NAME

       larmm - larmm: scale factor to avoid overflow, step in latrs

SYNOPSIS

   Functions
       double precision function dlarmm (anorm, bnorm, cnorm)
           DLARMM
       real function slarmm (anorm, bnorm, cnorm)
           SLARMM

Detailed Description

Function Documentation

   double precision function dlarmm (double precision anorm, double precision bnorm, double
       precision cnorm)
       DLARMM

       Purpose:

            DLARMM returns a factor s in (0, 1] such that the linear updates

               (s * C) - A * (s * B)  and  (s * C) - (s * A) * B

            cannot overflow, where A, B, and C are matrices of conforming
            dimensions.

            This is an auxiliary routine so there is no argument checking.

       Parameters
           ANORM

                     ANORM is DOUBLE PRECISION
                     The infinity norm of A. ANORM >= 0.
                     The number of rows of the matrix A.  M >= 0.

           BNORM

                     BNORM is DOUBLE PRECISION
                     The infinity norm of B. BNORM >= 0.

           CNORM

                     CNORM is DOUBLE PRECISION
                     The infinity norm of C. CNORM >= 0.

            References: C. C. Kjelgaard Mikkelsen and L. Karlsson, Blocked Algorithms for Robust
           Solution of Triangular Linear Systems. In: International Conference on Parallel
           Processing and Applied Mathematics, pages 68--78. Springer, 2017.

   real function slarmm (real anorm, real bnorm, real cnorm)
       SLARMM

       Purpose:

            SLARMM returns a factor s in (0, 1] such that the linear updates

               (s * C) - A * (s * B)  and  (s * C) - (s * A) * B

            cannot overflow, where A, B, and C are matrices of conforming
            dimensions.

            This is an auxiliary routine so there is no argument checking.

       Parameters
           ANORM

                     ANORM is REAL
                     The infinity norm of A. ANORM >= 0.
                     The number of rows of the matrix A.  M >= 0.

           BNORM

                     BNORM is REAL
                     The infinity norm of B. BNORM >= 0.

           CNORM

                     CNORM is REAL
                     The infinity norm of C. CNORM >= 0.

            References: C. C. Kjelgaard Mikkelsen and L. Karlsson, Blocked Algorithms for Robust
           Solution of Triangular Linear Systems. In: International Conference on Parallel
           Processing and Applied Mathematics, pages 68--78. Springer, 2017.

Author

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