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version 1.16, 2018/05/29 07:18:31
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*> \brief \b ZPBEQU |
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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 ZPBEQU + dependencies |
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zpbequ.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/zpbequ.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/zpbequ.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 ZPBEQU( UPLO, N, KD, AB, LDAB, S, SCOND, AMAX, 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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* DOUBLE PRECISION AMAX, SCOND |
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* .. |
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* .. Array Arguments .. |
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* DOUBLE PRECISION S( * ) |
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* COMPLEX*16 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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*> ZPBEQU computes row and column scalings intended to equilibrate a |
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*> Hermitian positive definite band matrix A and reduce its condition |
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*> number (with respect to the two-norm). S contains the scale factors, |
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*> S(i) = 1/sqrt(A(i,i)), chosen so that the scaled matrix B with |
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*> elements B(i,j) = S(i)*A(i,j)*S(j) has ones on the diagonal. This |
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*> choice of S puts the condition number of B within a factor N of the |
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*> smallest possible condition number over all possible diagonal |
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*> scalings. |
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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 triangular of A is stored; |
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*> = 'L': Lower triangular 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] AB |
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*> \verbatim |
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*> AB is COMPLEX*16 array, dimension (LDAB,N) |
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*> The upper or lower triangle of the Hermitian band matrix A, |
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*> stored in the first KD+1 rows of the array. The j-th column |
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*> of A is stored in the j-th column of the array AB 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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*> \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 >= KD+1. |
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*> \endverbatim |
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*> |
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*> \param[out] S |
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*> \verbatim |
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*> S is DOUBLE PRECISION array, dimension (N) |
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*> If INFO = 0, S contains the scale factors for A. |
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*> \endverbatim |
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*> |
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*> \param[out] SCOND |
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*> \verbatim |
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*> SCOND is DOUBLE PRECISION |
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*> If INFO = 0, S contains the ratio of the smallest S(i) to |
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*> the largest S(i). If SCOND >= 0.1 and AMAX is neither too |
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*> large nor too small, it is not worth scaling by S. |
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*> \endverbatim |
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*> |
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*> \param[out] AMAX |
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*> \verbatim |
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*> AMAX is DOUBLE PRECISION |
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*> Absolute value of largest matrix element. If AMAX is very |
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*> close to overflow or very close to underflow, the matrix |
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*> should be scaled. |
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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 i-th diagonal element is nonpositive. |
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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 complex16OTHERcomputational |
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* |
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* ===================================================================== |
SUBROUTINE ZPBEQU( UPLO, N, KD, AB, LDAB, S, SCOND, AMAX, INFO ) |
SUBROUTINE ZPBEQU( UPLO, N, KD, AB, LDAB, S, SCOND, AMAX, 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 |
CHARACTER UPLO |
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COMPLEX*16 AB( LDAB, * ) |
COMPLEX*16 AB( LDAB, * ) |
* .. |
* .. |
* |
* |
* Purpose |
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* ======= |
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* |
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* ZPBEQU computes row and column scalings intended to equilibrate a |
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* Hermitian positive definite band matrix A and reduce its condition |
|
* number (with respect to the two-norm). S contains the scale factors, |
|
* S(i) = 1/sqrt(A(i,i)), chosen so that the scaled matrix B with |
|
* elements B(i,j) = S(i)*A(i,j)*S(j) has ones on the diagonal. This |
|
* choice of S puts the condition number of B within a factor N of the |
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* smallest possible condition number over all possible diagonal |
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* scalings. |
|
* |
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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 triangular of A is stored; |
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* = 'L': Lower triangular 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) COMPLEX*16 array, dimension (LDAB,N) |
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* The upper or lower triangle of the Hermitian band matrix A, |
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* stored in the first KD+1 rows of the array. The j-th column |
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* of A is stored in the j-th column of the array AB 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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* LDAB (input) INTEGER |
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* The leading dimension of the array A. LDAB >= KD+1. |
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* |
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* S (output) DOUBLE PRECISION array, dimension (N) |
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* If INFO = 0, S contains the scale factors for A. |
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* |
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* SCOND (output) DOUBLE PRECISION |
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* If INFO = 0, S contains the ratio of the smallest S(i) to |
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* the largest S(i). If SCOND >= 0.1 and AMAX is neither too |
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* large nor too small, it is not worth scaling by S. |
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* |
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* AMAX (output) DOUBLE PRECISION |
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* Absolute value of largest matrix element. If AMAX is very |
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* close to overflow or very close to underflow, the matrix |
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* should be scaled. |
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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 i-th diagonal element is nonpositive. |
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* |
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* ===================================================================== |
* ===================================================================== |
* |
* |
* .. Parameters .. |
* .. Parameters .. |