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version 1.12, 2014/01/27 09:28:25
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*> \brief \b DPBTRF |
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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 DPBTRF + dependencies |
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dpbtrf.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/dpbtrf.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/dpbtrf.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 DPBTRF( UPLO, N, KD, AB, LDAB, INFO ) |
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* |
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* .. Scalar Arguments .. |
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* CHARACTER UPLO |
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* INTEGER INFO, KD, LDAB, N |
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* .. |
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* .. Array Arguments .. |
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* DOUBLE PRECISION AB( LDAB, * ) |
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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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*> DPBTRF computes the Cholesky factorization of a real symmetric |
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*> positive definite band matrix A. |
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*> |
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*> The factorization has the form |
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*> A = U**T * U, if UPLO = 'U', or |
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*> A = L * L**T, if UPLO = 'L', |
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*> where U is an upper triangular matrix and L is lower triangular. |
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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] 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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*> |
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*> On exit, if INFO = 0, the triangular factor U or L from the |
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*> Cholesky factorization A = U**T*U or A = L*L**T of the band |
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*> matrix A, in the same storage format as A. |
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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] 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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*> > 0: if INFO = i, the leading minor of order i is not |
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*> positive definite, and the factorization could not be |
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*> completed. |
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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 November 2011 |
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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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*> The band storage scheme is illustrated by the following example, when |
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*> N = 6, KD = 2, and UPLO = 'U': |
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*> |
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*> On entry: On exit: |
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*> |
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*> * * a13 a24 a35 a46 * * u13 u24 u35 u46 |
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*> * a12 a23 a34 a45 a56 * u12 u23 u34 u45 u56 |
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*> a11 a22 a33 a44 a55 a66 u11 u22 u33 u44 u55 u66 |
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*> |
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*> Similarly, if UPLO = 'L' the format of A is as follows: |
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*> |
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*> On entry: On exit: |
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*> |
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*> a11 a22 a33 a44 a55 a66 l11 l22 l33 l44 l55 l66 |
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*> a21 a32 a43 a54 a65 * l21 l32 l43 l54 l65 * |
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*> a31 a42 a53 a64 * * l31 l42 l53 l64 * * |
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*> |
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*> Array elements marked * are not used by the routine. |
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*> \endverbatim |
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* |
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*> \par Contributors: |
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* ================== |
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*> |
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*> Peter Mayes and Giuseppe Radicati, IBM ECSEC, Rome, March 23, 1989 |
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* |
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* ===================================================================== |
SUBROUTINE DPBTRF( UPLO, N, KD, AB, LDAB, INFO ) |
SUBROUTINE DPBTRF( UPLO, N, KD, AB, LDAB, INFO ) |
* |
* |
* -- LAPACK routine (version 3.2) -- |
* -- LAPACK computational routine (version 3.4.0) -- |
* -- 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 |
* November 2011 |
* |
* |
* .. Scalar Arguments .. |
* .. Scalar Arguments .. |
CHARACTER UPLO |
CHARACTER UPLO |
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DOUBLE PRECISION AB( LDAB, * ) |
DOUBLE PRECISION AB( LDAB, * ) |
* .. |
* .. |
* |
* |
* Purpose |
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* ======= |
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* |
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* DPBTRF computes the Cholesky factorization of a real symmetric |
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* positive definite band matrix A. |
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* |
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* The factorization has the form |
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* A = U**T * U, if UPLO = 'U', or |
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* A = L * L**T, if UPLO = 'L', |
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* where U is an upper triangular matrix and L is lower triangular. |
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* |
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* Arguments |
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* ========= |
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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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* |
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* On exit, if INFO = 0, the triangular factor U or L from the |
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* Cholesky factorization A = U**T*U or A = L*L**T of the band |
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* matrix A, in the same storage format as A. |
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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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* 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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* > 0: if INFO = i, the leading minor of order i is not |
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* positive definite, and the factorization could not be |
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* completed. |
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* |
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* Further Details |
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* =============== |
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* |
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* The band storage scheme is illustrated by the following example, when |
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* N = 6, KD = 2, and UPLO = 'U': |
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* |
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* On entry: On exit: |
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* |
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* * * a13 a24 a35 a46 * * u13 u24 u35 u46 |
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* * a12 a23 a34 a45 a56 * u12 u23 u34 u45 u56 |
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* a11 a22 a33 a44 a55 a66 u11 u22 u33 u44 u55 u66 |
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* |
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* Similarly, if UPLO = 'L' the format of A is as follows: |
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* |
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* On entry: On exit: |
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* |
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* a11 a22 a33 a44 a55 a66 l11 l22 l33 l44 l55 l66 |
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* a21 a32 a43 a54 a65 * l21 l32 l43 l54 l65 * |
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* a31 a42 a53 a64 * * l31 l42 l53 l64 * * |
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* |
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* Array elements marked * are not used by the routine. |
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* |
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* Contributed by |
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* Peter Mayes and Giuseppe Radicati, IBM ECSEC, Rome, March 23, 1989 |
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* |
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* ===================================================================== |
* ===================================================================== |
* |
* |
* .. Parameters .. |
* .. Parameters .. |