psblas3/test/computational_routines

Computational Routines Test

This is a directory containing all the tests done in order to analyze the correctness of the computational routines present in PSBLAS.

Test Environment

These tests are developed using a linux environment, in particular Rocky Linux 9.5 (Blue Onyx).

The compiler used is:

• gnu 12.2.1

The necessary dependnces are:

• mpich 4.2.2
• PSBLAS 3.9
• CUDA 12.5

Routines

In this test suite were considered only computational routines implemented by PSBLAS, according to the version 3.9 of the documentation. In the following table are reported all the kernels, their implementation and wheter or not they were tested yet.

Kernel	PSBLAS Subroutine	Description	Test
General Dense Matrix Sum	psb_geaxpby	This subroutine is an interface to the computational kernel for dense matrix sum: $Y \leftarrow \alpha X + \beta Y $	Work in progress 🛠️
Dot product	psb_gedot	This function computes dot product between two vectors x and y. dot \leftarrow x^T y If x and y are real vectors it computes dot-product as: dot \leftarrow x^H y	No ❌
Generalized Dot Product	psb_gedots	This subroutine computes a series of dot products among the columns of two dense matrices x and y: res(i) \leftarrow x(:,i)^T y(:,i) If the matrices are complex, then the usual convention applies, i.e. the conjugate transpose of x is used. If x and y are of rank one, then res is a scalar, else it is a rank one array.	No ❌
Infinity-Norm of Vector	psb_normi/psb_geamax	This function computes the infinity-norm of a vector x. If x is a real vector it computes infinity norm as: amax \leftarrow max \mid x_i \mid else if x is a complex vector then it computes the infinity-norm as: amax \leftarrow max(\mid re(x_i) \mid + \mid im(x_i) \mid)	No ❌
Generalized Infinity Norm	psb_geamaxs	This subroutine computes a series of infinity norms on the columns of a dense matrix x: res(i) \leftarrow max_k \mid x(k,i) \mid	No ❌
1-Norm of Vector	psb_norm1 / psb_geasums	This function computes the 1-norm of a vector x. If x is a real vector it computes 1-norm as: asum \leftarrow \mid \mid x_i \mid \mid else if x is a complex vector then it computes 1-norm as: asum \leftarrow \mid \mid re(x) \mid \mid_1 + \mid \mid im(x) \mid \mid_1	No ❌
Generalized 1-Norm of Vector	psb_geasums	This subroutine computes a series of 1-norms on the columns of a dense matrix x: res(i) \leftarrow max_k \mid x(k,i) \mid This function computes the 1-norm of a vector x. If x is a real vector it computes 1-norm as: res(i) \leftarrow \mid \mid x_i \mid \mid else if x is a complex vector then it computes 1-norm as: res(i) \leftarrow \mid \mid re(x) \mid \mid_\ + \mid \mid im(x) \mid \mid_1	No ❌
2-Norm of Vector	psb_norm2 / psb_genrm2	This function computes the 2-norm of a vector x. If x is a real vector it computes 2-norm as: nrm2 \leftarrow \sqrt{x^T x} else if x is a complex vector then it computes 2-norm as: nrm2 \leftarrow \sqrt{x^H x}	No ❌
Generalized 2-Norm of Vector	psb_genrm2s / psb_spnrm1	This subroutine computes a series of 2-norms on the columns of a dense matrix x: res(i) \leftarrow \mid \mid x(:,i) \mid \mid_2	No ❌
1-Norm of Sparse Matrix	psb_norm1	This function computes the 1-norm of a matrix A: nrm1 \leftarrow \mid \mid A \mid \mid_1 where A represents the global matrix A	No ❌
Infinity Norm of Sparse Matrix	psb_normi / psb_spnrmi	This function computes the infinity-norm of a matrix A: nrmi \leftarrow \mid \mid A \mid \mid_{\infty} where: A represents the global matrix A	No ❌
Sparse Matrix by Dense Matrix Product	psb_spmm	This subroutine computes the Sparse Matrix by Dense Matrix Product: y \leftarrow \alpha A x + \beta y$ y \leftarrow \alpha A^T x + \beta y y \leftarrow \alpha A^H x + \beta y$ where: x is the global dense matrix x_{:,:} y is the global dense matrix y_{:,:} A is the global sparse matrix A	Work in progress ✅
Triangular System Solve	psb_spsm	This subroutine computes the Triangular System Solve: y \leftarrow \alpha T^{-1} x + \beta y y \leftarrow \alpha D^{-1} x + \beta y y \leftarrow \alpha T^{-1} D x + \beta y y \leftarrow \alpha T^{-T} x + \beta y y \leftarrow \alpha D T^{-T} x + \beta y y \leftarrow \alpha T^{-T} D x + \beta y y \leftarrow \alpha T^{-H} x + \beta y y \leftarrow \alpha D T^{-H} x + \beta y y \leftarrow \alpha T^{-H} D x + \beta y where: x is the global dense matrix x_{:,:} y is the global dense matrix y_{:,:} T is the global sparse block triangular submatrix T D is the scaling diagonal matrix	No ❌
Entrywise Product	psb_gemlt	This function computes the entrywise product between two vectors x and y dot \leftarrow x(i)y(i)	No ❌
Entrywise Division	psb_gediv	This function computes the entrywise division between two vectors x and y div \leftarrow \frac{x(i)}{y(i)}	No ❌
Entrywise Inversion	psb_geinv	This function computes the entrywise inverse of a vector x and puts it into y inv \leftarrow \frac{1}{x(i)}	No ❌