version 1.5, 2010/08/07 13:22:25
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version 1.14, 2017/06/17 10:54:02
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*> \brief \b DSBTRD |
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* |
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* =========== DOCUMENTATION =========== |
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* |
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* Online html documentation available at |
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* http://www.netlib.org/lapack/explore-html/ |
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* |
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*> \htmlonly |
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*> Download DSBTRD + dependencies |
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dsbtrd.f"> |
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*> [TGZ]</a> |
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dsbtrd.f"> |
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*> [ZIP]</a> |
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dsbtrd.f"> |
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*> [TXT]</a> |
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*> \endhtmlonly |
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* |
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* Definition: |
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* =========== |
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* |
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* SUBROUTINE DSBTRD( VECT, UPLO, N, KD, AB, LDAB, D, E, Q, LDQ, |
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* WORK, INFO ) |
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* |
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* .. Scalar Arguments .. |
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* CHARACTER UPLO, VECT |
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* INTEGER INFO, KD, LDAB, LDQ, N |
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* .. |
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* .. Array Arguments .. |
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* DOUBLE PRECISION AB( LDAB, * ), D( * ), E( * ), Q( LDQ, * ), |
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* $ WORK( * ) |
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* .. |
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* |
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* |
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*> \par Purpose: |
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* ============= |
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*> |
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*> \verbatim |
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*> |
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*> DSBTRD reduces a real symmetric band matrix A to symmetric |
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*> tridiagonal form T by an orthogonal similarity transformation: |
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*> Q**T * A * Q = T. |
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*> \endverbatim |
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* |
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* Arguments: |
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* ========== |
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* |
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*> \param[in] VECT |
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*> \verbatim |
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*> VECT is CHARACTER*1 |
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*> = 'N': do not form Q; |
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*> = 'V': form Q; |
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*> = 'U': update a matrix X, by forming X*Q. |
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*> \endverbatim |
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*> |
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*> \param[in] UPLO |
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*> \verbatim |
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*> UPLO is CHARACTER*1 |
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*> = 'U': Upper triangle of A is stored; |
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*> = 'L': Lower triangle of A is stored. |
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*> \endverbatim |
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*> |
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*> \param[in] N |
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*> \verbatim |
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*> N is INTEGER |
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*> The order of the matrix A. N >= 0. |
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*> \endverbatim |
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*> |
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*> \param[in] KD |
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*> \verbatim |
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*> KD is INTEGER |
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*> The number of superdiagonals of the matrix A if UPLO = 'U', |
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*> or the number of subdiagonals if UPLO = 'L'. KD >= 0. |
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*> \endverbatim |
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*> |
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*> \param[in,out] AB |
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*> \verbatim |
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*> AB is DOUBLE PRECISION array, dimension (LDAB,N) |
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*> On entry, the upper or lower triangle of the symmetric band |
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*> matrix A, stored in the first KD+1 rows of the array. The |
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*> j-th column of A is stored in the j-th column of the array AB |
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*> as follows: |
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*> if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j; |
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*> if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd). |
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*> On exit, the diagonal elements of AB are overwritten by the |
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*> diagonal elements of the tridiagonal matrix T; if KD > 0, the |
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*> elements on the first superdiagonal (if UPLO = 'U') or the |
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*> first subdiagonal (if UPLO = 'L') are overwritten by the |
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*> off-diagonal elements of T; the rest of AB is overwritten by |
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*> values generated during the reduction. |
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*> \endverbatim |
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*> |
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*> \param[in] LDAB |
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*> \verbatim |
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*> LDAB is INTEGER |
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*> The leading dimension of the array AB. LDAB >= KD+1. |
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*> \endverbatim |
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*> |
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*> \param[out] D |
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*> \verbatim |
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*> D is DOUBLE PRECISION array, dimension (N) |
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*> The diagonal elements of the tridiagonal matrix T. |
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*> \endverbatim |
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*> |
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*> \param[out] E |
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*> \verbatim |
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*> E is DOUBLE PRECISION array, dimension (N-1) |
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*> The off-diagonal elements of the tridiagonal matrix T: |
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*> E(i) = T(i,i+1) if UPLO = 'U'; E(i) = T(i+1,i) if UPLO = 'L'. |
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*> \endverbatim |
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*> |
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*> \param[in,out] Q |
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*> \verbatim |
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*> Q is DOUBLE PRECISION array, dimension (LDQ,N) |
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*> On entry, if VECT = 'U', then Q must contain an N-by-N |
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*> matrix X; if VECT = 'N' or 'V', then Q need not be set. |
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*> |
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*> On exit: |
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*> if VECT = 'V', Q contains the N-by-N orthogonal matrix Q; |
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*> if VECT = 'U', Q contains the product X*Q; |
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*> if VECT = 'N', the array Q is not referenced. |
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*> \endverbatim |
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*> |
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*> \param[in] LDQ |
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*> \verbatim |
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*> LDQ is INTEGER |
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*> The leading dimension of the array Q. |
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*> LDQ >= 1, and LDQ >= N if VECT = 'V' or 'U'. |
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*> \endverbatim |
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*> |
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*> \param[out] WORK |
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*> \verbatim |
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*> WORK is DOUBLE PRECISION array, dimension (N) |
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*> \endverbatim |
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*> |
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*> \param[out] INFO |
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*> \verbatim |
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*> INFO is INTEGER |
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*> = 0: successful exit |
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*> < 0: if INFO = -i, the i-th argument had an illegal value |
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*> \endverbatim |
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* |
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* Authors: |
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* ======== |
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* |
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*> \author Univ. of Tennessee |
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*> \author Univ. of California Berkeley |
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*> \author Univ. of Colorado Denver |
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*> \author NAG Ltd. |
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* |
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*> \date December 2016 |
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* |
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*> \ingroup doubleOTHERcomputational |
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* |
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*> \par Further Details: |
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* ===================== |
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*> |
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*> \verbatim |
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*> |
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*> Modified by Linda Kaufman, Bell Labs. |
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*> \endverbatim |
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*> |
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* ===================================================================== |
SUBROUTINE DSBTRD( VECT, UPLO, N, KD, AB, LDAB, D, E, Q, LDQ, |
SUBROUTINE DSBTRD( VECT, UPLO, N, KD, AB, LDAB, D, E, Q, LDQ, |
$ WORK, INFO ) |
$ WORK, INFO ) |
* |
* |
* -- LAPACK routine (version 3.2) -- |
* -- LAPACK computational routine (version 3.7.0) -- |
* -- LAPACK is a software package provided by Univ. of Tennessee, -- |
* -- LAPACK is a software package provided by Univ. of Tennessee, -- |
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- |
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- |
* November 2006 |
* December 2016 |
* |
* |
* .. Scalar Arguments .. |
* .. Scalar Arguments .. |
CHARACTER UPLO, VECT |
CHARACTER UPLO, VECT |
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$ WORK( * ) |
$ WORK( * ) |
* .. |
* .. |
* |
* |
* Purpose |
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* ======= |
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* |
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* DSBTRD reduces a real symmetric band matrix A to symmetric |
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* tridiagonal form T by an orthogonal similarity transformation: |
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* Q**T * A * Q = T. |
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* |
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* Arguments |
|
* ========= |
|
* |
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* VECT (input) CHARACTER*1 |
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* = 'N': do not form Q; |
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* = 'V': form Q; |
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* = 'U': update a matrix X, by forming X*Q. |
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* |
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* UPLO (input) CHARACTER*1 |
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* = 'U': Upper triangle of A is stored; |
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* = 'L': Lower triangle of A is stored. |
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* |
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* N (input) INTEGER |
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* The order of the matrix A. N >= 0. |
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* |
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* KD (input) INTEGER |
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* The number of superdiagonals of the matrix A if UPLO = 'U', |
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* or the number of subdiagonals if UPLO = 'L'. KD >= 0. |
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* |
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* AB (input/output) DOUBLE PRECISION array, dimension (LDAB,N) |
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* On entry, the upper or lower triangle of the symmetric band |
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* matrix A, stored in the first KD+1 rows of the array. The |
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* j-th column of A is stored in the j-th column of the array AB |
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* as follows: |
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* if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j; |
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* if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd). |
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* On exit, the diagonal elements of AB are overwritten by the |
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* diagonal elements of the tridiagonal matrix T; if KD > 0, the |
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* elements on the first superdiagonal (if UPLO = 'U') or the |
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* first subdiagonal (if UPLO = 'L') are overwritten by the |
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* off-diagonal elements of T; the rest of AB is overwritten by |
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* values generated during the reduction. |
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* |
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* LDAB (input) INTEGER |
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* The leading dimension of the array AB. LDAB >= KD+1. |
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* |
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* D (output) DOUBLE PRECISION array, dimension (N) |
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* The diagonal elements of the tridiagonal matrix T. |
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* |
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* E (output) DOUBLE PRECISION array, dimension (N-1) |
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* The off-diagonal elements of the tridiagonal matrix T: |
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* E(i) = T(i,i+1) if UPLO = 'U'; E(i) = T(i+1,i) if UPLO = 'L'. |
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* |
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* Q (input/output) DOUBLE PRECISION array, dimension (LDQ,N) |
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* On entry, if VECT = 'U', then Q must contain an N-by-N |
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* matrix X; if VECT = 'N' or 'V', then Q need not be set. |
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* |
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* On exit: |
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* if VECT = 'V', Q contains the N-by-N orthogonal matrix Q; |
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* if VECT = 'U', Q contains the product X*Q; |
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* if VECT = 'N', the array Q is not referenced. |
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* |
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* LDQ (input) INTEGER |
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* The leading dimension of the array Q. |
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* LDQ >= 1, and LDQ >= N if VECT = 'V' or 'U'. |
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* |
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* WORK (workspace) DOUBLE PRECISION array, dimension (N) |
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* |
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* INFO (output) INTEGER |
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* = 0: successful exit |
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* < 0: if INFO = -i, the i-th argument had an illegal value |
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* |
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* Further Details |
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* =============== |
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* |
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* Modified by Linda Kaufman, Bell Labs. |
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* |
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* ===================================================================== |
* ===================================================================== |
* |
* |
* .. Parameters .. |
* .. Parameters .. |