wgblas
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    Function ssyr2k

    • Performs the symmetric rank-2k update $$C \leftarrow \mathrm{uplo}(\alpha \mathrm{op}(A) \mathrm{op}(B)^{T} + \alpha \mathrm{op}(B) \mathrm{op}(A)^{T} + \beta C)$$

      only the triangle of C named by uplo is read or written ('lower': col <= row, 'upper': col >= row). C is always n×n.

      • trans='no-transpose': op(A) = A, op(B) = B (both n×k)
      • trans='transpose': op(A) = A^T, op(B) = B^T (A, B stored k×n)

      No dedicated kernel — two passes of sgemmtr's kernel (sgemmtr_small.wgsl/sgemmtr_large.wgsl) on one command encoder, the second accumulating with beta=1 so C never leaves the GPU between them.

      import { init, cleanup } from "wgblas";
      import { ssyr2k } from "wgblas/ssyr2k";

      const device = await init();

      // C = uplo(alpha*A*B^T + alpha*B*A^T + beta*C). With B = A the two terms are
      // equal, so the result is exactly twice ssyrk's on the same A.
      const n = 3,
        k = 2;
      const A = new Float32Array([1, 0, 0, 1, 1, 1]);
      const B = new Float32Array([1, 0, 0, 1, 1, 1]);
      const C = new Float32Array(n * n);

      console.log("A = B =");
      console.table([A.slice(0, 2), A.slice(2, 4), A.slice(4, 6)]);

      const { C: result } = await ssyr2k(
        device,
        "upper",
        "no-transpose",
        n,
        k,
        1,
        A,
        k,
        B,
        k,
        0,
        C,
        n,
      );
      console.log("C = upper(A*B^T + B*A^T) =");
      console.table([result.slice(0, 3), result.slice(3, 6), result.slice(6, 9)]); // 2x ssyrk: [[2,0,2],[0,2,2],[0,0,4]]

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

      Browser (standalone HTML):

      <!doctype html>
      <html lang="en">
        <head>
          <meta charset="UTF-8" />
          <title>ssyr2k — 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, ssyr2k, cleanup } = window.wgblas;

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

              // With B = A the two rank-k terms are equal, so the result is exactly
              // twice ssyrk's on the same A.
              const n = 3, k = 2;
              const A = new Float32Array([1, 0,
                                          0, 1,
                                          1, 1]);
              const B = new Float32Array([1, 0,
                                          0, 1,
                                          1, 1]);
              const C = new Float32Array(n * n);

              const { C: result } = await ssyr2k(device, "upper", "no-transpose", n, k, 1, A, k, B, k, 0, C, n);

              document.getElementById("out").textContent = [
                "A = B =",
                "  [" + A.slice(0, 2).join(", ") + "]",
                "  [" + A.slice(2, 4).join(", ") + "]",
                "  [" + A.slice(4, 6).join(", ") + "]",
                "C = upper(A*B^T + B*A^T) =",
                "  [" + result.slice(0, 3).join(", ") + "]",
                "  [" + result.slice(3, 6).join(", ") + "]",
                "  [" + result.slice(6, 9).join(", ") + "]",
              ].join("\n");

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

      Parameters

      • device: GPUDevice

        GPUDevice from init()

      • uplo: "lower" | "upper"

        'lower' to update only col <= row, 'upper' for col >= row

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

        'no-transpose' for AB^T + BA^T, 'transpose' for A^TB + B^TA

      • n: number

        order of C (C is n×n); rows of op(A) and op(B)

      • k: number

        columns of op(A) and op(B) — the shared/contracted dimension

      • alpha: number

        scalar multiplier for both rank-k terms

      • A: Float32Array

        Float32Array, row-major or column-major (see layout)

      • lda: number

        leading dimension of A as stored

      • B: Float32Array

        Float32Array, row-major or column-major (see layout)

      • ldb: number

        leading dimension of B as stored

      • beta: number

        scalar multiplier for C

      • C: Float32Array

        Float32Array input/output matrix, row-major or column-major

      • ldc: number

        leading dimension of C as stored

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

        storage layout shared by A/B/C when they're Float32Array (default: 'row-major') — same handling as sgemmtr; column-major C flips uplo internally so it still names the triangle you asked for

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

      updated C as a Float32Array (only the requested triangle changed)

      Source code: ssyr2k.mjs (L20)

    • Performs the symmetric rank-2k update $$C \leftarrow \mathrm{uplo}(\alpha \mathrm{op}(A) \mathrm{op}(B)^{T} + \alpha \mathrm{op}(B) \mathrm{op}(A)^{T} + \beta C)$$

      A, B, and C are all kept GPU-resident. Each matrix's own layout (set at GpuMatrix.from time) determines the operation — there is no separate layout argument here. A and B must be GpuMatrix whenever C is, and vice versa — mixing a GpuMatrix with a plain Float32Array is not supported.

      import { init, cleanup } from "wgblas";
      import { ssyr2k } from "wgblas/ssyr2k";
      import { GpuMatrix } from "wgblas/classes/GpuMatrix";

      const device = await init();

      // With B = A the two rank-k terms are equal, so the result is exactly twice
      // ssyrk's on the same A.
      const n = 3,
        k = 2;
      const A = new Float32Array([1, 0, 0, 1, 1, 1]);

      const AGpu = GpuMatrix.from(A, n, k, k, "row-major");
      const BGpu = GpuMatrix.from(A.slice(), n, k, k, "row-major");
      const CGpu = GpuMatrix.from(new Float32Array(n * n), n, n, n, "row-major");

      console.log("A = B =");
      console.table([A.slice(0, 2), A.slice(2, 4), A.slice(4, 6)]);

      await ssyr2k(
        device,
        "upper",
        "no-transpose",
        n,
        k,
        1,
        AGpu,
        AGpu.lda,
        BGpu,
        BGpu.lda,
        0,
        CGpu,
        CGpu.lda,
      );

      const result = await CGpu.read();
      console.log("C = upper(A*B^T + B*A^T) =");
      console.table([result.slice(0, 3), result.slice(3, 6), result.slice(6, 9)]); // 2x ssyrk: [[2,0,2],[0,2,2],[0,0,4]]

      AGpu.destroy();
      BGpu.destroy();
      CGpu.destroy();
      if (typeof process !== "undefined") cleanup();

      Parameters

      • device: GPUDevice

        GPUDevice from init()

      • uplo: "lower" | "upper"

        'lower' to update only col <= row, 'upper' for col >= row

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

        'no-transpose' for AB^T + BA^T, 'transpose' for A^TB + B^TA

      • n: number

        order of C (C is n×n); rows of op(A) and op(B)

      • k: number

        columns of op(A) and op(B) — the shared/contracted dimension

      • alpha: number

        scalar multiplier for both rank-k terms

      • A: GpuMatrix

        GpuMatrix

      • lda: number

        leading dimension of A (must equal A.lda)

      • B: GpuMatrix

        GpuMatrix

      • ldb: number

        leading dimension of B (must equal B.lda)

      • beta: number

        scalar multiplier for C

      • C: GpuMatrix

        GpuMatrix (mutated in place; only the requested triangle changes)

      • ldc: number

        leading dimension of C (must equal C.lda)

      Returns Promise<{ gpuTimeMs?: number }>

      no C — it stays GPU-resident; call C.read() yourself for a CPU readback (see the example)

      Source code: ssyr2k.mjs (L20)

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