--- rpl/lapack/lapack/dspgst.f 2010/01/26 15:22:46 1.1
+++ rpl/lapack/lapack/dspgst.f 2023/08/07 08:39:06 1.18
@@ -1,9 +1,119 @@
+*> \brief \b DSPGST
+*
+* =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+* http://www.netlib.org/lapack/explore-html/
+*
+*> \htmlonly
+*> Download DSPGST + dependencies
+*>
+*> [TGZ]
+*>
+*> [ZIP]
+*>
+*> [TXT]
+*> \endhtmlonly
+*
+* Definition:
+* ===========
+*
+* SUBROUTINE DSPGST( ITYPE, UPLO, N, AP, BP, INFO )
+*
+* .. Scalar Arguments ..
+* CHARACTER UPLO
+* INTEGER INFO, ITYPE, N
+* ..
+* .. Array Arguments ..
+* DOUBLE PRECISION AP( * ), BP( * )
+* ..
+*
+*
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
+*>
+*> DSPGST reduces a real symmetric-definite generalized eigenproblem
+*> to standard form, using packed storage.
+*>
+*> If ITYPE = 1, the problem is A*x = lambda*B*x,
+*> and A is overwritten by inv(U**T)*A*inv(U) or inv(L)*A*inv(L**T)
+*>
+*> If ITYPE = 2 or 3, the problem is A*B*x = lambda*x or
+*> B*A*x = lambda*x, and A is overwritten by U*A*U**T or L**T*A*L.
+*>
+*> B must have been previously factorized as U**T*U or L*L**T by DPPTRF.
+*> \endverbatim
+*
+* Arguments:
+* ==========
+*
+*> \param[in] ITYPE
+*> \verbatim
+*> ITYPE is INTEGER
+*> = 1: compute inv(U**T)*A*inv(U) or inv(L)*A*inv(L**T);
+*> = 2 or 3: compute U*A*U**T or L**T*A*L.
+*> \endverbatim
+*>
+*> \param[in] UPLO
+*> \verbatim
+*> UPLO is CHARACTER*1
+*> = 'U': Upper triangle of A is stored and B is factored as
+*> U**T*U;
+*> = 'L': Lower triangle of A is stored and B is factored as
+*> L*L**T.
+*> \endverbatim
+*>
+*> \param[in] N
+*> \verbatim
+*> N is INTEGER
+*> The order of the matrices A and B. 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)*(2n-j)/2) = A(i,j) for j<=i<=n.
+*>
+*> On exit, if INFO = 0, the transformed matrix, stored in the
+*> same format as A.
+*> \endverbatim
+*>
+*> \param[in] BP
+*> \verbatim
+*> BP is DOUBLE PRECISION array, dimension (N*(N+1)/2)
+*> The triangular factor from the Cholesky factorization of B,
+*> stored in the same format as A, as returned by DPPTRF.
+*> \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
+*
+* =====================================================================
SUBROUTINE DSPGST( ITYPE, UPLO, N, AP, BP, 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
@@ -13,54 +123,6 @@
DOUBLE PRECISION AP( * ), BP( * )
* ..
*
-* Purpose
-* =======
-*
-* DSPGST reduces a real symmetric-definite generalized eigenproblem
-* to standard form, using packed storage.
-*
-* If ITYPE = 1, the problem is A*x = lambda*B*x,
-* and A is overwritten by inv(U**T)*A*inv(U) or inv(L)*A*inv(L**T)
-*
-* If ITYPE = 2 or 3, the problem is A*B*x = lambda*x or
-* B*A*x = lambda*x, and A is overwritten by U*A*U**T or L**T*A*L.
-*
-* B must have been previously factorized as U**T*U or L*L**T by DPPTRF.
-*
-* Arguments
-* =========
-*
-* ITYPE (input) INTEGER
-* = 1: compute inv(U**T)*A*inv(U) or inv(L)*A*inv(L**T);
-* = 2 or 3: compute U*A*U**T or L**T*A*L.
-*
-* UPLO (input) CHARACTER*1
-* = 'U': Upper triangle of A is stored and B is factored as
-* U**T*U;
-* = 'L': Lower triangle of A is stored and B is factored as
-* L*L**T.
-*
-* N (input) INTEGER
-* The order of the matrices A and B. 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)*(2n-j)/2) = A(i,j) for j<=i<=n.
-*
-* On exit, if INFO = 0, the transformed matrix, stored in the
-* same format as A.
-*
-* BP (input) DOUBLE PRECISION array, dimension (N*(N+1)/2)
-* The triangular factor from the Cholesky factorization of B,
-* stored in the same format as A, as returned by DPPTRF.
-*
-* INFO (output) INTEGER
-* = 0: successful exit
-* < 0: if INFO = -i, the i-th argument had an illegal value
-*
* =====================================================================
*
* .. Parameters ..
@@ -102,7 +164,7 @@
IF( ITYPE.EQ.1 ) THEN
IF( UPPER ) THEN
*
-* Compute inv(U')*A*inv(U)
+* Compute inv(U**T)*A*inv(U)
*
* J1 and JJ are the indices of A(1,j) and A(j,j)
*
@@ -124,7 +186,7 @@
10 CONTINUE
ELSE
*
-* Compute inv(L)*A*inv(L')
+* Compute inv(L)*A*inv(L**T)
*
* KK and K1K1 are the indices of A(k,k) and A(k+1,k+1)
*
@@ -154,7 +216,7 @@
ELSE
IF( UPPER ) THEN
*
-* Compute U*A*U'
+* Compute U*A*U**T
*
* K1 and KK are the indices of A(1,k) and A(k,k)
*
@@ -179,7 +241,7 @@
30 CONTINUE
ELSE
*
-* Compute L'*A*L
+* Compute L**T *A*L
*
* JJ and J1J1 are the indices of A(j,j) and A(j+1,j+1)
*