julie
be91086043
Those are just cosmetic changes to update version number and various other minor change.
298 lines
9.4 KiB
FortranFixed
298 lines
9.4 KiB
FortranFixed
SUBROUTINE CHETRD( UPLO, N, A, LDA, D, E, TAU, WORK, LWORK, INFO )
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*
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* -- LAPACK routine (version 3.2) --
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* -- LAPACK is a software package provided by Univ. of Tennessee, --
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* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
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* November 2006
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*
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* .. Scalar Arguments ..
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CHARACTER UPLO
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INTEGER INFO, LDA, LWORK, N
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* ..
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* .. Array Arguments ..
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REAL D( * ), E( * )
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COMPLEX A( LDA, * ), TAU( * ), WORK( * )
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* ..
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*
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* Purpose
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* =======
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*
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* CHETRD reduces a complex Hermitian matrix A to real symmetric
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* tridiagonal form T by a unitary similarity transformation:
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* Q**H * A * Q = T.
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*
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* Arguments
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* =========
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*
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* UPLO (input) CHARACTER*1
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* = 'U': Upper triangle of A is stored;
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* = 'L': Lower triangle of A is stored.
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*
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* N (input) INTEGER
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* The order of the matrix A. N >= 0.
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*
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* A (input/output) COMPLEX array, dimension (LDA,N)
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* On entry, the Hermitian matrix A. If UPLO = 'U', the leading
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* N-by-N upper triangular part of A contains the upper
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* triangular part of the matrix A, and the strictly lower
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* triangular part of A is not referenced. If UPLO = 'L', the
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* leading N-by-N lower triangular part of A contains the lower
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* triangular part of the matrix A, and the strictly upper
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* triangular part of A is not referenced.
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* On exit, if UPLO = 'U', the diagonal and first superdiagonal
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* of A are overwritten by the corresponding elements of the
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* tridiagonal matrix T, and the elements above the first
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* superdiagonal, with the array TAU, represent the unitary
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* matrix Q as a product of elementary reflectors; if UPLO
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* = 'L', the diagonal and first subdiagonal of A are over-
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* written by the corresponding elements of the tridiagonal
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* matrix T, and the elements below the first subdiagonal, with
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* the array TAU, represent the unitary matrix Q as a product
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* of elementary reflectors. See Further Details.
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*
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* LDA (input) INTEGER
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* The leading dimension of the array A. LDA >= max(1,N).
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*
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* D (output) REAL array, dimension (N)
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* The diagonal elements of the tridiagonal matrix T:
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* D(i) = A(i,i).
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*
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* E (output) REAL array, dimension (N-1)
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* The off-diagonal elements of the tridiagonal matrix T:
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* E(i) = A(i,i+1) if UPLO = 'U', E(i) = A(i+1,i) if UPLO = 'L'.
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*
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* TAU (output) COMPLEX array, dimension (N-1)
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* The scalar factors of the elementary reflectors (see Further
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* Details).
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*
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* WORK (workspace/output) COMPLEX array, dimension (MAX(1,LWORK))
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* On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
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*
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* LWORK (input) INTEGER
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* The dimension of the array WORK. LWORK >= 1.
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* For optimum performance LWORK >= N*NB, where NB is the
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* optimal blocksize.
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*
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* If LWORK = -1, then a workspace query is assumed; the routine
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* only calculates the optimal size of the WORK array, returns
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* this value as the first entry of the WORK array, and no error
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* message related to LWORK is issued by XERBLA.
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*
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* INFO (output) INTEGER
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* = 0: successful exit
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* < 0: if INFO = -i, the i-th argument had an illegal value
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*
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* Further Details
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* ===============
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*
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* If UPLO = 'U', the matrix Q is represented as a product of elementary
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* reflectors
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*
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* Q = H(n-1) . . . H(2) H(1).
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*
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* Each H(i) has the form
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*
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* H(i) = I - tau * v * v'
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*
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* where tau is a complex scalar, and v is a complex vector with
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* v(i+1:n) = 0 and v(i) = 1; v(1:i-1) is stored on exit in
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* A(1:i-1,i+1), and tau in TAU(i).
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*
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* If UPLO = 'L', the matrix Q is represented as a product of elementary
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* reflectors
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*
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* Q = H(1) H(2) . . . H(n-1).
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*
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* Each H(i) has the form
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*
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* H(i) = I - tau * v * v'
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*
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* where tau is a complex scalar, and v is a complex vector with
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* v(1:i) = 0 and v(i+1) = 1; v(i+2:n) is stored on exit in A(i+2:n,i),
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* and tau in TAU(i).
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*
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* The contents of A on exit are illustrated by the following examples
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* with n = 5:
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*
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* if UPLO = 'U': if UPLO = 'L':
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*
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* ( d e v2 v3 v4 ) ( d )
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* ( d e v3 v4 ) ( e d )
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* ( d e v4 ) ( v1 e d )
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* ( d e ) ( v1 v2 e d )
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* ( d ) ( v1 v2 v3 e d )
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*
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* where d and e denote diagonal and off-diagonal elements of T, and vi
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* denotes an element of the vector defining H(i).
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*
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* =====================================================================
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*
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* .. Parameters ..
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REAL ONE
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PARAMETER ( ONE = 1.0E+0 )
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COMPLEX CONE
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PARAMETER ( CONE = ( 1.0E+0, 0.0E+0 ) )
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* ..
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* .. Local Scalars ..
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LOGICAL LQUERY, UPPER
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INTEGER I, IINFO, IWS, J, KK, LDWORK, LWKOPT, NB,
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$ NBMIN, NX
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* ..
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* .. External Subroutines ..
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EXTERNAL CHER2K, CHETD2, CLATRD, XERBLA
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC MAX
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* ..
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* .. External Functions ..
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LOGICAL LSAME
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INTEGER ILAENV
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EXTERNAL LSAME, ILAENV
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* ..
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* .. Executable Statements ..
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*
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* Test the input parameters
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*
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INFO = 0
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UPPER = LSAME( UPLO, 'U' )
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LQUERY = ( LWORK.EQ.-1 )
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IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
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INFO = -1
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ELSE IF( N.LT.0 ) THEN
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INFO = -2
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ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
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INFO = -4
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ELSE IF( LWORK.LT.1 .AND. .NOT.LQUERY ) THEN
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INFO = -9
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END IF
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*
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IF( INFO.EQ.0 ) THEN
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*
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* Determine the block size.
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*
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NB = ILAENV( 1, 'CHETRD', UPLO, N, -1, -1, -1 )
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LWKOPT = N*NB
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WORK( 1 ) = LWKOPT
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END IF
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*
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IF( INFO.NE.0 ) THEN
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CALL XERBLA( 'CHETRD', -INFO )
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RETURN
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ELSE IF( LQUERY ) THEN
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RETURN
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END IF
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*
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* Quick return if possible
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*
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IF( N.EQ.0 ) THEN
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WORK( 1 ) = 1
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RETURN
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END IF
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*
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NX = N
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IWS = 1
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IF( NB.GT.1 .AND. NB.LT.N ) THEN
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*
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* Determine when to cross over from blocked to unblocked code
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* (last block is always handled by unblocked code).
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*
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NX = MAX( NB, ILAENV( 3, 'CHETRD', UPLO, N, -1, -1, -1 ) )
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IF( NX.LT.N ) THEN
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*
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* Determine if workspace is large enough for blocked code.
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*
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LDWORK = N
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IWS = LDWORK*NB
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IF( LWORK.LT.IWS ) THEN
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*
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* Not enough workspace to use optimal NB: determine the
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* minimum value of NB, and reduce NB or force use of
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* unblocked code by setting NX = N.
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*
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NB = MAX( LWORK / LDWORK, 1 )
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NBMIN = ILAENV( 2, 'CHETRD', UPLO, N, -1, -1, -1 )
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IF( NB.LT.NBMIN )
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$ NX = N
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END IF
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ELSE
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NX = N
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END IF
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ELSE
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NB = 1
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END IF
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*
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IF( UPPER ) THEN
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*
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* Reduce the upper triangle of A.
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* Columns 1:kk are handled by the unblocked method.
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*
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KK = N - ( ( N-NX+NB-1 ) / NB )*NB
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DO 20 I = N - NB + 1, KK + 1, -NB
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*
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* Reduce columns i:i+nb-1 to tridiagonal form and form the
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* matrix W which is needed to update the unreduced part of
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* the matrix
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*
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CALL CLATRD( UPLO, I+NB-1, NB, A, LDA, E, TAU, WORK,
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$ LDWORK )
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*
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* Update the unreduced submatrix A(1:i-1,1:i-1), using an
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* update of the form: A := A - V*W' - W*V'
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*
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CALL CHER2K( UPLO, 'No transpose', I-1, NB, -CONE,
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$ A( 1, I ), LDA, WORK, LDWORK, ONE, A, LDA )
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*
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* Copy superdiagonal elements back into A, and diagonal
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* elements into D
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*
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DO 10 J = I, I + NB - 1
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A( J-1, J ) = E( J-1 )
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D( J ) = A( J, J )
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10 CONTINUE
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20 CONTINUE
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*
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* Use unblocked code to reduce the last or only block
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*
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CALL CHETD2( UPLO, KK, A, LDA, D, E, TAU, IINFO )
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ELSE
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*
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* Reduce the lower triangle of A
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*
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DO 40 I = 1, N - NX, NB
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*
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* Reduce columns i:i+nb-1 to tridiagonal form and form the
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* matrix W which is needed to update the unreduced part of
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* the matrix
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*
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CALL CLATRD( UPLO, N-I+1, NB, A( I, I ), LDA, E( I ),
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$ TAU( I ), WORK, LDWORK )
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*
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* Update the unreduced submatrix A(i+nb:n,i+nb:n), using
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* an update of the form: A := A - V*W' - W*V'
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*
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CALL CHER2K( UPLO, 'No transpose', N-I-NB+1, NB, -CONE,
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$ A( I+NB, I ), LDA, WORK( NB+1 ), LDWORK, ONE,
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$ A( I+NB, I+NB ), LDA )
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*
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* Copy subdiagonal elements back into A, and diagonal
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* elements into D
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*
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DO 30 J = I, I + NB - 1
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A( J+1, J ) = E( J )
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D( J ) = A( J, J )
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30 CONTINUE
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40 CONTINUE
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*
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* Use unblocked code to reduce the last or only block
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*
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CALL CHETD2( UPLO, N-I+1, A( I, I ), LDA, D( I ), E( I ),
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$ TAU( I ), IINFO )
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END IF
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*
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WORK( 1 ) = LWKOPT
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RETURN
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*
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* End of CHETRD
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*
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END
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