.TH "TESTING/EIG/dlatm4.f" 3 "Version 3.12.0" "LAPACK" \" -*- nroff -*-
.ad l
.nh
.SH NAME
TESTING/EIG/dlatm4.f
.SH SYNOPSIS
.br
.PP
.SS "Functions/Subroutines"

.in +1c
.ti -1c
.RI "subroutine \fBdlatm4\fP (itype, n, nz1, nz2, isign, amagn, rcond, triang, idist, iseed, a, lda)"
.br
.RI "\fBDLATM4\fP "
.in -1c
.SH "Function/Subroutine Documentation"
.PP 
.SS "subroutine dlatm4 (integer itype, integer n, integer nz1, integer nz2, integer isign, double precision amagn, double precision rcond, double precision triang, integer idist, integer, dimension( 4 ) iseed, double precision, dimension( lda, * ) a, integer lda)"

.PP
\fBDLATM4\fP 
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 DLATM4 generates basic square matrices, which may later be
 multiplied by others in order to produce test matrices\&.  It is
 intended mainly to be used to test the generalized eigenvalue
 routines\&.

 It first generates the diagonal and (possibly) subdiagonal,
 according to the value of ITYPE, NZ1, NZ2, ISIGN, AMAGN, and RCOND\&.
 It then fills in the upper triangle with random numbers, if TRIANG is
 non-zero\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIITYPE\fP 
.PP
.nf
          ITYPE is INTEGER
          The 'type' of matrix on the diagonal and sub-diagonal\&.
          If ITYPE < 0, then type abs(ITYPE) is generated and then
             swapped end for end (A(I,J) := A'(N-J,N-I)\&.)  See also
             the description of AMAGN and ISIGN\&.

          Special types:
          = 0:  the zero matrix\&.
          = 1:  the identity\&.
          = 2:  a transposed Jordan block\&.
          = 3:  If N is odd, then a k+1 x k+1 transposed Jordan block
                followed by a k x k identity block, where k=(N-1)/2\&.
                If N is even, then k=(N-2)/2, and a zero diagonal entry
                is tacked onto the end\&.

          Diagonal types\&.  The diagonal consists of NZ1 zeros, then
             k=N-NZ1-NZ2 nonzeros\&.  The subdiagonal is zero\&.  ITYPE
             specifies the nonzero diagonal entries as follows:
          = 4:  1, \&.\&.\&., k
          = 5:  1, RCOND, \&.\&.\&., RCOND
          = 6:  1, \&.\&.\&., 1, RCOND
          = 7:  1, a, a^2, \&.\&.\&., a^(k-1)=RCOND
          = 8:  1, 1-d, 1-2*d, \&.\&.\&., 1-(k-1)*d=RCOND
          = 9:  random numbers chosen from (RCOND,1)
          = 10: random numbers with distribution IDIST (see DLARND\&.)
.fi
.PP
.br
\fIN\fP 
.PP
.nf
          N is INTEGER
          The order of the matrix\&.
.fi
.PP
.br
\fINZ1\fP 
.PP
.nf
          NZ1 is INTEGER
          If abs(ITYPE) > 3, then the first NZ1 diagonal entries will
          be zero\&.
.fi
.PP
.br
\fINZ2\fP 
.PP
.nf
          NZ2 is INTEGER
          If abs(ITYPE) > 3, then the last NZ2 diagonal entries will
          be zero\&.
.fi
.PP
.br
\fIISIGN\fP 
.PP
.nf
          ISIGN is INTEGER
          = 0: The sign of the diagonal and subdiagonal entries will
               be left unchanged\&.
          = 1: The diagonal and subdiagonal entries will have their
               sign changed at random\&.
          = 2: If ITYPE is 2 or 3, then the same as ISIGN=1\&.
               Otherwise, with probability 0\&.5, odd-even pairs of
               diagonal entries A(2*j-1,2*j-1), A(2*j,2*j) will be
               converted to a 2x2 block by pre- and post-multiplying
               by distinct random orthogonal rotations\&.  The remaining
               diagonal entries will have their sign changed at random\&.
.fi
.PP
.br
\fIAMAGN\fP 
.PP
.nf
          AMAGN is DOUBLE PRECISION
          The diagonal and subdiagonal entries will be multiplied by
          AMAGN\&.
.fi
.PP
.br
\fIRCOND\fP 
.PP
.nf
          RCOND is DOUBLE PRECISION
          If abs(ITYPE) > 4, then the smallest diagonal entry will be
          entry will be RCOND\&.  RCOND must be between 0 and 1\&.
.fi
.PP
.br
\fITRIANG\fP 
.PP
.nf
          TRIANG is DOUBLE PRECISION
          The entries above the diagonal will be random numbers with
          magnitude bounded by TRIANG (i\&.e\&., random numbers multiplied
          by TRIANG\&.)
.fi
.PP
.br
\fIIDIST\fP 
.PP
.nf
          IDIST is INTEGER
          Specifies the type of distribution to be used to generate a
          random matrix\&.
          = 1:  UNIFORM( 0, 1 )
          = 2:  UNIFORM( -1, 1 )
          = 3:  NORMAL ( 0, 1 )
.fi
.PP
.br
\fIISEED\fP 
.PP
.nf
          ISEED is INTEGER array, dimension (4)
          On entry ISEED specifies the seed of the random number
          generator\&.  The values of ISEED are changed on exit, and can
          be used in the next call to DLATM4 to continue the same
          random number sequence\&.
          Note: ISEED(4) should be odd, for the random number generator
          used at present\&.
.fi
.PP
.br
\fIA\fP 
.PP
.nf
          A is DOUBLE PRECISION array, dimension (LDA, N)
          Array to be computed\&.
.fi
.PP
.br
\fILDA\fP 
.PP
.nf
          LDA is INTEGER
          Leading dimension of A\&.  Must be at least 1 and at least N\&.
.fi
.PP
 
.RE
.PP
\fBAuthor\fP
.RS 4
Univ\&. of Tennessee 
.PP
Univ\&. of California Berkeley 
.PP
Univ\&. of Colorado Denver 
.PP
NAG Ltd\&. 
.RE
.PP

.PP
Definition at line \fB173\fP of file \fBdlatm4\&.f\fP\&.
.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.