NAME

       la_gerpvgrw - la_gerpvgrw: reciprocal pivot growth

SYNOPSIS

   Functions
       real function cla_gerpvgrw (n, ncols, a, lda, af, ldaf)
           CLA_GERPVGRW multiplies a square real matrix by a complex matrix.
       double precision function dla_gerpvgrw (n, ncols, a, lda, af, ldaf)
           DLA_GERPVGRW
       real function sla_gerpvgrw (n, ncols, a, lda, af, ldaf)
           SLA_GERPVGRW
       double precision function zla_gerpvgrw (n, ncols, a, lda, af, ldaf)
           ZLA_GERPVGRW multiplies a square real matrix by a complex matrix.

Detailed Description

Function Documentation

   real function cla_gerpvgrw (integer n, integer ncols, complex, dimension( lda, * ) a, integer lda, complex,
       dimension( ldaf, * ) af, integer ldaf)
       CLA_GERPVGRW multiplies a square real matrix by a complex matrix.

       Purpose:

            CLA_GERPVGRW computes the reciprocal pivot growth factor
            norm(A)/norm(U). The 'max absolute element' norm is used. If this is
            much less than 1, the stability of the LU factorization of the
            (equilibrated) matrix A could be poor. This also means that the
            solution X, estimated condition numbers, and error bounds could be
            unreliable.

       Parameters
           N

                     N is INTEGER
                The number of linear equations, i.e., the order of the
                matrix A.  N >= 0.

           NCOLS

                     NCOLS is INTEGER
                The number of columns of the matrix A. NCOLS >= 0.

           A

                     A is COMPLEX array, dimension (LDA,N)
                On entry, the N-by-N matrix A.

           LDA

                     LDA is INTEGER
                The leading dimension of the array A.  LDA >= max(1,N).

           AF

                     AF is COMPLEX array, dimension (LDAF,N)
                The factors L and U from the factorization
                A = P*L*U as computed by CGETRF.

           LDAF

                     LDAF is INTEGER
                The leading dimension of the array AF.  LDAF >= max(1,N).

       Author
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

   double precision function dla_gerpvgrw (integer n, integer ncols, double precision, dimension( lda, * ) a,
       integer lda, double precision, dimension( ldaf, * ) af, integer ldaf)
       DLA_GERPVGRW

       Purpose:

            DLA_GERPVGRW computes the reciprocal pivot growth factor
            norm(A)/norm(U). The 'max absolute element' norm is used. If this is
            much less than 1, the stability of the LU factorization of the
            (equilibrated) matrix A could be poor. This also means that the
            solution X, estimated condition numbers, and error bounds could be
            unreliable.

       Parameters
           N

                     N is INTEGER
                The number of linear equations, i.e., the order of the
                matrix A.  N >= 0.

           NCOLS

                     NCOLS is INTEGER
                The number of columns of the matrix A. NCOLS >= 0.

           A

                     A is DOUBLE PRECISION array, dimension (LDA,N)
                On entry, the N-by-N matrix A.

           LDA

                     LDA is INTEGER
                The leading dimension of the array A.  LDA >= max(1,N).

           AF

                     AF is DOUBLE PRECISION array, dimension (LDAF,N)
                The factors L and U from the factorization
                A = P*L*U as computed by DGETRF.

           LDAF

                     LDAF is INTEGER
                The leading dimension of the array AF.  LDAF >= max(1,N).

       Author
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

   real function sla_gerpvgrw (integer n, integer ncols, real, dimension( lda, * ) a, integer lda, real,
       dimension( ldaf, * ) af, integer ldaf)
       SLA_GERPVGRW

       Purpose:

            SLA_GERPVGRW computes the reciprocal pivot growth factor
            norm(A)/norm(U). The 'max absolute element' norm is used. If this is
            much less than 1, the stability of the LU factorization of the
            (equilibrated) matrix A could be poor. This also means that the
            solution X, estimated condition numbers, and error bounds could be
            unreliable.

       Parameters
           N

                     N is INTEGER
                The number of linear equations, i.e., the order of the
                matrix A.  N >= 0.

           NCOLS

                     NCOLS is INTEGER
                The number of columns of the matrix A. NCOLS >= 0.

           A

                     A is REAL array, dimension (LDA,N)
                On entry, the N-by-N matrix A.

           LDA

                     LDA is INTEGER
                The leading dimension of the array A.  LDA >= max(1,N).

           AF

                     AF is REAL array, dimension (LDAF,N)
                The factors L and U from the factorization
                A = P*L*U as computed by SGETRF.

           LDAF

                     LDAF is INTEGER
                The leading dimension of the array AF.  LDAF >= max(1,N).

       Author
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

   double precision function zla_gerpvgrw (integer n, integer ncols, complex*16, dimension( lda, * ) a, integer
       lda, complex*16, dimension( ldaf, * ) af, integer ldaf)
       ZLA_GERPVGRW multiplies a square real matrix by a complex matrix.

       Purpose:

            ZLA_GERPVGRW computes the reciprocal pivot growth factor
            norm(A)/norm(U). The 'max absolute element' norm is used. If this is
            much less than 1, the stability of the LU factorization of the
            (equilibrated) matrix A could be poor. This also means that the
            solution X, estimated condition numbers, and error bounds could be
            unreliable.

       Parameters
           N

                     N is INTEGER
                The number of linear equations, i.e., the order of the
                matrix A.  N >= 0.

           NCOLS

                     NCOLS is INTEGER
                The number of columns of the matrix A. NCOLS >= 0.

           A

                     A is COMPLEX*16 array, dimension (LDA,N)
                On entry, the N-by-N matrix A.

           LDA

                     LDA is INTEGER
                The leading dimension of the array A.  LDA >= max(1,N).

           AF

                     AF is COMPLEX*16 array, dimension (LDAF,N)
                The factors L and U from the factorization
                A = P*L*U as computed by ZGETRF.

           LDAF

                     LDAF is INTEGER
                The leading dimension of the array AF.  LDAF >= max(1,N).

       Author
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

Author

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Version 3.12.0                              Tue Jan 28 2025 00:54:31                              la_gerpvgrw(3)