diff options
Diffstat (limited to 'src/lib/lapack/dgelsx.f')
| -rw-r--r-- | src/lib/lapack/dgelsx.f | 349 |
1 files changed, 0 insertions, 349 deletions
diff --git a/src/lib/lapack/dgelsx.f b/src/lib/lapack/dgelsx.f deleted file mode 100644 index a597cd47..00000000 --- a/src/lib/lapack/dgelsx.f +++ /dev/null @@ -1,349 +0,0 @@ - SUBROUTINE DGELSX( M, N, NRHS, A, LDA, B, LDB, JPVT, RCOND, RANK, - $ WORK, 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, M, N, NRHS, RANK - DOUBLE PRECISION RCOND -* .. -* .. Array Arguments .. - INTEGER JPVT( * ) - DOUBLE PRECISION A( LDA, * ), B( LDB, * ), WORK( * ) -* .. -* -* Purpose -* ======= -* -* This routine is deprecated and has been replaced by routine DGELSY. -* -* DGELSX computes the minimum-norm solution to a real 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 orthogonal 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. -* -* 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) DOUBLE PRECISION 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) DOUBLE PRECISION array, dimension (LDB,NRHS) -* On entry, the M-by-NRHS right hand side matrix B. -* On exit, the N-by-NRHS solution matrix X. -* If m >= n and RANK = n, the residual sum-of-squares for -* the solution in the i-th column is given by the sum of -* squares of elements N+1:M in that column. -* -* 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 an -* initial column, otherwise it is a free column. Before -* the QR factorization of A, all initial columns are -* permuted to the leading positions; only the remaining -* free columns are moved as a result of column pivoting -* during the factorization. -* 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) DOUBLE PRECISION array, dimension -* (max( min(M,N)+3*N, 2*min(M,N)+NRHS )), -* -* INFO (output) INTEGER -* = 0: successful exit -* < 0: if INFO = -i, the i-th argument had an illegal value -* -* ===================================================================== -* -* .. Parameters .. - INTEGER IMAX, IMIN - PARAMETER ( IMAX = 1, IMIN = 2 ) - DOUBLE PRECISION ZERO, ONE, DONE, NTDONE - PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0, DONE = ZERO, - $ NTDONE = ONE ) -* .. -* .. Local Scalars .. - INTEGER I, IASCL, IBSCL, ISMAX, ISMIN, J, K, MN - DOUBLE PRECISION ANRM, BIGNUM, BNRM, C1, C2, S1, S2, SMAX, - $ SMAXPR, SMIN, SMINPR, SMLNUM, T1, T2 -* .. -* .. External Functions .. - DOUBLE PRECISION DLAMCH, DLANGE - EXTERNAL DLAMCH, DLANGE -* .. -* .. External Subroutines .. - EXTERNAL DGEQPF, DLAIC1, DLASCL, DLASET, DLATZM, DORM2R, - $ DTRSM, DTZRQF, XERBLA -* .. -* .. Intrinsic Functions .. - INTRINSIC ABS, MAX, MIN -* .. -* .. Executable Statements .. -* - MN = MIN( M, N ) - ISMIN = MN + 1 - ISMAX = 2*MN + 1 -* -* Test the input arguments. -* - INFO = 0 - 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 - END IF -* - IF( INFO.NE.0 ) THEN - CALL XERBLA( 'DGELSX', -INFO ) - 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 elements outside range [SMLNUM,BIGNUM] -* - ANRM = DLANGE( 'M', M, N, A, LDA, WORK ) - IASCL = 0 - IF( ANRM.GT.ZERO .AND. ANRM.LT.SMLNUM ) THEN -* -* Scale matrix norm up to SMLNUM -* - CALL DLASCL( '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 DLASCL( '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 DLASET( 'F', MAX( M, N ), NRHS, ZERO, ZERO, B, LDB ) - RANK = 0 - GO TO 100 - END IF -* - BNRM = DLANGE( 'M', M, NRHS, B, LDB, WORK ) - IBSCL = 0 - IF( BNRM.GT.ZERO .AND. BNRM.LT.SMLNUM ) THEN -* -* Scale matrix norm up to SMLNUM -* - CALL DLASCL( '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 DLASCL( '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 DGEQPF( M, N, A, LDA, JPVT, WORK( 1 ), WORK( MN+1 ), INFO ) -* -* workspace 3*N. Details of Householder rotations stored -* in WORK(1:MN). -* -* Determine RANK using incremental condition estimation -* - WORK( ISMIN ) = ONE - WORK( ISMAX ) = ONE - SMAX = ABS( A( 1, 1 ) ) - SMIN = SMAX - IF( ABS( A( 1, 1 ) ).EQ.ZERO ) THEN - RANK = 0 - CALL DLASET( 'F', MAX( M, N ), NRHS, ZERO, ZERO, B, LDB ) - GO TO 100 - ELSE - RANK = 1 - END IF -* - 10 CONTINUE - IF( RANK.LT.MN ) THEN - I = RANK + 1 - CALL DLAIC1( IMIN, RANK, WORK( ISMIN ), SMIN, A( 1, I ), - $ A( I, I ), SMINPR, S1, C1 ) - CALL DLAIC1( 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 -* -* Logically partition R = [ R11 R12 ] -* [ 0 R22 ] -* where R11 = R(1:RANK,1:RANK) -* -* [R11,R12] = [ T11, 0 ] * Y -* - IF( RANK.LT.N ) - $ CALL DTZRQF( RANK, N, A, LDA, WORK( MN+1 ), INFO ) -* -* Details of Householder rotations stored in WORK(MN+1:2*MN) -* -* B(1:M,1:NRHS) := Q' * B(1:M,1:NRHS) -* - CALL DORM2R( 'Left', 'Transpose', M, NRHS, MN, A, LDA, WORK( 1 ), - $ B, LDB, WORK( 2*MN+1 ), INFO ) -* -* workspace NRHS -* -* B(1:RANK,1:NRHS) := inv(T11) * B(1:RANK,1:NRHS) -* - CALL DTRSM( 'Left', 'Upper', 'No transpose', 'Non-unit', RANK, - $ NRHS, ONE, A, LDA, B, LDB ) -* - DO 40 I = RANK + 1, N - DO 30 J = 1, NRHS - B( I, J ) = ZERO - 30 CONTINUE - 40 CONTINUE -* -* B(1:N,1:NRHS) := Y' * B(1:N,1:NRHS) -* - IF( RANK.LT.N ) THEN - DO 50 I = 1, RANK - CALL DLATZM( 'Left', N-RANK+1, NRHS, A( I, RANK+1 ), LDA, - $ WORK( MN+I ), B( I, 1 ), B( RANK+1, 1 ), LDB, - $ WORK( 2*MN+1 ) ) - 50 CONTINUE - END IF -* -* workspace NRHS -* -* B(1:N,1:NRHS) := P * B(1:N,1:NRHS) -* - DO 90 J = 1, NRHS - DO 60 I = 1, N - WORK( 2*MN+I ) = NTDONE - 60 CONTINUE - DO 80 I = 1, N - IF( WORK( 2*MN+I ).EQ.NTDONE ) THEN - IF( JPVT( I ).NE.I ) THEN - K = I - T1 = B( K, J ) - T2 = B( JPVT( K ), J ) - 70 CONTINUE - B( JPVT( K ), J ) = T1 - WORK( 2*MN+K ) = DONE - T1 = T2 - K = JPVT( K ) - T2 = B( JPVT( K ), J ) - IF( JPVT( K ).NE.I ) - $ GO TO 70 - B( I, J ) = T1 - WORK( 2*MN+K ) = DONE - END IF - END IF - 80 CONTINUE - 90 CONTINUE -* -* Undo scaling -* - IF( IASCL.EQ.1 ) THEN - CALL DLASCL( 'G', 0, 0, ANRM, SMLNUM, N, NRHS, B, LDB, INFO ) - CALL DLASCL( 'U', 0, 0, SMLNUM, ANRM, RANK, RANK, A, LDA, - $ INFO ) - ELSE IF( IASCL.EQ.2 ) THEN - CALL DLASCL( 'G', 0, 0, ANRM, BIGNUM, N, NRHS, B, LDB, INFO ) - CALL DLASCL( 'U', 0, 0, BIGNUM, ANRM, RANK, RANK, A, LDA, - $ INFO ) - END IF - IF( IBSCL.EQ.1 ) THEN - CALL DLASCL( 'G', 0, 0, SMLNUM, BNRM, N, NRHS, B, LDB, INFO ) - ELSE IF( IBSCL.EQ.2 ) THEN - CALL DLASCL( 'G', 0, 0, BIGNUM, BNRM, N, NRHS, B, LDB, INFO ) - END IF -* - 100 CONTINUE -* - RETURN -* -* End of DGELSX -* - END |