version 1.3, 2010/08/06 15:28:35
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version 1.15, 2017/06/17 10:53:46
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*> \brief \b DGBBRD |
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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 DGBBRD + dependencies |
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dgbbrd.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/dgbbrd.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/dgbbrd.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 DGBBRD( VECT, M, N, NCC, KL, KU, AB, LDAB, D, E, Q, |
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* LDQ, PT, LDPT, C, LDC, WORK, INFO ) |
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* |
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* .. Scalar Arguments .. |
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* CHARACTER VECT |
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* INTEGER INFO, KL, KU, LDAB, LDC, LDPT, LDQ, M, N, NCC |
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* .. |
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* .. Array Arguments .. |
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* DOUBLE PRECISION AB( LDAB, * ), C( LDC, * ), D( * ), E( * ), |
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* $ PT( LDPT, * ), Q( LDQ, * ), 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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*> DGBBRD reduces a real general m-by-n band matrix A to upper |
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*> bidiagonal form B by an orthogonal transformation: Q**T * A * P = B. |
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*> |
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*> The routine computes B, and optionally forms Q or P**T, or computes |
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*> Q**T*C for a given matrix C. |
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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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*> Specifies whether or not the matrices Q and P**T are to be |
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*> formed. |
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*> = 'N': do not form Q or P**T; |
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*> = 'Q': form Q only; |
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*> = 'P': form P**T only; |
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*> = 'B': form both. |
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*> \endverbatim |
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*> |
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*> \param[in] M |
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*> \verbatim |
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*> M is INTEGER |
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*> The number of rows of the matrix A. M >= 0. |
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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 number of columns of the matrix A. N >= 0. |
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*> \endverbatim |
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*> |
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*> \param[in] NCC |
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*> \verbatim |
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*> NCC is INTEGER |
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*> The number of columns of the matrix C. NCC >= 0. |
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*> \endverbatim |
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*> |
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*> \param[in] KL |
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*> \verbatim |
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*> KL is INTEGER |
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*> The number of subdiagonals of the matrix A. KL >= 0. |
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*> \endverbatim |
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*> |
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*> \param[in] KU |
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*> \verbatim |
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*> KU is INTEGER |
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*> The number of superdiagonals of the matrix A. KU >= 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 m-by-n band matrix A, stored in rows 1 to |
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*> KL+KU+1. The j-th column of A is stored in the j-th column of |
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*> the array AB as follows: |
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*> AB(ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(m,j+kl). |
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*> On exit, A is overwritten by values generated during the |
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*> 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 A. LDAB >= KL+KU+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 (min(M,N)) |
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*> The diagonal elements of the bidiagonal matrix B. |
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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 (min(M,N)-1) |
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*> The superdiagonal elements of the bidiagonal matrix B. |
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*> \endverbatim |
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*> |
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*> \param[out] Q |
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*> \verbatim |
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*> Q is DOUBLE PRECISION array, dimension (LDQ,M) |
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*> If VECT = 'Q' or 'B', the m-by-m orthogonal matrix Q. |
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*> If VECT = 'N' or 'P', 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 >= max(1,M) if VECT = 'Q' or 'B'; LDQ >= 1 otherwise. |
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*> \endverbatim |
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*> |
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*> \param[out] PT |
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*> \verbatim |
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*> PT is DOUBLE PRECISION array, dimension (LDPT,N) |
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*> If VECT = 'P' or 'B', the n-by-n orthogonal matrix P'. |
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*> If VECT = 'N' or 'Q', the array PT is not referenced. |
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*> \endverbatim |
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*> |
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*> \param[in] LDPT |
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*> \verbatim |
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*> LDPT is INTEGER |
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*> The leading dimension of the array PT. |
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*> LDPT >= max(1,N) if VECT = 'P' or 'B'; LDPT >= 1 otherwise. |
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*> \endverbatim |
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*> |
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*> \param[in,out] C |
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*> \verbatim |
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*> C is DOUBLE PRECISION array, dimension (LDC,NCC) |
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*> On entry, an m-by-ncc matrix C. |
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*> On exit, C is overwritten by Q**T*C. |
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*> C is not referenced if NCC = 0. |
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*> \endverbatim |
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*> |
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*> \param[in] LDC |
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*> \verbatim |
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*> LDC is INTEGER |
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*> The leading dimension of the array C. |
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*> LDC >= max(1,M) if NCC > 0; LDC >= 1 if NCC = 0. |
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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 (2*max(M,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 doubleGBcomputational |
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* |
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* ===================================================================== |
SUBROUTINE DGBBRD( VECT, M, N, NCC, KL, KU, AB, LDAB, D, E, Q, |
SUBROUTINE DGBBRD( VECT, M, N, NCC, KL, KU, AB, LDAB, D, E, Q, |
$ LDQ, PT, LDPT, C, LDC, WORK, INFO ) |
$ LDQ, PT, LDPT, C, LDC, 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 VECT |
CHARACTER VECT |
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$ PT( LDPT, * ), Q( LDQ, * ), WORK( * ) |
$ PT( LDPT, * ), Q( LDQ, * ), WORK( * ) |
* .. |
* .. |
* |
* |
* Purpose |
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* ======= |
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* |
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* DGBBRD reduces a real general m-by-n band matrix A to upper |
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* bidiagonal form B by an orthogonal transformation: Q' * A * P = B. |
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* |
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* The routine computes B, and optionally forms Q or P', or computes |
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* Q'*C for a given matrix C. |
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* |
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* Arguments |
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* ========= |
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* |
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* VECT (input) CHARACTER*1 |
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* Specifies whether or not the matrices Q and P' are to be |
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* formed. |
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* = 'N': do not form Q or P'; |
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* = 'Q': form Q only; |
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* = 'P': form P' only; |
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* = 'B': form both. |
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* |
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* M (input) INTEGER |
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* The number of rows of the matrix A. M >= 0. |
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* |
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* N (input) INTEGER |
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* The number of columns of the matrix A. N >= 0. |
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* |
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* NCC (input) INTEGER |
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* The number of columns of the matrix C. NCC >= 0. |
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* |
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* KL (input) INTEGER |
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* The number of subdiagonals of the matrix A. KL >= 0. |
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* |
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* KU (input) INTEGER |
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* The number of superdiagonals of the matrix A. KU >= 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 m-by-n band matrix A, stored in rows 1 to |
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* KL+KU+1. The j-th column of A is stored in the j-th column of |
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* the array AB as follows: |
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* AB(ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(m,j+kl). |
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* On exit, A is overwritten by values generated during the |
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* reduction. |
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* |
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* LDAB (input) INTEGER |
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* The leading dimension of the array A. LDAB >= KL+KU+1. |
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* |
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* D (output) DOUBLE PRECISION array, dimension (min(M,N)) |
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* The diagonal elements of the bidiagonal matrix B. |
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* |
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* E (output) DOUBLE PRECISION array, dimension (min(M,N)-1) |
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* The superdiagonal elements of the bidiagonal matrix B. |
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* |
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* Q (output) DOUBLE PRECISION array, dimension (LDQ,M) |
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* If VECT = 'Q' or 'B', the m-by-m orthogonal matrix Q. |
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* If VECT = 'N' or 'P', 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 >= max(1,M) if VECT = 'Q' or 'B'; LDQ >= 1 otherwise. |
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* |
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* PT (output) DOUBLE PRECISION array, dimension (LDPT,N) |
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* If VECT = 'P' or 'B', the n-by-n orthogonal matrix P'. |
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* If VECT = 'N' or 'Q', the array PT is not referenced. |
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* |
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* LDPT (input) INTEGER |
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* The leading dimension of the array PT. |
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* LDPT >= max(1,N) if VECT = 'P' or 'B'; LDPT >= 1 otherwise. |
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* |
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* C (input/output) DOUBLE PRECISION array, dimension (LDC,NCC) |
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* On entry, an m-by-ncc matrix C. |
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* On exit, C is overwritten by Q'*C. |
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* C is not referenced if NCC = 0. |
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* |
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* LDC (input) INTEGER |
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* The leading dimension of the array C. |
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* LDC >= max(1,M) if NCC > 0; LDC >= 1 if NCC = 0. |
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* |
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* WORK (workspace) DOUBLE PRECISION array, dimension (2*max(M,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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* ===================================================================== |
* ===================================================================== |
* |
* |
* .. Parameters .. |
* .. Parameters .. |
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RETURN |
RETURN |
END IF |
END IF |
* |
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* Initialize Q and P' to the unit matrix, if needed |
* Initialize Q and P**T to the unit matrix, if needed |
* |
* |
IF( WANTQ ) |
IF( WANTQ ) |
$ CALL DLASET( 'Full', M, M, ZERO, ONE, Q, LDQ ) |
$ CALL DLASET( 'Full', M, M, ZERO, ONE, Q, LDQ ) |
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* |
* |
IF( WANTPT ) THEN |
IF( WANTPT ) THEN |
* |
* |
* accumulate product of plane rotations in P' |
* accumulate product of plane rotations in P**T |
* |
* |
DO 60 J = J1, J2, KB1 |
DO 60 J = J1, J2, KB1 |
CALL DROT( N, PT( J+KUN-1, 1 ), LDPT, |
CALL DROT( N, PT( J+KUN-1, 1 ), LDPT, |