From 8c8d2f518968ce7057eec6aa5cd5aec8faab861a Mon Sep 17 00:00:00 2001 From: jofret Date: Tue, 28 Apr 2009 07:17:00 +0000 Subject: Moving lapack to right place --- src/lib/lapack/zhetrd.f | 296 ------------------------------------------------ 1 file changed, 296 deletions(-) delete mode 100644 src/lib/lapack/zhetrd.f (limited to 'src/lib/lapack/zhetrd.f') diff --git a/src/lib/lapack/zhetrd.f b/src/lib/lapack/zhetrd.f deleted file mode 100644 index fb0cd0b2..00000000 --- a/src/lib/lapack/zhetrd.f +++ /dev/null @@ -1,296 +0,0 @@ - SUBROUTINE ZHETRD( UPLO, N, A, LDA, D, E, TAU, WORK, LWORK, INFO ) -* -* -- LAPACK routine (version 3.1) -- -* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. -* November 2006 -* -* .. Scalar Arguments .. - CHARACTER UPLO - INTEGER INFO, LDA, LWORK, N -* .. -* .. Array Arguments .. - DOUBLE PRECISION D( * ), E( * ) - COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * ) -* .. -* -* Purpose -* ======= -* -* ZHETRD reduces a complex Hermitian matrix A to real symmetric -* tridiagonal form T by a unitary similarity transformation: -* Q**H * A * Q = T. -* -* 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) 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 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 unitary -* 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 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). -* -* 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) COMPLEX*16 array, dimension (N-1) -* The scalar factors of the elementary reflectors (see Further -* Details). -* -* WORK (workspace/output) COMPLEX*16 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 -* -* Further Details -* =============== -* -* 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' -* -* where tau is a complex scalar, and v is a complex 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' -* -* where tau is a complex scalar, and v is a complex 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). -* -* ===================================================================== -* -* .. Parameters .. - DOUBLE PRECISION ONE - PARAMETER ( ONE = 1.0D+0 ) - COMPLEX*16 CONE - PARAMETER ( CONE = ( 1.0D+0, 0.0D+0 ) ) -* .. -* .. Local Scalars .. - LOGICAL LQUERY, UPPER - INTEGER I, IINFO, IWS, J, KK, LDWORK, LWKOPT, NB, - $ NBMIN, NX -* .. -* .. External Subroutines .. - EXTERNAL XERBLA, ZHER2K, ZHETD2, ZLATRD -* .. -* .. Intrinsic Functions .. - INTRINSIC MAX -* .. -* .. External Functions .. - LOGICAL LSAME - INTEGER ILAENV - EXTERNAL LSAME, ILAENV -* .. -* .. Executable Statements .. -* -* Test the input parameters -* - INFO = 0 - UPPER = LSAME( UPLO, 'U' ) - LQUERY = ( LWORK.EQ.-1 ) - IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN - INFO = -1 - ELSE IF( N.LT.0 ) THEN - INFO = -2 - ELSE IF( LDA.LT.MAX( 1, N ) ) THEN - INFO = -4 - ELSE IF( LWORK.LT.1 .AND. .NOT.LQUERY ) THEN - INFO = -9 - END IF -* - IF( INFO.EQ.0 ) THEN -* -* Determine the block size. -* - NB = ILAENV( 1, 'ZHETRD', UPLO, N, -1, -1, -1 ) - LWKOPT = N*NB - WORK( 1 ) = LWKOPT - END IF -* - IF( INFO.NE.0 ) THEN - CALL XERBLA( 'ZHETRD', -INFO ) - RETURN - ELSE IF( LQUERY ) THEN - RETURN - END IF -* -* Quick return if possible -* - IF( N.EQ.0 ) THEN - WORK( 1 ) = 1 - RETURN - END IF -* - NX = N - IWS = 1 - IF( NB.GT.1 .AND. NB.LT.N ) THEN -* -* Determine when to cross over from blocked to unblocked code -* (last block is always handled by unblocked code). -* - NX = MAX( NB, ILAENV( 3, 'ZHETRD', UPLO, N, -1, -1, -1 ) ) - IF( NX.LT.N ) THEN -* -* Determine if workspace is large enough for blocked code. -* - LDWORK = N - IWS = LDWORK*NB - IF( LWORK.LT.IWS ) THEN -* -* Not enough workspace to use optimal NB: determine the -* minimum value of NB, and reduce NB or force use of -* unblocked code by setting NX = N. -* - NB = MAX( LWORK / LDWORK, 1 ) - NBMIN = ILAENV( 2, 'ZHETRD', UPLO, N, -1, -1, -1 ) - IF( NB.LT.NBMIN ) - $ NX = N - END IF - ELSE - NX = N - END IF - ELSE - NB = 1 - END IF -* - IF( UPPER ) THEN -* -* Reduce the upper triangle of A. -* Columns 1:kk are handled by the unblocked method. -* - KK = N - ( ( N-NX+NB-1 ) / NB )*NB - DO 20 I = N - NB + 1, KK + 1, -NB -* -* Reduce columns i:i+nb-1 to tridiagonal form and form the -* matrix W which is needed to update the unreduced part of -* the matrix -* - CALL ZLATRD( UPLO, I+NB-1, NB, A, LDA, E, TAU, WORK, - $ LDWORK ) -* -* Update the unreduced submatrix A(1:i-1,1:i-1), using an -* update of the form: A := A - V*W' - W*V' -* - CALL ZHER2K( UPLO, 'No transpose', I-1, NB, -CONE, - $ A( 1, I ), LDA, WORK, LDWORK, ONE, A, LDA ) -* -* Copy superdiagonal elements back into A, and diagonal -* elements into D -* - DO 10 J = I, I + NB - 1 - A( J-1, J ) = E( J-1 ) - D( J ) = A( J, J ) - 10 CONTINUE - 20 CONTINUE -* -* Use unblocked code to reduce the last or only block -* - CALL ZHETD2( UPLO, KK, A, LDA, D, E, TAU, IINFO ) - ELSE -* -* Reduce the lower triangle of A -* - DO 40 I = 1, N - NX, NB -* -* Reduce columns i:i+nb-1 to tridiagonal form and form the -* matrix W which is needed to update the unreduced part of -* the matrix -* - CALL ZLATRD( UPLO, N-I+1, NB, A( I, I ), LDA, E( I ), - $ TAU( I ), WORK, LDWORK ) -* -* Update the unreduced submatrix A(i+nb:n,i+nb:n), using -* an update of the form: A := A - V*W' - W*V' -* - CALL ZHER2K( UPLO, 'No transpose', N-I-NB+1, NB, -CONE, - $ A( I+NB, I ), LDA, WORK( NB+1 ), LDWORK, ONE, - $ A( I+NB, I+NB ), LDA ) -* -* Copy subdiagonal elements back into A, and diagonal -* elements into D -* - DO 30 J = I, I + NB - 1 - A( J+1, J ) = E( J ) - D( J ) = A( J, J ) - 30 CONTINUE - 40 CONTINUE -* -* Use unblocked code to reduce the last or only block -* - CALL ZHETD2( UPLO, N-I+1, A( I, I ), LDA, D( I ), E( I ), - $ TAU( I ), IINFO ) - END IF -* - WORK( 1 ) = LWKOPT - RETURN -* -* End of ZHETRD -* - END -- cgit