--- rpl/lapack/lapack/dsptrd.f	2010/01/26 15:22:46	1.1.1.1
+++ rpl/lapack/lapack/dsptrd.f	2023/08/07 08:39:06	1.18
@@ -1,9 +1,156 @@
+*> \brief \b DSPTRD
+*
+*  =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+*            http://www.netlib.org/lapack/explore-html/
+*
+*> \htmlonly
+*> Download DSPTRD + dependencies
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dsptrd.f">
+*> [TGZ]</a>
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dsptrd.f">
+*> [ZIP]</a>
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dsptrd.f">
+*> [TXT]</a>
+*> \endhtmlonly
+*
+*  Definition:
+*  ===========
+*
+*       SUBROUTINE DSPTRD( UPLO, N, AP, D, E, TAU, INFO )
+*
+*       .. Scalar Arguments ..
+*       CHARACTER          UPLO
+*       INTEGER            INFO, N
+*       ..
+*       .. Array Arguments ..
+*       DOUBLE PRECISION   AP( * ), D( * ), E( * ), TAU( * )
+*       ..
+*
+*
+*> \par Purpose:
+*  =============
+*>
+*> \verbatim
+*>
+*> DSPTRD reduces a real symmetric matrix A stored in packed form to
+*> symmetric tridiagonal form T by an orthogonal similarity
+*> transformation: Q**T * A * Q = T.
+*> \endverbatim
+*
+*  Arguments:
+*  ==========
+*
+*> \param[in] UPLO
+*> \verbatim
+*>          UPLO is CHARACTER*1
+*>          = 'U':  Upper triangle of A is stored;
+*>          = 'L':  Lower triangle of A is stored.
+*> \endverbatim
+*>
+*> \param[in] N
+*> \verbatim
+*>          N is INTEGER
+*>          The order of the matrix A.  N >= 0.
+*> \endverbatim
+*>
+*> \param[in,out] AP
+*> \verbatim
+*>          AP is DOUBLE PRECISION array, dimension (N*(N+1)/2)
+*>          On entry, the upper or lower triangle of the symmetric matrix
+*>          A, packed columnwise in a linear array.  The j-th column of A
+*>          is stored in the array AP as follows:
+*>          if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
+*>          if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n.
+*>          On exit, if UPLO = 'U', the diagonal and first superdiagonal
+*>          of A are overwritten by the corresponding elements of the
+*>          tridiagonal matrix T, and the elements above the first
+*>          superdiagonal, with the array TAU, represent the orthogonal
+*>          matrix Q as a product of elementary reflectors; if UPLO
+*>          = 'L', the diagonal and first subdiagonal of A are over-
+*>          written by the corresponding elements of the tridiagonal
+*>          matrix T, and the elements below the first subdiagonal, with
+*>          the array TAU, represent the orthogonal matrix Q as a product
+*>          of elementary reflectors. See Further Details.
+*> \endverbatim
+*>
+*> \param[out] D
+*> \verbatim
+*>          D is DOUBLE PRECISION array, dimension (N)
+*>          The diagonal elements of the tridiagonal matrix T:
+*>          D(i) = A(i,i).
+*> \endverbatim
+*>
+*> \param[out] E
+*> \verbatim
+*>          E is DOUBLE PRECISION array, dimension (N-1)
+*>          The off-diagonal elements of the tridiagonal matrix T:
+*>          E(i) = A(i,i+1) if UPLO = 'U', E(i) = A(i+1,i) if UPLO = 'L'.
+*> \endverbatim
+*>
+*> \param[out] TAU
+*> \verbatim
+*>          TAU is DOUBLE PRECISION array, dimension (N-1)
+*>          The scalar factors of the elementary reflectors (see Further
+*>          Details).
+*> \endverbatim
+*>
+*> \param[out] INFO
+*> \verbatim
+*>          INFO is INTEGER
+*>          = 0:  successful exit
+*>          < 0:  if INFO = -i, the i-th argument had an illegal value
+*> \endverbatim
+*
+*  Authors:
+*  ========
+*
+*> \author Univ. of Tennessee
+*> \author Univ. of California Berkeley
+*> \author Univ. of Colorado Denver
+*> \author NAG Ltd.
+*
+*> \ingroup doubleOTHERcomputational
+*
+*> \par Further Details:
+*  =====================
+*>
+*> \verbatim
+*>
+*>  If UPLO = 'U', the matrix Q is represented as a product of elementary
+*>  reflectors
+*>
+*>     Q = H(n-1) . . . H(2) H(1).
+*>
+*>  Each H(i) has the form
+*>
+*>     H(i) = I - tau * v * v**T
+*>
+*>  where tau is a real scalar, and v is a real vector with
+*>  v(i+1:n) = 0 and v(i) = 1; v(1:i-1) is stored on exit in AP,
+*>  overwriting A(1:i-1,i+1), and tau is stored in TAU(i).
+*>
+*>  If UPLO = 'L', the matrix Q is represented as a product of elementary
+*>  reflectors
+*>
+*>     Q = H(1) H(2) . . . H(n-1).
+*>
+*>  Each H(i) has the form
+*>
+*>     H(i) = I - tau * v * v**T
+*>
+*>  where tau is a real scalar, and v is a real vector with
+*>  v(1:i) = 0 and v(i+1) = 1; v(i+2:n) is stored on exit in AP,
+*>  overwriting A(i+2:n,i), and tau is stored in TAU(i).
+*> \endverbatim
+*>
+*  =====================================================================
       SUBROUTINE DSPTRD( UPLO, N, AP, D, E, TAU, INFO )
 *
-*  -- LAPACK routine (version 3.2) --
+*  -- LAPACK computational routine --
 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
-*     November 2006
 *
 *     .. Scalar Arguments ..
       CHARACTER          UPLO
@@ -13,85 +160,6 @@
       DOUBLE PRECISION   AP( * ), D( * ), E( * ), TAU( * )
 *     ..
 *
-*  Purpose
-*  =======
-*
-*  DSPTRD reduces a real symmetric matrix A stored in packed form to
-*  symmetric tridiagonal form T by an orthogonal similarity
-*  transformation: Q**T * A * Q = T.
-*
-*  Arguments
-*  =========
-*
-*  UPLO    (input) CHARACTER*1
-*          = 'U':  Upper triangle of A is stored;
-*          = 'L':  Lower triangle of A is stored.
-*
-*  N       (input) INTEGER
-*          The order of the matrix A.  N >= 0.
-*
-*  AP      (input/output) DOUBLE PRECISION array, dimension (N*(N+1)/2)
-*          On entry, the upper or lower triangle of the symmetric matrix
-*          A, packed columnwise in a linear array.  The j-th column of A
-*          is stored in the array AP as follows:
-*          if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
-*          if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n.
-*          On exit, if UPLO = 'U', the diagonal and first superdiagonal
-*          of A are overwritten by the corresponding elements of the
-*          tridiagonal matrix T, and the elements above the first
-*          superdiagonal, with the array TAU, represent the orthogonal
-*          matrix Q as a product of elementary reflectors; if UPLO
-*          = 'L', the diagonal and first subdiagonal of A are over-
-*          written by the corresponding elements of the tridiagonal
-*          matrix T, and the elements below the first subdiagonal, with
-*          the array TAU, represent the orthogonal matrix Q as a product
-*          of elementary reflectors. See Further Details.
-*
-*  D       (output) DOUBLE PRECISION array, dimension (N)
-*          The diagonal elements of the tridiagonal matrix T:
-*          D(i) = A(i,i).
-*
-*  E       (output) DOUBLE PRECISION array, dimension (N-1)
-*          The off-diagonal elements of the tridiagonal matrix T:
-*          E(i) = A(i,i+1) if UPLO = 'U', E(i) = A(i+1,i) if UPLO = 'L'.
-*
-*  TAU     (output) DOUBLE PRECISION array, dimension (N-1)
-*          The scalar factors of the elementary reflectors (see Further
-*          Details).
-*
-*  INFO    (output) INTEGER
-*          = 0:  successful exit
-*          < 0:  if INFO = -i, the i-th argument had an illegal value
-*
-*  Further Details
-*  ===============
-*
-*  If UPLO = 'U', the matrix Q is represented as a product of elementary
-*  reflectors
-*
-*     Q = H(n-1) . . . H(2) H(1).
-*
-*  Each H(i) has the form
-*
-*     H(i) = I - tau * v * v'
-*
-*  where tau is a real scalar, and v is a real vector with
-*  v(i+1:n) = 0 and v(i) = 1; v(1:i-1) is stored on exit in AP,
-*  overwriting A(1:i-1,i+1), and tau is stored in TAU(i).
-*
-*  If UPLO = 'L', the matrix Q is represented as a product of elementary
-*  reflectors
-*
-*     Q = H(1) H(2) . . . H(n-1).
-*
-*  Each H(i) has the form
-*
-*     H(i) = I - tau * v * v'
-*
-*  where tau is a real scalar, and v is a real vector with
-*  v(1:i) = 0 and v(i+1) = 1; v(i+2:n) is stored on exit in AP,
-*  overwriting A(i+2:n,i), and tau is stored in TAU(i).
-*
 *  =====================================================================
 *
 *     .. Parameters ..
@@ -141,7 +209,7 @@
          I1 = N*( N-1 ) / 2 + 1
          DO 10 I = N - 1, 1, -1
 *
-*           Generate elementary reflector H(i) = I - tau * v * v'
+*           Generate elementary reflector H(i) = I - tau * v * v**T
 *           to annihilate A(1:i-1,i+1)
 *
             CALL DLARFG( I, AP( I1+I-1 ), AP( I1 ), 1, TAUI )
@@ -158,13 +226,13 @@
                CALL DSPMV( UPLO, I, TAUI, AP, AP( I1 ), 1, ZERO, TAU,
      $                     1 )
 *
-*              Compute  w := y - 1/2 * tau * (y'*v) * v
+*              Compute  w := y - 1/2 * tau * (y**T *v) * v
 *
                ALPHA = -HALF*TAUI*DDOT( I, TAU, 1, AP( I1 ), 1 )
                CALL DAXPY( I, ALPHA, AP( I1 ), 1, TAU, 1 )
 *
 *              Apply the transformation as a rank-2 update:
-*                 A := A - v * w' - w * v'
+*                 A := A - v * w**T - w * v**T
 *
                CALL DSPR2( UPLO, I, -ONE, AP( I1 ), 1, TAU, 1, AP )
 *
@@ -184,7 +252,7 @@
          DO 20 I = 1, N - 1
             I1I1 = II + N - I + 1
 *
-*           Generate elementary reflector H(i) = I - tau * v * v'
+*           Generate elementary reflector H(i) = I - tau * v * v**T
 *           to annihilate A(i+2:n,i)
 *
             CALL DLARFG( N-I, AP( II+1 ), AP( II+2 ), 1, TAUI )
@@ -201,14 +269,14 @@
                CALL DSPMV( UPLO, N-I, TAUI, AP( I1I1 ), AP( II+1 ), 1,
      $                     ZERO, TAU( I ), 1 )
 *
-*              Compute  w := y - 1/2 * tau * (y'*v) * v
+*              Compute  w := y - 1/2 * tau * (y**T *v) * v
 *
                ALPHA = -HALF*TAUI*DDOT( N-I, TAU( I ), 1, AP( II+1 ),
      $                 1 )
                CALL DAXPY( N-I, ALPHA, AP( II+1 ), 1, TAU( I ), 1 )
 *
 *              Apply the transformation as a rank-2 update:
-*                 A := A - v * w' - w * v'
+*                 A := A - v * w**T - w * v**T
 *
                CALL DSPR2( UPLO, N-I, -ONE, AP( II+1 ), 1, TAU( I ), 1,
      $                     AP( I1I1 ) )