--- rpl/lapack/lapack/dspgvd.f 2010/04/21 13:45:24 1.2
+++ rpl/lapack/lapack/dspgvd.f 2023/08/07 08:39:06 1.20
@@ -1,10 +1,216 @@
+*> \brief \b DSPGVD
+*
+* =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+* http://www.netlib.org/lapack/explore-html/
+*
+*> \htmlonly
+*> Download DSPGVD + dependencies
+*>
+*> [TGZ]
+*>
+*> [ZIP]
+*>
+*> [TXT]
+*> \endhtmlonly
+*
+* Definition:
+* ===========
+*
+* SUBROUTINE DSPGVD( ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ, WORK,
+* LWORK, IWORK, LIWORK, INFO )
+*
+* .. Scalar Arguments ..
+* CHARACTER JOBZ, UPLO
+* INTEGER INFO, ITYPE, LDZ, LIWORK, LWORK, N
+* ..
+* .. Array Arguments ..
+* INTEGER IWORK( * )
+* DOUBLE PRECISION AP( * ), BP( * ), W( * ), WORK( * ),
+* $ Z( LDZ, * )
+* ..
+*
+*
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
+*>
+*> DSPGVD computes all the eigenvalues, and optionally, the eigenvectors
+*> of a real generalized symmetric-definite eigenproblem, of the form
+*> A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x. Here A and
+*> B are assumed to be symmetric, stored in packed format, and B is also
+*> positive definite.
+*> If eigenvectors are desired, it uses a divide and conquer algorithm.
+*>
+*> The divide and conquer algorithm makes very mild assumptions about
+*> floating point arithmetic. It will work on machines with a guard
+*> digit in add/subtract, or on those binary machines without guard
+*> digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
+*> Cray-2. It could conceivably fail on hexadecimal or decimal machines
+*> without guard digits, but we know of none.
+*> \endverbatim
+*
+* Arguments:
+* ==========
+*
+*> \param[in] ITYPE
+*> \verbatim
+*> ITYPE is INTEGER
+*> Specifies the problem type to be solved:
+*> = 1: A*x = (lambda)*B*x
+*> = 2: A*B*x = (lambda)*x
+*> = 3: B*A*x = (lambda)*x
+*> \endverbatim
+*>
+*> \param[in] JOBZ
+*> \verbatim
+*> JOBZ is CHARACTER*1
+*> = 'N': Compute eigenvalues only;
+*> = 'V': Compute eigenvalues and eigenvectors.
+*> \endverbatim
+*>
+*> \param[in] UPLO
+*> \verbatim
+*> UPLO is CHARACTER*1
+*> = 'U': Upper triangles of A and B are stored;
+*> = 'L': Lower triangles of A and B are stored.
+*> \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)*(2*n-j)/2) = A(i,j) for j<=i<=n.
+*>
+*> On exit, the contents of AP are destroyed.
+*> \endverbatim
+*>
+*> \param[in,out] BP
+*> \verbatim
+*> BP is DOUBLE PRECISION array, dimension (N*(N+1)/2)
+*> On entry, the upper or lower triangle of the symmetric matrix
+*> B, packed columnwise in a linear array. The j-th column of B
+*> is stored in the array BP as follows:
+*> if UPLO = 'U', BP(i + (j-1)*j/2) = B(i,j) for 1<=i<=j;
+*> if UPLO = 'L', BP(i + (j-1)*(2*n-j)/2) = B(i,j) for j<=i<=n.
+*>
+*> On exit, the triangular factor U or L from the Cholesky
+*> factorization B = U**T*U or B = L*L**T, in the same storage
+*> format as B.
+*> \endverbatim
+*>
+*> \param[out] W
+*> \verbatim
+*> W is DOUBLE PRECISION array, dimension (N)
+*> If INFO = 0, the eigenvalues in ascending order.
+*> \endverbatim
+*>
+*> \param[out] Z
+*> \verbatim
+*> Z is DOUBLE PRECISION array, dimension (LDZ, N)
+*> If JOBZ = 'V', then if INFO = 0, Z contains the matrix Z of
+*> eigenvectors. The eigenvectors are normalized as follows:
+*> if ITYPE = 1 or 2, Z**T*B*Z = I;
+*> if ITYPE = 3, Z**T*inv(B)*Z = I.
+*> If JOBZ = 'N', then Z is not referenced.
+*> \endverbatim
+*>
+*> \param[in] LDZ
+*> \verbatim
+*> LDZ is INTEGER
+*> The leading dimension of the array Z. LDZ >= 1, and if
+*> JOBZ = 'V', LDZ >= max(1,N).
+*> \endverbatim
+*>
+*> \param[out] WORK
+*> \verbatim
+*> WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK))
+*> On exit, if INFO = 0, WORK(1) returns the required LWORK.
+*> \endverbatim
+*>
+*> \param[in] LWORK
+*> \verbatim
+*> LWORK is INTEGER
+*> The dimension of the array WORK.
+*> If N <= 1, LWORK >= 1.
+*> If JOBZ = 'N' and N > 1, LWORK >= 2*N.
+*> If JOBZ = 'V' and N > 1, LWORK >= 1 + 6*N + 2*N**2.
+*>
+*> If LWORK = -1, then a workspace query is assumed; the routine
+*> only calculates the required sizes of the WORK and IWORK
+*> arrays, returns these values as the first entries of the WORK
+*> and IWORK arrays, and no error message related to LWORK or
+*> LIWORK is issued by XERBLA.
+*> \endverbatim
+*>
+*> \param[out] IWORK
+*> \verbatim
+*> IWORK is INTEGER array, dimension (MAX(1,LIWORK))
+*> On exit, if INFO = 0, IWORK(1) returns the required LIWORK.
+*> \endverbatim
+*>
+*> \param[in] LIWORK
+*> \verbatim
+*> LIWORK is INTEGER
+*> The dimension of the array IWORK.
+*> If JOBZ = 'N' or N <= 1, LIWORK >= 1.
+*> If JOBZ = 'V' and N > 1, LIWORK >= 3 + 5*N.
+*>
+*> If LIWORK = -1, then a workspace query is assumed; the
+*> routine only calculates the required sizes of the WORK and
+*> IWORK arrays, returns these values as the first entries of
+*> the WORK and IWORK arrays, and no error message related to
+*> LWORK or LIWORK is issued by XERBLA.
+*> \endverbatim
+*>
+*> \param[out] INFO
+*> \verbatim
+*> INFO is INTEGER
+*> = 0: successful exit
+*> < 0: if INFO = -i, the i-th argument had an illegal value
+*> > 0: DPPTRF or DSPEVD returned an error code:
+*> <= N: if INFO = i, DSPEVD failed to converge;
+*> i off-diagonal elements of an intermediate
+*> tridiagonal form did not converge to zero;
+*> > N: if INFO = N + i, for 1 <= i <= N, then the leading
+*> minor of order i of B is not positive definite.
+*> The factorization of B could not be completed and
+*> no eigenvalues or eigenvectors were computed.
+*> \endverbatim
+*
+* Authors:
+* ========
+*
+*> \author Univ. of Tennessee
+*> \author Univ. of California Berkeley
+*> \author Univ. of Colorado Denver
+*> \author NAG Ltd.
+*
+*> \ingroup doubleOTHEReigen
+*
+*> \par Contributors:
+* ==================
+*>
+*> Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA
+*
+* =====================================================================
SUBROUTINE DSPGVD( ITYPE, JOBZ, UPLO, N, AP, BP, W, Z, LDZ, WORK,
$ LWORK, IWORK, LIWORK, INFO )
*
-* -- LAPACK driver routine (version 3.2) --
+* -- LAPACK driver 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 JOBZ, UPLO
@@ -16,130 +222,8 @@
$ Z( LDZ, * )
* ..
*
-* Purpose
-* =======
-*
-* DSPGVD computes all the eigenvalues, and optionally, the eigenvectors
-* of a real generalized symmetric-definite eigenproblem, of the form
-* A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x. Here A and
-* B are assumed to be symmetric, stored in packed format, and B is also
-* positive definite.
-* If eigenvectors are desired, it uses a divide and conquer algorithm.
-*
-* The divide and conquer algorithm makes very mild assumptions about
-* floating point arithmetic. It will work on machines with a guard
-* digit in add/subtract, or on those binary machines without guard
-* digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
-* Cray-2. It could conceivably fail on hexadecimal or decimal machines
-* without guard digits, but we know of none.
-*
-* Arguments
-* =========
-*
-* ITYPE (input) INTEGER
-* Specifies the problem type to be solved:
-* = 1: A*x = (lambda)*B*x
-* = 2: A*B*x = (lambda)*x
-* = 3: B*A*x = (lambda)*x
-*
-* JOBZ (input) CHARACTER*1
-* = 'N': Compute eigenvalues only;
-* = 'V': Compute eigenvalues and eigenvectors.
-*
-* UPLO (input) CHARACTER*1
-* = 'U': Upper triangles of A and B are stored;
-* = 'L': Lower triangles of A and B are stored.
-*
-* 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)*(2*n-j)/2) = A(i,j) for j<=i<=n.
-*
-* On exit, the contents of AP are destroyed.
-*
-* BP (input/output) DOUBLE PRECISION array, dimension (N*(N+1)/2)
-* On entry, the upper or lower triangle of the symmetric matrix
-* B, packed columnwise in a linear array. The j-th column of B
-* is stored in the array BP as follows:
-* if UPLO = 'U', BP(i + (j-1)*j/2) = B(i,j) for 1<=i<=j;
-* if UPLO = 'L', BP(i + (j-1)*(2*n-j)/2) = B(i,j) for j<=i<=n.
-*
-* On exit, the triangular factor U or L from the Cholesky
-* factorization B = U**T*U or B = L*L**T, in the same storage
-* format as B.
-*
-* W (output) DOUBLE PRECISION array, dimension (N)
-* If INFO = 0, the eigenvalues in ascending order.
-*
-* Z (output) DOUBLE PRECISION array, dimension (LDZ, N)
-* If JOBZ = 'V', then if INFO = 0, Z contains the matrix Z of
-* eigenvectors. The eigenvectors are normalized as follows:
-* if ITYPE = 1 or 2, Z**T*B*Z = I;
-* if ITYPE = 3, Z**T*inv(B)*Z = I.
-* If JOBZ = 'N', then Z is not referenced.
-*
-* LDZ (input) INTEGER
-* The leading dimension of the array Z. LDZ >= 1, and if
-* JOBZ = 'V', LDZ >= max(1,N).
-*
-* WORK (workspace/output) DOUBLE PRECISION array, dimension (MAX(1,LWORK))
-* On exit, if INFO = 0, WORK(1) returns the required LWORK.
-*
-* LWORK (input) INTEGER
-* The dimension of the array WORK.
-* If N <= 1, LWORK >= 1.
-* If JOBZ = 'N' and N > 1, LWORK >= 2*N.
-* If JOBZ = 'V' and N > 1, LWORK >= 1 + 6*N + 2*N**2.
-*
-* If LWORK = -1, then a workspace query is assumed; the routine
-* only calculates the required sizes of the WORK and IWORK
-* arrays, returns these values as the first entries of the WORK
-* and IWORK arrays, and no error message related to LWORK or
-* LIWORK is issued by XERBLA.
-*
-* IWORK (workspace/output) INTEGER array, dimension (MAX(1,LIWORK))
-* On exit, if INFO = 0, IWORK(1) returns the required LIWORK.
-*
-* LIWORK (input) INTEGER
-* The dimension of the array IWORK.
-* If JOBZ = 'N' or N <= 1, LIWORK >= 1.
-* If JOBZ = 'V' and N > 1, LIWORK >= 3 + 5*N.
-*
-* If LIWORK = -1, then a workspace query is assumed; the
-* routine only calculates the required sizes of the WORK and
-* IWORK arrays, returns these values as the first entries of
-* the WORK and IWORK arrays, and no error message related to
-* LWORK or LIWORK is issued by XERBLA.
-*
-* INFO (output) INTEGER
-* = 0: successful exit
-* < 0: if INFO = -i, the i-th argument had an illegal value
-* > 0: DPPTRF or DSPEVD returned an error code:
-* <= N: if INFO = i, DSPEVD failed to converge;
-* i off-diagonal elements of an intermediate
-* tridiagonal form did not converge to zero;
-* > N: if INFO = N + i, for 1 <= i <= N, then the leading
-* minor of order i of B is not positive definite.
-* The factorization of B could not be completed and
-* no eigenvalues or eigenvectors were computed.
-*
-* Further Details
-* ===============
-*
-* Based on contributions by
-* Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA
-*
* =====================================================================
*
-* .. Parameters ..
- DOUBLE PRECISION TWO
- PARAMETER ( TWO = 2.0D+0 )
-* ..
* .. Local Scalars ..
LOGICAL LQUERY, UPPER, WANTZ
CHARACTER TRANS
@@ -191,7 +275,6 @@
END IF
WORK( 1 ) = LWMIN
IWORK( 1 ) = LIWMIN
-*
IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY ) THEN
INFO = -11
ELSE IF( LIWORK.LT.LIWMIN .AND. .NOT.LQUERY ) THEN
@@ -224,8 +307,8 @@
CALL DSPGST( ITYPE, UPLO, N, AP, BP, INFO )
CALL DSPEVD( JOBZ, UPLO, N, AP, W, Z, LDZ, WORK, LWORK, IWORK,
$ LIWORK, INFO )
- LWMIN = MAX( DBLE( LWMIN ), DBLE( WORK( 1 ) ) )
- LIWMIN = MAX( DBLE( LIWMIN ), DBLE( IWORK( 1 ) ) )
+ LWMIN = INT( MAX( DBLE( LWMIN ), DBLE( WORK( 1 ) ) ) )
+ LIWMIN = INT( MAX( DBLE( LIWMIN ), DBLE( IWORK( 1 ) ) ) )
*
IF( WANTZ ) THEN
*
@@ -237,7 +320,7 @@
IF( ITYPE.EQ.1 .OR. ITYPE.EQ.2 ) THEN
*
* For A*x=(lambda)*B*x and A*B*x=(lambda)*x;
-* backtransform eigenvectors: x = inv(L)'*y or inv(U)*y
+* backtransform eigenvectors: x = inv(L)**T *y or inv(U)*y
*
IF( UPPER ) THEN
TRANS = 'N'
@@ -253,7 +336,7 @@
ELSE IF( ITYPE.EQ.3 ) THEN
*
* For B*A*x=(lambda)*x;
-* backtransform eigenvectors: x = L*y or U'*y
+* backtransform eigenvectors: x = L*y or U**T *y
*
IF( UPPER ) THEN
TRANS = 'T'