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authorjulie <julielangou@users.noreply.github.com>2011-10-06 06:53:11 +0000
committerjulie <julielangou@users.noreply.github.com>2011-10-06 06:53:11 +0000
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- SUBROUTINE DGEBAL( JOB, N, A, LDA, ILO, IHI, SCALE, INFO )
-*
-* -- LAPACK routine (version 3.2.2) --
-* -- LAPACK is a software package provided by Univ. of Tennessee, --
-* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
-* June 2010
-*
-* .. Scalar Arguments ..
- CHARACTER JOB
- INTEGER IHI, ILO, INFO, LDA, N
-* ..
-* .. Array Arguments ..
- DOUBLE PRECISION A( LDA, * ), SCALE( * )
-* ..
-*
+*> \brief \b DGEBAL
+*
+* =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+* http://www.netlib.org/lapack/explore-html/
+*
+* Definition
+* ==========
+*
+* SUBROUTINE DGEBAL( JOB, N, A, LDA, ILO, IHI, SCALE, INFO )
+*
+* .. Scalar Arguments ..
+* CHARACTER JOB
+* INTEGER IHI, ILO, INFO, LDA, N
+* ..
+* .. Array Arguments ..
+* DOUBLE PRECISION A( LDA, * ), SCALE( * )
+* ..
+*
* Purpose
* =======
*
-* DGEBAL balances a general real matrix A. This involves, first,
-* permuting A by a similarity transformation to isolate eigenvalues
-* in the first 1 to ILO-1 and last IHI+1 to N elements on the
-* diagonal; and second, applying a diagonal similarity transformation
-* to rows and columns ILO to IHI to make the rows and columns as
-* close in norm as possible. Both steps are optional.
-*
-* Balancing may reduce the 1-norm of the matrix, and improve the
-* accuracy of the computed eigenvalues and/or eigenvectors.
+*>\details \b Purpose:
+*>\verbatim
+*>
+*> DGEBAL balances a general real matrix A. This involves, first,
+*> permuting A by a similarity transformation to isolate eigenvalues
+*> in the first 1 to ILO-1 and last IHI+1 to N elements on the
+*> diagonal; and second, applying a diagonal similarity transformation
+*> to rows and columns ILO to IHI to make the rows and columns as
+*> close in norm as possible. Both steps are optional.
+*>
+*> Balancing may reduce the 1-norm of the matrix, and improve the
+*> accuracy of the computed eigenvalues and/or eigenvectors.
+*>
+*>\endverbatim
*
* Arguments
* =========
*
-* JOB (input) CHARACTER*1
-* Specifies the operations to be performed on A:
-* = 'N': none: simply set ILO = 1, IHI = N, SCALE(I) = 1.0
-* for i = 1,...,N;
-* = 'P': permute only;
-* = 'S': scale only;
-* = 'B': both permute and scale.
-*
-* N (input) INTEGER
-* The order of the matrix A. N >= 0.
-*
-* A (input/output) DOUBLE PRECISION array, dimension (LDA,N)
-* On entry, the input matrix A.
-* On exit, A is overwritten by the balanced matrix.
-* If JOB = 'N', A is not referenced.
-* See Further Details.
-*
-* LDA (input) INTEGER
-* The leading dimension of the array A. LDA >= max(1,N).
+*> \param[in] JOB
+*> \verbatim
+*> JOB is CHARACTER*1
+*> Specifies the operations to be performed on A:
+*> = 'N': none: simply set ILO = 1, IHI = N, SCALE(I) = 1.0
+*> for i = 1,...,N;
+*> = 'P': permute only;
+*> = 'S': scale only;
+*> = 'B': both permute and scale.
+*> \endverbatim
+*>
+*> \param[in] N
+*> \verbatim
+*> N is INTEGER
+*> The order of the matrix A. N >= 0.
+*> \endverbatim
+*>
+*
+* Authors
+* =======
*
-* ILO (output) INTEGER
+*> \author Univ. of Tennessee
+*> \author Univ. of California Berkeley
+*> \author Univ. of Colorado Denver
+*> \author NAG Ltd.
*
-* IHI (output) INTEGER
-* ILO and IHI are set to integers such that on exit
-* A(i,j) = 0 if i > j and j = 1,...,ILO-1 or I = IHI+1,...,N.
-* If JOB = 'N' or 'S', ILO = 1 and IHI = N.
+*> \date November 2011
*
-* SCALE (output) DOUBLE PRECISION array, dimension (N)
-* Details of the permutations and scaling factors applied to
-* A. If P(j) is the index of the row and column interchanged
-* with row and column j and D(j) is the scaling factor
-* applied to row and column j, then
-* SCALE(j) = P(j) for j = 1,...,ILO-1
-* = D(j) for j = ILO,...,IHI
-* = P(j) for j = IHI+1,...,N.
-* The order in which the interchanges are made is N to IHI+1,
-* then 1 to ILO-1.
+*> \ingroup doubleGEcomputational
*
-* INFO (output) INTEGER
-* = 0: successful exit.
-* < 0: if INFO = -i, the i-th argument had an illegal value.
*
* Further Details
* ===============
+*>\details \b Further \b Details
+*> \verbatim
+* See Further Details.
+*>
+*> LDA (input) INTEGER
+*> The leading dimension of the array A. LDA >= max(1,N).
+*>
+*> ILO (output) INTEGER
+*>
+*> IHI (output) INTEGER
+*> ILO and IHI are set to integers such that on exit
+*> A(i,j) = 0 if i > j and j = 1,...,ILO-1 or I = IHI+1,...,N.
+*> If JOB = 'N' or 'S', ILO = 1 and IHI = N.
+*>
+*> SCALE (output) DOUBLE PRECISION array, dimension (N)
+*> Details of the permutations and scaling factors applied to
+*> A. If P(j) is the index of the row and column interchanged
+*> with row and column j and D(j) is the scaling factor
+*> applied to row and column j, then
+*> SCALE(j) = P(j) for j = 1,...,ILO-1
+*> = D(j) for j = ILO,...,IHI
+*> = P(j) for j = IHI+1,...,N.
+*> The order in which the interchanges are made is N to IHI+1,
+*> then 1 to ILO-1.
+*>
+*> INFO (output) INTEGER
+*> = 0: successful exit.
+*> < 0: if INFO = -i, the i-th argument had an illegal value.
+*>
+*>
+*> The permutations consist of row and column interchanges which put
+*> the matrix in the form
+*>
+*> ( T1 X Y )
+*> P A P = ( 0 B Z )
+*> ( 0 0 T2 )
+*>
+*> where T1 and T2 are upper triangular matrices whose eigenvalues lie
+*> along the diagonal. The column indices ILO and IHI mark the starting
+*> and ending columns of the submatrix B. Balancing consists of applying
+*> a diagonal similarity transformation inv(D) * B * D to make the
+*> 1-norms of each row of B and its corresponding column nearly equal.
+*> The output matrix is
+*>
+*> ( T1 X*D Y )
+*> ( 0 inv(D)*B*D inv(D)*Z ).
+*> ( 0 0 T2 )
+*>
+*> Information about the permutations P and the diagonal matrix D is
+*> returned in the vector SCALE.
+*>
+*> This subroutine is based on the EISPACK routine BALANC.
+*>
+*> Modified by Tzu-Yi Chen, Computer Science Division, University of
+*> California at Berkeley, USA
+*>
+*> \endverbatim
+*>
+* =====================================================================
+ SUBROUTINE DGEBAL( JOB, N, A, LDA, ILO, IHI, SCALE, INFO )
*
-* The permutations consist of row and column interchanges which put
-* the matrix in the form
-*
-* ( T1 X Y )
-* P A P = ( 0 B Z )
-* ( 0 0 T2 )
-*
-* where T1 and T2 are upper triangular matrices whose eigenvalues lie
-* along the diagonal. The column indices ILO and IHI mark the starting
-* and ending columns of the submatrix B. Balancing consists of applying
-* a diagonal similarity transformation inv(D) * B * D to make the
-* 1-norms of each row of B and its corresponding column nearly equal.
-* The output matrix is
-*
-* ( T1 X*D Y )
-* ( 0 inv(D)*B*D inv(D)*Z ).
-* ( 0 0 T2 )
-*
-* Information about the permutations P and the diagonal matrix D is
-* returned in the vector SCALE.
-*
-* This subroutine is based on the EISPACK routine BALANC.
+* -- LAPACK computational routine (version 3.2.2) --
+* -- LAPACK is a software package provided by Univ. of Tennessee, --
+* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+* November 2011
*
-* Modified by Tzu-Yi Chen, Computer Science Division, University of
-* California at Berkeley, USA
+* .. Scalar Arguments ..
+ CHARACTER JOB
+ INTEGER IHI, ILO, INFO, LDA, N
+* ..
+* .. Array Arguments ..
+ DOUBLE PRECISION A( LDA, * ), SCALE( * )
+* ..
*
* =====================================================================
*