From e1d39294aee16fa6db9ba079b14442358217db71 Mon Sep 17 00:00:00 2001 From: julie Date: Thu, 6 Oct 2011 06:53:11 +0000 Subject: Integrating Doxygen in comments --- SRC/dsytrd.f | 254 +++++++++++++++++++++++++++++++++-------------------------- 1 file changed, 144 insertions(+), 110 deletions(-) (limited to 'SRC/dsytrd.f') diff --git a/SRC/dsytrd.f b/SRC/dsytrd.f index 53bbab73..b53e61da 100644 --- a/SRC/dsytrd.f +++ b/SRC/dsytrd.f @@ -1,129 +1,163 @@ - SUBROUTINE DSYTRD( UPLO, N, A, LDA, D, E, TAU, WORK, LWORK, INFO ) -* -* -- LAPACK 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 INFO, LDA, LWORK, N -* .. -* .. Array Arguments .. - DOUBLE PRECISION A( LDA, * ), D( * ), E( * ), TAU( * ), - $ WORK( * ) -* .. -* +*> \brief \b DSYTRD +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +* Definition +* ========== +* +* SUBROUTINE DSYTRD( UPLO, N, A, LDA, D, E, TAU, WORK, LWORK, INFO ) +* +* .. Scalar Arguments .. +* CHARACTER UPLO +* INTEGER INFO, LDA, LWORK, N +* .. +* .. Array Arguments .. +* DOUBLE PRECISION A( LDA, * ), D( * ), E( * ), TAU( * ), +* $ WORK( * ) +* .. +* * Purpose * ======= * -* DSYTRD reduces a real symmetric matrix A to real symmetric -* tridiagonal form T by an orthogonal similarity transformation: -* Q**T * A * Q = T. +*>\details \b Purpose: +*>\verbatim +*> +*> DSYTRD reduces a real symmetric matrix A to real symmetric +*> tridiagonal form T by an orthogonal similarity transformation: +*> Q**T * A * Q = T. +*> +*>\endverbatim * * Arguments * ========= * -* UPLO (input) CHARACTER*1 -* = 'U': Upper triangle of A is stored; -* = 'L': Lower triangle of A is stored. -* -* N (input) INTEGER -* The order of the matrix A. N >= 0. -* -* A (input/output) DOUBLE PRECISION 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 diagonal and first superdiagonal -* of A are overwritten by the corresponding elements of the -* tridiagonal matrix T, and the elements above the first -* superdiagonal, with the array TAU, represent the orthogonal -* matrix Q as a product of elementary reflectors; if UPLO -* = 'L', the diagonal and first subdiagonal of A are over- -* written by the corresponding elements of the tridiagonal -* matrix T, and the elements below the first subdiagonal, 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 >= max(1,N). -* -* D (output) DOUBLE PRECISION array, dimension (N) -* The diagonal elements of the tridiagonal matrix T: -* D(i) = A(i,i). -* -* E (output) DOUBLE PRECISION array, dimension (N-1) -* The off-diagonal elements of the tridiagonal matrix T: -* E(i) = A(i,i+1) if UPLO = 'U', E(i) = A(i+1,i) if UPLO = 'L'. -* -* TAU (output) DOUBLE PRECISION array, dimension (N-1) -* The scalar factors of the elementary reflectors (see Further -* Details). +*> \param[in] UPLO +*> \verbatim +*> UPLO is CHARACTER*1 +*> = 'U': Upper triangle of A is stored; +*> = 'L': Lower triangle of A is stored. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> The order of the matrix A. N >= 0. +*> \endverbatim +*> +* +* Authors +* ======= * -* WORK (workspace/output) DOUBLE PRECISION array, dimension (MAX(1,LWORK)) -* On exit, if INFO = 0, WORK(1) returns the optimal LWORK. +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. * -* LWORK (input) INTEGER -* The dimension of the array WORK. LWORK >= 1. -* For optimum performance LWORK >= N*NB, where NB is the -* optimal blocksize. +*> \date November 2011 * -* If LWORK = -1, then a workspace query is assumed; the routine -* only calculates the optimal size of the WORK array, returns -* this value as the first entry of the WORK array, and no error -* message related to LWORK is issued by XERBLA. +*> \ingroup doubleSYcomputational * -* 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 +* of elementary reflectors. See Further Details. +*> +*> LDA (input) INTEGER +*> The leading dimension of the array A. LDA >= max(1,N). +*> +*> D (output) DOUBLE PRECISION array, dimension (N) +*> The diagonal elements of the tridiagonal matrix T: +*> D(i) = A(i,i). +*> +*> E (output) DOUBLE PRECISION array, dimension (N-1) +*> The off-diagonal elements of the tridiagonal matrix T: +*> E(i) = A(i,i+1) if UPLO = 'U', E(i) = A(i+1,i) if UPLO = 'L'. +*> +*> TAU (output) DOUBLE PRECISION array, dimension (N-1) +*> The scalar factors of the elementary reflectors (see Further +*> Details). +*> +*> WORK (workspace/output) DOUBLE PRECISION array, dimension (MAX(1,LWORK)) +*> On exit, if INFO = 0, WORK(1) returns the optimal LWORK. +*> +*> LWORK (input) INTEGER +*> The dimension of the array WORK. LWORK >= 1. +*> For optimum performance LWORK >= N*NB, where NB is the +*> optimal blocksize. +*> +*> If LWORK = -1, then a workspace query is assumed; the routine +*> only calculates the optimal size of the WORK array, returns +*> this value as the first entry of the WORK array, and no error +*> message related to LWORK is issued by XERBLA. +*> +*> INFO (output) INTEGER +*> = 0: successful exit +*> < 0: if INFO = -i, the i-th argument had an illegal value +*> +*> +*> If UPLO = 'U', the matrix Q is represented as a product of elementary +*> reflectors +*> +*> Q = H(n-1) . . . H(2) H(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+1:n) = 0 and v(i) = 1; v(1:i-1) is stored on exit in +*> A(1:i-1,i+1), and tau in TAU(i). +*> +*> If UPLO = 'L', the matrix Q is represented as a product of elementary +*> reflectors +*> +*> Q = H(1) H(2) . . . H(n-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(1:i) = 0 and v(i+1) = 1; v(i+2:n) is stored on exit in A(i+2:n,i), +*> and tau in TAU(i). +*> +*> The contents of A on exit are illustrated by the following examples +*> with n = 5: +*> +*> if UPLO = 'U': if UPLO = 'L': +*> +*> ( d e v2 v3 v4 ) ( d ) +*> ( d e v3 v4 ) ( e d ) +*> ( d e v4 ) ( v1 e d ) +*> ( d e ) ( v1 v2 e d ) +*> ( d ) ( v1 v2 v3 e d ) +*> +*> where d and e denote diagonal and off-diagonal elements of T, and vi +*> denotes an element of the vector defining H(i). +*> +*> \endverbatim +*> +* ===================================================================== + SUBROUTINE DSYTRD( UPLO, N, A, LDA, D, E, TAU, WORK, LWORK, INFO ) * -* If UPLO = 'U', the matrix Q is represented as a product of elementary -* reflectors -* -* Q = H(n-1) . . . H(2) H(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+1:n) = 0 and v(i) = 1; v(1:i-1) is stored on exit in -* A(1:i-1,i+1), and tau in TAU(i). -* -* If UPLO = 'L', the matrix Q is represented as a product of elementary -* reflectors -* -* Q = H(1) H(2) . . . H(n-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(1:i) = 0 and v(i+1) = 1; v(i+2:n) is stored on exit in A(i+2:n,i), -* and tau in TAU(i). -* -* The contents of A on exit are illustrated by the following examples -* with n = 5: -* -* if UPLO = 'U': if UPLO = 'L': -* -* ( d e v2 v3 v4 ) ( d ) -* ( d e v3 v4 ) ( e d ) -* ( d e v4 ) ( v1 e d ) -* ( d e ) ( v1 v2 e d ) -* ( d ) ( v1 v2 v3 e d ) +* -- LAPACK computational 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 and e denote diagonal and off-diagonal elements of T, and vi -* denotes an element of the vector defining H(i). +* .. Scalar Arguments .. + CHARACTER UPLO + INTEGER INFO, LDA, LWORK, N +* .. +* .. Array Arguments .. + DOUBLE PRECISION A( LDA, * ), D( * ), E( * ), TAU( * ), + $ WORK( * ) +* .. * * ===================================================================== * -- cgit v1.2.3