin : 0 +descrip : b'TE=2.7;Time=150734.828;phase=1' +aux_file : b'' +qform_code : scanner +sform_code : scanner +quatern_b : 0.00042526424 +quatern_c : -0.027039066 +quatern_d : 0.01571919 +qoffset_x : -81.5222 +qoffset_y : -130.72974 +qoffset_z : -144.47054 +srow_x : [ 9.9804670e-01 -3.1445995e-02 -5.4038301e-02 -8.1522202e+01] +srow_y : [ 3.1400096e-02 9.9950546e-01 -1.7001767e-03 -1.3072974e+02] +srow_z : [ 5.4065209e-02 4.7863640e-08 9.9853742e-01 -1.4447054e+02] +intent_name : b'' +magic : b'n+1' +``` +### 3. Access data in the NIfTI object +``` +brain_vol_data = brain_vol.get_fdata() +type(brain_vol_data) +``` +### Output +``` +numpy.ndarray +``` +### Dimensions of the image +``` +brain_vol_data.shape +``` +### Output +``` +(192, 256, 256) +``` +### 4. Visualize a Slice +``` +plt.imshow(brain_vol_data[96], cmap='bone') +plt.axis('off') +plt.show() +``` + + + + From ad7ec8797e02a99f21194fbb3486f3cf8d039b96 Mon Sep 17 00:00:00 2001 From: Niyonika Gaur <83643952+niyonikagaur@users.noreply.github.com> Date: Sun, 2 Jun 2024 11:37:11 +0530 Subject: [PATCH 02/16] Add files via upload --- images/1.png | Bin 0 -> 267708 bytes images/2.png | Bin 0 -> 761399 bytes images/3.png | Bin 0 -> 1384689 bytes 3 files changed, 0 insertions(+), 0 deletions(-) create mode 100644 images/1.png create mode 100644 images/2.png create mode 100644 images/3.png diff --git a/images/1.png b/images/1.png new file mode 100644 index 0000000000000000000000000000000000000000..bdf458ac3a056ee8d2e550ec215b8cbcd26f750a GIT binary patch literal 267708 zcmZ6yc{E$=A3oX-YBT**m^_j7drCUJ-)vpLb7tBktM!wWq90WombD!0(#fwLN<(2-2HA z2Y1JZLT`FR?AasR^1ov*Go;XW&z_yUTi35S$3SMb1}o3m5c4HH_xwg5P_g>s&v5lq zH_}etez7bc@_Z&G>n7da;t)ls8#AJHGCR`k)jLJSW2usoD&}&bfAk2!j4hj#Dc36G 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z9b2o*fm=w5VBL!L^s|Nmq2L11XzpYhX5=t!hLzu?n1z{(q}_0lmkD%K(BSlkGt5Vh zGi5D#n1!bbcFcE133u5CsV2+6(=M@;=2Q&Q(%wYHr1W?>q~W#Ze(0{DnQ9$QD4{&y zwZIuiCCN5Hg`s<@pA|4?zg(s?-L%|eyhk(rPUE0cv>_GQFVvWkLF5su<`en0ca*l? zdp5)&&@eCnLzoBUPUtsU?b+}g_GcZ+o6-%@7GPfp1xx`Qgymf|h>vjYbBfN?<@Ntk zo5riM%j~F#GMoZObb{B&jQQ#%&daCb!kRl0BYAocXW36Sv7?z~SeOke?Jn=V407;# z(pZS!o8kk(l4CPbZ-(in%Rmv(laSDs7zXR!*j$lb-9Zn*y!CB6HQxyCm+YeP_ zGqoO5b_}r^$lO{MLRW-!r@1hS)LyNtfjv;H#akYHiGqda;L{gVw(N9W*)pL^!}rB1 z&1NA7Mk#%U``6T4U(&TVfi-Si$yH+0G^L({iFTcR`PbSrR-v|;mSJ^xLG#IMQ_`;^ zd#NT`zDMb%Rl$+hsF{ql*C<|1jvHXcWLXdw^IxB&AqeySg89v$?FQmzED;)ax%UXR zJ>p`rwDfDe-uC&8ZDByu(eFRvhw0!B$D`Il{&hcoWfPj={?9*4`|o3Xw%dr%v;X%$ zU)iw#xv%X1+_&bbRQ!K<;eX!NpNNb9G(7+Fy+sHA_l^Fi)dUyyf3IlXfB%X9_pQTH f|9^i*w-CB(w@e=&@;Lk*_-AQ)`C`TSKkxk?I=MGT From dbe3af270ac69849229c450609d23dd25eb8f3e2 Mon Sep 17 00:00:00 2001 From: Niyonika Gaur <83643952+niyonikagaur@users.noreply.github.com> Date: Sun, 2 Jun 2024 11:51:34 +0530 Subject: [PATCH 06/16] Visualizing_nifti_files.md --- .../Visualizing_nifti_files.md | 31 +++++++++++++++++++ 1 file changed, 31 insertions(+) diff --git a/contrib/plotting-visualization/Visualizing_nifti_files.md b/contrib/plotting-visualization/Visualizing_nifti_files.md index 4baaca3..bcd2619 100644 --- a/contrib/plotting-visualization/Visualizing_nifti_files.md +++ b/contrib/plotting-visualization/Visualizing_nifti_files.md @@ -84,6 +84,37 @@ plt.imshow(brain_vol_data[96], cmap='bone') plt.axis('off') plt.show() ``` +The image can be rotated +``` +plt.imshow(ndi.rotate(brain_vol_data[96], 90), cmap='bone') +plt.axis('off') +plt.show() +``` +### Plot a series of slices +``` +fig_rows = 4 +fig_cols = 4 +n_subplots = fig_rows * fig_cols +n_slice = brain_vol_data.shape[0] +step_size = n_slice // n_subplots +plot_range = n_subplots * step_size +start_stop = int((n_slice - plot_range) / 2) + +fig, axs = plt.subplots(fig_rows, fig_cols, figsize=[10, 10]) + +for idx, img in enumerate(range(start_stop, plot_range, step_size)): + axs.flat[idx].imshow(ndi.rotate(brain_vol_data[img, :, :], 90), cmap='gray') + axs.flat[idx].axis('off') + +plt.tight_layout() +plt.show() +``` +### Multiples slices at once +``` +plotting.plot_img(brain_vol, display_mode='mosaic', cmap='gray') +plt.show() +``` + From cd3e090e703ab3b3812614a4590a062ce8e81ce3 Mon Sep 17 00:00:00 2001 From: Niyonika Gaur <83643952+niyonikagaur@users.noreply.github.com> Date: Sun, 2 Jun 2024 11:53:31 +0530 Subject: [PATCH 07/16] index.md --- contrib/plotting-visualization/index.md | 1 + 1 file changed, 1 insertion(+) diff --git a/contrib/plotting-visualization/index.md b/contrib/plotting-visualization/index.md index 67bee6d..74558c4 100644 --- a/contrib/plotting-visualization/index.md +++ b/contrib/plotting-visualization/index.md @@ -1,3 +1,4 @@ # List of sections - [Installing Matplotlib](matplotlib_installation.md) +- [Visualizing NIfTI files](Visualizing_NIfTI_files.md) From b519834b34a998805d9fc76343b224ad7220f7ff Mon Sep 17 00:00:00 2001 From: Niyonika Gaur <83643952+niyonikagaur@users.noreply.github.com> Date: Sun, 2 Jun 2024 11:54:24 +0530 Subject: [PATCH 08/16] index.md --- contrib/plotting-visualization/index.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/contrib/plotting-visualization/index.md b/contrib/plotting-visualization/index.md index 74558c4..03994ec 100644 --- a/contrib/plotting-visualization/index.md +++ b/contrib/plotting-visualization/index.md @@ -1,4 +1,4 @@ # List of sections - [Installing Matplotlib](matplotlib_installation.md) -- [Visualizing NIfTI files](Visualizing_NIfTI_files.md) +- [Visualizing NIfTI files](Visualizing_nifti_files.md) From a0e9936ce91dcbb26e2a3230e5f4d9c0c1d3f976 Mon Sep 17 00:00:00 2001 From: Niyonika Gaur <83643952+niyonikagaur@users.noreply.github.com> Date: Mon, 10 Jun 2024 12:09:17 +0530 Subject: [PATCH 09/16] SciPy_Graphs.md --- contrib/scipy/SciPy_Graphs.md | 137 ++++++++++++++++++++++++++++++++++ 1 file changed, 137 insertions(+) create mode 100644 contrib/scipy/SciPy_Graphs.md diff --git a/contrib/scipy/SciPy_Graphs.md b/contrib/scipy/SciPy_Graphs.md new file mode 100644 index 0000000..747ede7 --- /dev/null +++ b/contrib/scipy/SciPy_Graphs.md @@ -0,0 +1,137 @@ +# SciPy Graphs +Graphs are also a type of data structure, SciPy provides a module called scipy.sparse.csgraph for working with graphs. +## Adjacency Matrix +An adjacency matrix is a way of representing a graph using a square matrix. In the matrix, the element at the i-th row and j-th column indicates whether there is an edge from vertex +i to vertex j. +``` +import numpy as np +from scipy.sparse import csr_matrix + +adj_matrix = np.array([ + [0, 1, 0, 0], + [1, 0, 1, 0], + [0, 1, 0, 1], + [0, 0, 1, 0] +]) + + +sparse_matrix = csr_matrix(adj_matrix) + +print(sparse_matrix) +``` +In this example: + +1. The graph has 4 nodes. +2. is an edge between node 0 and node 1, node 1 and node 2, and node 2 and node 3. +3. The csr_matrix function converts the dense adjacency matrix into a compressed sparse row (CSR) format, which is efficient for storing large, sparse matrices. +## Floyd Warshall +The Floyd-Warshall algorithm is a classic algorithm used to find the shortest paths between all pairs of nodes in a weighted graph. +``` +import numpy as np +from scipy.sparse.csgraph import floyd_warshall +from scipy.sparse import csr_matrix + +arr = np.array([ + [0, 1, 2], + [1, 0, 0], + [2, 0, 0] +]) + +newarr = csr_matrix(arr) + +print(floyd_warshall(newarr, return_predecessors=True)) +``` +### Output +``` +(array([[0., 1., 2.], + [1., 0., 3.], + [2., 3., 0.]]), array([[-9999, 0, 0], + [ 1, -9999, 0], + [ 2, 0, -9999]], dtype=int32)) +``` +## Dijkstra +Dijkstra's algorithm is used to find the shortest path from a source node to all other nodes in a graph with non-negative edge weights. +``` +import numpy as np +from scipy.sparse.csgraph import dijkstra +from scipy.sparse import csr_matrix + +arr = np.array([ + [0, 1, 2], + [1, 0, 0], + [2, 0, 0] +]) + +newarr = csr_matrix(arr) + +print(dijkstra(newarr, return_predecessors=True, indices=0)) +``` +### Output +``` +(array([ 0., 1., 2.]), array([-9999, 0, 0], dtype=int32)) +``` +## Bellman Ford +The Bellman-Ford algorithm is used to find the shortest path from a single source vertex to all other vertices in a weighted graph. It can handle graphs with negative weights, and it also detects negative weight cycles. +``` +import numpy as np +from scipy.sparse.csgraph import bellman_ford +from scipy.sparse import csr_matrix + +arr = np.array([ + [0, -1, 2], + [1, 0, 0], + [2, 0, 0] +]) + +newarr = csr_matrix(arr) + +print(bellman_ford(newarr, return_predecessors=True, indices=0)) +``` +### Output +``` +(array([ 0., -1., 2.]), array([-9999, 0, 0], dtype=int32)) +``` +## Depth First Order +Depth-First Search (DFS) is an algorithm for traversing or searching tree or graph data structures. The algorithm starts at the root and explores as far as possible along each branch before backtracking. +``` +import numpy as np +from scipy.sparse.csgraph import depth_first_order +from scipy.sparse import csr_matrix + +arr = np.array([ + [0, 1, 0, 1], + [1, 1, 1, 1], + [2, 1, 1, 0], + [0, 1, 0, 1] +]) + +newarr = csr_matrix(arr) + +print(depth_first_order(newarr, 1)) +``` +### Output +``` +(array([1, 0, 3, 2], dtype=int32), array([ 1, -9999, 1, 0], dtype=int32)) +``` +## Breadth First Order +Breadth-First Search (BFS) is an algorithm for traversing or searching tree or graph data structures. It starts at the root present depth level before moving on to nodes at the next depth level. +``` +import numpy as np +from scipy.sparse.csgraph import breadth_first_order +from scipy.sparse import csr_matrix + +arr = np.array([ + [0, 1, 0, 1], + [1, 1, 1, 1], + [2, 1, 1, 0], + [0, 1, 0, 1] +]) + +newarr = csr_matrix(arr) + +print(breadth_first_order(newarr, 1)) +``` +### Output +``` +(array([1, 0, 2, 3], dtype=int32), array([ 1, -9999, 1, 1], dtype=int32)) +``` From 8dfaed116e75ea44d56b47dbf851d0c20b8c10e8 Mon Sep 17 00:00:00 2001 From: Niyonika Gaur <83643952+niyonikagaur@users.noreply.github.com> Date: Mon, 10 Jun 2024 12:11:06 +0530 Subject: [PATCH 10/16] Delete contrib/plotting-visualization/Visualizing_nifti_files.md --- .../Visualizing_nifti_files.md | 121 ------------------ 1 file changed, 121 deletions(-) delete mode 100644 contrib/plotting-visualization/Visualizing_nifti_files.md diff --git a/contrib/plotting-visualization/Visualizing_nifti_files.md b/contrib/plotting-visualization/Visualizing_nifti_files.md deleted file mode 100644 index bcd2619..0000000 --- a/contrib/plotting-visualization/Visualizing_nifti_files.md +++ /dev/null @@ -1,121 +0,0 @@ -## NIfTI Files -Neuroimaging Informatics Technology Initiative is a data format for storage. Functional Magnetic Resonance Imaging (fMRI) and other medical images. -## In this, we'll be using different packages: -1. Matplotlib -2. Nibabel: It gives access to a variety of imaging formats, it provides a common interface for various formats produced by different scanners. - -## Various Methods for viewing a NIfTI file -### 1. Load NIfTI file -``` -brain_vol = nib.load("") #Enter the path to NIfTI file here -type(brain_vol) -``` -### 2. View Metadata -``` -print(brain_vol.header) -``` -### Output -``` - object, endian='<' -sizeof_hdr : 348 -data_type : b'' -db_name : b'' -extents : 0 -session_error : 0 -regular : b'r' -dim_info : 54 -dim : [ 3 192 256 256 1 1 1 1] -intent_p1 : 0.0 -intent_p2 : 0.0 -intent_p3 : 0.0 -intent_code : none -datatype : int16 -bitpix : 16 -slice_start : 0 -pixdim : [1. 1. 1. 1. 2.3 0. 0. 0. ] -vox_offset : 0.0 -scl_slope : nan -scl_inter : nan -slice_end : 0 -slice_code : unknown -xyzt_units : 10 -cal_max : 0.0 -cal_min : 0.0 -slice_duration : 0.0 -toffset : 0.0 -glmax : 0 -glmin : 0 -descrip : b'TE=2.7;Time=150734.828;phase=1' -aux_file : b'' -qform_code : scanner -sform_code : scanner -quatern_b : 0.00042526424 -quatern_c : -0.027039066 -quatern_d : 0.01571919 -qoffset_x : -81.5222 -qoffset_y : -130.72974 -qoffset_z : -144.47054 -srow_x : [ 9.9804670e-01 -3.1445995e-02 -5.4038301e-02 -8.1522202e+01] -srow_y : [ 3.1400096e-02 9.9950546e-01 -1.7001767e-03 -1.3072974e+02] -srow_z : [ 5.4065209e-02 4.7863640e-08 9.9853742e-01 -1.4447054e+02] -intent_name : b'' -magic : b'n+1' -``` -### 3. Access data in the NIfTI object -``` -brain_vol_data = brain_vol.get_fdata() -type(brain_vol_data) -``` -### Output -``` -numpy.ndarray -``` -### Dimensions of the image -``` -brain_vol_data.shape -``` -### Output -``` -(192, 256, 256) -``` -### 4. Visualize a Slice -``` -plt.imshow(brain_vol_data[96], cmap='bone') -plt.axis('off') -plt.show() -``` -The image can be rotated -``` -plt.imshow(ndi.rotate(brain_vol_data[96], 90), cmap='bone') -plt.axis('off') -plt.show() -``` -### Plot a series of slices -``` -fig_rows = 4 -fig_cols = 4 -n_subplots = fig_rows * fig_cols -n_slice = brain_vol_data.shape[0] -step_size = n_slice // n_subplots -plot_range = n_subplots * step_size -start_stop = int((n_slice - plot_range) / 2) - -fig, axs = plt.subplots(fig_rows, fig_cols, figsize=[10, 10]) - -for idx, img in enumerate(range(start_stop, plot_range, step_size)): - axs.flat[idx].imshow(ndi.rotate(brain_vol_data[img, :, :], 90), cmap='gray') - axs.flat[idx].axis('off') - -plt.tight_layout() -plt.show() -``` -### Multiples slices at once -``` -plotting.plot_img(brain_vol, display_mode='mosaic', cmap='gray') -plt.show() -``` - - - - - From 35ca73c13ab69728a317ee32859a770e45d8a948 Mon Sep 17 00:00:00 2001 From: Niyonika Gaur <83643952+niyonikagaur@users.noreply.github.com> Date: Mon, 10 Jun 2024 12:13:15 +0530 Subject: [PATCH 11/16] index.md --- contrib/scipy/index.md | 1 + 1 file changed, 1 insertion(+) diff --git a/contrib/scipy/index.md b/contrib/scipy/index.md index 5737114..4916bff 100644 --- a/contrib/scipy/index.md +++ b/contrib/scipy/index.md @@ -1,4 +1,5 @@ # List of sections - [Installation of Scipy and its key uses](installation_features.md) +- [SciPy Graphs](SciPy_Graphs.md) From 23e146c14508dbec01ed1f3fcc2d72fa1c7320f9 Mon Sep 17 00:00:00 2001 From: Niyonika Gaur <83643952+niyonikagaur@users.noreply.github.com> Date: Mon, 10 Jun 2024 12:13:53 +0530 Subject: [PATCH 12/16] index.md --- contrib/plotting-visualization/index.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/contrib/plotting-visualization/index.md b/contrib/plotting-visualization/index.md index 03994ec..7a33cc1 100644 --- a/contrib/plotting-visualization/index.md +++ b/contrib/plotting-visualization/index.md @@ -1,4 +1,4 @@ # List of sections - [Installing Matplotlib](matplotlib_installation.md) -- [Visualizing NIfTI files](Visualizing_nifti_files.md) + From f86cdffb92bec774a65f726d218f6fcc222c8e21 Mon Sep 17 00:00:00 2001 From: Ashita Prasad Date: Sat, 22 Jun 2024 16:02:57 +0530 Subject: [PATCH 13/16] Update index.md --- contrib/plotting-visualization/index.md | 1 - 1 file changed, 1 deletion(-) diff --git a/contrib/plotting-visualization/index.md b/contrib/plotting-visualization/index.md index 7a33cc1..67bee6d 100644 --- a/contrib/plotting-visualization/index.md +++ b/contrib/plotting-visualization/index.md @@ -1,4 +1,3 @@ # List of sections - [Installing Matplotlib](matplotlib_installation.md) - From 4a6f2692cbe50d0e778682edbcd1a795cad1e2f2 Mon Sep 17 00:00:00 2001 From: Ashita Prasad Date: Sat, 22 Jun 2024 16:03:21 +0530 Subject: [PATCH 14/16] Rename SciPy_Graphs.md to scipy-graphs.md --- contrib/scipy/{SciPy_Graphs.md => scipy-graphs.md} | 0 1 file changed, 0 insertions(+), 0 deletions(-) rename contrib/scipy/{SciPy_Graphs.md => scipy-graphs.md} (100%) diff --git a/contrib/scipy/SciPy_Graphs.md b/contrib/scipy/scipy-graphs.md similarity index 100% rename from contrib/scipy/SciPy_Graphs.md rename to contrib/scipy/scipy-graphs.md From 915f810b0080d64fb1c651656abe7e3b5b95ad16 Mon Sep 17 00:00:00 2001 From: Ashita Prasad Date: Sat, 22 Jun 2024 16:03:38 +0530 Subject: [PATCH 15/16] Update index.md --- contrib/scipy/index.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/contrib/scipy/index.md b/contrib/scipy/index.md index 4916bff..5425c4a 100644 --- a/contrib/scipy/index.md +++ b/contrib/scipy/index.md @@ -1,5 +1,5 @@ # List of sections - [Installation of Scipy and its key uses](installation_features.md) -- [SciPy Graphs](SciPy_Graphs.md) +- [SciPy Graphs](scipy-graphs.md) From eacf86cec5b3a8089f7697339a7b7bb5e475a3a9 Mon Sep 17 00:00:00 2001 From: Ashita Prasad Date: Sat, 22 Jun 2024 16:06:16 +0530 Subject: [PATCH 16/16] Update scipy-graphs.md --- contrib/scipy/scipy-graphs.md | 48 +++++++++++++++++++++++++++-------- 1 file changed, 38 insertions(+), 10 deletions(-) diff --git a/contrib/scipy/scipy-graphs.md b/contrib/scipy/scipy-graphs.md index 747ede7..60bb565 100644 --- a/contrib/scipy/scipy-graphs.md +++ b/contrib/scipy/scipy-graphs.md @@ -1,9 +1,11 @@ # SciPy Graphs Graphs are also a type of data structure, SciPy provides a module called scipy.sparse.csgraph for working with graphs. + ## Adjacency Matrix An adjacency matrix is a way of representing a graph using a square matrix. In the matrix, the element at the i-th row and j-th column indicates whether there is an edge from vertex i to vertex j. -``` + +```python import numpy as np from scipy.sparse import csr_matrix @@ -19,14 +21,18 @@ sparse_matrix = csr_matrix(adj_matrix) print(sparse_matrix) ``` + In this example: 1. The graph has 4 nodes. 2. is an edge between node 0 and node 1, node 1 and node 2, and node 2 and node 3. 3. The csr_matrix function converts the dense adjacency matrix into a compressed sparse row (CSR) format, which is efficient for storing large, sparse matrices. + ## Floyd Warshall + The Floyd-Warshall algorithm is a classic algorithm used to find the shortest paths between all pairs of nodes in a weighted graph. -``` + +```python import numpy as np from scipy.sparse.csgraph import floyd_warshall from scipy.sparse import csr_matrix @@ -41,7 +47,9 @@ newarr = csr_matrix(arr) print(floyd_warshall(newarr, return_predecessors=True)) ``` -### Output + +#### Output + ``` (array([[0., 1., 2.], [1., 0., 3.], @@ -49,9 +57,12 @@ print(floyd_warshall(newarr, return_predecessors=True)) [ 1, -9999, 0], [ 2, 0, -9999]], dtype=int32)) ``` + ## Dijkstra + Dijkstra's algorithm is used to find the shortest path from a source node to all other nodes in a graph with non-negative edge weights. -``` + +```python import numpy as np from scipy.sparse.csgraph import dijkstra from scipy.sparse import csr_matrix @@ -66,13 +77,18 @@ newarr = csr_matrix(arr) print(dijkstra(newarr, return_predecessors=True, indices=0)) ``` -### Output + +#### Output + ``` (array([ 0., 1., 2.]), array([-9999, 0, 0], dtype=int32)) ``` + ## Bellman Ford + The Bellman-Ford algorithm is used to find the shortest path from a single source vertex to all other vertices in a weighted graph. It can handle graphs with negative weights, and it also detects negative weight cycles. -``` + +```python import numpy as np from scipy.sparse.csgraph import bellman_ford from scipy.sparse import csr_matrix @@ -87,13 +103,18 @@ newarr = csr_matrix(arr) print(bellman_ford(newarr, return_predecessors=True, indices=0)) ``` -### Output + +#### Output + ``` (array([ 0., -1., 2.]), array([-9999, 0, 0], dtype=int32)) ``` + ## Depth First Order + Depth-First Search (DFS) is an algorithm for traversing or searching tree or graph data structures. The algorithm starts at the root and explores as far as possible along each branch before backtracking. -``` + +```python import numpy as np from scipy.sparse.csgraph import depth_first_order from scipy.sparse import csr_matrix @@ -109,13 +130,18 @@ newarr = csr_matrix(arr) print(depth_first_order(newarr, 1)) ``` -### Output + +#### Output + ``` (array([1, 0, 3, 2], dtype=int32), array([ 1, -9999, 1, 0], dtype=int32)) ``` + ## Breadth First Order + Breadth-First Search (BFS) is an algorithm for traversing or searching tree or graph data structures. It starts at the root present depth level before moving on to nodes at the next depth level. -``` + +```python import numpy as np from scipy.sparse.csgraph import breadth_first_order from scipy.sparse import csr_matrix @@ -131,7 +157,9 @@ newarr = csr_matrix(arr) print(breadth_first_order(newarr, 1)) ``` + ### Output + ``` (array([1, 0, 2, 3], dtype=int32), array([ 1, -9999, 1, 1], dtype=int32)) ```