--- rpl/lapack/lapack/zlatrd.f 2011/07/22 07:38:18 1.8
+++ rpl/lapack/lapack/zlatrd.f 2011/11/21 20:43:18 1.9
@@ -1,9 +1,208 @@
+*> \brief \b ZLATRD
+*
+* =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+* http://www.netlib.org/lapack/explore-html/
+*
+*> \htmlonly
+*> Download ZLATRD + dependencies
+*>
+*> [TGZ]
+*>
+*> [ZIP]
+*>
+*> [TXT]
+*> \endhtmlonly
+*
+* Definition:
+* ===========
+*
+* SUBROUTINE ZLATRD( UPLO, N, NB, A, LDA, E, TAU, W, LDW )
+*
+* .. Scalar Arguments ..
+* CHARACTER UPLO
+* INTEGER LDA, LDW, N, NB
+* ..
+* .. Array Arguments ..
+* DOUBLE PRECISION E( * )
+* COMPLEX*16 A( LDA, * ), TAU( * ), W( LDW, * )
+* ..
+*
+*
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
+*>
+*> ZLATRD reduces NB rows and columns of a complex Hermitian matrix A to
+*> Hermitian tridiagonal form by a unitary similarity
+*> transformation Q**H * 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', ZLATRD reduces the last NB rows and columns of a
+*> matrix, of which the upper triangle is supplied;
+*> if UPLO = 'L', ZLATRD reduces the first NB rows and columns of a
+*> matrix, of which the lower triangle is supplied.
+*>
+*> This is an auxiliary routine called by ZHETRD.
+*> \endverbatim
+*
+* Arguments:
+* ==========
+*
+*> \param[in] UPLO
+*> \verbatim
+*> UPLO is CHARACTER*1
+*> Specifies whether the upper or lower triangular part of the
+*> Hermitian 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
+*>
+*> \param[in,out] A
+*> \verbatim
+*> A is COMPLEX*16 array, dimension (LDA,N)
+*> On entry, the Hermitian 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 unitary 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 unitary matrix Q as a
+*> product of elementary reflectors.
+*> See Further Details.
+*> \endverbatim
+*>
+*> \param[in] LDA
+*> \verbatim
+*> LDA is INTEGER
+*> The leading dimension of the array A. LDA >= max(1,N).
+*> \endverbatim
+*>
+*> \param[out] E
+*> \verbatim
+*> E is DOUBLE PRECISION 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.
+*> \endverbatim
+*>
+*> \param[out] TAU
+*> \verbatim
+*> TAU is COMPLEX*16 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.
+*> \endverbatim
+*>
+*> \param[out] W
+*> \verbatim
+*> W is COMPLEX*16 array, dimension (LDW,NB)
+*> The n-by-nb matrix W required to update the unreduced part
+*> of A.
+*> \endverbatim
+*>
+*> \param[in] LDW
+*> \verbatim
+*> LDW is INTEGER
+*> The leading dimension of the array W. LDW >= max(1,N).
+*> \endverbatim
+*
+* Authors:
+* ========
+*
+*> \author Univ. of Tennessee
+*> \author Univ. of California Berkeley
+*> \author Univ. of Colorado Denver
+*> \author NAG Ltd.
+*
+*> \date November 2011
+*
+*> \ingroup complex16OTHERauxiliary
+*
+*> \par Further Details:
+* =====================
+*>
+*> \verbatim
+*>
+*> 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**H
+*>
+*> where tau is a complex scalar, and v is a complex 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**H
+*>
+*> where tau is a complex scalar, and v is a complex 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 Hermitian rank-2k update of the form:
+*> A := A - V*W**H - W*V**H.
+*>
+*> 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 ZLATRD( UPLO, N, NB, A, LDA, E, TAU, W, LDW )
*
-* -- LAPACK auxiliary routine (version 3.3.1) --
+* -- LAPACK auxiliary routine (version 3.4.0) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
-* -- April 2011 --
+* November 2011
*
* .. Scalar Arguments ..
CHARACTER UPLO
@@ -14,127 +213,6 @@
COMPLEX*16 A( LDA, * ), TAU( * ), W( LDW, * )
* ..
*
-* Purpose
-* =======
-*
-* ZLATRD reduces NB rows and columns of a complex Hermitian matrix A to
-* Hermitian tridiagonal form by a unitary similarity
-* transformation Q**H * 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', ZLATRD reduces the last NB rows and columns of a
-* matrix, of which the upper triangle is supplied;
-* if UPLO = 'L', ZLATRD reduces the first NB rows and columns of a
-* matrix, of which the lower triangle is supplied.
-*
-* This is an auxiliary routine called by ZHETRD.
-*
-* Arguments
-* =========
-*
-* UPLO (input) CHARACTER*1
-* Specifies whether the upper or lower triangular part of the
-* Hermitian 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) COMPLEX*16 array, dimension (LDA,N)
-* On entry, the Hermitian 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 unitary 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 unitary 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).
-*
-* E (output) DOUBLE PRECISION 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) COMPLEX*16 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) COMPLEX*16 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).
-*
-* Further Details
-* ===============
-*
-* 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**H
-*
-* where tau is a complex scalar, and v is a complex 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**H
-*
-* where tau is a complex scalar, and v is a complex 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 Hermitian rank-2k update of the form:
-* A := A - V*W**H - W*V**H.
-*
-* 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).
-*
* =====================================================================
*
* .. Parameters ..