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author | julie <julielangou@users.noreply.github.com> | 2011-10-06 06:53:11 +0000 |
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committer | julie <julielangou@users.noreply.github.com> | 2011-10-06 06:53:11 +0000 |
commit | e1d39294aee16fa6db9ba079b14442358217db71 (patch) | |
tree | 30e5aa04c1f6596991fda5334f63dfb9b8027849 /SRC/dgebal.f | |
parent | 5fe0466a14e395641f4f8a300ecc9dcb8058081b (diff) | |
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Integrating Doxygen in comments
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-rw-r--r-- | SRC/dgebal.f | 216 |
1 files changed, 131 insertions, 85 deletions
diff --git a/SRC/dgebal.f b/SRC/dgebal.f index 0cbe0999..a8e297da 100644 --- a/SRC/dgebal.f +++ b/SRC/dgebal.f @@ -1,104 +1,150 @@ - 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( * ) +* .. * * ===================================================================== * |