New term entry on the built in function for Numpy named 'svd' #4547

doroodianMostafa · 2024-04-19T08:57:33Z

new term entry on the built in function for Numpy named SVD(Singular Value Decomposition) under svd.md

Description

This is a new term entry on the built-in-functions term for [Numpy]: Singular Value Decomposition. The is in a new file under docs/content/numpy/concepts/built-in-functions/terms/svd/svd.md

I'd like to acknowledge that the following link served as my source of motivation or inspiration for the provided example: numpy.linalg.svd() documentation.

Issue Solved

Closes #4479

Type of Change

Adding a new entry

Checklist

All writings are my own.
My entry follows the Codecademy Docs style guide.
My changes generate no new warnings.
I have performed a self-review of my own writing and code.
I have checked my entry and corrected any misspellings.
I have made corresponding changes to the documentation if needed.
I have confirmed my changes are not being pushed from my forked main branch.
I have confirmed that I'm pushing from a new branch named after the changes I'm making.
I have linked any issues that are relevant to this PR in the Issues Solved section.

… Value Decomposition) under svd.md

CLAassistant · 2024-04-19T08:57:38Z

All committers have signed the CLA.

doroodianMostafa · 2024-04-19T10:30:13Z

Thank you for your comment, I tried to redo it through the provided link, I hope this time it's addressed. Otherwise I do appreciate further instructions.

Besides I do not understand why it's mentioned that there are two committers, since my account is doroodianMostafa.

mamtawardhani · 2024-04-20T06:44:02Z

@doroodianMostafa it appears that you've submitted this PR using two accounts (The other one is @doroodian ). Therefore, please sign this CLA with both accounts or close this and resubmit a new PR using only one account.

doroodianMostafa · 2024-04-20T09:46:04Z

Thanks for clarification, I found it easier to sign the CLA with other account as well, since I have no idea how I submitted with two accounts. I hope now the matter is addressed.

…

________________________________ From: mamtawardhani ***@***.***> Sent: Saturday, April 20, 2024 8:44 To: Codecademy/docs ***@***.***> Cc: Doroodian, M. (Mostafa) ***@***.***>; Mention ***@***.***> Subject: Re: [Codecademy/docs] New term entry on the built in function for Numpy named 'svd' (PR #4547) @doroodianMostafa<https://github.com/doroodianMostafa> it appears that you've submitted this PR using two accounts (The other one is @doroodian<https://github.com/doroodian> ). Therefore, please sign this CLA with both accounts or close this and resubmit a new PR using only one account. — Reply to this email directly, view it on GitHub<#4547 (comment)>, or unsubscribe<https://github.com/notifications/unsubscribe-auth/AQ3XQOCWXP76KFJ7NVWRM6LY6IFERAVCNFSM6AAAAABGOY52GWVHI2DSMVQWIX3LMV43OSLTON2WKQ3PNVWWK3TUHMZDANRXGU3TQOBUGA>. You are receiving this because you were mentioned.Message ID: ***@***.***>

mamtawardhani

Hey @doroodianMostafa
Thank you for contributing at Codecademy!

I've suggested some changes in the entry, please review and modify them at your earliest convenience. Also, please change or replace the example given with a new one, since this one is plagiarized.

Thanks!

mamtawardhani · 2024-04-23T10:39:32Z

content/numpy/concepts/built-in-functions/terms/svd/svd.md

@@ -0,0 +1,93 @@
+---
+Title: '.svd()'
+Description: 'Singular Value Decomposition'


Suggested change

Description: 'Singular Value Decomposition'

Description: 'The `.svd()` built-in function performs the Singular Value Decomposition (SVD) on a matrix, breaking it down into singular vectors and values.'

mamtawardhani · 2024-04-23T11:59:39Z

content/numpy/concepts/built-in-functions/terms/svd/svd.md

+The **`.svd()`** is a mathematical technique that decomposes a matrix into three simpler matrices.Factorizes the matrix `a` into two unitary matrices `U` and `Vh`, 
+along with a 1-D array `s` of singular values (real and non-negative), such that `a` equals `U @ S @ Vh`, where `S` is a suitably shaped matrix of zeros with `s` as 
+its main diagonal.


Suggested change

The **`.svd()`** is a mathematical technique that decomposes a matrix into three simpler matrices.Factorizes the matrix `a` into two unitary matrices `U` and `Vh`,

along with a 1-D array `s` of singular values (real and non-negative), such that `a` equals `U @ S @ Vh`, where `S` is a suitably shaped matrix of zeros with `s` as

its main diagonal.

The **`.svd()`** function is a mathematical technique that decomposes a matrix into three simpler matrices: it factorizes the matrix `a` into two unitary matrices `U` and `Vh`, along with a 1-D array `s` of singular values (real and non-negative). This decomposition satisfies the equation `a = U @ S @ Vh`, where `S` is a suitably shaped matrix of zeros with `s` as its main diagonal.

mamtawardhani · 2024-04-23T12:00:10Z

content/numpy/concepts/built-in-functions/terms/svd/svd.md

+
+

Please remove the extra one line spacing here.

mamtawardhani · 2024-04-23T12:18:11Z

content/numpy/concepts/built-in-functions/terms/svd/svd.md

+- `a`: This is the input matrix to be decomposed with a.ndim >= 2. It is the matrix you want to perform Singular Value Decomposition on.
+- `full_matrices`:This parameter determines whether to compute the full-sized or reduced-sized matrices U and VT. If full_matrices is set to True, the function 
+computes the full-sized matrices. If set to False, it computes only the essential parts of U and VT. By default, it's set to True.
+- `compute_uv`: This parameter specifies whether to compute the left-singular vectors (U) and right-singular vectors (transpose of V) in addition to the singular 
+values. If compute_uv is set to True, the function computes U and VT. If set to False, it only computes the singular values. By default, it's set to True.
+- `hermitian':This parameter indicates whether the input matrix a is Hermitian (equal to its conjugate transpose). If hermitian is set to True, the function assumes 
+that a is Hermitian and uses a more efficient algorithm tailored for Hermitian matrices. If set to False, it uses a general algorithm. By default, it's set to 
+False.


Suggested change

- `a`: This is the input matrix to be decomposed with a.ndim >= 2. It is the matrix you want to perform Singular Value Decomposition on.

- `full_matrices`:This parameter determines whether to compute the full-sized or reduced-sized matrices U and VT. If full_matrices is set to True, the function

computes the full-sized matrices. If set to False, it computes only the essential parts of U and VT. By default, it's set to True.

- `compute_uv`: This parameter specifies whether to compute the left-singular vectors (U) and right-singular vectors (transpose of V) in addition to the singular

values. If compute_uv is set to True, the function computes U and VT. If set to False, it only computes the singular values. By default, it's set to True.

- `hermitian':This parameter indicates whether the input matrix a is Hermitian (equal to its conjugate transpose). If hermitian is set to True, the function assumes

that a is Hermitian and uses a more efficient algorithm tailored for Hermitian matrices. If set to False, it uses a general algorithm. By default, it's set to

False.

- `a`: This parameter represents the input matrix to be decomposed, where `a.ndim>=2`. It is the matrix on which Singular Value Decomposition will be performed.

- `full_matrices`: This parameter determines whether the function computes full-sized or reduced-sized matrices `U` and `Vh`. If `full_matrices` is set to `True`, the function computes the full-sized matrices. If set to `False`, it computes only the essential parts of `U` and `Vh`. The default value is `True`.

- `compute_uv`: This parameter specifies whether the function computes the left-singular vectors (`U`) and right-singular vectors (transpose of `V`) in addition to the singular values. When `compute_uv` is set to `True`, the function computes `U` and `Vh`. If set to `False`, it only computes the singular values. The default value is `True`.

- `hermitian': This parameter indicates whether the input matrix `a` is Hermitian, meaning it is equal to its conjugate transpose. When `hermitian` is set to `True`, the function assumes that a is Hermitian and uses a more efficient algorithm tailored for such matrices. If set to `False`, it uses a general algorithm. The default value is `False`.

mamtawardhani · 2024-04-23T12:21:20Z

content/numpy/concepts/built-in-functions/terms/svd/svd.md

+# The following example demonstrates various scenarios of Singular Value Decomposition (SVD) using NumPy:
+
+a = np.random.randn(9, 6) + 1j*np.random.randn(9, 6)
+b = np.random.randn(2, 7, 8, 3) + 1j*np.random.randn(2, 7, 8, 3)
+
+## Reconstruction based on full SVD, 2D case:
+
+U, S, Vh = np.linalg.svd(a, full_matrices=True)
+U.shape, S.shape, Vh.shape
+((9, 9), (6,), (6, 6))
+np.allclose(a, np.dot(U[:, :6] * S, Vh))
+True
+smat = np.zeros((9, 6), dtype=complex)
+smat[:6, :6] = np.diag(S)
+np.allclose(a, np.dot(U, np.dot(smat, Vh)))
+True
+
+## Reconstruction based on reduced SVD, 2D case:
+
+U, S, Vh = np.linalg.svd(a, full_matrices=False)
+U.shape, S.shape, Vh.shape
+((9, 6), (6,), (6, 6))
+np.allclose(a, np.dot(U * S, Vh))
+True
+smat = np.diag(S)
+np.allclose(a, np.dot(U, np.dot(smat, Vh)))
+True
+
+## Reconstruction based on full SVD, 4D case:
+
+U, S, Vh = np.linalg.svd(b, full_matrices=True)
+U.shape, S.shape, Vh.shape
+((2, 7, 8, 8), (2, 7, 3), (2, 7, 3, 3))
+np.allclose(b, np.matmul(U[..., :3] * S[..., None, :], Vh))
+True
+np.allclose(b, np.matmul(U[..., :3], S[..., None] * Vh))
+True
+
+## Reconstruction based on reduced SVD, 4D case:
+
+U, S, Vh = np.linalg.svd(b, full_matrices=False)
+U.shape, S.shape, Vh.shape
+((2, 7, 8, 3), (2, 7, 3), (2, 7, 3, 3))
+np.allclose(b, np.matmul(U * S[..., None, :], Vh))
+True
+np.allclose(b, np.matmul(U, S[..., None] * Vh))
+True


Please modify or replace this example with a new one, this is plagiarized.
Plagiarized from: https://numpy.org/doc/stable/reference/generated/numpy.linalg.svd.html

Thanks for your comment. To clarify, I specifically mentioned the source of the examples in the commit comment to avoid plagiarism. However, I wasn't aware that it could still be considered plagiarism even when the resource is provided. Thanks for correcting me!

mamtawardhani

Hey @doroodianMostafa! Please review the changes suggested and modify them. Thanks!

mamtawardhani · 2024-04-30T06:22:22Z

content/numpy/concepts/built-in-functions/terms/svd/svd.md

+- `a`: This parameter represents the input matrix to be decomposed, where `a.ndim>=2`. It is the matrix on which Singular Value Decomposition will be performed.
+- `full_matrices`: This parameter determines whether the function computes full-sized or reduced-sized matrices `U` and `Vh`. If `full_matrices` is set to `True`, the function computes the full-sized matrices. If set to `False`, it computes only the essential parts of `U` and `Vh`. The default value is `True`.
+- `compute_uv`: This parameter specifies whether the function computes the left-singular vectors (`U`) and right-singular vectors (transpose of `V`) in addition to the singular values. When `compute_uv` is set to `True`, the function computes `U` and `Vh`. If set to `False`, it only computes the singular values. The default value is `True`.
+- `hermitian': This parameter indicates whether the input matrix `a` is Hermitian, meaning it is equal to its conjugate transpose. When `hermitian` is set to `True`, the function assumes that a is Hermitian and uses a more efficient algorithm tailored for such matrices. If set to `False`, it uses a general algorithm. The default value is `False`.


Suggested change

- `hermitian': This parameter indicates whether the input matrix `a` is Hermitian, meaning it is equal to its conjugate transpose. When `hermitian` is set to `True`, the function assumes that a is Hermitian and uses a more efficient algorithm tailored for such matrices. If set to `False`, it uses a general algorithm. The default value is `False`.

- `hermitian`: This parameter indicates whether the input matrix `a` is Hermitian, meaning it is equal to its conjugate transpose. When `hermitian` is set to `True`, the function assumes that a is Hermitian and uses a more efficient algorithm tailored for such matrices. If set to `False`, it uses a general algorithm. The default value is `False`.

mamtawardhani · 2024-04-30T06:22:48Z

content/numpy/concepts/built-in-functions/terms/svd/svd.md

+- `hermitian': This parameter indicates whether the input matrix `a` is Hermitian, meaning it is equal to its conjugate transpose. When `hermitian` is set to `True`, the function assumes that a is Hermitian and uses a more efficient algorithm tailored for such matrices. If set to `False`, it uses a general algorithm. The default value is `False`.
+
+## Example
+The following example demonstrates various scenarios of Singular Value Decomposition (SVD) and uses `.svd()` using NumPy:


Suggested change

The following example demonstrates various scenarios of Singular Value Decomposition (SVD) and uses `.svd()` using NumPy:

The following example demonstrates various scenarios of Singular Value Decomposition (SVD) and uses `.svd()` using `NumPy`:

mamtawardhani · 2024-04-30T08:01:45Z

content/numpy/concepts/built-in-functions/terms/svd/svd.md

+import numpy as np
+
+# Example 1: Full SVD, 2D Case
+A = np.random.randn(5, 3)
+U, S, Vt = np.linalg.svd(A, full_matrices=True)
+U.shape, S.shape, Vt.shape
+((5, 5), (3,), (3, 3))
+np.allclose(A, np.dot(U[:, :3] * S, Vt))
+True
+Sigma = np.zeros((5, 3))
+Sigma[:3, :3] = np.diag(S)
+np.allclose(A, np.dot(U, np.dot(Sigma, Vt)))
+True
+
+# Example 2: Reduced SVD, 2D Case
+B = np.random.randn(4, 6)
+U, S, Vt = np.linalg.svd(B, full_matrices=False)
+U.shape, S.shape, Vt.shape
+((4, 4), (4,), (4, 6))
+np.allclose(B, np.dot(U * S, Vt))
+True
+Sigma = np.diag(S)
+np.allclose(B, np.dot(U, np.dot(Sigma, Vt)))
+True
+
+# Example 3: Full SVD, 3D Case
+C = np.random.randn(3, 4, 5)
+U, S, Vt = np.linalg.svd(C, full_matrices=True)
+U.shape, S.shape, Vt.shape
+((3, 3, 3), (3,), (3, 4, 5))
+np.allclose(C, np.matmul(U[..., :3] * S[..., None, :], Vt))
+True
+np.allclose(C, np.matmul(U, np.matmul(np.diag(S), Vt)))
+True
+
+# Example 4: Reduced SVD, 3D Case
+D = np.random.randn(2, 2, 3)
+U, S, Vt = np.linalg.svd(D, full_matrices=False)
+U.shape, S.shape, Vt.shape
+((2, 2, 2), (2,), (2, 2, 3))
+np.allclose(D, np.matmul(U * S[..., None, :], Vt))
+True
+np.allclose(D, np.matmul(U, np.matmul(np.diag(S), Vt)))
+True


Hey @doroodianMostafa, based on the entry you made, the .svd() computes the singular value decomposition and produces the U', Vh, and s` matrices, the example should be something similar to that. Please refer to the following links for reference:

https://www.geeksforgeeks.org/compute-the-factor-of-a-given-array-by-singular-value-decomposition-using-numpy/

https://python.quantecon.org/svd_intro.html

Please modify the example so that it fits your description.
Thanks!

Hi @mamtawardhani,

Thanks for the feedback! I took a look at the links and tried to create a similar, but simpler example. To keep things clear, I skipped the 3D matrix example and left the other input parameters at their defaults.

mamtawardhani

Hey @doroodianMostafa! Thank you for changing the example!

Just a few more suggestions are added (like leaving a line after every heading, and, adding the output block, etc); please review them and merge those suggestions at your earliest convenience.
Thank you!

mamtawardhani · 2024-05-02T08:11:14Z

content/numpy/concepts/built-in-functions/terms/svd/svd.md

@@ -0,0 +1,51 @@
+---
+Title: '.svd()'
+Description: 'The `.svd()` built-in function performs the Singular Value Decomposition (SVD) on a matrix, breaking it down into singular vectors and values.'


Suggested change

Description: 'The `.svd()` built-in function performs the Singular Value Decomposition (SVD) on a matrix, breaking it down into singular vectors and values.'

Description: 'Performs the Singular Value Decomposition (SVD) on a matrix, breaking it down into singular vectors and values.'

content/numpy/concepts/built-in-functions/terms/svd/svd.md

mamtawardhani

Good for the next review

doroodianMostafa · 2024-05-13T09:40:17Z

Hi @letsbuildanything, Thanks for taking responsibility for the second review.
Looking forward to hear your feedbacks.
Thank you.

new term entry on the built in function for Numpy named svd (Singular…

7798cd4

… Value Decomposition) under svd.md

Merge branch 'main' into svd-branch

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New term entry on the built in function for Numpy named 'svd' #4547

New term entry on the built in function for Numpy named 'svd' #4547

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doroodianMostafa commented May 13, 2024

	Description: 'Singular Value Decomposition'
	Description: 'The `.svd()` built-in function performs the Singular Value Decomposition (SVD) on a matrix, breaking it down into singular vectors and values.'

	- `hermitian': This parameter indicates whether the input matrix `a` is Hermitian, meaning it is equal to its conjugate transpose. When `hermitian` is set to `True`, the function assumes that a is Hermitian and uses a more efficient algorithm tailored for such matrices. If set to `False`, it uses a general algorithm. The default value is `False`.
	- `hermitian`: This parameter indicates whether the input matrix `a` is Hermitian, meaning it is equal to its conjugate transpose. When `hermitian` is set to `True`, the function assumes that a is Hermitian and uses a more efficient algorithm tailored for such matrices. If set to `False`, it uses a general algorithm. The default value is `False`.

	The following example demonstrates various scenarios of Singular Value Decomposition (SVD) and uses `.svd()` using NumPy:
	The following example demonstrates various scenarios of Singular Value Decomposition (SVD) and uses `.svd()` using `NumPy`:

	Description: 'The `.svd()` built-in function performs the Singular Value Decomposition (SVD) on a matrix, breaking it down into singular vectors and values.'
	Description: 'Performs the Singular Value Decomposition (SVD) on a matrix, breaking it down into singular vectors and values.'

New term entry on the built in function for Numpy named 'svd' #4547

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New term entry on the built in function for Numpy named 'svd' #4547

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doroodianMostafa commented Apr 19, 2024 • edited

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