feat: Add generalized lagtm routine supporting arbitrary values for alpha and beta #1068

Mahmood-Sinan · 2025-12-09T05:14:50Z

This PR adds a generalized lagtm routine that supports arbitrary values of alpha and beta for the operation:

y = alpha * A * x + beta * y

where A is a tridiagonal matrix. The existing LAPACK lagtm restricts alpha and beta to the set { -1, 0, 1 }, which limits its applicability in several higher-level routines.
The routine can be called as follows:

glagtm(trans, n, nrhs, alpha, dl, d, du, x, ldx, beta, b, ldb)

which is similar to the LAPACK version:

lagtm( trans, n, nrhs, alpha, dl, d, du, x, ldx, beta,b, ldb )

except that alpha and beta can be arbitrary(including complex values).

This new subroutine is placed inside
src/lapack_extended/stdlib_extended_lapack_base.fypp (interface) and
src/lapack_extended/stdlib_extended_lapack.fypp (implementation).

codecov · 2025-12-09T05:49:14Z

Codecov Report

❌ Patch coverage is 0% with 17 lines in your changes missing coverage. Please review.
✅ Project coverage is 68.57%. Comparing base (34723c7) to head (21a5435).

Files with missing lines	Patch %	Lines
...ecialmatrices/example_specialmatrices_cdp_spmv.f90	0.00%	17 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##           master    #1068      +/-   ##
==========================================
- Coverage   68.69%   68.57%   -0.13%     
==========================================
  Files         392      393       +1     
  Lines       12693    12710      +17     
  Branches     1377     1377              
==========================================
- Hits         8720     8716       -4     
- Misses       3973     3994      +21

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jalvesz · 2025-12-10T17:33:52Z

Hi @Mahmood-Sinan, this looks pretty neat! the only thing I would suggest would be to keep the files and folders naming somewhat coherent with respect to the name lapack_extended.

Copilot

Pull request overview

This PR adds a generalized glagtm routine that extends LAPACK's lagtm function to support arbitrary scalar values for alpha and beta (not just -1, 0, 1), including complex values. This enables the operation y = alpha * A * x + beta * y for tridiagonal matrices with greater flexibility.

Key Changes:

Implemented new glagtm subroutine supporting arbitrary alpha/beta values for real and complex types
Updated spmv interface to accept complex alpha/beta parameters (previously restricted to real)
Added fallback logic to use standard LAPACK lagtm when alpha/beta are special values (-1, 0, 1) for performance

Reviewed changes

Copilot reviewed 9 out of 9 changed files in this pull request and generated 4 comments.

Show a summary per file

File	Description
src/lapack_extended/stdlib_extended_lapack_base.fypp	Interface definition for new `glagtm` subroutine
src/lapack_extended/stdlib_extended_lapack.fypp	Implementation of `glagtm` routine handling N/T/C transpose operations
src/lapack_extended/CMakeLists.txt	Build configuration for new lapack_extended module
src/CMakeLists.txt	Integration of lapack_extended module into main build
src/stdlib_specialmatrices.fypp	Updated interface signatures to accept complex alpha/beta
src/stdlib_specialmatrices_tridiagonal.fypp	Logic to dispatch between `lagtm` and `glagtm` based on parameter values
test/linalg/test_linalg_specialmatrices.fypp	Added tests for random alpha/beta values across N/T/H operations
example/specialmatrices/example_specialmatrices_cdp_spmv.f90	Example demonstrating complex alpha/beta usage
example/specialmatrices/CMakeLists.txt	Build configuration for new example

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Copilot · 2025-12-10T17:39:08Z

src/stdlib_specialmatrices_tridiagonal.fypp


+        is_alpha_special = (alpha_ ==  1.0_${k1}$  .or. alpha_ ==  0.0_${k1}$  .or. alpha_ == -1.0_${k1}$)
+        is_beta_special  = (beta_  ==  1.0_${k1}$  .or. beta_  ==  0.0_${k1}$  .or. beta_  == -1.0_${k1}$)


For complex types, comparing complex values directly against real literals (e.g., alpha_ == 1.0_${k1}$) will not work correctly. Complex equality checks require both real and imaginary parts to match, so a complex value like (1.0, 0.1) would fail this check even though it should. Consider using abs(alpha_ - 1.0_${k1}$) < epsilon or checking real(alpha_) == 1.0_${k1}$ .and. aimag(alpha_) == 0.0_${k1}$ for each special value.

Suggested change

is_alpha_special = (alpha_ == 1.0_${k1}$ .or. alpha_ == 0.0_${k1}$ .or. alpha_ == -1.0_${k1}$)

is_beta_special = (beta_ == 1.0_${k1}$ .or. beta_ == 0.0_${k1}$ .or. beta_ == -1.0_${k1}$)

#:if t1.startswith('complex')

is_alpha_special = ((real(alpha_) == 1.0_${k1}$ .and. aimag(alpha_) == 0.0_${k1}$) .or. &

(real(alpha_) == 0.0_${k1}$ .and. aimag(alpha_) == 0.0_${k1}$) .or. &

(real(alpha_) == -1.0_${k1}$ .and. aimag(alpha_) == 0.0_${k1}$))

is_beta_special = ((real(beta_) == 1.0_${k1}$ .and. aimag(beta_) == 0.0_${k1}$) .or. &

(real(beta_) == 0.0_${k1}$ .and. aimag(beta_) == 0.0_${k1}$) .or. &

(real(beta_) == -1.0_${k1}$ .and. aimag(beta_) == 0.0_${k1}$))

#:else

is_alpha_special = (alpha_ == 1.0_${k1}$ .or. alpha_ == 0.0_${k1}$ .or. alpha_ == -1.0_${k1}$)

is_beta_special = (beta_ == 1.0_${k1}$ .or. beta_ == 0.0_${k1}$ .or. beta_ == -1.0_${k1}$)

#:endif

An easier solution is to use stdlib_constants where constants zero and one have been added for all kinds. So simply replacing the real values with the respective constants would do the job.

An easier solution is to use stdlib_constants where constants zero and one have been added for all kinds. So simply replacing the real values with the respective constants would do the job.

Another solution would be to wrap those two lines and the declaration of is_alpha_special and is_beta_special in an #:if t1.startswith('real') block. Then we can avoid the checks for is_alpha_special and is_beta_special in case of complex types. This works because for complex types we always call glagtm regardless of the values of alpha and beta.
Let me know which approach you’d prefer.

Sounds good to me!

Copilot · 2025-12-10T17:39:08Z

src/lapack_extended/stdlib_extended_lapack.fypp

+                    b(1_${ik}$, j) = b(1_${ik}$, j) + alpha * temp
+                    do i = 2, n - 1
+                        temp = dl(i - 1) * x(i - 1, j) + d(i) * x(i, j) + du(i) * x(i + 1, j)
+                        b(i, j) = b (i, j) + alpha * temp


Inconsistent spacing: extra space between 'b' and '(i, j)' compared to other lines.

src/lapack_extended/stdlib_extended_lapack.fypp

Co-authored-by: Copilot <175728472+Copilot@users.noreply.github.com>

Mahmood-Sinan · 2025-12-11T05:59:56Z

Hi @Mahmood-Sinan, this looks pretty neat! the only thing I would suggest would be to keep the files and folders naming somewhat coherent with respect to the name lapack_extended.

Sure, I will do that in the next commit.

Mahmood-Sinan · 2025-12-11T06:19:17Z

I also noticed that the documentation in
doc/specs/stdlib_specialmatrices.md contains the following warning:

@warning
Due to limitations of the underlying `lapack` driver, currently `alpha` and `beta` can only take one of the values [-1, 0, 1] for `tridiagonal` and `symtridiagonal` matrices. See `lagtm` for more details.
@endwarning

Since the specialmatrices routines now call glagtm when alpha or beta take arbitrary values, this warning is no longer entirely accurate. Should I update this as well?

…ocs, updated alpha and beta checks

Mahmood-Sinan · 2025-12-11T08:32:13Z

I’ve applied the changes. Please let me know if anything else is needed.

Mahmood-Sinan added 4 commits December 8, 2025 22:17

extended lagtm implemented, but only for real alpha and beta values

27906b3

alpha and beta now supports complex values also

d2d9aef

modularized extended lapack, but cmakefile has to be changed

c6b1a33

changed cmakefiles.txt

d18b50c

Mahmood-Sinan force-pushed the generalized_lagtm branch from 07228b0 to d18b50c Compare December 9, 2025 14:19

added tests for random values of alpha and beta

d50fd87

jalvesz requested review from Copilot, loiseaujc and perazz December 10, 2025 17:33

Copilot started reviewing on behalf of jalvesz December 10, 2025 17:34 View session

Copilot AI reviewed Dec 10, 2025

View reviewed changes

jalvesz and others added 2 commits December 10, 2025 18:47

Update src/lapack_extended/stdlib_extended_lapack.fypp

608f8ad

Co-authored-by: Copilot <175728472+Copilot@users.noreply.github.com>

Update src/lapack_extended/stdlib_extended_lapack.fypp

a27ebf8

Co-authored-by: Copilot <175728472+Copilot@users.noreply.github.com>

Mahmood-Sinan added 2 commits December 11, 2025 13:50

changed file names from extended_lapack to lapack_extended, updated d…

3428d45

…ocs, updated alpha and beta checks

updated the docs

21a5435


		is_alpha_special = (alpha_ == 1.0_${k1}$ .or. alpha_ == 0.0_${k1}$ .or. alpha_ == -1.0_${k1}$)
		is_beta_special = (beta_ == 1.0_${k1}$ .or. beta_ == 0.0_${k1}$ .or. beta_ == -1.0_${k1}$)

-        is_alpha_special = (alpha_ ==  1.0_${k1}$  .or. alpha_ ==  0.0_${k1}$  .or. alpha_ == -1.0_${k1}$)
-        is_beta_special  = (beta_  ==  1.0_${k1}$  .or. beta_  ==  0.0_${k1}$  .or. beta_  == -1.0_${k1}$)
+        #:if t1.startswith('complex')
+        is_alpha_special = ((real(alpha_) ==  1.0_${k1}$ .and. aimag(alpha_) == 0.0_${k1}$) .or. &
+                            (real(alpha_) ==  0.0_${k1}$ .and. aimag(alpha_) == 0.0_${k1}$) .or. &
+                            (real(alpha_) == -1.0_${k1}$ .and. aimag(alpha_) == 0.0_${k1}$))
+        is_beta_special  = ((real(beta_)  ==  1.0_${k1}$ .and. aimag(beta_) == 0.0_${k1}$) .or. &
+                            (real(beta_)  ==  0.0_${k1}$ .and. aimag(beta_) == 0.0_${k1}$) .or. &
+                            (real(beta_)  == -1.0_${k1}$ .and. aimag(beta_) == 0.0_${k1}$))
+        #:else
+        is_alpha_special = (alpha_ ==  1.0_${k1}$  .or. alpha_ ==  0.0_${k1}$  .or. alpha_ == -1.0_${k1}$)
+        is_beta_special  = (beta_  ==  1.0_${k1}$  .or. beta_  ==  0.0_${k1}$  .or. beta_  == -1.0_${k1}$)
+        #:endif

feat: Add generalized lagtm routine supporting arbitrary values for alpha and beta #1068

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