Solvers for triangular matrix

[Stan Tomov]

This is implemented in CUBLAS. In MAGMA we use TRSM to solve triangular systems. As an example, you can see the code in src/sgetrs_gpu.cpp:

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...
if (notran) {
        inc = 1;

        /* Solve A * X = B. */
        cublasGetMatrix( n, nrhs, sizeof(float), dB, lddb, work, n);
        lapackf77_slaswp(&nrhs, work, &n, &i1, &i2, ipiv, &inc);
        cublasSetMatrix( n, nrhs, sizeof(float), work, n, dB, lddb);

        if ( nrhs == 1) {
            cublasStrsv(MagmaLower, MagmaNoTrans, MagmaUnit,    n, dA, ldda, dB, 1 );
            cublasStrsv(MagmaUpper, MagmaNoTrans, MagmaNonUnit, n, dA, ldda, dB, 1 );
        } else {
            cublasStrsm(MagmaLeft, MagmaLower, MagmaNoTrans, MagmaUnit,    n, nrhs, c_one, dA, ldda, dB, lddb );
            cublasStrsm(MagmaLeft, MagmaUpper, MagmaNoTrans, MagmaNonUnit, n, nrhs, c_one, dA, ldda, dB, lddb );
        }
    } else {
        inc = -1;

        /* Solve A' * X = B. */
        if ( nrhs == 1) {
            cublasStrsv(MagmaUpper, trans, MagmaNonUnit, n, dA, ldda, dB, 1 );
            cublasStrsv(MagmaLower, trans, MagmaUnit,    n, dA, ldda, dB, 1 );
        } else {
            cublasStrsm(MagmaLeft, MagmaUpper, trans, MagmaNonUnit, n, nrhs, c_one, dA, ldda, dB, lddb );
            cublasStrsm(MagmaLeft, MagmaLower, trans, MagmaUnit,    n, nrhs, c_one, dA, ldda, dB, lddb );
        }

        cublasGetMatrix( n, nrhs, sizeof(float), dB, lddb, work, n );
        lapackf77_slaswp(&nrhs, work, &n, &i1, &i2, ipiv, &inc);
        cublasSetMatrix( n, nrhs, sizeof(float), work, n, dB, lddb);
    }


Stan

[Stan Tomov]

That's good to hear!
In general, all magma routines are coded in terms of cublas, but if for some routines magmablas is faster, we redefine it for the particular routine at the beginning with a define pragma statement, e.g., for the file mentioned above cublas is faster for one right-hand side and we use it, but for multiple we have redefined the cublas calls to call magmablas with a

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  #define cublasStrsm magmablas_strsm


at the beginning of the file.
Stan