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Diffstat (limited to 'src/lib/lapack/zgelsy.f')
| -rw-r--r-- | src/lib/lapack/zgelsy.f | 385 |
1 files changed, 0 insertions, 385 deletions
diff --git a/src/lib/lapack/zgelsy.f b/src/lib/lapack/zgelsy.f deleted file mode 100644 index 95aece58..00000000 --- a/src/lib/lapack/zgelsy.f +++ /dev/null @@ -1,385 +0,0 @@ - SUBROUTINE ZGELSY( M, N, NRHS, A, LDA, B, LDB, JPVT, RCOND, RANK, - $ WORK, LWORK, RWORK, INFO ) -* -* -- LAPACK driver routine (version 3.1) -- -* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. -* November 2006 -* -* .. Scalar Arguments .. - INTEGER INFO, LDA, LDB, LWORK, M, N, NRHS, RANK - DOUBLE PRECISION RCOND -* .. -* .. Array Arguments .. - INTEGER JPVT( * ) - DOUBLE PRECISION RWORK( * ) - COMPLEX*16 A( LDA, * ), B( LDB, * ), WORK( * ) -* .. -* -* Purpose -* ======= -* -* ZGELSY computes the minimum-norm solution to a complex linear least -* squares problem: -* minimize || A * X - B || -* using a complete orthogonal factorization of A. A is an M-by-N -* matrix which may be rank-deficient. -* -* Several right hand side vectors b and solution vectors x can be -* handled in a single call; they are stored as the columns of the -* M-by-NRHS right hand side matrix B and the N-by-NRHS solution -* matrix X. -* -* The routine first computes a QR factorization with column pivoting: -* A * P = Q * [ R11 R12 ] -* [ 0 R22 ] -* with R11 defined as the largest leading submatrix whose estimated -* condition number is less than 1/RCOND. The order of R11, RANK, -* is the effective rank of A. -* -* Then, R22 is considered to be negligible, and R12 is annihilated -* by unitary transformations from the right, arriving at the -* complete orthogonal factorization: -* A * P = Q * [ T11 0 ] * Z -* [ 0 0 ] -* The minimum-norm solution is then -* X = P * Z' [ inv(T11)*Q1'*B ] -* [ 0 ] -* where Q1 consists of the first RANK columns of Q. -* -* This routine is basically identical to the original xGELSX except -* three differences: -* o The permutation of matrix B (the right hand side) is faster and -* more simple. -* o The call to the subroutine xGEQPF has been substituted by the -* the call to the subroutine xGEQP3. This subroutine is a Blas-3 -* version of the QR factorization with column pivoting. -* o Matrix B (the right hand side) is updated with Blas-3. -* -* Arguments -* ========= -* -* M (input) INTEGER -* The number of rows of the matrix A. M >= 0. -* -* N (input) INTEGER -* The number of columns of the matrix A. N >= 0. -* -* NRHS (input) INTEGER -* The number of right hand sides, i.e., the number of -* columns of matrices B and X. NRHS >= 0. -* -* A (input/output) COMPLEX*16 array, dimension (LDA,N) -* On entry, the M-by-N matrix A. -* On exit, A has been overwritten by details of its -* complete orthogonal factorization. -* -* LDA (input) INTEGER -* The leading dimension of the array A. LDA >= max(1,M). -* -* B (input/output) COMPLEX*16 array, dimension (LDB,NRHS) -* On entry, the M-by-NRHS right hand side matrix B. -* On exit, the N-by-NRHS solution matrix X. -* -* LDB (input) INTEGER -* The leading dimension of the array B. LDB >= max(1,M,N). -* -* JPVT (input/output) INTEGER array, dimension (N) -* On entry, if JPVT(i) .ne. 0, the i-th column of A is permuted -* to the front of AP, otherwise column i is a free column. -* On exit, if JPVT(i) = k, then the i-th column of A*P -* was the k-th column of A. -* -* RCOND (input) DOUBLE PRECISION -* RCOND is used to determine the effective rank of A, which -* is defined as the order of the largest leading triangular -* submatrix R11 in the QR factorization with pivoting of A, -* whose estimated condition number < 1/RCOND. -* -* RANK (output) INTEGER -* The effective rank of A, i.e., the order of the submatrix -* R11. This is the same as the order of the submatrix T11 -* in the complete orthogonal factorization of A. -* -* 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. -* The unblocked strategy requires that: -* LWORK >= MN + MAX( 2*MN, N+1, MN+NRHS ) -* where MN = min(M,N). -* The block algorithm requires that: -* LWORK >= MN + MAX( 2*MN, NB*(N+1), MN+MN*NB, MN+NB*NRHS ) -* where NB is an upper bound on the blocksize returned -* by ILAENV for the routines ZGEQP3, ZTZRZF, CTZRQF, ZUNMQR, -* and ZUNMRZ. -* -* 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 -* -* Further Details -* =============== -* -* Based on contributions by -* A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA -* E. Quintana-Orti, Depto. de Informatica, Universidad Jaime I, Spain -* G. Quintana-Orti, Depto. de Informatica, Universidad Jaime I, Spain -* -* ===================================================================== -* -* .. Parameters .. - INTEGER IMAX, IMIN - PARAMETER ( IMAX = 1, IMIN = 2 ) - DOUBLE PRECISION ZERO, ONE - PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 ) - COMPLEX*16 CZERO, CONE - PARAMETER ( CZERO = ( 0.0D+0, 0.0D+0 ), - $ CONE = ( 1.0D+0, 0.0D+0 ) ) -* .. -* .. Local Scalars .. - LOGICAL LQUERY - INTEGER I, IASCL, IBSCL, ISMAX, ISMIN, J, LWKOPT, MN, - $ NB, NB1, NB2, NB3, NB4 - DOUBLE PRECISION ANRM, BIGNUM, BNRM, SMAX, SMAXPR, SMIN, SMINPR, - $ SMLNUM, WSIZE - COMPLEX*16 C1, C2, S1, S2 -* .. -* .. External Subroutines .. - EXTERNAL DLABAD, XERBLA, ZCOPY, ZGEQP3, ZLAIC1, ZLASCL, - $ ZLASET, ZTRSM, ZTZRZF, ZUNMQR, ZUNMRZ -* .. -* .. External Functions .. - INTEGER ILAENV - DOUBLE PRECISION DLAMCH, ZLANGE - EXTERNAL ILAENV, DLAMCH, ZLANGE -* .. -* .. Intrinsic Functions .. - INTRINSIC ABS, DBLE, DCMPLX, MAX, MIN -* .. -* .. Executable Statements .. -* - MN = MIN( M, N ) - ISMIN = MN + 1 - ISMAX = 2*MN + 1 -* -* Test the input arguments. -* - INFO = 0 - NB1 = ILAENV( 1, 'ZGEQRF', ' ', M, N, -1, -1 ) - NB2 = ILAENV( 1, 'ZGERQF', ' ', M, N, -1, -1 ) - NB3 = ILAENV( 1, 'ZUNMQR', ' ', M, N, NRHS, -1 ) - NB4 = ILAENV( 1, 'ZUNMRQ', ' ', M, N, NRHS, -1 ) - NB = MAX( NB1, NB2, NB3, NB4 ) - LWKOPT = MAX( 1, MN+2*N+NB*( N+1 ), 2*MN+NB*NRHS ) - WORK( 1 ) = DCMPLX( LWKOPT ) - LQUERY = ( LWORK.EQ.-1 ) - IF( M.LT.0 ) THEN - INFO = -1 - ELSE IF( N.LT.0 ) THEN - INFO = -2 - ELSE IF( NRHS.LT.0 ) THEN - INFO = -3 - ELSE IF( LDA.LT.MAX( 1, M ) ) THEN - INFO = -5 - ELSE IF( LDB.LT.MAX( 1, M, N ) ) THEN - INFO = -7 - ELSE IF( LWORK.LT.( MN+MAX( 2*MN, N+1, MN+NRHS ) ) .AND. .NOT. - $ LQUERY ) THEN - INFO = -12 - END IF -* - IF( INFO.NE.0 ) THEN - CALL XERBLA( 'ZGELSY', -INFO ) - RETURN - ELSE IF( LQUERY ) THEN - RETURN - END IF -* -* Quick return if possible -* - IF( MIN( M, N, NRHS ).EQ.0 ) THEN - RANK = 0 - RETURN - END IF -* -* Get machine parameters -* - SMLNUM = DLAMCH( 'S' ) / DLAMCH( 'P' ) - BIGNUM = ONE / SMLNUM - CALL DLABAD( SMLNUM, BIGNUM ) -* -* Scale A, B if max entries outside range [SMLNUM,BIGNUM] -* - ANRM = ZLANGE( 'M', M, N, A, LDA, RWORK ) - IASCL = 0 - IF( ANRM.GT.ZERO .AND. ANRM.LT.SMLNUM ) THEN -* -* Scale matrix norm up to SMLNUM -* - CALL ZLASCL( 'G', 0, 0, ANRM, SMLNUM, M, N, A, LDA, INFO ) - IASCL = 1 - ELSE IF( ANRM.GT.BIGNUM ) THEN -* -* Scale matrix norm down to BIGNUM -* - CALL ZLASCL( 'G', 0, 0, ANRM, BIGNUM, M, N, A, LDA, INFO ) - IASCL = 2 - ELSE IF( ANRM.EQ.ZERO ) THEN -* -* Matrix all zero. Return zero solution. -* - CALL ZLASET( 'F', MAX( M, N ), NRHS, CZERO, CZERO, B, LDB ) - RANK = 0 - GO TO 70 - END IF -* - BNRM = ZLANGE( 'M', M, NRHS, B, LDB, RWORK ) - IBSCL = 0 - IF( BNRM.GT.ZERO .AND. BNRM.LT.SMLNUM ) THEN -* -* Scale matrix norm up to SMLNUM -* - CALL ZLASCL( 'G', 0, 0, BNRM, SMLNUM, M, NRHS, B, LDB, INFO ) - IBSCL = 1 - ELSE IF( BNRM.GT.BIGNUM ) THEN -* -* Scale matrix norm down to BIGNUM -* - CALL ZLASCL( 'G', 0, 0, BNRM, BIGNUM, M, NRHS, B, LDB, INFO ) - IBSCL = 2 - END IF -* -* Compute QR factorization with column pivoting of A: -* A * P = Q * R -* - CALL ZGEQP3( M, N, A, LDA, JPVT, WORK( 1 ), WORK( MN+1 ), - $ LWORK-MN, RWORK, INFO ) - WSIZE = MN + DBLE( WORK( MN+1 ) ) -* -* complex workspace: MN+NB*(N+1). real workspace 2*N. -* Details of Householder rotations stored in WORK(1:MN). -* -* Determine RANK using incremental condition estimation -* - WORK( ISMIN ) = CONE - WORK( ISMAX ) = CONE - SMAX = ABS( A( 1, 1 ) ) - SMIN = SMAX - IF( ABS( A( 1, 1 ) ).EQ.ZERO ) THEN - RANK = 0 - CALL ZLASET( 'F', MAX( M, N ), NRHS, CZERO, CZERO, B, LDB ) - GO TO 70 - ELSE - RANK = 1 - END IF -* - 10 CONTINUE - IF( RANK.LT.MN ) THEN - I = RANK + 1 - CALL ZLAIC1( IMIN, RANK, WORK( ISMIN ), SMIN, A( 1, I ), - $ A( I, I ), SMINPR, S1, C1 ) - CALL ZLAIC1( IMAX, RANK, WORK( ISMAX ), SMAX, A( 1, I ), - $ A( I, I ), SMAXPR, S2, C2 ) -* - IF( SMAXPR*RCOND.LE.SMINPR ) THEN - DO 20 I = 1, RANK - WORK( ISMIN+I-1 ) = S1*WORK( ISMIN+I-1 ) - WORK( ISMAX+I-1 ) = S2*WORK( ISMAX+I-1 ) - 20 CONTINUE - WORK( ISMIN+RANK ) = C1 - WORK( ISMAX+RANK ) = C2 - SMIN = SMINPR - SMAX = SMAXPR - RANK = RANK + 1 - GO TO 10 - END IF - END IF -* -* complex workspace: 3*MN. -* -* Logically partition R = [ R11 R12 ] -* [ 0 R22 ] -* where R11 = R(1:RANK,1:RANK) -* -* [R11,R12] = [ T11, 0 ] * Y -* -c IF( RANK.LT.N ) -c $ CALL ZTZRZF( RANK, N, A, LDA, WORK( MN+1 ), WORK( 2*MN+1 ), -c $ LWORK-2*MN, INFO ) -* -* complex workspace: 2*MN. -* Details of Householder rotations stored in WORK(MN+1:2*MN) -* -* B(1:M,1:NRHS) := Q' * B(1:M,1:NRHS) -* - CALL ZUNMQR( 'Left', 'Conjugate transpose', M, NRHS, MN, A, LDA, - $ WORK( 1 ), B, LDB, WORK( 2*MN+1 ), LWORK-2*MN, INFO ) - WSIZE = MAX( WSIZE, 2*MN+DBLE( WORK( 2*MN+1 ) ) ) -* -* complex workspace: 2*MN+NB*NRHS. -* -* B(1:RANK,1:NRHS) := inv(T11) * B(1:RANK,1:NRHS) -* - CALL ZTRSM( 'Left', 'Upper', 'No transpose', 'Non-unit', RANK, - $ NRHS, CONE, A, LDA, B, LDB ) -* - DO 40 J = 1, NRHS - DO 30 I = RANK + 1, N - B( I, J ) = CZERO - 30 CONTINUE - 40 CONTINUE -* -* B(1:N,1:NRHS) := Y' * B(1:N,1:NRHS) -* -c IF( RANK.LT.N ) THEN -c CALL ZUNMRZ( 'Left', 'Conjugate transpose', N, NRHS, RANK, -c $ N-RANK, A, LDA, WORK( MN+1 ), B, LDB, -c $ WORK( 2*MN+1 ), LWORK-2*MN, INFO ) -c END IF -* -* complex workspace: 2*MN+NRHS. -* -* B(1:N,1:NRHS) := P * B(1:N,1:NRHS) -* - DO 60 J = 1, NRHS - DO 50 I = 1, N - WORK( JPVT( I ) ) = B( I, J ) - 50 CONTINUE - CALL ZCOPY( N, WORK( 1 ), 1, B( 1, J ), 1 ) - 60 CONTINUE -* -* complex workspace: N. -* -* Undo scaling -* - IF( IASCL.EQ.1 ) THEN - CALL ZLASCL( 'G', 0, 0, ANRM, SMLNUM, N, NRHS, B, LDB, INFO ) - CALL ZLASCL( 'U', 0, 0, SMLNUM, ANRM, RANK, RANK, A, LDA, - $ INFO ) - ELSE IF( IASCL.EQ.2 ) THEN - CALL ZLASCL( 'G', 0, 0, ANRM, BIGNUM, N, NRHS, B, LDB, INFO ) - CALL ZLASCL( 'U', 0, 0, BIGNUM, ANRM, RANK, RANK, A, LDA, - $ INFO ) - END IF - IF( IBSCL.EQ.1 ) THEN - CALL ZLASCL( 'G', 0, 0, SMLNUM, BNRM, N, NRHS, B, LDB, INFO ) - ELSE IF( IBSCL.EQ.2 ) THEN - CALL ZLASCL( 'G', 0, 0, BIGNUM, BNRM, N, NRHS, B, LDB, INFO ) - END IF -* - 70 CONTINUE - WORK( 1 ) = DCMPLX( LWKOPT ) -* - RETURN -* -* End of ZGELSY -* - END |