Update LAPACK to 3.9.0

lapack-netlib/SRC/dbdsqr.f

@@ -166,7 +166,7 @@
 *>
 *> \param[out] WORK
 *> \verbatim
-*>          WORK is DOUBLE PRECISION array, dimension (4*N)
+*>          WORK is DOUBLE PRECISION array, dimension (4*(N-1))
 *> \endverbatim
 *>
 *> \param[out] INFO

lapack-netlib/SRC/dbdsvdx.f

@@ -165,7 +165,7 @@
 *>
 *> \param[out] Z
 *> \verbatim
-*>          Z is DOUBLE PRECISION array, dimension (2*N,K) )
+*>          Z is DOUBLE PRECISION array, dimension (2*N,K)
 *>          If JOBZ = 'V', then if INFO = 0 the first NS columns of Z
 *>          contain the singular vectors of the matrix B corresponding to
 *>          the selected singular values, with U in rows 1 to N and V

lapack-netlib/SRC/dcombssq.f

@@ -0,0 +1,92 @@
+*> \brief \b DCOMBSSQ adds two scaled sum of squares quantities.
+*
+*  =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+*            http://www.netlib.org/lapack/explore-html/
+*
+*
+*  Definition:
+*  ===========
+*
+*       SUBROUTINE DCOMBSSQ( V1, V2 )
+*
+*       .. Array Arguments ..
+*       DOUBLE PRECISION   V1( 2 ), V2( 2 )
+*       ..
+*
+*
+*> \par Purpose:
+*  =============
+*>
+*> \verbatim
+*>
+*> DCOMBSSQ adds two scaled sum of squares quantities, V1 := V1 + V2.
+*> That is,
+*>
+*>    V1_scale**2 * V1_sumsq := V1_scale**2 * V1_sumsq
+*>                            + V2_scale**2 * V2_sumsq
+*> \endverbatim
+*
+*  Arguments:
+*  ==========
+*
+*> \param[in,out] V1
+*> \verbatim
+*>          V1 is DOUBLE PRECISION array, dimension (2).
+*>          The first scaled sum.
+*>          V1(1) = V1_scale, V1(2) = V1_sumsq.
+*> \endverbatim
+*>
+*> \param[in] V2
+*> \verbatim
+*>          V2 is DOUBLE PRECISION array, dimension (2).
+*>          The second scaled sum.
+*>          V2(1) = V2_scale, V2(2) = V2_sumsq.
+*> \endverbatim
+*
+*  Authors:
+*  ========
+*
+*> \author Univ. of Tennessee
+*> \author Univ. of California Berkeley
+*> \author Univ. of Colorado Denver
+*> \author NAG Ltd.
+*
+*> \date November 2018
+*
+*> \ingroup OTHERauxiliary
+*
+*  =====================================================================
+      SUBROUTINE DCOMBSSQ( V1, V2 )
+*
+*  -- LAPACK auxiliary 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 2018
+*
+*     .. Array Arguments ..
+      DOUBLE PRECISION   V1( 2 ), V2( 2 )
+*     ..
+*
+* =====================================================================
+*
+*     .. Parameters ..
+      DOUBLE PRECISION   ZERO
+      PARAMETER          ( ZERO = 0.0D+0 )
+*     ..
+*     .. Executable Statements ..
+*
+      IF( V1( 1 ).GE.V2( 1 ) ) THEN
+         IF( V1( 1 ).NE.ZERO ) THEN
+            V1( 2 ) = V1( 2 ) + ( V2( 1 ) / V1( 1 ) )**2 * V2( 2 )
+         END IF
+      ELSE
+         V1( 2 ) = V2( 2 ) + ( V1( 1 ) / V2( 1 ) )**2 * V1( 2 )
+         V1( 1 ) = V2( 1 )
+      END IF
+      RETURN
+*
+*     End of DCOMBSSQ
+*
+      END

lapack-netlib/SRC/dgbrfsx.f

@@ -308,7 +308,7 @@
 *>     information as described below. There currently are up to three
 *>     pieces of information returned for each right-hand side. If
 *>     componentwise accuracy is not requested (PARAMS(3) = 0.0), then
-*>     ERR_BNDS_COMP is not accessed.  If N_ERR_BNDS .LT. 3, then at most
+*>     ERR_BNDS_COMP is not accessed.  If N_ERR_BNDS < 3, then at most
 *>     the first (:,N_ERR_BNDS) entries are returned.
 *>
 *>     The first index in ERR_BNDS_COMP(i,:) corresponds to the ith
@@ -344,14 +344,14 @@
 *> \param[in] NPARAMS
 *> \verbatim
 *>          NPARAMS is INTEGER
-*>     Specifies the number of parameters set in PARAMS.  If .LE. 0, the
+*>     Specifies the number of parameters set in PARAMS.  If <= 0, the
 *>     PARAMS array is never referenced and default values are used.
 *> \endverbatim
 *>
 *> \param[in,out] PARAMS
 *> \verbatim
 *>          PARAMS is DOUBLE PRECISION array, dimension (NPARAMS)
-*>     Specifies algorithm parameters.  If an entry is .LT. 0.0, then
+*>     Specifies algorithm parameters.  If an entry is < 0.0, then
 *>     that entry will be filled with default value used for that
 *>     parameter.  Only positions up to NPARAMS are accessed; defaults
 *>     are used for higher-numbered parameters.
@@ -359,9 +359,9 @@
 *>       PARAMS(LA_LINRX_ITREF_I = 1) : Whether to perform iterative
 *>            refinement or not.
 *>         Default: 1.0D+0
-*>            = 0.0 : No refinement is performed, and no error bounds are
+*>            = 0.0:  No refinement is performed, and no error bounds are
 *>                    computed.
-*>            = 1.0 : Use the double-precision refinement algorithm,
+*>            = 1.0:  Use the double-precision refinement algorithm,
 *>                    possibly with doubled-single computations if the
 *>                    compilation environment does not support DOUBLE
 *>                    PRECISION.

lapack-netlib/SRC/dgbsvxx.f

@@ -431,7 +431,7 @@
 *>     information as described below. There currently are up to three
 *>     pieces of information returned for each right-hand side. If
 *>     componentwise accuracy is not requested (PARAMS(3) = 0.0), then
-*>     ERR_BNDS_COMP is not accessed.  If N_ERR_BNDS .LT. 3, then at most
+*>     ERR_BNDS_COMP is not accessed.  If N_ERR_BNDS < 3, then at most
 *>     the first (:,N_ERR_BNDS) entries are returned.
 *>
 *>     The first index in ERR_BNDS_COMP(i,:) corresponds to the ith
@@ -467,14 +467,14 @@
 *> \param[in] NPARAMS
 *> \verbatim
 *>          NPARAMS is INTEGER
-*>     Specifies the number of parameters set in PARAMS.  If .LE. 0, the
+*>     Specifies the number of parameters set in PARAMS.  If <= 0, the
 *>     PARAMS array is never referenced and default values are used.
 *> \endverbatim
 *>
 *> \param[in,out] PARAMS
 *> \verbatim
 *>          PARAMS is DOUBLE PRECISION array, dimension (NPARAMS)
-*>     Specifies algorithm parameters.  If an entry is .LT. 0.0, then
+*>     Specifies algorithm parameters.  If an entry is < 0.0, then
 *>     that entry will be filled with default value used for that
 *>     parameter.  Only positions up to NPARAMS are accessed; defaults
 *>     are used for higher-numbered parameters.
@@ -482,9 +482,9 @@
 *>       PARAMS(LA_LINRX_ITREF_I = 1) : Whether to perform iterative
 *>            refinement or not.
 *>         Default: 1.0D+0
-*>            = 0.0 : No refinement is performed, and no error bounds are
+*>            = 0.0:  No refinement is performed, and no error bounds are
 *>                    computed.
-*>            = 1.0 : Use the extra-precise refinement algorithm.
+*>            = 1.0:  Use the extra-precise refinement algorithm.
 *>              (other values are reserved for future use)
 *>
 *>       PARAMS(LA_LINRX_ITHRESH_I = 2) : Maximum number of residual

lapack-netlib/SRC/dgebak.f

@@ -47,10 +47,10 @@
 *> \verbatim
 *>          JOB is CHARACTER*1
 *>          Specifies the type of backward transformation required:
-*>          = 'N', do nothing, return immediately;
+*>          = 'N': do nothing, return immediately;
-*>          = 'P', do backward transformation for permutation only;
+*>          = 'P': do backward transformation for permutation only;
-*>          = 'S', do backward transformation for scaling only;
+*>          = 'S': do backward transformation for scaling only;
-*>          = 'B', do backward transformations for both permutation and
+*>          = 'B': do backward transformations for both permutation and
 *>                 scaling.
 *>          JOB must be the same as the argument JOB supplied to DGEBAL.
 *> \endverbatim

lapack-netlib/SRC/dgeesx.f

@@ -583,7 +583,9 @@
                      IF( N.GT.I+1 )
      $                  CALL DSWAP( N-I-1, A( I, I+2 ), LDA,
      $                              A( I+1, I+2 ), LDA )
-                     CALL DSWAP( N, VS( 1, I ), 1, VS( 1, I+1 ), 1 )
+                     IF( WANTVS ) THEN
+                       CALL DSWAP( N, VS( 1, I ), 1, VS( 1, I+1 ), 1 )
+                     END IF
                      A( I, I+1 ) = A( I+1, I )
                      A( I+1, I ) = ZERO
                   END IF

lapack-netlib/SRC/dgejsv.f

@@ -82,7 +82,7 @@
 *>             desirable, then this option is advisable. The input matrix A
 *>             is preprocessed with QR factorization with FULL (row and
 *>             column) pivoting.
-*>       = 'G'  Computation as with 'F' with an additional estimate of the
+*>       = 'G': Computation as with 'F' with an additional estimate of the
 *>             condition number of B, where A=D*B. If A has heavily weighted
 *>             rows, then using this condition number gives too pessimistic
 *>             error bound.
@@ -133,7 +133,7 @@
 *>        specified range. If A .NE. 0 is scaled so that the largest singular
 *>        value of c*A is around DSQRT(BIG), BIG=SLAMCH('O'), then JOBR issues
 *>        the licence to kill columns of A whose norm in c*A is less than
-*>        DSQRT(SFMIN) (for JOBR.EQ.'R'), or less than SMALL=SFMIN/EPSLN,
+*>        DSQRT(SFMIN) (for JOBR = 'R'), or less than SMALL=SFMIN/EPSLN,
 *>        where SFMIN=SLAMCH('S'), EPSLN=SLAMCH('E').
 *>       = 'N': Do not kill small columns of c*A. This option assumes that
 *>             BLAS and QR factorizations and triangular solvers are
@@ -230,7 +230,7 @@
 *>          If JOBU = 'F', then U contains on exit the M-by-M matrix of
 *>                         the left singular vectors, including an ONB
 *>                         of the orthogonal complement of the Range(A).
-*>          If JOBU = 'W'  .AND. (JOBV.EQ.'V' .AND. JOBT.EQ.'T' .AND. M.EQ.N),
+*>          If JOBU = 'W'  .AND. (JOBV = 'V' .AND. JOBT = 'T' .AND. M = N),
 *>                         then U is used as workspace if the procedure
 *>                         replaces A with A^t. In that case, [V] is computed
 *>                         in U as left singular vectors of A^t and then
@@ -252,7 +252,7 @@
 *>          V is DOUBLE PRECISION array, dimension ( LDV, N )
 *>          If JOBV = 'V', 'J' then V contains on exit the N-by-N matrix of
 *>                         the right singular vectors;
-*>          If JOBV = 'W', AND (JOBU.EQ.'U' AND JOBT.EQ.'T' AND M.EQ.N),
+*>          If JOBV = 'W', AND (JOBU = 'U' AND JOBT = 'T' AND M = N),
 *>                         then V is used as workspace if the pprocedure
 *>                         replaces A with A^t. In that case, [U] is computed
 *>                         in V as right singular vectors of A^t and then
@@ -272,13 +272,13 @@
 *> \param[out] WORK
 *> \verbatim
 *>          WORK is DOUBLE PRECISION array, dimension (LWORK)
-*>          On exit, if N.GT.0 .AND. M.GT.0 (else not referenced),
+*>          On exit, if N > 0 .AND. M > 0 (else not referenced),
 *>          WORK(1) = SCALE = WORK(2) / WORK(1) is the scaling factor such
 *>                    that SCALE*SVA(1:N) are the computed singular values
 *>                    of A. (See the description of SVA().)
 *>          WORK(2) = See the description of WORK(1).
 *>          WORK(3) = SCONDA is an estimate for the condition number of
-*>                    column equilibrated A. (If JOBA .EQ. 'E' or 'G')
+*>                    column equilibrated A. (If JOBA = 'E' or 'G')
 *>                    SCONDA is an estimate of DSQRT(||(R^t * R)^(-1)||_1).
 *>                    It is computed using DPOCON. It holds
 *>                    N^(-1/4) * SCONDA <= ||R^(-1)||_2 <= N^(1/4) * SCONDA
@@ -297,7 +297,7 @@
 *>                    triangular factor in the first QR factorization.
 *>          WORK(5) = an estimate of the scaled condition number of the
 *>                    triangular factor in the second QR factorization.
-*>          The following two parameters are computed if JOBT .EQ. 'T'.
+*>          The following two parameters are computed if JOBT = 'T'.
 *>          They are provided for a developer/implementer who is familiar
 *>          with the details of the method.
 *>
@@ -313,8 +313,8 @@
 *>          Length of WORK to confirm proper allocation of work space.
 *>          LWORK depends on the job:
 *>
-*>          If only SIGMA is needed ( JOBU.EQ.'N', JOBV.EQ.'N' ) and
+*>          If only SIGMA is needed (JOBU = 'N', JOBV = 'N') and
-*>            -> .. no scaled condition estimate required (JOBE.EQ.'N'):
+*>            -> .. no scaled condition estimate required (JOBE = 'N'):
 *>               LWORK >= max(2*M+N,4*N+1,7). This is the minimal requirement.
 *>               ->> For optimal performance (blocked code) the optimal value
 *>               is LWORK >= max(2*M+N,3*N+(N+1)*NB,7). Here NB is the optimal
@@ -330,7 +330,7 @@
 *>               LWORK >= max(2*M+N,N+LWORK(DGEQP3),N+LWORK(DGEQRF),
 *>                                                     N+N*N+LWORK(DPOCON),7).
 *>
-*>          If SIGMA and the right singular vectors are needed (JOBV.EQ.'V'),
+*>          If SIGMA and the right singular vectors are needed (JOBV = 'V'),
 *>            -> the minimal requirement is LWORK >= max(2*M+N,4*N+1,7).
 *>            -> For optimal performance, LWORK >= max(2*M+N,3*N+(N+1)*NB,7),
 *>               where NB is the optimal block size for DGEQP3, DGEQRF, DGELQF,
@@ -341,19 +341,19 @@
 *>          If SIGMA and the left singular vectors are needed
 *>            -> the minimal requirement is LWORK >= max(2*M+N,4*N+1,7).
 *>            -> For optimal performance:
-*>               if JOBU.EQ.'U' :: LWORK >= max(2*M+N,3*N+(N+1)*NB,7),
+*>               if JOBU = 'U' :: LWORK >= max(2*M+N,3*N+(N+1)*NB,7),
-*>               if JOBU.EQ.'F' :: LWORK >= max(2*M+N,3*N+(N+1)*NB,N+M*NB,7),
+*>               if JOBU = 'F' :: LWORK >= max(2*M+N,3*N+(N+1)*NB,N+M*NB,7),
 *>               where NB is the optimal block size for DGEQP3, DGEQRF, DORMQR.
 *>               In general, the optimal length LWORK is computed as
 *>               LWORK >= max(2*M+N,N+LWORK(DGEQP3),N+LWORK(DPOCON),
 *>                        2*N+LWORK(DGEQRF), N+LWORK(DORMQR)).
-*>               Here LWORK(DORMQR) equals N*NB (for JOBU.EQ.'U') or
+*>               Here LWORK(DORMQR) equals N*NB (for JOBU = 'U') or
-*>               M*NB (for JOBU.EQ.'F').
+*>               M*NB (for JOBU = 'F').
 *>
-*>          If the full SVD is needed: (JOBU.EQ.'U' or JOBU.EQ.'F') and
+*>          If the full SVD is needed: (JOBU = 'U' or JOBU = 'F') and
-*>            -> if JOBV.EQ.'V'
+*>            -> if JOBV = 'V'
 *>               the minimal requirement is LWORK >= max(2*M+N,6*N+2*N*N).
-*>            -> if JOBV.EQ.'J' the minimal requirement is
+*>            -> if JOBV = 'J' the minimal requirement is
 *>               LWORK >= max(2*M+N, 4*N+N*N,2*N+N*N+6).
 *>            -> For optimal performance, LWORK should be additionally
 *>               larger than N+M*NB, where NB is the optimal block size
@@ -369,7 +369,7 @@
 *>                     of JOBA and JOBR.
 *>          IWORK(2) = the number of the computed nonzero singular values
 *>          IWORK(3) = if nonzero, a warning message:
-*>                     If IWORK(3).EQ.1 then some of the column norms of A
+*>                     If IWORK(3) = 1 then some of the column norms of A
 *>                     were denormalized floats. The requested high accuracy
 *>                     is not warranted by the data.
 *> \endverbatim
@@ -377,10 +377,10 @@
 *> \param[out] INFO
 *> \verbatim
 *>          INFO is INTEGER
-*>           < 0  : if INFO = -i, then the i-th argument had an illegal value.
+*>           < 0:  if INFO = -i, then the i-th argument had an illegal value.
-*>           = 0 :  successful exit;
+*>           = 0:  successful exit;
-*>           > 0 :  DGEJSV  did not converge in the maximal allowed number
+*>           > 0:  DGEJSV  did not converge in the maximal allowed number
-*>                  of sweeps. The computed values may be inaccurate.
+*>                 of sweeps. The computed values may be inaccurate.
 *> \endverbatim
 *
 *  Authors:
@@ -953,7 +953,7 @@
       IF ( L2ABER ) THEN
 *        Standard absolute error bound suffices. All sigma_i with
 *        sigma_i < N*EPSLN*||A|| are flushed to zero. This is an
-*        agressive enforcement of lower numerical rank by introducing a
+*        aggressive enforcement of lower numerical rank by introducing a
 *        backward error of the order of N*EPSLN*||A||.
          TEMP1 = DSQRT(DBLE(N))*EPSLN
          DO 3001 p = 2, N
@@ -965,7 +965,7 @@
  3001    CONTINUE
  3002    CONTINUE
       ELSE IF ( L2RANK ) THEN
-*        .. similarly as above, only slightly more gentle (less agressive).
+*        .. similarly as above, only slightly more gentle (less aggressive).
 *        Sudden drop on the diagonal of R1 is used as the criterion for
 *        close-to-rank-deficient.
          TEMP1 = DSQRT(SFMIN)
@@ -1294,7 +1294,7 @@
             CALL DPOCON('Lower',NR,WORK(2*N+1),NR,ONE,TEMP1,
      $                   WORK(2*N+NR*NR+1),IWORK(M+2*N+1),IERR)
             CONDR1 = ONE / DSQRT(TEMP1)
-*           .. here need a second oppinion on the condition number
+*           .. here need a second opinion on the condition number
 *           .. then assume worst case scenario
 *           R1 is OK for inverse <=> CONDR1 .LT. DBLE(N)
 *           more conservative    <=> CONDR1 .LT. DSQRT(DBLE(N))
@@ -1335,7 +1335,7 @@
             ELSE
 *
 *              .. ill-conditioned case: second QRF with pivoting
-*              Note that windowed pivoting would be equaly good
+*              Note that windowed pivoting would be equally good
 *              numerically, and more run-time efficient. So, in
 *              an optimal implementation, the next call to DGEQP3
 *              should be replaced with eg. CALL SGEQPX (ACM TOMS #782)
@@ -1388,7 +1388,7 @@
 *
                IF ( CONDR2 .GE. COND_OK ) THEN
 *                 .. save the Householder vectors used for Q3
-*                 (this overwrittes the copy of R2, as it will not be
+*                 (this overwrites the copy of R2, as it will not be
 *                 needed in this branch, but it does not overwritte the
 *                 Huseholder vectors of Q2.).
                   CALL DLACPY( 'U', NR, NR, V, LDV, WORK(2*N+1), N )
@@ -1638,7 +1638,7 @@
 *
 *        This branch deploys a preconditioned Jacobi SVD with explicitly
 *        accumulated rotations. It is included as optional, mainly for
-*        experimental purposes. It does perfom well, and can also be used.
+*        experimental purposes. It does perform well, and can also be used.
 *        In this implementation, this branch will be automatically activated
 *        if the  condition number sigma_max(A) / sigma_min(A) is predicted
 *        to be greater than the overflow threshold. This is because the

lapack-netlib/SRC/dgelq.f

@@ -1,3 +1,4 @@
+*> \brief \b DGELQ
 *
 *  Definition:
 *  ===========
@@ -17,7 +18,17 @@
 *  =============
 *>
 *> \verbatim
-*> DGELQ computes a LQ factorization of an M-by-N matrix A.
+*>
+*> DGELQ computes an LQ factorization of a real M-by-N matrix A:
+*>
+*>    A = ( L 0 ) *  Q
+*>
+*> where:
+*>
+*>    Q is a N-by-N orthogonal matrix;
+*>    L is an lower-triangular M-by-M matrix;
+*>    0 is a M-by-(N-M) zero matrix, if M < N.
+*>
 *> \endverbatim
 *
 *  Arguments:
@@ -138,7 +149,7 @@
 *> \verbatim
 *>
 *> These details are particular for this LAPACK implementation. Users should not 
-*> take them for granted. These details may change in the future, and are unlikely not
+*> take them for granted. These details may change in the future, and are not likely
 *> true for another LAPACK implementation. These details are relevant if one wants
 *> to try to understand the code. They are not part of the interface.
 *>
@@ -159,10 +170,10 @@
       SUBROUTINE DGELQ( M, N, A, LDA, T, TSIZE, WORK, LWORK,
      $                  INFO )
 *
-*  -- LAPACK computational routine (version 3.7.0) --
+*  -- LAPACK computational routine (version 3.9.0) --
 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd. --
-*     December 2016
+*     November 2019
 *
 *     .. Scalar Arguments ..
       INTEGER            INFO, LDA, M, N, TSIZE, LWORK

lapack-netlib/SRC/dgelq2.f

@@ -33,8 +33,16 @@
 *>
 *> \verbatim
 *>
-*> DGELQ2 computes an LQ factorization of a real m by n matrix A:
+*> DGELQ2 computes an LQ factorization of a real m-by-n matrix A:
-*> A = L * Q.
+*>
+*>    A = ( L 0 ) *  Q
+*>
+*> where:
+*>
+*>    Q is a n-by-n orthogonal matrix;
+*>    L is an lower-triangular m-by-m matrix;
+*>    0 is a m-by-(n-m) zero matrix, if m < n.
+*>
 *> \endverbatim
 *
 *  Arguments:
@@ -96,7 +104,7 @@
 *> \author Univ. of Colorado Denver
 *> \author NAG Ltd.
 *
-*> \date December 2016
+*> \date November 2019
 *
 *> \ingroup doubleGEcomputational
 *
@@ -121,10 +129,10 @@
 *  =====================================================================
       SUBROUTINE DGELQ2( M, N, A, LDA, TAU, WORK, INFO )
 *
-*  -- LAPACK computational routine (version 3.7.0) --
+*  -- LAPACK computational routine (version 3.9.0) --
 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
-*     December 2016
+*     November 2019
 *
 *     .. Scalar Arguments ..
       INTEGER            INFO, LDA, M, N

lapack-netlib/SRC/dgelqf.f

@@ -34,7 +34,15 @@
 *> \verbatim
 *>
 *> DGELQF computes an LQ factorization of a real M-by-N matrix A:
-*> A = L * Q.
+*>
+*>    A = ( L 0 ) *  Q
+*>
+*> where:
+*>
+*>    Q is a N-by-N orthogonal matrix;
+*>    L is an lower-triangular M-by-M matrix;
+*>    0 is a M-by-(N-M) zero matrix, if M < N.
+*>
 *> \endverbatim
 *
 *  Arguments:
@@ -110,7 +118,7 @@
 *> \author Univ. of Colorado Denver
 *> \author NAG Ltd.
 *
-*> \date December 2016
+*> \date November 2019
 *
 *> \ingroup doubleGEcomputational
 *
@@ -135,10 +143,10 @@
 *  =====================================================================
       SUBROUTINE DGELQF( M, N, A, LDA, TAU, WORK, LWORK, INFO )
 *
-*  -- LAPACK computational routine (version 3.7.0) --
+*  -- LAPACK computational routine (version 3.9.0) --
 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
-*     December 2016
+*     November 2019
 *
 *     .. Scalar Arguments ..
       INTEGER            INFO, LDA, LWORK, M, N

lapack-netlib/SRC/dgemlq.f

@@ -1,3 +1,4 @@
+*> \brief \b DGEMLQ
 *
 *  Definition:
 *  ===========
@@ -144,7 +145,7 @@
 *> \verbatim
 *>
 *> These details are particular for this LAPACK implementation. Users should not 
-*> take them for granted. These details may change in the future, and are unlikely not
+*> take them for granted. These details may change in the future, and are not likely
 *> true for another LAPACK implementation. These details are relevant if one wants
 *> to try to understand the code. They are not part of the interface.
 *>

lapack-netlib/SRC/dgemqr.f

@@ -1,3 +1,4 @@
+*> \brief \b DGEMQR
 *
 *  Definition:
 *  ===========
@@ -144,7 +145,7 @@
 *> \verbatim
 *>
 *> These details are particular for this LAPACK implementation. Users should not 
-*> take them for granted. These details may change in the future, and are unlikely not
+*> take them for granted. These details may change in the future, and are not likely
 *> true for another LAPACK implementation. These details are relevant if one wants
 *> to try to understand the code. They are not part of the interface.
 *>

lapack-netlib/SRC/dgeqr.f

@@ -1,3 +1,4 @@
+*> \brief \b DGEQR
 *
 *  Definition:
 *  ===========
@@ -17,7 +18,18 @@
 *  =============
 *>
 *> \verbatim
-*> DGEQR computes a QR factorization of an M-by-N matrix A.
+*>
+*> DGEQR computes a QR factorization of a real M-by-N matrix A:
+*>
+*>    A = Q * ( R ),
+*>            ( 0 )
+*>
+*> where:
+*>
+*>    Q is a M-by-M orthogonal matrix;
+*>    R is an upper-triangular N-by-N matrix;
+*>    0 is a (M-N)-by-N zero matrix, if M > N.
+*>
 *> \endverbatim
 *
 *  Arguments:
@@ -138,7 +150,7 @@
 *> \verbatim
 *>
 *> These details are particular for this LAPACK implementation. Users should not 
-*> take them for granted. These details may change in the future, and are unlikely not
+*> take them for granted. These details may change in the future, and are not likely
 *> true for another LAPACK implementation. These details are relevant if one wants
 *> to try to understand the code. They are not part of the interface.
 *>
@@ -160,10 +172,10 @@
       SUBROUTINE DGEQR( M, N, A, LDA, T, TSIZE, WORK, LWORK,
      $                  INFO )
 *
-*  -- LAPACK computational routine (version 3.7.0) --
+*  -- LAPACK computational routine (version 3.9.0) --
 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd. --
-*     December 2016
+*     November 2019
 *
 *     .. Scalar Arguments ..
       INTEGER            INFO, LDA, M, N, TSIZE, LWORK

lapack-netlib/SRC/dgeqr2.f

@@ -33,8 +33,17 @@
 *>
 *> \verbatim
 *>
-*> DGEQR2 computes a QR factorization of a real m by n matrix A:
+*> DGEQR2 computes a QR factorization of a real m-by-n matrix A:
-*> A = Q * R.
+*>
+*>    A = Q * ( R ),
+*>            ( 0 )
+*>
+*> where:
+*>
+*>    Q is a m-by-m orthogonal matrix;
+*>    R is an upper-triangular n-by-n matrix;
+*>    0 is a (m-n)-by-n zero matrix, if m > n.
+*>
 *> \endverbatim
 *
 *  Arguments:
@@ -96,7 +105,7 @@
 *> \author Univ. of Colorado Denver
 *> \author NAG Ltd.
 *
-*> \date December 2016
+*> \date November 2019
 *
 *> \ingroup doubleGEcomputational
 *
@@ -121,10 +130,10 @@
 *  =====================================================================
       SUBROUTINE DGEQR2( M, N, A, LDA, TAU, WORK, INFO )
 *
-*  -- LAPACK computational routine (version 3.7.0) --
+*  -- LAPACK computational routine (version 3.9.0) --
 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
-*     December 2016
+*     November 2019
 *
 *     .. Scalar Arguments ..
       INTEGER            INFO, LDA, M, N

lapack-netlib/SRC/dgeqr2p.f

@@ -33,8 +33,18 @@
 *>
 *> \verbatim
 *>
-*> DGEQR2P computes a QR factorization of a real m by n matrix A:
+*> DGEQR2P computes a QR factorization of a real m-by-n matrix A:
-*> A = Q * R. The diagonal entries of R are nonnegative.
+*>
+*>    A = Q * ( R ),
+*>            ( 0 )
+*>
+*> where:
+*>
+*>    Q is a m-by-m orthogonal matrix;
+*>    R is an upper-triangular n-by-n matrix with nonnegative diagonal
+*>    entries;
+*>    0 is a (m-n)-by-n zero matrix, if m > n.
+*>
 *> \endverbatim
 *
 *  Arguments:
@@ -97,7 +107,7 @@
 *> \author Univ. of Colorado Denver
 *> \author NAG Ltd.
 *
-*> \date December 2016
+*> \date November 2019
 *
 *> \ingroup doubleGEcomputational
 *
@@ -124,10 +134,10 @@
 *  =====================================================================
       SUBROUTINE DGEQR2P( M, N, A, LDA, TAU, WORK, INFO )
 *
-*  -- LAPACK computational routine (version 3.7.0) --
+*  -- LAPACK computational routine (version 3.9.0) --
 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
-*     December 2016
+*     November 2019
 *
 *     .. Scalar Arguments ..
       INTEGER            INFO, LDA, M, N

lapack-netlib/SRC/dgeqrf.f

@@ -34,7 +34,16 @@
 *> \verbatim
 *>
 *> DGEQRF computes a QR factorization of a real M-by-N matrix A:
-*> A = Q * R.
+*>
+*>    A = Q * ( R ),
+*>            ( 0 )
+*>
+*> where:
+*>
+*>    Q is a M-by-M orthogonal matrix;
+*>    R is an upper-triangular N-by-N matrix;
+*>    0 is a (M-N)-by-N zero matrix, if M > N.
+*>
 *> \endverbatim
 *
 *  Arguments:
@@ -111,7 +120,7 @@
 *> \author Univ. of Colorado Denver
 *> \author NAG Ltd.
 *
-*> \date December 2016
+*> \date November 2019
 *
 *> \ingroup doubleGEcomputational
 *
@@ -136,10 +145,10 @@
 *  =====================================================================
       SUBROUTINE DGEQRF( M, N, A, LDA, TAU, WORK, LWORK, INFO )
 *
-*  -- LAPACK computational routine (version 3.7.0) --
+*  -- LAPACK computational routine (version 3.9.0) --
 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
-*     December 2016
+*     November 2019
 *
 *     .. Scalar Arguments ..
       INTEGER            INFO, LDA, LWORK, M, N

lapack-netlib/SRC/dgeqrfp.f

@@ -33,8 +33,18 @@
 *>
 *> \verbatim
 *>
-*> DGEQRFP computes a QR factorization of a real M-by-N matrix A:
+*> DGEQR2P computes a QR factorization of a real M-by-N matrix A:
-*> A = Q * R. The diagonal entries of R are nonnegative.
+*>
+*>    A = Q * ( R ),
+*>            ( 0 )
+*>
+*> where:
+*>
+*>    Q is a M-by-M orthogonal matrix;
+*>    R is an upper-triangular N-by-N matrix with nonnegative diagonal
+*>    entries;
+*>    0 is a (M-N)-by-N zero matrix, if M > N.
+*>
 *> \endverbatim
 *
 *  Arguments:
@@ -112,7 +122,7 @@
 *> \author Univ. of Colorado Denver
 *> \author NAG Ltd.
 *
-*> \date December 2016
+*> \date November 2019
 *
 *> \ingroup doubleGEcomputational
 *
@@ -139,10 +149,10 @@
 *  =====================================================================
       SUBROUTINE DGEQRFP( M, N, A, LDA, TAU, WORK, LWORK, INFO )
 *
-*  -- LAPACK computational routine (version 3.7.0) --
+*  -- LAPACK computational routine (version 3.9.0) --
 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
-*     December 2016
+*     November 2019
 *
 *     .. Scalar Arguments ..
       INTEGER            INFO, LDA, LWORK, M, N

lapack-netlib/SRC/dgerfsx.f

@@ -283,7 +283,7 @@
 *>     information as described below. There currently are up to three
 *>     pieces of information returned for each right-hand side. If
 *>     componentwise accuracy is not requested (PARAMS(3) = 0.0), then
-*>     ERR_BNDS_COMP is not accessed.  If N_ERR_BNDS .LT. 3, then at most
+*>     ERR_BNDS_COMP is not accessed.  If N_ERR_BNDS < 3, then at most
 *>     the first (:,N_ERR_BNDS) entries are returned.
 *>
 *>     The first index in ERR_BNDS_COMP(i,:) corresponds to the ith
@@ -319,14 +319,14 @@
 *> \param[in] NPARAMS
 *> \verbatim
 *>          NPARAMS is INTEGER
-*>     Specifies the number of parameters set in PARAMS.  If .LE. 0, the
+*>     Specifies the number of parameters set in PARAMS.  If <= 0, the
 *>     PARAMS array is never referenced and default values are used.
 *> \endverbatim
 *>
 *> \param[in,out] PARAMS
 *> \verbatim
 *>          PARAMS is DOUBLE PRECISION array, dimension (NPARAMS)
-*>     Specifies algorithm parameters.  If an entry is .LT. 0.0, then
+*>     Specifies algorithm parameters.  If an entry is < 0.0, then
 *>     that entry will be filled with default value used for that
 *>     parameter.  Only positions up to NPARAMS are accessed; defaults
 *>     are used for higher-numbered parameters.
@@ -334,9 +334,9 @@
 *>       PARAMS(LA_LINRX_ITREF_I = 1) : Whether to perform iterative
 *>            refinement or not.
 *>         Default: 1.0D+0
-*>            = 0.0 : No refinement is performed, and no error bounds are
+*>            = 0.0:  No refinement is performed, and no error bounds are
 *>                    computed.
-*>            = 1.0 : Use the double-precision refinement algorithm,
+*>            = 1.0:  Use the double-precision refinement algorithm,
 *>                    possibly with doubled-single computations if the
 *>                    compilation environment does not support DOUBLE
 *>                    PRECISION.

lapack-netlib/SRC/dgesc2.f

@@ -90,7 +90,7 @@
 *> \verbatim
 *>          SCALE is DOUBLE PRECISION
 *>          On exit, SCALE contains the scale factor. SCALE is chosen
-*>          0 <= SCALE <= 1 to prevent owerflow in the solution.
+*>          0 <= SCALE <= 1 to prevent overflow in the solution.
 *> \endverbatim
 *
 *  Authors:
@@ -151,7 +151,7 @@
 *     ..
 *     .. Executable Statements ..
 *
-*      Set constant to control owerflow
+*      Set constant to control overflow
 *
       EPS = DLAMCH( 'P' )
       SMLNUM = DLAMCH( 'S' ) / EPS

lapack-netlib/SRC/dgesdd.f

@@ -322,7 +322,7 @@
 *
             IF( WNTQN ) THEN
 *              dbdsdc needs only 4*N (or 6*N for uplo=L for LAPACK <= 3.6)
-*              keep 7*N for backwards compatability.
+*              keep 7*N for backwards compatibility.
                BDSPAC = 7*N
             ELSE
                BDSPAC = 3*N*N + 4*N
@@ -448,7 +448,7 @@
 *
             IF( WNTQN ) THEN
 *              dbdsdc needs only 4*N (or 6*N for uplo=L for LAPACK <= 3.6)
-*              keep 7*N for backwards compatability.
+*              keep 7*N for backwards compatibility.
                BDSPAC = 7*M
             ELSE
                BDSPAC = 3*M*M + 4*M

lapack-netlib/SRC/dgesvj.f

@@ -90,13 +90,13 @@
 *>          JOBV is CHARACTER*1
 *>          Specifies whether to compute the right singular vectors, that
 *>          is, the matrix V:
-*>          = 'V' : the matrix V is computed and returned in the array V
+*>          = 'V':  the matrix V is computed and returned in the array V
-*>          = 'A' : the Jacobi rotations are applied to the MV-by-N
+*>          = 'A':  the Jacobi rotations are applied to the MV-by-N
 *>                  array V. In other words, the right singular vector
 *>                  matrix V is not computed explicitly, instead it is
 *>                  applied to an MV-by-N matrix initially stored in the
 *>                  first MV rows of V.
-*>          = 'N' : the matrix V is not computed and the array V is not
+*>          = 'N':  the matrix V is not computed and the array V is not
 *>                  referenced
 *> \endverbatim
 *>
@@ -118,8 +118,8 @@
 *>          A is DOUBLE PRECISION array, dimension (LDA,N)
 *>          On entry, the M-by-N matrix A.
 *>          On exit :
-*>          If JOBU .EQ. 'U' .OR. JOBU .EQ. 'C' :
+*>          If JOBU = 'U' .OR. JOBU = 'C' :
-*>                 If INFO .EQ. 0 :
+*>                 If INFO = 0 :
 *>                 RANKA orthonormal columns of U are returned in the
 *>                 leading RANKA columns of the array A. Here RANKA <= N
 *>                 is the number of computed singular values of A that are
@@ -129,9 +129,9 @@
 *>                 in the array WORK as RANKA=NINT(WORK(2)). Also see the
 *>                 descriptions of SVA and WORK. The computed columns of U
 *>                 are mutually numerically orthogonal up to approximately
-*>                 TOL=DSQRT(M)*EPS (default); or TOL=CTOL*EPS (JOBU.EQ.'C'),
+*>                 TOL=DSQRT(M)*EPS (default); or TOL=CTOL*EPS (JOBU = 'C'),
 *>                 see the description of JOBU.
-*>                 If INFO .GT. 0 :
+*>                 If INFO > 0 :
 *>                 the procedure DGESVJ did not converge in the given number
 *>                 of iterations (sweeps). In that case, the computed
 *>                 columns of U may not be orthogonal up to TOL. The output
@@ -140,8 +140,8 @@
 *>                 input matrix A in the sense that the residual
 *>                 ||A-SCALE*U*SIGMA*V^T||_2 / ||A||_2 is small.
 *>
-*>          If JOBU .EQ. 'N' :
+*>          If JOBU = 'N' :
-*>                 If INFO .EQ. 0 :
+*>                 If INFO = 0 :
 *>                 Note that the left singular vectors are 'for free' in the
 *>                 one-sided Jacobi SVD algorithm. However, if only the
 *>                 singular values are needed, the level of numerical
@@ -150,7 +150,7 @@
 *>                 numerically orthogonal up to approximately M*EPS. Thus,
 *>                 on exit, A contains the columns of U scaled with the
 *>                 corresponding singular values.
-*>                 If INFO .GT. 0 :
+*>                 If INFO > 0 :
 *>                 the procedure DGESVJ did not converge in the given number
 *>                 of iterations (sweeps).
 *> \endverbatim
@@ -165,9 +165,9 @@
 *> \verbatim
 *>          SVA is DOUBLE PRECISION array, dimension (N)
 *>          On exit :
-*>          If INFO .EQ. 0 :
+*>          If INFO = 0 :
 *>          depending on the value SCALE = WORK(1), we have:
-*>                 If SCALE .EQ. ONE :
+*>                 If SCALE = ONE :
 *>                 SVA(1:N) contains the computed singular values of A.
 *>                 During the computation SVA contains the Euclidean column
 *>                 norms of the iterated matrices in the array A.
@@ -175,7 +175,7 @@
 *>                 The singular values of A are SCALE*SVA(1:N), and this
 *>                 factored representation is due to the fact that some of the
 *>                 singular values of A might underflow or overflow.
-*>          If INFO .GT. 0 :
+*>          If INFO > 0 :
 *>          the procedure DGESVJ did not converge in the given number of
 *>          iterations (sweeps) and SCALE*SVA(1:N) may not be accurate.
 *> \endverbatim
@@ -183,7 +183,7 @@
 *> \param[in] MV
 *> \verbatim
 *>          MV is INTEGER
-*>          If JOBV .EQ. 'A', then the product of Jacobi rotations in DGESVJ
+*>          If JOBV = 'A', then the product of Jacobi rotations in DGESVJ
 *>          is applied to the first MV rows of V. See the description of JOBV.
 *> \endverbatim
 *>
@@ -201,16 +201,16 @@
 *> \param[in] LDV
 *> \verbatim
 *>          LDV is INTEGER
-*>          The leading dimension of the array V, LDV .GE. 1.
+*>          The leading dimension of the array V, LDV >= 1.
-*>          If JOBV .EQ. 'V', then LDV .GE. max(1,N).
+*>          If JOBV = 'V', then LDV >= max(1,N).
-*>          If JOBV .EQ. 'A', then LDV .GE. max(1,MV) .
+*>          If JOBV = 'A', then LDV >= max(1,MV) .
 *> \endverbatim
 *>
 *> \param[in,out] WORK
 *> \verbatim
 *>          WORK is DOUBLE PRECISION array, dimension (LWORK)
 *>          On entry :
-*>          If JOBU .EQ. 'C' :
+*>          If JOBU = 'C' :
 *>          WORK(1) = CTOL, where CTOL defines the threshold for convergence.
 *>                    The process stops if all columns of A are mutually
 *>                    orthogonal up to CTOL*EPS, EPS=DLAMCH('E').
@@ -230,7 +230,7 @@
 *>          WORK(5) = max_{i.NE.j} |COS(A(:,i),A(:,j))| in the last sweep.
 *>                    This is useful information in cases when DGESVJ did
 *>                    not converge, as it can be used to estimate whether
-*>                    the output is stil useful and for post festum analysis.
+*>                    the output is still useful and for post festum analysis.
 *>          WORK(6) = the largest absolute value over all sines of the
 *>                    Jacobi rotation angles in the last sweep. It can be
 *>                    useful for a post festum analysis.
@@ -245,9 +245,9 @@
 *> \param[out] INFO
 *> \verbatim
 *>          INFO is INTEGER
-*>          = 0 : successful exit.
+*>          = 0:  successful exit.
-*>          < 0 : if INFO = -i, then the i-th argument had an illegal value
+*>          < 0:  if INFO = -i, then the i-th argument had an illegal value
-*>          > 0 : DGESVJ did not converge in the maximal allowed number (30)
+*>          > 0:  DGESVJ did not converge in the maximal allowed number (30)
 *>                of sweeps. The output may still be useful. See the
 *>                description of WORK.
 *> \endverbatim

lapack-netlib/SRC/dgesvxx.f

@@ -411,7 +411,7 @@
 *>     information as described below. There currently are up to three
 *>     pieces of information returned for each right-hand side. If
 *>     componentwise accuracy is not requested (PARAMS(3) = 0.0), then
-*>     ERR_BNDS_COMP is not accessed.  If N_ERR_BNDS .LT. 3, then at most
+*>     ERR_BNDS_COMP is not accessed.  If N_ERR_BNDS < 3, then at most
 *>     the first (:,N_ERR_BNDS) entries are returned.
 *>
 *>     The first index in ERR_BNDS_COMP(i,:) corresponds to the ith
@@ -447,14 +447,14 @@
 *> \param[in] NPARAMS
 *> \verbatim
 *>          NPARAMS is INTEGER
-*>     Specifies the number of parameters set in PARAMS.  If .LE. 0, the
+*>     Specifies the number of parameters set in PARAMS.  If <= 0, the
 *>     PARAMS array is never referenced and default values are used.
 *> \endverbatim
 *>
 *> \param[in,out] PARAMS
 *> \verbatim
 *>          PARAMS is DOUBLE PRECISION array, dimension (NPARAMS)
-*>     Specifies algorithm parameters.  If an entry is .LT. 0.0, then
+*>     Specifies algorithm parameters.  If an entry is < 0.0, then
 *>     that entry will be filled with default value used for that
 *>     parameter.  Only positions up to NPARAMS are accessed; defaults
 *>     are used for higher-numbered parameters.
@@ -462,9 +462,9 @@
 *>       PARAMS(LA_LINRX_ITREF_I = 1) : Whether to perform iterative
 *>            refinement or not.
 *>         Default: 1.0D+0
-*>            = 0.0 : No refinement is performed, and no error bounds are
+*>            = 0.0:  No refinement is performed, and no error bounds are
 *>                    computed.
-*>            = 1.0 : Use the extra-precise refinement algorithm.
+*>            = 1.0:  Use the extra-precise refinement algorithm.
 *>              (other values are reserved for future use)
 *>
 *>       PARAMS(LA_LINRX_ITHRESH_I = 2) : Maximum number of residual

lapack-netlib/SRC/dgetc2.f

@@ -85,7 +85,7 @@
 *> \verbatim
 *>          INFO is INTEGER
 *>           = 0: successful exit
-*>           > 0: if INFO = k, U(k, k) is likely to produce owerflow if
+*>           > 0: if INFO = k, U(k, k) is likely to produce overflow if
 *>                we try to solve for x in Ax = b. So U is perturbed to
 *>                avoid the overflow.
 *> \endverbatim

lapack-netlib/SRC/dgetsls.f

@@ -1,3 +1,5 @@
+*> \brief \b DGETSLS
+*
 *  Definition:
 *  ===========
 *

lapack-netlib/SRC/dggesx.f

@@ -131,10 +131,10 @@
 *> \verbatim
 *>          SENSE is CHARACTER*1
 *>          Determines which reciprocal condition numbers are computed.
-*>          = 'N' : None are computed;
+*>          = 'N':  None are computed;
-*>          = 'E' : Computed for average of selected eigenvalues only;
+*>          = 'E':  Computed for average of selected eigenvalues only;
-*>          = 'V' : Computed for selected deflating subspaces only;
+*>          = 'V':  Computed for selected deflating subspaces only;
-*>          = 'B' : Computed for both.
+*>          = 'B':  Computed for both.
 *>          If SENSE = 'E', 'V', or 'B', SORT must equal 'S'.
 *> \endverbatim
 *>

lapack-netlib/SRC/dgsvj0.f

@@ -117,7 +117,7 @@
 *> \param[in] MV
 *> \verbatim
 *>          MV is INTEGER
-*>          If JOBV .EQ. 'A', then MV rows of V are post-multipled by a
+*>          If JOBV = 'A', then MV rows of V are post-multipled by a
 *>                           sequence of Jacobi rotations.
 *>          If JOBV = 'N',   then MV is not referenced.
 *> \endverbatim
@@ -125,9 +125,9 @@
 *> \param[in,out] V
 *> \verbatim
 *>          V is DOUBLE PRECISION array, dimension (LDV,N)
-*>          If JOBV .EQ. 'V' then N rows of V are post-multipled by a
+*>          If JOBV = 'V' then N rows of V are post-multipled by a
 *>                           sequence of Jacobi rotations.
-*>          If JOBV .EQ. 'A' then MV rows of V are post-multipled by a
+*>          If JOBV = 'A' then MV rows of V are post-multipled by a
 *>                           sequence of Jacobi rotations.
 *>          If JOBV = 'N',   then V is not referenced.
 *> \endverbatim
@@ -136,8 +136,8 @@
 *> \verbatim
 *>          LDV is INTEGER
 *>          The leading dimension of the array V,  LDV >= 1.
-*>          If JOBV = 'V', LDV .GE. N.
+*>          If JOBV = 'V', LDV >= N.
-*>          If JOBV = 'A', LDV .GE. MV.
+*>          If JOBV = 'A', LDV >= MV.
 *> \endverbatim
 *>
 *> \param[in] EPS
@@ -157,7 +157,7 @@
 *>          TOL is DOUBLE PRECISION
 *>          TOL is the threshold for Jacobi rotations. For a pair
 *>          A(:,p), A(:,q) of pivot columns, the Jacobi rotation is
-*>          applied only if DABS(COS(angle(A(:,p),A(:,q)))) .GT. TOL.
+*>          applied only if DABS(COS(angle(A(:,p),A(:,q)))) > TOL.
 *> \endverbatim
 *>
 *> \param[in] NSWEEP
@@ -175,14 +175,14 @@
 *> \param[in] LWORK
 *> \verbatim
 *>          LWORK is INTEGER
-*>          LWORK is the dimension of WORK. LWORK .GE. M.
+*>          LWORK is the dimension of WORK. LWORK >= M.
 *> \endverbatim
 *>
 *> \param[out] INFO
 *> \verbatim
 *>          INFO is INTEGER
-*>          = 0 : successful exit.
+*>          = 0:  successful exit.
-*>          < 0 : if INFO = -i, then the i-th argument had an illegal value
+*>          < 0:  if INFO = -i, then the i-th argument had an illegal value
 *> \endverbatim
 *
 *  Authors:
@@ -1045,7 +1045,7 @@
 
  1993 CONTINUE
 *     end i=1:NSWEEP loop
-* #:) Reaching this point means that the procedure has comleted the given
+* #:) Reaching this point means that the procedure has completed the given
 *     number of iterations.
       INFO = NSWEEP - 1
       GO TO 1995

lapack-netlib/SRC/dgsvj1.f

@@ -61,7 +61,7 @@
 *> In terms of the columns of A, the first N1 columns are rotated 'against'
 *> the remaining N-N1 columns, trying to increase the angle between the
 *> corresponding subspaces. The off-diagonal block is N1-by(N-N1) and it is
-*> tiled using quadratic tiles of side KBL. Here, KBL is a tunning parmeter.
+*> tiled using quadratic tiles of side KBL. Here, KBL is a tunning parameter.
 *> The number of sweeps is given in NSWEEP and the orthogonality threshold
 *> is given in TOL.
 *> \endverbatim
@@ -147,27 +147,27 @@
 *> \param[in] MV
 *> \verbatim
 *>          MV is INTEGER
-*>          If JOBV .EQ. 'A', then MV rows of V are post-multipled by a
+*>          If JOBV = 'A', then MV rows of V are post-multipled by a
-*>                           sequence of Jacobi rotations.
+*>                         sequence of Jacobi rotations.
-*>          If JOBV = 'N',   then MV is not referenced.
+*>          If JOBV = 'N', then MV is not referenced.
 *> \endverbatim
 *>
 *> \param[in,out] V
 *> \verbatim
 *>          V is DOUBLE PRECISION array, dimension (LDV,N)
-*>          If JOBV .EQ. 'V' then N rows of V are post-multipled by a
+*>          If JOBV = 'V', then N rows of V are post-multipled by a
-*>                           sequence of Jacobi rotations.
+*>                         sequence of Jacobi rotations.
-*>          If JOBV .EQ. 'A' then MV rows of V are post-multipled by a
+*>          If JOBV = 'A', then MV rows of V are post-multipled by a
-*>                           sequence of Jacobi rotations.
+*>                         sequence of Jacobi rotations.
-*>          If JOBV = 'N',   then V is not referenced.
+*>          If JOBV = 'N', then V is not referenced.
 *> \endverbatim
 *>
 *> \param[in] LDV
 *> \verbatim
 *>          LDV is INTEGER
 *>          The leading dimension of the array V,  LDV >= 1.
-*>          If JOBV = 'V', LDV .GE. N.
+*>          If JOBV = 'V', LDV >= N.
-*>          If JOBV = 'A', LDV .GE. MV.
+*>          If JOBV = 'A', LDV >= MV.
 *> \endverbatim
 *>
 *> \param[in] EPS
@@ -187,7 +187,7 @@
 *>          TOL is DOUBLE PRECISION
 *>          TOL is the threshold for Jacobi rotations. For a pair
 *>          A(:,p), A(:,q) of pivot columns, the Jacobi rotation is
-*>          applied only if DABS(COS(angle(A(:,p),A(:,q)))) .GT. TOL.
+*>          applied only if DABS(COS(angle(A(:,p),A(:,q)))) > TOL.
 *> \endverbatim
 *>
 *> \param[in] NSWEEP
@@ -205,14 +205,14 @@
 *> \param[in] LWORK
 *> \verbatim
 *>          LWORK is INTEGER
-*>          LWORK is the dimension of WORK. LWORK .GE. M.
+*>          LWORK is the dimension of WORK. LWORK >= M.
 *> \endverbatim
 *>
 *> \param[out] INFO
 *> \verbatim
 *>          INFO is INTEGER
-*>          = 0 : successful exit.
+*>          = 0:  successful exit.
-*>          < 0 : if INFO = -i, then the i-th argument had an illegal value
+*>          < 0:  if INFO = -i, then the i-th argument had an illegal value
 *> \endverbatim
 *
 *  Authors:

lapack-netlib/SRC/dhseqr.f

@@ -70,7 +70,7 @@
 *> \param[in] N
 *> \verbatim
 *>          N is INTEGER
-*>           The order of the matrix H.  N .GE. 0.
+*>           The order of the matrix H.  N >= 0.
 *> \endverbatim
 *>
 *> \param[in] ILO
@@ -87,7 +87,7 @@
 *>           set by a previous call to DGEBAL, and then passed to ZGEHRD
 *>           when the matrix output by DGEBAL is reduced to Hessenberg
 *>           form. Otherwise ILO and IHI should be set to 1 and N
-*>           respectively.  If N.GT.0, then 1.LE.ILO.LE.IHI.LE.N.
+*>           respectively.  If N > 0, then 1 <= ILO <= IHI <= N.
 *>           If N = 0, then ILO = 1 and IHI = 0.
 *> \endverbatim
 *>
@@ -100,20 +100,20 @@
 *>           (the Schur form); 2-by-2 diagonal blocks (corresponding to
 *>           complex conjugate pairs of eigenvalues) are returned in
 *>           standard form, with H(i,i) = H(i+1,i+1) and
-*>           H(i+1,i)*H(i,i+1).LT.0. If INFO = 0 and JOB = 'E', the
+*>           H(i+1,i)*H(i,i+1) < 0. If INFO = 0 and JOB = 'E', the
 *>           contents of H are unspecified on exit.  (The output value of
-*>           H when INFO.GT.0 is given under the description of INFO
+*>           H when INFO > 0 is given under the description of INFO
 *>           below.)
 *>
 *>           Unlike earlier versions of DHSEQR, this subroutine may
-*>           explicitly H(i,j) = 0 for i.GT.j and j = 1, 2, ... ILO-1
+*>           explicitly H(i,j) = 0 for i > j and j = 1, 2, ... ILO-1
 *>           or j = IHI+1, IHI+2, ... N.
 *> \endverbatim
 *>
 *> \param[in] LDH
 *> \verbatim
 *>          LDH is INTEGER
-*>           The leading dimension of the array H. LDH .GE. max(1,N).
+*>           The leading dimension of the array H. LDH >= max(1,N).
 *> \endverbatim
 *>
 *> \param[out] WR
@@ -128,8 +128,8 @@
 *>           The real and imaginary parts, respectively, of the computed
 *>           eigenvalues. If two eigenvalues are computed as a complex
 *>           conjugate pair, they are stored in consecutive elements of
-*>           WR and WI, say the i-th and (i+1)th, with WI(i) .GT. 0 and
+*>           WR and WI, say the i-th and (i+1)th, with WI(i) > 0 and
-*>           WI(i+1) .LT. 0. If JOB = 'S', the eigenvalues are stored in
+*>           WI(i+1) < 0. If JOB = 'S', the eigenvalues are stored in
 *>           the same order as on the diagonal of the Schur form returned
 *>           in H, with WR(i) = H(i,i) and, if H(i:i+1,i:i+1) is a 2-by-2
 *>           diagonal block, WI(i) = sqrt(-H(i+1,i)*H(i,i+1)) and
@@ -148,7 +148,7 @@
 *>           if INFO = 0, Z contains Q*Z.
 *>           Normally Q is the orthogonal matrix generated by DORGHR
 *>           after the call to DGEHRD which formed the Hessenberg matrix
-*>           H. (The output value of Z when INFO.GT.0 is given under
+*>           H. (The output value of Z when INFO > 0 is given under
 *>           the description of INFO below.)
 *> \endverbatim
 *>
@@ -156,7 +156,7 @@
 *> \verbatim
 *>          LDZ is INTEGER
 *>           The leading dimension of the array Z.  if COMPZ = 'I' or
-*>           COMPZ = 'V', then LDZ.GE.MAX(1,N).  Otherwize, LDZ.GE.1.
+*>           COMPZ = 'V', then LDZ >= MAX(1,N).  Otherwise, LDZ >= 1.
 *> \endverbatim
 *>
 *> \param[out] WORK
@@ -169,7 +169,7 @@
 *> \param[in] LWORK
 *> \verbatim
 *>          LWORK is INTEGER
-*>           The dimension of the array WORK.  LWORK .GE. max(1,N)
+*>           The dimension of the array WORK.  LWORK >= max(1,N)
 *>           is sufficient and delivers very good and sometimes
 *>           optimal performance.  However, LWORK as large as 11*N
 *>           may be required for optimal performance.  A workspace
@@ -187,21 +187,21 @@
 *> \param[out] INFO
 *> \verbatim
 *>          INFO is INTEGER
-*>             =  0:  successful exit
+*>             = 0:  successful exit
-*>           .LT. 0:  if INFO = -i, the i-th argument had an illegal
+*>             < 0:  if INFO = -i, the i-th argument had an illegal
 *>                    value
-*>           .GT. 0:  if INFO = i, DHSEQR failed to compute all of
+*>             > 0:  if INFO = i, DHSEQR failed to compute all of
 *>                the eigenvalues.  Elements 1:ilo-1 and i+1:n of WR
 *>                and WI contain those eigenvalues which have been
 *>                successfully computed.  (Failures are rare.)
 *>
-*>                If INFO .GT. 0 and JOB = 'E', then on exit, the
+*>                If INFO > 0 and JOB = 'E', then on exit, the
 *>                remaining unconverged eigenvalues are the eigen-
 *>                values of the upper Hessenberg matrix rows and
 *>                columns ILO through INFO of the final, output
 *>                value of H.
 *>
-*>                If INFO .GT. 0 and JOB   = 'S', then on exit
+*>                If INFO > 0 and JOB   = 'S', then on exit
 *>
 *>           (*)  (initial value of H)*U  = U*(final value of H)
 *>
@@ -209,19 +209,19 @@
 *>                value of H is upper Hessenberg and quasi-triangular
 *>                in rows and columns INFO+1 through IHI.
 *>
-*>                If INFO .GT. 0 and COMPZ = 'V', then on exit
+*>                If INFO > 0 and COMPZ = 'V', then on exit
 *>
 *>                  (final value of Z)  =  (initial value of Z)*U
 *>
 *>                where U is the orthogonal matrix in (*) (regard-
 *>                less of the value of JOB.)
 *>
-*>                If INFO .GT. 0 and COMPZ = 'I', then on exit
+*>                If INFO > 0 and COMPZ = 'I', then on exit
 *>                      (final value of Z)  = U
 *>                where U is the orthogonal matrix in (*) (regard-
 *>                less of the value of JOB.)
 *>
-*>                If INFO .GT. 0 and COMPZ = 'N', then Z is not
+*>                If INFO > 0 and COMPZ = 'N', then Z is not
 *>                accessed.
 *> \endverbatim
 *
@@ -261,8 +261,8 @@
 *>                      This depends on ILO, IHI and NS.  NS is the
 *>                      number of simultaneous shifts returned
 *>                      by ILAENV(ISPEC=15).  (See ISPEC=15 below.)
-*>                      The default for (IHI-ILO+1).LE.500 is NS.
+*>                      The default for (IHI-ILO+1) <= 500 is NS.
-*>                      The default for (IHI-ILO+1).GT.500 is 3*NS/2.
+*>                      The default for (IHI-ILO+1) >  500 is 3*NS/2.
 *>
 *>            ISPEC=14: Nibble crossover point. (See IPARMQ for
 *>                      details.)  Default: 14% of deflation window
@@ -341,8 +341,8 @@
       PARAMETER          ( NTINY = 11 )
 *
 *     ==== NL allocates some local workspace to help small matrices
-*     .    through a rare DLAHQR failure.  NL .GT. NTINY = 11 is
+*     .    through a rare DLAHQR failure.  NL > NTINY = 11 is
-*     .    required and NL .LE. NMIN = ILAENV(ISPEC=12,...) is recom-
+*     .    required and NL <= NMIN = ILAENV(ISPEC=12,...) is recom-
 *     .    mended.  (The default value of NMIN is 75.)  Using NL = 49
 *     .    allows up to six simultaneous shifts and a 16-by-16
 *     .    deflation window.  ====

lapack-netlib/SRC/dla_gbrcond.f

@@ -141,13 +141,13 @@
 *>     i > 0:  The ith argument is invalid.
 *> \endverbatim
 *>
-*> \param[in] WORK
+*> \param[out] WORK
 *> \verbatim
 *>          WORK is DOUBLE PRECISION array, dimension (5*N).
 *>     Workspace.
 *> \endverbatim
 *>
-*> \param[in] IWORK
+*> \param[out] IWORK
 *> \verbatim
 *>          IWORK is INTEGER array, dimension (N).
 *>     Workspace.

lapack-netlib/SRC/dla_gbrfsx_extended.f

@@ -66,19 +66,19 @@
 *> \verbatim
 *>          PREC_TYPE is INTEGER
 *>     Specifies the intermediate precision to be used in refinement.
-*>     The value is defined by ILAPREC(P) where P is a CHARACTER and
+*>     The value is defined by ILAPREC(P) where P is a CHARACTER and P
-*>     P    = 'S':  Single
+*>          = 'S':  Single
 *>          = 'D':  Double
 *>          = 'I':  Indigenous
-*>          = 'X', 'E':  Extra
+*>          = 'X' or 'E':  Extra
 *> \endverbatim
 *>
 *> \param[in] TRANS_TYPE
 *> \verbatim
 *>          TRANS_TYPE is INTEGER
 *>     Specifies the transposition operation on A.
-*>     The value is defined by ILATRANS(T) where T is a CHARACTER and
+*>     The value is defined by ILATRANS(T) where T is a CHARACTER and T
-*>     T    = 'N':  No transpose
+*>          = 'N':  No transpose
 *>          = 'T':  Transpose
 *>          = 'C':  Conjugate transpose
 *> \endverbatim
@@ -270,7 +270,7 @@
 *>     information as described below. There currently are up to three
 *>     pieces of information returned for each right-hand side. If
 *>     componentwise accuracy is not requested (PARAMS(3) = 0.0), then
-*>     ERR_BNDS_COMP is not accessed.  If N_ERR_BNDS .LT. 3, then at most
+*>     ERR_BNDS_COMP is not accessed.  If N_ERR_BNDS < 3, then at most
 *>     the first (:,N_ERR_BNDS) entries are returned.
 *>
 *>     The first index in ERR_BNDS_COMP(i,:) corresponds to the ith

lapack-netlib/SRC/dla_gercond.f

@@ -123,13 +123,13 @@
 *>     i > 0:  The ith argument is invalid.
 *> \endverbatim
 *>
-*> \param[in] WORK
+*> \param[out] WORK
 *> \verbatim
 *>          WORK is DOUBLE PRECISION array, dimension (3*N).
 *>     Workspace.
 *> \endverbatim
 *>
-*> \param[in] IWORK
+*> \param[out] IWORK
 *> \verbatim
 *>          IWORK is INTEGER array, dimension (N).
 *>     Workspace.

lapack-netlib/SRC/dla_gerfsx_extended.f

@@ -64,19 +64,19 @@
 *> \verbatim
 *>          PREC_TYPE is INTEGER
 *>     Specifies the intermediate precision to be used in refinement.
-*>     The value is defined by ILAPREC(P) where P is a CHARACTER and
+*>     The value is defined by ILAPREC(P) where P is a CHARACTER and P
-*>     P    = 'S':  Single
+*>          = 'S':  Single
 *>          = 'D':  Double
 *>          = 'I':  Indigenous
-*>          = 'X', 'E':  Extra
+*>          = 'X' or 'E':  Extra
 *> \endverbatim
 *>
 *> \param[in] TRANS_TYPE
 *> \verbatim
 *>          TRANS_TYPE is INTEGER
 *>     Specifies the transposition operation on A.
-*>     The value is defined by ILATRANS(T) where T is a CHARACTER and
+*>     The value is defined by ILATRANS(T) where T is a CHARACTER and T
-*>     T    = 'N':  No transpose
+*>          = 'N':  No transpose
 *>          = 'T':  Transpose
 *>          = 'C':  Conjugate transpose
 *> \endverbatim
@@ -256,7 +256,7 @@
 *>     information as described below. There currently are up to three
 *>     pieces of information returned for each right-hand side. If
 *>     componentwise accuracy is not requested (PARAMS(3) = 0.0), then
-*>     ERRS_C is not accessed.  If N_ERR_BNDS .LT. 3, then at most
+*>     ERRS_C is not accessed.  If N_ERR_BNDS < 3, then at most
 *>     the first (:,N_ERR_BNDS) entries are returned.
 *>
 *>     The first index in ERRS_C(i,:) corresponds to the ith

lapack-netlib/SRC/dla_porcond.f

@@ -113,13 +113,13 @@
 *>     i > 0:  The ith argument is invalid.
 *> \endverbatim
 *>
-*> \param[in] WORK
+*> \param[out] WORK
 *> \verbatim
 *>          WORK is DOUBLE PRECISION array, dimension (3*N).
 *>     Workspace.
 *> \endverbatim
 *>
-*> \param[in] IWORK
+*> \param[out] IWORK
 *> \verbatim
 *>          IWORK is INTEGER array, dimension (N).
 *>     Workspace.

lapack-netlib/SRC/dla_porfsx_extended.f

@@ -65,11 +65,11 @@
 *> \verbatim
 *>          PREC_TYPE is INTEGER
 *>     Specifies the intermediate precision to be used in refinement.
-*>     The value is defined by ILAPREC(P) where P is a CHARACTER and
+*>     The value is defined by ILAPREC(P) where P is a CHARACTER and P
-*>     P    = 'S':  Single
+*>          = 'S':  Single
 *>          = 'D':  Double
 *>          = 'I':  Indigenous
-*>          = 'X', 'E':  Extra
+*>          = 'X' or 'E':  Extra
 *> \endverbatim
 *>
 *> \param[in] UPLO
@@ -246,7 +246,7 @@
 *>     information as described below. There currently are up to three
 *>     pieces of information returned for each right-hand side. If
 *>     componentwise accuracy is not requested (PARAMS(3) = 0.0), then
-*>     ERR_BNDS_COMP is not accessed.  If N_ERR_BNDS .LT. 3, then at most
+*>     ERR_BNDS_COMP is not accessed.  If N_ERR_BNDS < 3, then at most
 *>     the first (:,N_ERR_BNDS) entries are returned.
 *>
 *>     The first index in ERR_BNDS_COMP(i,:) corresponds to the ith

lapack-netlib/SRC/dla_porpvgrw.f

@@ -85,7 +85,7 @@
 *>     The leading dimension of the array AF.  LDAF >= max(1,N).
 *> \endverbatim
 *>
-*> \param[in] WORK
+*> \param[out] WORK
 *> \verbatim
 *>          WORK is DOUBLE PRECISION array, dimension (2*N)
 *> \endverbatim

lapack-netlib/SRC/dla_syrcond.f

@@ -119,13 +119,13 @@
 *>     i > 0:  The ith argument is invalid.
 *> \endverbatim
 *>
-*> \param[in] WORK
+*> \param[out] WORK
 *> \verbatim
 *>          WORK is DOUBLE PRECISION array, dimension (3*N).
 *>     Workspace.
 *> \endverbatim
 *>
-*> \param[in] IWORK
+*> \param[out] IWORK
 *> \verbatim
 *>          IWORK is INTEGER array, dimension (N).
 *>     Workspace.

lapack-netlib/SRC/dla_syrfsx_extended.f

@@ -67,11 +67,11 @@
 *> \verbatim
 *>          PREC_TYPE is INTEGER
 *>     Specifies the intermediate precision to be used in refinement.
-*>     The value is defined by ILAPREC(P) where P is a CHARACTER and
+*>     The value is defined by ILAPREC(P) where P is a CHARACTER and P
-*>     P    = 'S':  Single
+*>          = 'S':  Single
 *>          = 'D':  Double
 *>          = 'I':  Indigenous
-*>          = 'X', 'E':  Extra
+*>          = 'X' or 'E':  Extra
 *> \endverbatim
 *>
 *> \param[in] UPLO
@@ -255,7 +255,7 @@
 *>     information as described below. There currently are up to three
 *>     pieces of information returned for each right-hand side. If
 *>     componentwise accuracy is not requested (PARAMS(3) = 0.0), then
-*>     ERR_BNDS_COMP is not accessed.  If N_ERR_BNDS .LT. 3, then at most
+*>     ERR_BNDS_COMP is not accessed.  If N_ERR_BNDS < 3, then at most
 *>     the first (:,N_ERR_BNDS) entries are returned.
 *>
 *>     The first index in ERR_BNDS_COMP(i,:) corresponds to the ith

lapack-netlib/SRC/dla_syrpvgrw.f

@@ -101,7 +101,7 @@
 *>     as determined by DSYTRF.
 *> \endverbatim
 *>
-*> \param[in] WORK
+*> \param[out] WORK
 *> \verbatim
 *>          WORK is DOUBLE PRECISION array, dimension (2*N)
 *> \endverbatim

lapack-netlib/SRC/dla_wwaddw.f

@@ -36,7 +36,7 @@
 *>    DLA_WWADDW adds a vector W into a doubled-single vector (X, Y).
 *>
 *>    This works for all extant IBM's hex and binary floating point
-*>    arithmetics, but not for decimal.
+*>    arithmetic, but not for decimal.
 *> \endverbatim
 *
 *  Arguments: