wgblas
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    Function strsv

    • Solves the triangular system op(A) * x = b for x, in place (x holds b on input, the solution on output).

      A is an n×n triangular matrix stored in row-major order. Only the triangle specified by uplo is referenced; the other triangle is not accessed.

      import { init, cleanup } from "wgblas";
      import { strsv } from "wgblas/strsv";
      import { randomFloat32Array, randomTriangularFloat32Array } from "wgblas/random";

      const device = await init();

      // 4×4 triangular matrix, lower triangular storage; lda = n
      const n = 4, lda = n;
      const A = randomTriangularFloat32Array(n, lda, "lower", -10, 10);
      const b = randomFloat32Array(n, -10, 10);

      console.log("A (lower triangle):", A);
      console.log("b:", b);
      const { x } = await strsv(device, "lower", "no-transpose", "non-unit", n, A, lda, Float32Array.from(b), 1, "row-major");
      console.log("x (solves A*x = b):", x);
      if (typeof process !== "undefined") cleanup();

      Browser (standalone HTML):

      <!doctype html>
      <html lang="en">
        <head>
          <meta charset="UTF-8" />
          <title>strsv — wgblas browser example</title>
          <script src="https://unpkg.com/wgblas/dist/wgblas.browser.js"></script>
        </head>
        <body>
          <pre id="out">Running…</pre>
          <script>
            const { init, strsv, randomFloat32Array, randomTriangularFloat32Array, cleanup } = window.wgblas;

            (async () => {
              const device = await init();

              const n = 4, lda = n;
              const A = randomTriangularFloat32Array(n, lda, "lower", -10, 10);
              const b = randomFloat32Array(n, -10, 10);

              const { x } = await strsv(device, "lower", "no-transpose", "non-unit", n, A, lda, Float32Array.from(b), 1, "row-major");

              document.getElementById("out").textContent =
                "A (lower triangle): " + Array.from(A).map(v => v.toFixed(4)).join(", ") +
                "\nb: " + Array.from(b).map(v => v.toFixed(4)).join(", ") +
                "\nx (solves A*x = b): " + Array.from(x).map(v => v.toFixed(4)).join(", ");

              cleanup();
            })();
          </script>
        </body>
      </html>

      Parameters

      • device: GPUDevice

        GPUDevice from init()

      • uplo: "lower" | "upper"

        'lower' to use the lower triangle, 'upper' to use the upper triangle

      • trans: "no-transpose" | "transpose"

        'no-transpose' to solve Ax=b, 'transpose' to solve A^Tx=b

      • diag: "unit" | "non-unit"

        'unit' to treat the diagonal as all-ones (A's diagonal is not read), 'non-unit' to read it

      • n: number

        order of the matrix A (number of rows and columns)

      • A: Float32Array

        Float32Array, row-major or column-major (see layout), at least (n-1)*lda+n elements

      • lda: number

        leading dimension of A (>= n either way — A is square)

      • x: Float32Array

        Float32Array holding b on input, the solution on output; length at least (n-1)*incx+1

      • incx: number

        stride for x (must be a positive integer)

      • Optionallayout: "column-major" | "row-major"

        storage layout of A (default: 'row-major'); column-major flips both the stored triangle and the effective trans (the system being solved stays what you asked for either way)

      Returns Promise<{ gpuTimeMs?: number; x: Float32Array }>

      Source code: strsv.mjs (L15)

    • Solves the triangular system op(A) * x = b for x, in place.

      A is kept GPU-resident; x is a CPU Float32Array. A's own layout (set at GpuMatrix.from time) determines the operation — there is no separate layout argument here.

      Parameters

      • device: GPUDevice

        GPUDevice from init()

      • uplo: "lower" | "upper"

        'lower' to use the lower triangle, 'upper' to use the upper triangle

      • trans: "no-transpose" | "transpose"

        'no-transpose' to solve Ax=b, 'transpose' to solve A^Tx=b

      • diag: "unit" | "non-unit"

        'unit' to treat the diagonal as all-ones (A's diagonal is not read), 'non-unit' to read it

      • n: number

        order of the matrix A

      • A: GpuMatrix

        GpuMatrix, GPU-resident

      • lda: number

        leading dimension of A (must equal A.lda)

      • x: Float32Array

        Float32Array holding b on input, the solution on output

      • incx: number

        stride for x (must be a positive integer)

      Returns Promise<{ gpuTimeMs?: number; x: Float32Array }>

      Source code: strsv.mjs (L15)

    • Solves the triangular system op(A) * x = b for x, in place.

      x is kept resident on the GPU (mutated in place). A must be a GpuMatrix; its own layout (set at GpuMatrix.from time) determines the operation — there is no separate layout argument here.

      import { init, cleanup } from "wgblas";
      import { strsv } from "wgblas/strsv";
      import { GpuVector } from "wgblas/classes/GpuVector";
      import { GpuMatrix } from "wgblas/classes/GpuMatrix";
      import { randomFloat32Array, randomTriangularFloat32Array } from "wgblas/random";

      const device = await init();

      const n = 4;
      const A = randomTriangularFloat32Array(n, n, "lower", -10, 10);
      const b = randomFloat32Array(n, -10, 10);

      const AGpu = GpuMatrix.from(A, n, n, n, "row-major");
      const xGpu = GpuVector.from(Float32Array.from(b));

      console.log("A (lower triangle):", A);
      console.log("b:", b);

      // x is mutated in place on the GPU: holds b on input, the solution on output
      await strsv(device, "lower", "no-transpose", "non-unit", n, AGpu, AGpu.lda, xGpu, 1);

      // single readback
      const result = await xGpu.read();
      console.log("x (solves A*x = b):", result);

      AGpu.destroy();
      xGpu.destroy();

      if (typeof process !== "undefined") cleanup();

      Parameters

      • device: GPUDevice

        GPUDevice from init()

      • uplo: "lower" | "upper"

        'lower' to use the lower triangle, 'upper' to use the upper triangle

      • trans: "no-transpose" | "transpose"

        'no-transpose' to solve Ax=b, 'transpose' to solve A^Tx=b

      • diag: "unit" | "non-unit"

        'unit' to treat the diagonal as all-ones (A's diagonal is not read), 'non-unit' to read it

      • n: number

        order of the matrix A

      • A: GpuMatrix

        GpuMatrix, GPU-resident

      • lda: number

        leading dimension of A (must equal A.lda)

      • x: GpuVector

        GpuVector holding b on input, the solution on output (mutated in place)

      • incx: number

        stride for x (must be a positive integer)

      Returns Promise<{ gpuTimeMs?: number }>

      Source code: strsv.mjs (L15)

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