# DOUBLE PRECISION routines for (real) orthogonal, packed storage matrix

## dopgtr

```USAGE:
q, info = NumRu::Lapack.dopgtr( uplo, ap, tau, [:usage => usage, :help => help])

FORTRAN MANUAL
SUBROUTINE DOPGTR( UPLO, N, AP, TAU, Q, LDQ, WORK, INFO )

*  Purpose
*  =======
*
*  DOPGTR generates a real orthogonal matrix Q which is defined as the
*  product of n-1 elementary reflectors H(i) of order n, as returned by
*  DSPTRD using packed storage:
*
*  if UPLO = 'U', Q = H(n-1) . . . H(2) H(1),
*
*  if UPLO = 'L', Q = H(1) H(2) . . . H(n-1).
*

*  Arguments
*  =========
*
*  UPLO    (input) CHARACTER*1
*          = 'U': Upper triangular packed storage used in previous
*                 call to DSPTRD;
*          = 'L': Lower triangular packed storage used in previous
*                 call to DSPTRD.
*
*  N       (input) INTEGER
*          The order of the matrix Q. N >= 0.
*
*  AP      (input) DOUBLE PRECISION array, dimension (N*(N+1)/2)
*          The vectors which define the elementary reflectors, as
*          returned by DSPTRD.
*
*  TAU     (input) DOUBLE PRECISION array, dimension (N-1)
*          TAU(i) must contain the scalar factor of the elementary
*          reflector H(i), as returned by DSPTRD.
*
*  Q       (output) DOUBLE PRECISION array, dimension (LDQ,N)
*          The N-by-N orthogonal matrix Q.
*
*  LDQ     (input) INTEGER
*          The leading dimension of the array Q. LDQ >= max(1,N).
*
*  WORK    (workspace) DOUBLE PRECISION array, dimension (N-1)
*
*  INFO    (output) INTEGER
*          = 0:  successful exit
*          < 0:  if INFO = -i, the i-th argument had an illegal value
*

*  =====================================================================
*

```
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## dopmtr

```USAGE:
info, c = NumRu::Lapack.dopmtr( side, uplo, trans, m, ap, tau, c, [:usage => usage, :help => help])

FORTRAN MANUAL
SUBROUTINE DOPMTR( SIDE, UPLO, TRANS, M, N, AP, TAU, C, LDC, WORK, INFO )

*  Purpose
*  =======
*
*  DOPMTR overwrites the general real M-by-N matrix C with
*
*                  SIDE = 'L'     SIDE = 'R'
*  TRANS = 'N':      Q * C          C * Q
*  TRANS = 'T':      Q**T * C       C * Q**T
*
*  where Q is a real orthogonal matrix of order nq, with nq = m if
*  SIDE = 'L' and nq = n if SIDE = 'R'. Q is defined as the product of
*  nq-1 elementary reflectors, as returned by DSPTRD using packed
*  storage:
*
*  if UPLO = 'U', Q = H(nq-1) . . . H(2) H(1);
*
*  if UPLO = 'L', Q = H(1) H(2) . . . H(nq-1).
*

*  Arguments
*  =========
*
*  SIDE    (input) CHARACTER*1
*          = 'L': apply Q or Q**T from the Left;
*          = 'R': apply Q or Q**T from the Right.
*
*  UPLO    (input) CHARACTER*1
*          = 'U': Upper triangular packed storage used in previous
*                 call to DSPTRD;
*          = 'L': Lower triangular packed storage used in previous
*                 call to DSPTRD.
*
*  TRANS   (input) CHARACTER*1
*          = 'N':  No transpose, apply Q;
*          = 'T':  Transpose, apply Q**T.
*
*  M       (input) INTEGER
*          The number of rows of the matrix C. M >= 0.
*
*  N       (input) INTEGER
*          The number of columns of the matrix C. N >= 0.
*
*  AP      (input) DOUBLE PRECISION array, dimension
*                               (M*(M+1)/2) if SIDE = 'L'
*                               (N*(N+1)/2) if SIDE = 'R'
*          The vectors which define the elementary reflectors, as
*          returned by DSPTRD.  AP is modified by the routine but
*          restored on exit.
*
*  TAU     (input) DOUBLE PRECISION array, dimension (M-1) if SIDE = 'L'
*                                     or (N-1) if SIDE = 'R'
*          TAU(i) must contain the scalar factor of the elementary
*          reflector H(i), as returned by DSPTRD.
*
*  C       (input/output) DOUBLE PRECISION array, dimension (LDC,N)
*          On entry, the M-by-N matrix C.
*          On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q.
*
*  LDC     (input) INTEGER
*          The leading dimension of the array C. LDC >= max(1,M).
*
*  WORK    (workspace) DOUBLE PRECISION array, dimension
*                                   (N) if SIDE = 'L'
*                                   (M) if SIDE = 'R'
*
*  INFO    (output) INTEGER
*          = 0:  successful exit
*          < 0:  if INFO = -i, the i-th argument had an illegal value
*

*  =====================================================================
*

```
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