--- rpl/lapack/lapack/zgeev.f 2010/08/06 15:28:51 1.3 +++ rpl/lapack/lapack/zgeev.f 2017/06/17 11:06:41 1.16 @@ -1,10 +1,189 @@ +*> \brief ZGEEV computes the eigenvalues and, optionally, the left and/or right eigenvectors for GE matrices +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +*> \htmlonly +*> Download ZGEEV + dependencies +*> +*> [TGZ] +*> +*> [ZIP] +*> +*> [TXT] +*> \endhtmlonly +* +* Definition: +* =========== +* +* SUBROUTINE ZGEEV( JOBVL, JOBVR, N, A, LDA, W, VL, LDVL, VR, LDVR, +* WORK, LWORK, RWORK, INFO ) +* +* .. Scalar Arguments .. +* CHARACTER JOBVL, JOBVR +* INTEGER INFO, LDA, LDVL, LDVR, LWORK, N +* .. +* .. Array Arguments .. +* DOUBLE PRECISION RWORK( * ) +* COMPLEX*16 A( LDA, * ), VL( LDVL, * ), VR( LDVR, * ), +* $ W( * ), WORK( * ) +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> ZGEEV computes for an N-by-N complex nonsymmetric matrix A, the +*> eigenvalues and, optionally, the left and/or right eigenvectors. +*> +*> The right eigenvector v(j) of A satisfies +*> A * v(j) = lambda(j) * v(j) +*> where lambda(j) is its eigenvalue. +*> The left eigenvector u(j) of A satisfies +*> u(j)**H * A = lambda(j) * u(j)**H +*> where u(j)**H denotes the conjugate transpose of u(j). +*> +*> The computed eigenvectors are normalized to have Euclidean norm +*> equal to 1 and largest component real. +*> \endverbatim +* +* Arguments: +* ========== +* +*> \param[in] JOBVL +*> \verbatim +*> JOBVL is CHARACTER*1 +*> = 'N': left eigenvectors of A are not computed; +*> = 'V': left eigenvectors of are computed. +*> \endverbatim +*> +*> \param[in] JOBVR +*> \verbatim +*> JOBVR is CHARACTER*1 +*> = 'N': right eigenvectors of A are not computed; +*> = 'V': right eigenvectors of A are computed. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> The order of the matrix A. N >= 0. +*> \endverbatim +*> +*> \param[in,out] A +*> \verbatim +*> A is COMPLEX*16 array, dimension (LDA,N) +*> On entry, the N-by-N matrix A. +*> On exit, A has been overwritten. +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> The leading dimension of the array A. LDA >= max(1,N). +*> \endverbatim +*> +*> \param[out] W +*> \verbatim +*> W is COMPLEX*16 array, dimension (N) +*> W contains the computed eigenvalues. +*> \endverbatim +*> +*> \param[out] VL +*> \verbatim +*> VL is COMPLEX*16 array, dimension (LDVL,N) +*> If JOBVL = 'V', the left eigenvectors u(j) are stored one +*> after another in the columns of VL, in the same order +*> as their eigenvalues. +*> If JOBVL = 'N', VL is not referenced. +*> u(j) = VL(:,j), the j-th column of VL. +*> \endverbatim +*> +*> \param[in] LDVL +*> \verbatim +*> LDVL is INTEGER +*> The leading dimension of the array VL. LDVL >= 1; if +*> JOBVL = 'V', LDVL >= N. +*> \endverbatim +*> +*> \param[out] VR +*> \verbatim +*> VR is COMPLEX*16 array, dimension (LDVR,N) +*> If JOBVR = 'V', the right eigenvectors v(j) are stored one +*> after another in the columns of VR, in the same order +*> as their eigenvalues. +*> If JOBVR = 'N', VR is not referenced. +*> v(j) = VR(:,j), the j-th column of VR. +*> \endverbatim +*> +*> \param[in] LDVR +*> \verbatim +*> LDVR is INTEGER +*> The leading dimension of the array VR. LDVR >= 1; if +*> JOBVR = 'V', LDVR >= N. +*> \endverbatim +*> +*> \param[out] WORK +*> \verbatim +*> WORK is COMPLEX*16 array, dimension (MAX(1,LWORK)) +*> On exit, if INFO = 0, WORK(1) returns the optimal LWORK. +*> \endverbatim +*> +*> \param[in] LWORK +*> \verbatim +*> LWORK is INTEGER +*> The dimension of the array WORK. LWORK >= max(1,2*N). +*> For good performance, LWORK must generally be larger. +*> +*> 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. +*> \endverbatim +*> +*> \param[out] RWORK +*> \verbatim +*> RWORK is DOUBLE PRECISION array, dimension (2*N) +*> \endverbatim +*> +*> \param[out] INFO +*> \verbatim +*> INFO is INTEGER +*> = 0: successful exit +*> < 0: if INFO = -i, the i-th argument had an illegal value. +*> > 0: if INFO = i, the QR algorithm failed to compute all the +*> eigenvalues, and no eigenvectors have been computed; +*> elements and i+1:N of W contain eigenvalues which have +*> converged. +*> \endverbatim +* +* Authors: +* ======== +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date June 2016 +* +* @precisions fortran z -> c +* +*> \ingroup complex16GEeigen +* +* ===================================================================== SUBROUTINE ZGEEV( JOBVL, JOBVR, N, A, LDA, W, VL, LDVL, VR, LDVR, $ WORK, LWORK, RWORK, INFO ) + implicit none * -* -- LAPACK driver routine (version 3.2) -- +* -- LAPACK driver routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* November 2006 +* June 2016 * * .. Scalar Arguments .. CHARACTER JOBVL, JOBVR @@ -16,90 +195,6 @@ $ W( * ), WORK( * ) * .. * -* Purpose -* ======= -* -* ZGEEV computes for an N-by-N complex nonsymmetric matrix A, the -* eigenvalues and, optionally, the left and/or right eigenvectors. -* -* The right eigenvector v(j) of A satisfies -* A * v(j) = lambda(j) * v(j) -* where lambda(j) is its eigenvalue. -* The left eigenvector u(j) of A satisfies -* u(j)**H * A = lambda(j) * u(j)**H -* where u(j)**H denotes the conjugate transpose of u(j). -* -* The computed eigenvectors are normalized to have Euclidean norm -* equal to 1 and largest component real. -* -* Arguments -* ========= -* -* JOBVL (input) CHARACTER*1 -* = 'N': left eigenvectors of A are not computed; -* = 'V': left eigenvectors of are computed. -* -* JOBVR (input) CHARACTER*1 -* = 'N': right eigenvectors of A are not computed; -* = 'V': right eigenvectors of A are computed. -* -* N (input) INTEGER -* The order of the matrix A. N >= 0. -* -* A (input/output) COMPLEX*16 array, dimension (LDA,N) -* On entry, the N-by-N matrix A. -* On exit, A has been overwritten. -* -* LDA (input) INTEGER -* The leading dimension of the array A. LDA >= max(1,N). -* -* W (output) COMPLEX*16 array, dimension (N) -* W contains the computed eigenvalues. -* -* VL (output) COMPLEX*16 array, dimension (LDVL,N) -* If JOBVL = 'V', the left eigenvectors u(j) are stored one -* after another in the columns of VL, in the same order -* as their eigenvalues. -* If JOBVL = 'N', VL is not referenced. -* u(j) = VL(:,j), the j-th column of VL. -* -* LDVL (input) INTEGER -* The leading dimension of the array VL. LDVL >= 1; if -* JOBVL = 'V', LDVL >= N. -* -* VR (output) COMPLEX*16 array, dimension (LDVR,N) -* If JOBVR = 'V', the right eigenvectors v(j) are stored one -* after another in the columns of VR, in the same order -* as their eigenvalues. -* If JOBVR = 'N', VR is not referenced. -* v(j) = VR(:,j), the j-th column of VR. -* -* LDVR (input) INTEGER -* The leading dimension of the array VR. LDVR >= 1; if -* JOBVR = 'V', LDVR >= N. -* -* 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 >= max(1,2*N). -* For good performance, LWORK must generally be larger. -* -* 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. -* -* RWORK (workspace) DOUBLE PRECISION array, dimension (2*N) -* -* INFO (output) INTEGER -* = 0: successful exit -* < 0: if INFO = -i, the i-th argument had an illegal value. -* > 0: if INFO = i, the QR algorithm failed to compute all the -* eigenvalues, and no eigenvectors have been computed; -* elements and i+1:N of W contain eigenvalues which have -* converged. -* * ===================================================================== * * .. Parameters .. @@ -110,7 +205,7 @@ LOGICAL LQUERY, SCALEA, WANTVL, WANTVR CHARACTER SIDE INTEGER HSWORK, I, IBAL, IERR, IHI, ILO, IRWORK, ITAU, - $ IWRK, K, MAXWRK, MINWRK, NOUT + $ IWRK, K, LWORK_TREVC, MAXWRK, MINWRK, NOUT DOUBLE PRECISION ANRM, BIGNUM, CSCALE, EPS, SCL, SMLNUM COMPLEX*16 TMP * .. @@ -120,7 +215,7 @@ * .. * .. External Subroutines .. EXTERNAL DLABAD, XERBLA, ZDSCAL, ZGEBAK, ZGEBAL, ZGEHRD, - $ ZHSEQR, ZLACPY, ZLASCL, ZSCAL, ZTREVC, ZUNGHR + $ ZHSEQR, ZLACPY, ZLASCL, ZSCAL, ZTREVC3, ZUNGHR * .. * .. External Functions .. LOGICAL LSAME @@ -129,7 +224,7 @@ EXTERNAL LSAME, IDAMAX, ILAENV, DLAMCH, DZNRM2, ZLANGE * .. * .. Intrinsic Functions .. - INTRINSIC DBLE, DCMPLX, DCONJG, DIMAG, MAX, SQRT + INTRINSIC DBLE, DCMPLX, CONJG, AIMAG, MAX, SQRT * .. * .. Executable Statements .. * @@ -174,18 +269,28 @@ IF( WANTVL ) THEN MAXWRK = MAX( MAXWRK, N + ( N - 1 )*ILAENV( 1, 'ZUNGHR', $ ' ', N, 1, N, -1 ) ) + CALL ZTREVC3( 'L', 'B', SELECT, N, A, LDA, + $ VL, LDVL, VR, LDVR, + $ N, NOUT, WORK, -1, RWORK, -1, IERR ) + LWORK_TREVC = INT( WORK(1) ) + MAXWRK = MAX( MAXWRK, N + LWORK_TREVC ) CALL ZHSEQR( 'S', 'V', N, 1, N, A, LDA, W, VL, LDVL, - $ WORK, -1, INFO ) + $ WORK, -1, INFO ) ELSE IF( WANTVR ) THEN MAXWRK = MAX( MAXWRK, N + ( N - 1 )*ILAENV( 1, 'ZUNGHR', $ ' ', N, 1, N, -1 ) ) + CALL ZTREVC3( 'R', 'B', SELECT, N, A, LDA, + $ VL, LDVL, VR, LDVR, + $ N, NOUT, WORK, -1, RWORK, -1, IERR ) + LWORK_TREVC = INT( WORK(1) ) + MAXWRK = MAX( MAXWRK, N + LWORK_TREVC ) CALL ZHSEQR( 'S', 'V', N, 1, N, A, LDA, W, VR, LDVR, - $ WORK, -1, INFO ) + $ WORK, -1, INFO ) ELSE CALL ZHSEQR( 'E', 'N', N, 1, N, A, LDA, W, VR, LDVR, - $ WORK, -1, INFO ) + $ WORK, -1, INFO ) END IF - HSWORK = WORK( 1 ) + HSWORK = INT( WORK(1) ) MAXWRK = MAX( MAXWRK, HSWORK, MINWRK ) END IF WORK( 1 ) = MAXWRK @@ -312,20 +417,21 @@ $ WORK( IWRK ), LWORK-IWRK+1, INFO ) END IF * -* If INFO > 0 from ZHSEQR, then quit +* If INFO .NE. 0 from ZHSEQR, then quit * - IF( INFO.GT.0 ) + IF( INFO.NE.0 ) $ GO TO 50 * IF( WANTVL .OR. WANTVR ) THEN * * Compute left and/or right eigenvectors -* (CWorkspace: need 2*N) +* (CWorkspace: need 2*N, prefer N + 2*N*NB) * (RWorkspace: need 2*N) * IRWORK = IBAL + N - CALL ZTREVC( SIDE, 'B', SELECT, N, A, LDA, VL, LDVL, VR, LDVR, - $ N, NOUT, WORK( IWRK ), RWORK( IRWORK ), IERR ) + CALL ZTREVC3( SIDE, 'B', SELECT, N, A, LDA, VL, LDVL, VR, LDVR, + $ N, NOUT, WORK( IWRK ), LWORK-IWRK+1, + $ RWORK( IRWORK ), N, IERR ) END IF * IF( WANTVL ) THEN @@ -344,10 +450,10 @@ CALL ZDSCAL( N, SCL, VL( 1, I ), 1 ) DO 10 K = 1, N RWORK( IRWORK+K-1 ) = DBLE( VL( K, I ) )**2 + - $ DIMAG( VL( K, I ) )**2 + $ AIMAG( VL( K, I ) )**2 10 CONTINUE K = IDAMAX( N, RWORK( IRWORK ), 1 ) - TMP = DCONJG( VL( K, I ) ) / SQRT( RWORK( IRWORK+K-1 ) ) + TMP = CONJG( VL( K, I ) ) / SQRT( RWORK( IRWORK+K-1 ) ) CALL ZSCAL( N, TMP, VL( 1, I ), 1 ) VL( K, I ) = DCMPLX( DBLE( VL( K, I ) ), ZERO ) 20 CONTINUE @@ -369,10 +475,10 @@ CALL ZDSCAL( N, SCL, VR( 1, I ), 1 ) DO 30 K = 1, N RWORK( IRWORK+K-1 ) = DBLE( VR( K, I ) )**2 + - $ DIMAG( VR( K, I ) )**2 + $ AIMAG( VR( K, I ) )**2 30 CONTINUE K = IDAMAX( N, RWORK( IRWORK ), 1 ) - TMP = DCONJG( VR( K, I ) ) / SQRT( RWORK( IRWORK+K-1 ) ) + TMP = CONJG( VR( K, I ) ) / SQRT( RWORK( IRWORK+K-1 ) ) CALL ZSCAL( N, TMP, VR( 1, I ), 1 ) VR( K, I ) = DCMPLX( DBLE( VR( K, I ) ), ZERO ) 40 CONTINUE