--- rpl/lapack/lapack/dgejsv.f 2018/05/29 07:17:51 1.19 +++ rpl/lapack/lapack/dgejsv.f 2020/05/21 21:45:56 1.20 @@ -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 -*> -> .. no scaled condition estimate required (JOBE.EQ.'N'): +*> If only SIGMA is needed (JOBU = 'N', JOBV = 'N') and +*> -> .. 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.EQ.'F' :: LWORK >= max(2*M+N,3*N+(N+1)*NB,N+M*NB,7), +*> if JOBU = 'U' :: LWORK >= max(2*M+N,3*N+(N+1)*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 -*> M*NB (for JOBU.EQ.'F'). +*> Here LWORK(DORMQR) equals N*NB (for JOBU = 'U') or +*> M*NB (for JOBU = 'F'). *> -*> If the full SVD is needed: (JOBU.EQ.'U' or JOBU.EQ.'F') and -*> -> if JOBV.EQ.'V' +*> If the full SVD is needed: (JOBU = 'U' or JOBU = 'F') and +*> -> 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 : successful exit; -*> > 0 : DGEJSV did not converge in the maximal allowed number -*> of sweeps. The computed values may be inaccurate. +*> < 0: if INFO = -i, then the i-th argument had an illegal value. +*> = 0: successful exit; +*> > 0: DGEJSV did not converge in the maximal allowed number +*> 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