.TH "TESTING/EIG/dsyt22.f" 3 "Version 3.12.0" "LAPACK" \" -*- nroff -*-
.ad l
.nh
.SH NAME
TESTING/EIG/dsyt22.f
.SH SYNOPSIS
.br
.PP
.SS "Functions/Subroutines"

.in +1c
.ti -1c
.RI "subroutine \fBdsyt22\fP (itype, uplo, n, m, kband, a, lda, d, e, u, ldu, v, ldv, tau, work, result)"
.br
.RI "\fBDSYT22\fP "
.in -1c
.SH "Function/Subroutine Documentation"
.PP 
.SS "subroutine dsyt22 (integer itype, character uplo, integer n, integer m, integer kband, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( * ) d, double precision, dimension( * ) e, double precision, dimension( ldu, * ) u, integer ldu, double precision, dimension( ldv, * ) v, integer ldv, double precision, dimension( * ) tau, double precision, dimension( * ) work, double precision, dimension( 2 ) result)"

.PP
\fBDSYT22\fP 
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
      DSYT22  generally checks a decomposition of the form

              A U = U S

      where A is symmetric, the columns of U are orthonormal, and S
      is diagonal (if KBAND=0) or symmetric tridiagonal (if
      KBAND=1)\&.  If ITYPE=1, then U is represented as a dense matrix,
      otherwise the U is expressed as a product of Householder
      transformations, whose vectors are stored in the array 'V' and
      whose scaling constants are in 'TAU'; we shall use the letter
      'V' to refer to the product of Householder transformations
      (which should be equal to U)\&.

      Specifically, if ITYPE=1, then:

              RESULT(1) = | U**T A U - S | / ( |A| m ulp ) and
              RESULT(2) = | I - U**T U | / ( m ulp )
.fi
.PP
 
.PP
.nf
  ITYPE   INTEGER
          Specifies the type of tests to be performed\&.
          1: U expressed as a dense orthogonal matrix:
             RESULT(1) = | A - U S U**T | / ( |A| n ulp )  and
             RESULT(2) = | I - U U**T | / ( n ulp )

  UPLO    CHARACTER
          If UPLO='U', the upper triangle of A will be used and the
          (strictly) lower triangle will not be referenced\&.  If
          UPLO='L', the lower triangle of A will be used and the
          (strictly) upper triangle will not be referenced\&.
          Not modified\&.

  N       INTEGER
          The size of the matrix\&.  If it is zero, DSYT22 does nothing\&.
          It must be at least zero\&.
          Not modified\&.

  M       INTEGER
          The number of columns of U\&.  If it is zero, DSYT22 does
          nothing\&.  It must be at least zero\&.
          Not modified\&.

  KBAND   INTEGER
          The bandwidth of the matrix\&.  It may only be zero or one\&.
          If zero, then S is diagonal, and E is not referenced\&.  If
          one, then S is symmetric tri-diagonal\&.
          Not modified\&.

  A       DOUBLE PRECISION array, dimension (LDA , N)
          The original (unfactored) matrix\&.  It is assumed to be
          symmetric, and only the upper (UPLO='U') or only the lower
          (UPLO='L') will be referenced\&.
          Not modified\&.

  LDA     INTEGER
          The leading dimension of A\&.  It must be at least 1
          and at least N\&.
          Not modified\&.

  D       DOUBLE PRECISION array, dimension (N)
          The diagonal of the (symmetric tri-) diagonal matrix\&.
          Not modified\&.

  E       DOUBLE PRECISION array, dimension (N)
          The off-diagonal of the (symmetric tri-) diagonal matrix\&.
          E(1) is ignored, E(2) is the (1,2) and (2,1) element, etc\&.
          Not referenced if KBAND=0\&.
          Not modified\&.

  U       DOUBLE PRECISION array, dimension (LDU, N)
          If ITYPE=1 or 3, this contains the orthogonal matrix in
          the decomposition, expressed as a dense matrix\&.  If ITYPE=2,
          then it is not referenced\&.
          Not modified\&.

  LDU     INTEGER
          The leading dimension of U\&.  LDU must be at least N and
          at least 1\&.
          Not modified\&.

  V       DOUBLE PRECISION array, dimension (LDV, N)
          If ITYPE=2 or 3, the lower triangle of this array contains
          the Householder vectors used to describe the orthogonal
          matrix in the decomposition\&.  If ITYPE=1, then it is not
          referenced\&.
          Not modified\&.

  LDV     INTEGER
          The leading dimension of V\&.  LDV must be at least N and
          at least 1\&.
          Not modified\&.

  TAU     DOUBLE PRECISION array, dimension (N)
          If ITYPE >= 2, then TAU(j) is the scalar factor of
          v(j) v(j)**T in the Householder transformation H(j) of
          the product  U = H(1)\&.\&.\&.H(n-2)
          If ITYPE < 2, then TAU is not referenced\&.
          Not modified\&.

  WORK    DOUBLE PRECISION array, dimension (2*N**2)
          Workspace\&.
          Modified\&.

  RESULT  DOUBLE PRECISION array, dimension (2)
          The values computed by the two tests described above\&.  The
          values are currently limited to 1/ulp, to avoid overflow\&.
          RESULT(1) is always modified\&.  RESULT(2) is modified only
          if LDU is at least N\&.
          Modified\&.
.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 \fB155\fP of file \fBdsyt22\&.f\fP\&.
.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.