aboutsummaryrefslogtreecommitdiff
path: root/SRC/slatrd.f
diff options
context:
space:
mode:
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
commite1d39294aee16fa6db9ba079b14442358217db71 (patch)
tree30e5aa04c1f6596991fda5334f63dfb9b8027849 /SRC/slatrd.f
parent5fe0466a14e395641f4f8a300ecc9dcb8058081b (diff)
Integrating Doxygen in comments
Diffstat (limited to 'SRC/slatrd.f')
-rw-r--r--SRC/slatrd.f272
1 files changed, 153 insertions, 119 deletions
diff --git a/SRC/slatrd.f b/SRC/slatrd.f
index 76116636..2d694237 100644
--- a/SRC/slatrd.f
+++ b/SRC/slatrd.f
@@ -1,138 +1,172 @@
- SUBROUTINE SLATRD( UPLO, N, NB, A, LDA, E, TAU, W, LDW )
-*
-* -- LAPACK auxiliary routine (version 3.3.1) --
-* -- LAPACK is a software package provided by Univ. of Tennessee, --
-* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
-* -- April 2011 --
-*
-* .. Scalar Arguments ..
- CHARACTER UPLO
- INTEGER LDA, LDW, N, NB
-* ..
-* .. Array Arguments ..
- REAL A( LDA, * ), E( * ), TAU( * ), W( LDW, * )
-* ..
-*
+*> \brief \b SLATRD
+*
+* =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+* http://www.netlib.org/lapack/explore-html/
+*
+* Definition
+* ==========
+*
+* SUBROUTINE SLATRD( UPLO, N, NB, A, LDA, E, TAU, W, LDW )
+*
+* .. Scalar Arguments ..
+* CHARACTER UPLO
+* INTEGER LDA, LDW, N, NB
+* ..
+* .. Array Arguments ..
+* REAL A( LDA, * ), E( * ), TAU( * ), W( LDW, * )
+* ..
+*
* Purpose
* =======
*
-* SLATRD reduces NB rows and columns of a real symmetric matrix A to
-* symmetric tridiagonal form by an orthogonal similarity
-* transformation Q**T * A * Q, and returns the matrices V and W which are
-* needed to apply the transformation to the unreduced part of A.
-*
-* If UPLO = 'U', SLATRD reduces the last NB rows and columns of a
-* matrix, of which the upper triangle is supplied;
-* if UPLO = 'L', SLATRD reduces the first NB rows and columns of a
-* matrix, of which the lower triangle is supplied.
-*
-* This is an auxiliary routine called by SSYTRD.
+*>\details \b Purpose:
+*>\verbatim
+*>
+*> SLATRD reduces NB rows and columns of a real symmetric matrix A to
+*> symmetric tridiagonal form by an orthogonal similarity
+*> transformation Q**T * A * Q, and returns the matrices V and W which are
+*> needed to apply the transformation to the unreduced part of A.
+*>
+*> If UPLO = 'U', SLATRD reduces the last NB rows and columns of a
+*> matrix, of which the upper triangle is supplied;
+*> if UPLO = 'L', SLATRD reduces the first NB rows and columns of a
+*> matrix, of which the lower triangle is supplied.
+*>
+*> This is an auxiliary routine called by SSYTRD.
+*>
+*>\endverbatim
*
* Arguments
* =========
*
-* UPLO (input) CHARACTER*1
-* Specifies whether the upper or lower triangular part of the
-* symmetric matrix A is stored:
-* = 'U': Upper triangular
-* = 'L': Lower triangular
-*
-* N (input) INTEGER
-* The order of the matrix A.
-*
-* NB (input) INTEGER
-* The number of rows and columns to be reduced.
-*
-* A (input/output) REAL array, dimension (LDA,N)
-* On entry, the symmetric matrix A. If UPLO = 'U', the leading
-* n-by-n upper triangular part of A contains the upper
-* triangular part of the matrix A, and the strictly lower
-* triangular part of A is not referenced. If UPLO = 'L', the
-* leading n-by-n lower triangular part of A contains the lower
-* triangular part of the matrix A, and the strictly upper
-* triangular part of A is not referenced.
-* On exit:
-* if UPLO = 'U', the last NB columns have been reduced to
-* tridiagonal form, with the diagonal elements overwriting
-* the diagonal elements of A; the elements above the diagonal
-* with the array TAU, represent the orthogonal matrix Q as a
-* product of elementary reflectors;
-* if UPLO = 'L', the first NB columns have been reduced to
-* tridiagonal form, with the diagonal elements overwriting
-* the diagonal elements of A; the elements below the diagonal
-* with the array TAU, represent the orthogonal matrix Q as a
-* product of elementary reflectors.
-* See Further Details.
-*
-* LDA (input) INTEGER
-* The leading dimension of the array A. LDA >= (1,N).
+*> \param[in] UPLO
+*> \verbatim
+*> UPLO is CHARACTER*1
+*> Specifies whether the upper or lower triangular part of the
+*> symmetric matrix A is stored:
+*> = 'U': Upper triangular
+*> = 'L': Lower triangular
+*> \endverbatim
+*>
+*> \param[in] N
+*> \verbatim
+*> N is INTEGER
+*> The order of the matrix A.
+*> \endverbatim
+*>
+*> \param[in] NB
+*> \verbatim
+*> NB is INTEGER
+*> The number of rows and columns to be reduced.
+*> \endverbatim
+*>
+*
+* Authors
+* =======
*
-* E (output) REAL array, dimension (N-1)
-* If UPLO = 'U', E(n-nb:n-1) contains the superdiagonal
-* elements of the last NB columns of the reduced matrix;
-* if UPLO = 'L', E(1:nb) contains the subdiagonal elements of
-* the first NB columns of the reduced matrix.
+*> \author Univ. of Tennessee
+*> \author Univ. of California Berkeley
+*> \author Univ. of Colorado Denver
+*> \author NAG Ltd.
*
-* TAU (output) REAL array, dimension (N-1)
-* The scalar factors of the elementary reflectors, stored in
-* TAU(n-nb:n-1) if UPLO = 'U', and in TAU(1:nb) if UPLO = 'L'.
-* See Further Details.
+*> \date November 2011
*
-* W (output) REAL array, dimension (LDW,NB)
-* The n-by-nb matrix W required to update the unreduced part
-* of A.
+*> \ingroup realOTHERauxiliary
*
-* LDW (input) INTEGER
-* The leading dimension of the array W. LDW >= max(1,N).
*
* Further Details
* ===============
+*>\details \b Further \b Details
+*> \verbatim
+* See Further Details.
+*>
+*> LDA (input) INTEGER
+*> The leading dimension of the array A. LDA >= (1,N).
+*>
+*> E (output) REAL array, dimension (N-1)
+*> If UPLO = 'U', E(n-nb:n-1) contains the superdiagonal
+*> elements of the last NB columns of the reduced matrix;
+*> if UPLO = 'L', E(1:nb) contains the subdiagonal elements of
+*> the first NB columns of the reduced matrix.
+*>
+*> TAU (output) REAL array, dimension (N-1)
+*> The scalar factors of the elementary reflectors, stored in
+*> TAU(n-nb:n-1) if UPLO = 'U', and in TAU(1:nb) if UPLO = 'L'.
+*> See Further Details.
+*>
+*> W (output) REAL array, dimension (LDW,NB)
+*> The n-by-nb matrix W required to update the unreduced part
+*> of A.
+*>
+*> LDW (input) INTEGER
+*> The leading dimension of the array W. LDW >= max(1,N).
+*>
+*>
+*> If UPLO = 'U', the matrix Q is represented as a product of elementary
+*> reflectors
+*>
+*> Q = H(n) H(n-1) . . . H(n-nb+1).
+*>
+*> Each H(i) has the form
+*>
+*> H(i) = I - tau * v * v**T
+*>
+*> where tau is a real scalar, and v is a real vector with
+*> v(i:n) = 0 and v(i-1) = 1; v(1:i-1) is stored on exit in A(1:i-1,i),
+*> and tau in TAU(i-1).
+*>
+*> If UPLO = 'L', the matrix Q is represented as a product of elementary
+*> reflectors
+*>
+*> Q = H(1) H(2) . . . H(nb).
+*>
+*> Each H(i) has the form
+*>
+*> H(i) = I - tau * v * v**T
+*>
+*> where tau is a real scalar, and v is a real vector with
+*> v(1:i) = 0 and v(i+1) = 1; v(i+1:n) is stored on exit in A(i+1:n,i),
+*> and tau in TAU(i).
+*>
+*> The elements of the vectors v together form the n-by-nb matrix V
+*> which is needed, with W, to apply the transformation to the unreduced
+*> part of the matrix, using a symmetric rank-2k update of the form:
+*> A := A - V*W**T - W*V**T.
+*>
+*> The contents of A on exit are illustrated by the following examples
+*> with n = 5 and nb = 2:
+*>
+*> if UPLO = 'U': if UPLO = 'L':
+*>
+*> ( a a a v4 v5 ) ( d )
+*> ( a a v4 v5 ) ( 1 d )
+*> ( a 1 v5 ) ( v1 1 a )
+*> ( d 1 ) ( v1 v2 a a )
+*> ( d ) ( v1 v2 a a a )
+*>
+*> where d denotes a diagonal element of the reduced matrix, a denotes
+*> an element of the original matrix that is unchanged, and vi denotes
+*> an element of the vector defining H(i).
+*>
+*> \endverbatim
+*>
+* =====================================================================
+ SUBROUTINE SLATRD( UPLO, N, NB, A, LDA, E, TAU, W, LDW )
*
-* If UPLO = 'U', the matrix Q is represented as a product of elementary
-* reflectors
-*
-* Q = H(n) H(n-1) . . . H(n-nb+1).
-*
-* Each H(i) has the form
-*
-* H(i) = I - tau * v * v**T
-*
-* where tau is a real scalar, and v is a real vector with
-* v(i:n) = 0 and v(i-1) = 1; v(1:i-1) is stored on exit in A(1:i-1,i),
-* and tau in TAU(i-1).
-*
-* If UPLO = 'L', the matrix Q is represented as a product of elementary
-* reflectors
-*
-* Q = H(1) H(2) . . . H(nb).
-*
-* Each H(i) has the form
-*
-* H(i) = I - tau * v * v**T
-*
-* where tau is a real scalar, and v is a real vector with
-* v(1:i) = 0 and v(i+1) = 1; v(i+1:n) is stored on exit in A(i+1:n,i),
-* and tau in TAU(i).
-*
-* The elements of the vectors v together form the n-by-nb matrix V
-* which is needed, with W, to apply the transformation to the unreduced
-* part of the matrix, using a symmetric rank-2k update of the form:
-* A := A - V*W**T - W*V**T.
-*
-* The contents of A on exit are illustrated by the following examples
-* with n = 5 and nb = 2:
-*
-* if UPLO = 'U': if UPLO = 'L':
-*
-* ( a a a v4 v5 ) ( d )
-* ( a a v4 v5 ) ( 1 d )
-* ( a 1 v5 ) ( v1 1 a )
-* ( d 1 ) ( v1 v2 a a )
-* ( d ) ( v1 v2 a a a )
+* -- LAPACK auxiliary routine (version 3.3.1) --
+* -- LAPACK is a software package provided by Univ. of Tennessee, --
+* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
+* November 2011
*
-* where d denotes a diagonal element of the reduced matrix, a denotes
-* an element of the original matrix that is unchanged, and vi denotes
-* an element of the vector defining H(i).
+* .. Scalar Arguments ..
+ CHARACTER UPLO
+ INTEGER LDA, LDW, N, NB
+* ..
+* .. Array Arguments ..
+ REAL A( LDA, * ), E( * ), TAU( * ), W( LDW, * )
+* ..
*
* =====================================================================
*