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Fix typos in comments and documentation (Reference-LAPACK PR 820)

pull/4045/head
Martin Kroeker GitHub 3 years ago
parent
9e22527b66
commit
2ba22b8473
No known key found for this signature in database GPG Key ID: 4AEE18F83AFDEB23
100 changed files with 146 additions and 150 deletions
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  1. +1
    -1
      lapack-netlib/SRC/cgejsv.f
  2. +1
    -1
      lapack-netlib/SRC/cgesvdq.f
  3. +2
    -2
      lapack-netlib/SRC/cgsvj0.f
  4. +2
    -2
      lapack-netlib/SRC/cgsvj1.f
  5. +1
    -1
      lapack-netlib/SRC/chesv_aa_2stage.f
  6. +4
    -4
      lapack-netlib/SRC/chetf2_rk.f
  7. +4
    -4
      lapack-netlib/SRC/chetf2_rook.f
  8. +1
    -1
      lapack-netlib/SRC/chetrf_aa.f
  9. +1
    -1
      lapack-netlib/SRC/chetrf_aa_2stage.f
  10. +3
    -3
      lapack-netlib/SRC/cla_gbrfsx_extended.f
  11. +1
    -1
      lapack-netlib/SRC/cla_gerfsx_extended.f
  12. +1
    -1
      lapack-netlib/SRC/cla_herfsx_extended.f
  13. +1
    -1
      lapack-netlib/SRC/cla_porfsx_extended.f
  14. +1
    -1
      lapack-netlib/SRC/cla_syrfsx_extended.f
  15. +1
    -1
      lapack-netlib/SRC/claed7.f
  16. +3
    -4
      lapack-netlib/SRC/claqz0.f
  17. +1
    -1
      lapack-netlib/SRC/clarfb_gett.f
  18. +1
    -1
      lapack-netlib/SRC/clatdf.f
  19. +1
    -1
      lapack-netlib/SRC/clatrs3.f
  20. +5
    -5
      lapack-netlib/SRC/csyconvf.f
  21. +1
    -1
      lapack-netlib/SRC/csyconvf_rook.f
  22. +1
    -1
      lapack-netlib/SRC/csysv_aa_2stage.f
  23. +1
    -1
      lapack-netlib/SRC/csytrf_aa.f
  24. +1
    -1
      lapack-netlib/SRC/csytrf_aa_2stage.f
  25. +1
    -1
      lapack-netlib/SRC/ctrexc.f
  26. +1
    -1
      lapack-netlib/SRC/cunbdb1.f
  27. +1
    -1
      lapack-netlib/SRC/cunbdb2.f
  28. +1
    -1
      lapack-netlib/SRC/cunbdb3.f
  29. +1
    -1
      lapack-netlib/SRC/cunbdb4.f
  30. +1
    -1
      lapack-netlib/SRC/dbdsvdx.f
  31. +1
    -1
      lapack-netlib/SRC/dgejsv.f
  32. +1
    -1
      lapack-netlib/SRC/dgesvdq.f
  33. +2
    -2
      lapack-netlib/SRC/dgsvj0.f
  34. +2
    -2
      lapack-netlib/SRC/dgsvj1.f
  35. +1
    -1
      lapack-netlib/SRC/dla_gbrfsx_extended.f
  36. +1
    -1
      lapack-netlib/SRC/dla_gerfsx_extended.f
  37. +1
    -1
      lapack-netlib/SRC/dla_porfsx_extended.f
  38. +1
    -1
      lapack-netlib/SRC/dla_syrfsx_extended.f
  39. +3
    -4
      lapack-netlib/SRC/dlaqz0.f
  40. +1
    -1
      lapack-netlib/SRC/dlarfb_gett.f
  41. +1
    -1
      lapack-netlib/SRC/dlatrs3.f
  42. +1
    -1
      lapack-netlib/SRC/dorbdb1.f
  43. +1
    -1
      lapack-netlib/SRC/dorbdb2.f
  44. +1
    -1
      lapack-netlib/SRC/dorbdb3.f
  45. +1
    -1
      lapack-netlib/SRC/dorbdb4.f
  46. +5
    -5
      lapack-netlib/SRC/dsyconvf.f
  47. +1
    -1
      lapack-netlib/SRC/dsyconvf_rook.f
  48. +1
    -1
      lapack-netlib/SRC/dsysv_aa_2stage.f
  49. +1
    -1
      lapack-netlib/SRC/dsytrf_aa.f
  50. +1
    -1
      lapack-netlib/SRC/dsytrf_aa_2stage.f
  51. +1
    -1
      lapack-netlib/SRC/sbdsvdx.f
  52. +1
    -1
      lapack-netlib/SRC/sgejsv.f
  53. +1
    -1
      lapack-netlib/SRC/sgesvdq.f
  54. +2
    -2
      lapack-netlib/SRC/sgsvj0.f
  55. +2
    -2
      lapack-netlib/SRC/sgsvj1.f
  56. +1
    -1
      lapack-netlib/SRC/sla_gbrfsx_extended.f
  57. +1
    -1
      lapack-netlib/SRC/sla_gerfsx_extended.f
  58. +1
    -1
      lapack-netlib/SRC/sla_porfsx_extended.f
  59. +1
    -1
      lapack-netlib/SRC/sla_syrfsx_extended.f
  60. +3
    -4
      lapack-netlib/SRC/slaqz0.f
  61. +1
    -1
      lapack-netlib/SRC/slarfb_gett.f
  62. +1
    -1
      lapack-netlib/SRC/slatrs3.f
  63. +1
    -1
      lapack-netlib/SRC/sorbdb1.f
  64. +1
    -1
      lapack-netlib/SRC/sorbdb2.f
  65. +1
    -1
      lapack-netlib/SRC/sorbdb3.f
  66. +1
    -1
      lapack-netlib/SRC/sorbdb4.f
  67. +5
    -5
      lapack-netlib/SRC/ssyconvf.f
  68. +1
    -1
      lapack-netlib/SRC/ssyconvf_rook.f
  69. +1
    -1
      lapack-netlib/SRC/ssysv_aa_2stage.f
  70. +1
    -1
      lapack-netlib/SRC/ssytrf_aa.f
  71. +1
    -1
      lapack-netlib/SRC/ssytrf_aa_2stage.f
  72. +1
    -1
      lapack-netlib/SRC/zgejsv.f
  73. +1
    -1
      lapack-netlib/SRC/zgesvdq.f
  74. +2
    -2
      lapack-netlib/SRC/zgsvj0.f
  75. +2
    -2
      lapack-netlib/SRC/zgsvj1.f
  76. +1
    -1
      lapack-netlib/SRC/zhesv_aa_2stage.f
  77. +4
    -4
      lapack-netlib/SRC/zhetf2_rk.f
  78. +4
    -4
      lapack-netlib/SRC/zhetf2_rook.f
  79. +1
    -1
      lapack-netlib/SRC/zhetrf_aa.f
  80. +1
    -1
      lapack-netlib/SRC/zhetrf_aa_2stage.f
  81. +1
    -1
      lapack-netlib/SRC/zla_gbrfsx_extended.f
  82. +1
    -1
      lapack-netlib/SRC/zla_gerfsx_extended.f
  83. +1
    -1
      lapack-netlib/SRC/zla_herfsx_extended.f
  84. +1
    -1
      lapack-netlib/SRC/zla_porfsx_extended.f
  85. +1
    -1
      lapack-netlib/SRC/zla_syrfsx_extended.f
  86. +1
    -1
      lapack-netlib/SRC/zlaed7.f
  87. +3
    -4
      lapack-netlib/SRC/zlaqz0.f
  88. +1
    -1
      lapack-netlib/SRC/zlarfb_gett.f
  89. +1
    -1
      lapack-netlib/SRC/zlatdf.f
  90. +1
    -1
      lapack-netlib/SRC/zlatrs3.f
  91. +5
    -5
      lapack-netlib/SRC/zsyconvf.f
  92. +1
    -1
      lapack-netlib/SRC/zsyconvf_rook.f
  93. +1
    -1
      lapack-netlib/SRC/zsysv_aa_2stage.f
  94. +1
    -1
      lapack-netlib/SRC/zsytrf_aa.f
  95. +1
    -1
      lapack-netlib/SRC/zsytrf_aa_2stage.f
  96. +1
    -1
      lapack-netlib/SRC/ztrexc.f
  97. +1
    -1
      lapack-netlib/SRC/zunbdb1.f
  98. +1
    -1
      lapack-netlib/SRC/zunbdb2.f
  99. +1
    -1
      lapack-netlib/SRC/zunbdb3.f
  100. +1
    -1
      lapack-netlib/SRC/zunbdb4.f

+ 1
- 1
lapack-netlib/SRC/cgejsv.f View File

@@ -252,7 +252,7 @@
*> If JOBV = 'V', 'J' then V contains on exit the N-by-N matrix of *> If JOBV = 'V', 'J' then V contains on exit the N-by-N matrix of
*> the right singular vectors; *> the right singular vectors;
*> If JOBV = 'W', AND (JOBU = 'U' AND JOBT = 'T' AND M = N), *> If JOBV = 'W', AND (JOBU = 'U' AND JOBT = 'T' AND M = N),
*> then V is used as workspace if the pprocedure
*> then V is used as workspace if the procedure
*> replaces A with A^*. In that case, [U] is computed *> replaces A with A^*. In that case, [U] is computed
*> in V as right singular vectors of A^* and then *> in V as right singular vectors of A^* and then
*> copied back to the U array. This 'W' option is just *> copied back to the U array. This 'W' option is just


+ 1
- 1
lapack-netlib/SRC/cgesvdq.f View File

@@ -363,7 +363,7 @@
*> an optimal implementation would do all necessary scaling before calling *> an optimal implementation would do all necessary scaling before calling
*> CGESVD and the scaling in CGESVD can be switched off. *> CGESVD and the scaling in CGESVD can be switched off.
*> 3. Other comments related to code optimization are given in comments in the *> 3. Other comments related to code optimization are given in comments in the
*> code, enlosed in [[double brackets]].
*> code, enclosed in [[double brackets]].
*> \endverbatim *> \endverbatim
* *
*> \par Bugs, examples and comments *> \par Bugs, examples and comments


+ 2
- 2
lapack-netlib/SRC/cgsvj0.f View File

@@ -52,10 +52,10 @@
*> Specifies whether the output from this procedure is used *> Specifies whether the output from this procedure is used
*> to compute the matrix V: *> to compute the matrix V:
*> = 'V': the product of the Jacobi rotations is accumulated *> = 'V': the product of the Jacobi rotations is accumulated
*> by postmulyiplying the N-by-N array V.
*> by postmultiplying the N-by-N array V.
*> (See the description of V.) *> (See the description of V.)
*> = 'A': the product of the Jacobi rotations is accumulated *> = 'A': the product of the Jacobi rotations is accumulated
*> by postmulyiplying the MV-by-N array V.
*> by postmultiplying the MV-by-N array V.
*> (See the descriptions of MV and V.) *> (See the descriptions of MV and V.)
*> = 'N': the Jacobi rotations are not accumulated. *> = 'N': the Jacobi rotations are not accumulated.
*> \endverbatim *> \endverbatim


+ 2
- 2
lapack-netlib/SRC/cgsvj1.f View File

@@ -75,10 +75,10 @@
*> Specifies whether the output from this procedure is used *> Specifies whether the output from this procedure is used
*> to compute the matrix V: *> to compute the matrix V:
*> = 'V': the product of the Jacobi rotations is accumulated *> = 'V': the product of the Jacobi rotations is accumulated
*> by postmulyiplying the N-by-N array V.
*> by postmultiplying the N-by-N array V.
*> (See the description of V.) *> (See the description of V.)
*> = 'A': the product of the Jacobi rotations is accumulated *> = 'A': the product of the Jacobi rotations is accumulated
*> by postmulyiplying the MV-by-N array V.
*> by postmultiplying the MV-by-N array V.
*> (See the descriptions of MV and V.) *> (See the descriptions of MV and V.)
*> = 'N': the Jacobi rotations are not accumulated. *> = 'N': the Jacobi rotations are not accumulated.
*> \endverbatim *> \endverbatim


+ 1
- 1
lapack-netlib/SRC/chesv_aa_2stage.f View File

@@ -87,7 +87,7 @@
*> triangular part of the matrix A, and the strictly upper *> triangular part of the matrix A, and the strictly upper
*> triangular part of A is not referenced. *> triangular part of A is not referenced.
*> *>
*> On exit, L is stored below (or above) the subdiaonal blocks,
*> On exit, L is stored below (or above) the subdiagonal blocks,
*> when UPLO is 'L' (or 'U'). *> when UPLO is 'L' (or 'U').
*> \endverbatim *> \endverbatim
*> *>


+ 4
- 4
lapack-netlib/SRC/chetf2_rk.f View File

@@ -480,7 +480,7 @@
A( J, K ) = CONJG( A( P, J ) ) A( J, K ) = CONJG( A( P, J ) )
A( P, J ) = T A( P, J ) = T
14 CONTINUE 14 CONTINUE
* (3) Swap and conjugate corner elements at row-col interserction
* (3) Swap and conjugate corner elements at row-col intersection
A( P, K ) = CONJG( A( P, K ) ) A( P, K ) = CONJG( A( P, K ) )
* (4) Swap diagonal elements at row-col intersection * (4) Swap diagonal elements at row-col intersection
R1 = REAL( A( K, K ) ) R1 = REAL( A( K, K ) )
@@ -508,7 +508,7 @@
A( J, KK ) = CONJG( A( KP, J ) ) A( J, KK ) = CONJG( A( KP, J ) )
A( KP, J ) = T A( KP, J ) = T
15 CONTINUE 15 CONTINUE
* (3) Swap and conjugate corner elements at row-col interserction
* (3) Swap and conjugate corner elements at row-col intersection
A( KP, KK ) = CONJG( A( KP, KK ) ) A( KP, KK ) = CONJG( A( KP, KK ) )
* (4) Swap diagonal elements at row-col intersection * (4) Swap diagonal elements at row-col intersection
R1 = REAL( A( KK, KK ) ) R1 = REAL( A( KK, KK ) )
@@ -834,7 +834,7 @@
A( J, K ) = CONJG( A( P, J ) ) A( J, K ) = CONJG( A( P, J ) )
A( P, J ) = T A( P, J ) = T
44 CONTINUE 44 CONTINUE
* (3) Swap and conjugate corner elements at row-col interserction
* (3) Swap and conjugate corner elements at row-col intersection
A( P, K ) = CONJG( A( P, K ) ) A( P, K ) = CONJG( A( P, K ) )
* (4) Swap diagonal elements at row-col intersection * (4) Swap diagonal elements at row-col intersection
R1 = REAL( A( K, K ) ) R1 = REAL( A( K, K ) )
@@ -862,7 +862,7 @@
A( J, KK ) = CONJG( A( KP, J ) ) A( J, KK ) = CONJG( A( KP, J ) )
A( KP, J ) = T A( KP, J ) = T
45 CONTINUE 45 CONTINUE
* (3) Swap and conjugate corner elements at row-col interserction
* (3) Swap and conjugate corner elements at row-col intersection
A( KP, KK ) = CONJG( A( KP, KK ) ) A( KP, KK ) = CONJG( A( KP, KK ) )
* (4) Swap diagonal elements at row-col intersection * (4) Swap diagonal elements at row-col intersection
R1 = REAL( A( KK, KK ) ) R1 = REAL( A( KK, KK ) )


+ 4
- 4
lapack-netlib/SRC/chetf2_rook.f View File

@@ -420,7 +420,7 @@
A( J, K ) = CONJG( A( P, J ) ) A( J, K ) = CONJG( A( P, J ) )
A( P, J ) = T A( P, J ) = T
14 CONTINUE 14 CONTINUE
* (3) Swap and conjugate corner elements at row-col interserction
* (3) Swap and conjugate corner elements at row-col intersection
A( P, K ) = CONJG( A( P, K ) ) A( P, K ) = CONJG( A( P, K ) )
* (4) Swap diagonal elements at row-col intersection * (4) Swap diagonal elements at row-col intersection
R1 = REAL( A( K, K ) ) R1 = REAL( A( K, K ) )
@@ -441,7 +441,7 @@
A( J, KK ) = CONJG( A( KP, J ) ) A( J, KK ) = CONJG( A( KP, J ) )
A( KP, J ) = T A( KP, J ) = T
15 CONTINUE 15 CONTINUE
* (3) Swap and conjugate corner elements at row-col interserction
* (3) Swap and conjugate corner elements at row-col intersection
A( KP, KK ) = CONJG( A( KP, KK ) ) A( KP, KK ) = CONJG( A( KP, KK ) )
* (4) Swap diagonal elements at row-col intersection * (4) Swap diagonal elements at row-col intersection
R1 = REAL( A( KK, KK ) ) R1 = REAL( A( KK, KK ) )
@@ -733,7 +733,7 @@
A( J, K ) = CONJG( A( P, J ) ) A( J, K ) = CONJG( A( P, J ) )
A( P, J ) = T A( P, J ) = T
44 CONTINUE 44 CONTINUE
* (3) Swap and conjugate corner elements at row-col interserction
* (3) Swap and conjugate corner elements at row-col intersection
A( P, K ) = CONJG( A( P, K ) ) A( P, K ) = CONJG( A( P, K ) )
* (4) Swap diagonal elements at row-col intersection * (4) Swap diagonal elements at row-col intersection
R1 = REAL( A( K, K ) ) R1 = REAL( A( K, K ) )
@@ -754,7 +754,7 @@
A( J, KK ) = CONJG( A( KP, J ) ) A( J, KK ) = CONJG( A( KP, J ) )
A( KP, J ) = T A( KP, J ) = T
45 CONTINUE 45 CONTINUE
* (3) Swap and conjugate corner elements at row-col interserction
* (3) Swap and conjugate corner elements at row-col intersection
A( KP, KK ) = CONJG( A( KP, KK ) ) A( KP, KK ) = CONJG( A( KP, KK ) )
* (4) Swap diagonal elements at row-col intersection * (4) Swap diagonal elements at row-col intersection
R1 = REAL( A( KK, KK ) ) R1 = REAL( A( KK, KK ) )


+ 1
- 1
lapack-netlib/SRC/chetrf_aa.f View File

@@ -74,7 +74,7 @@
*> *>
*> On exit, the tridiagonal matrix is stored in the diagonals *> On exit, the tridiagonal matrix is stored in the diagonals
*> and the subdiagonals of A just below (or above) the diagonals, *> and the subdiagonals of A just below (or above) the diagonals,
*> and L is stored below (or above) the subdiaonals, when UPLO
*> and L is stored below (or above) the subdiagonals, when UPLO
*> is 'L' (or 'U'). *> is 'L' (or 'U').
*> \endverbatim *> \endverbatim
*> *>


+ 1
- 1
lapack-netlib/SRC/chetrf_aa_2stage.f View File

@@ -75,7 +75,7 @@
*> triangular part of the matrix A, and the strictly upper *> triangular part of the matrix A, and the strictly upper
*> triangular part of A is not referenced. *> triangular part of A is not referenced.
*> *>
*> On exit, L is stored below (or above) the subdiaonal blocks,
*> On exit, L is stored below (or above) the subdiagonal blocks,
*> when UPLO is 'L' (or 'U'). *> when UPLO is 'L' (or 'U').
*> \endverbatim *> \endverbatim
*> *>


+ 3
- 3
lapack-netlib/SRC/cla_gbrfsx_extended.f View File

@@ -18,7 +18,7 @@
* Definition: * Definition:
* =========== * ===========
* *
* SUBROUTINE CLA_GBRFSX_EXTENDED ( PREC_TYPE, TRANS_TYPE, N, KL, KU,
* SUBROUTINE CLA_GBRFSX_EXTENDED( PREC_TYPE, TRANS_TYPE, N, KL, KU,
* NRHS, AB, LDAB, AFB, LDAFB, IPIV, * NRHS, AB, LDAB, AFB, LDAFB, IPIV,
* COLEQU, C, B, LDB, Y, LDY, * COLEQU, C, B, LDB, Y, LDY,
* BERR_OUT, N_NORMS, ERR_BNDS_NORM, * BERR_OUT, N_NORMS, ERR_BNDS_NORM,
@@ -400,7 +400,7 @@
*> \ingroup complexGBcomputational *> \ingroup complexGBcomputational
* *
* ===================================================================== * =====================================================================
SUBROUTINE CLA_GBRFSX_EXTENDED ( PREC_TYPE, TRANS_TYPE, N, KL, KU,
SUBROUTINE CLA_GBRFSX_EXTENDED( PREC_TYPE, TRANS_TYPE, N, KL, KU,
$ NRHS, AB, LDAB, AFB, LDAFB, IPIV, $ NRHS, AB, LDAB, AFB, LDAFB, IPIV,
$ COLEQU, C, B, LDB, Y, LDY, $ COLEQU, C, B, LDB, Y, LDY,
$ BERR_OUT, N_NORMS, ERR_BNDS_NORM, $ BERR_OUT, N_NORMS, ERR_BNDS_NORM,
@@ -651,7 +651,7 @@
PREVNORMDX = NORMDX PREVNORMDX = NORMDX
PREV_DZ_Z = DZ_Z PREV_DZ_Z = DZ_Z
* *
* Update soluton.
* Update solution.
* *
IF ( Y_PREC_STATE .LT. EXTRA_Y ) THEN IF ( Y_PREC_STATE .LT. EXTRA_Y ) THEN
CALL CAXPY( N, (1.0E+0,0.0E+0), DY, 1, Y(1,J), 1 ) CALL CAXPY( N, (1.0E+0,0.0E+0), DY, 1, Y(1,J), 1 )


+ 1
- 1
lapack-netlib/SRC/cla_gerfsx_extended.f View File

@@ -637,7 +637,7 @@
PREVNORMDX = NORMDX PREVNORMDX = NORMDX
PREV_DZ_Z = DZ_Z PREV_DZ_Z = DZ_Z
* *
* Update soluton.
* Update solution.
* *
IF ( Y_PREC_STATE .LT. EXTRA_Y ) THEN IF ( Y_PREC_STATE .LT. EXTRA_Y ) THEN
CALL CAXPY( N, (1.0E+0,0.0E+0), DY, 1, Y(1,J), 1 ) CALL CAXPY( N, (1.0E+0,0.0E+0), DY, 1, Y(1,J), 1 )


+ 1
- 1
lapack-netlib/SRC/cla_herfsx_extended.f View File

@@ -654,7 +654,7 @@
PREVNORMDX = NORMDX PREVNORMDX = NORMDX
PREV_DZ_Z = DZ_Z PREV_DZ_Z = DZ_Z
* *
* Update soluton.
* Update solution.
* *
IF ( Y_PREC_STATE .LT. EXTRA_Y ) THEN IF ( Y_PREC_STATE .LT. EXTRA_Y ) THEN
CALL CAXPY( N, CMPLX(1.0), DY, 1, Y(1,J), 1 ) CALL CAXPY( N, CMPLX(1.0), DY, 1, Y(1,J), 1 )


+ 1
- 1
lapack-netlib/SRC/cla_porfsx_extended.f View File

@@ -625,7 +625,7 @@
PREVNORMDX = NORMDX PREVNORMDX = NORMDX
PREV_DZ_Z = DZ_Z PREV_DZ_Z = DZ_Z
* *
* Update soluton.
* Update solution.
* *
IF (Y_PREC_STATE .LT. EXTRA_Y) THEN IF (Y_PREC_STATE .LT. EXTRA_Y) THEN
CALL CAXPY( N, CMPLX(1.0), DY, 1, Y(1,J), 1 ) CALL CAXPY( N, CMPLX(1.0), DY, 1, Y(1,J), 1 )


+ 1
- 1
lapack-netlib/SRC/cla_syrfsx_extended.f View File

@@ -654,7 +654,7 @@
PREVNORMDX = NORMDX PREVNORMDX = NORMDX
PREV_DZ_Z = DZ_Z PREV_DZ_Z = DZ_Z
* *
* Update soluton.
* Update solution.
* *
IF ( Y_PREC_STATE .LT. EXTRA_Y ) THEN IF ( Y_PREC_STATE .LT. EXTRA_Y ) THEN
CALL CAXPY( N, CMPLX(1.0), DY, 1, Y(1,J), 1 ) CALL CAXPY( N, CMPLX(1.0), DY, 1, Y(1,J), 1 )


+ 1
- 1
lapack-netlib/SRC/claed7.f View File

@@ -363,7 +363,7 @@
RETURN RETURN
END IF END IF
* *
* Prepare the INDXQ sorting premutation.
* Prepare the INDXQ sorting permutation.
* *
N1 = K N1 = K
N2 = N - K N2 = N - K


+ 3
- 4
lapack-netlib/SRC/claqz0.f View File

@@ -89,7 +89,7 @@
*> Anal., 29(2006), pp. 199--227. *> Anal., 29(2006), pp. 199--227.
*> *>
*> Ref: T. Steel, D. Camps, K. Meerbergen, R. Vandebril "A multishift, *> Ref: T. Steel, D. Camps, K. Meerbergen, R. Vandebril "A multishift,
*> multipole rational QZ method with agressive early deflation"
*> multipole rational QZ method with aggressive early deflation"
*> \endverbatim *> \endverbatim
* *
* Arguments: * Arguments:
@@ -310,7 +310,7 @@
CHARACTER :: JBCMPZ*3 CHARACTER :: JBCMPZ*3


* External Functions * External Functions
EXTERNAL :: XERBLA, CHGEQZ, CLAQZ2, CLAQZ3, CLASET, SLABAD,
EXTERNAL :: XERBLA, CHGEQZ, CLAQZ2, CLAQZ3, CLASET,
$ CLARTG, CROT $ CLARTG, CROT
REAL, EXTERNAL :: SLAMCH, CLANHS REAL, EXTERNAL :: SLAMCH, CLANHS
LOGICAL, EXTERNAL :: LSAME LOGICAL, EXTERNAL :: LSAME
@@ -462,7 +462,6 @@
* Get machine constants * Get machine constants
SAFMIN = SLAMCH( 'SAFE MINIMUM' ) SAFMIN = SLAMCH( 'SAFE MINIMUM' )
SAFMAX = ONE/SAFMIN SAFMAX = ONE/SAFMIN
CALL SLABAD( SAFMIN, SAFMAX )
ULP = SLAMCH( 'PRECISION' ) ULP = SLAMCH( 'PRECISION' )
SMLNUM = SAFMIN*( REAL( N )/ULP ) SMLNUM = SAFMIN*( REAL( N )/ULP )


@@ -533,7 +532,7 @@
DO WHILE ( K.GE.ISTART2 ) DO WHILE ( K.GE.ISTART2 )


IF( ABS( B( K, K ) ) .LT. BTOL ) THEN IF( ABS( B( K, K ) ) .LT. BTOL ) THEN
* A diagonal element of B is negligable, move it
* A diagonal element of B is negligible, move it
* to the top and deflate it * to the top and deflate it
DO K2 = K, ISTART2+1, -1 DO K2 = K, ISTART2+1, -1


+ 1
- 1
lapack-netlib/SRC/clarfb_gett.f View File

@@ -452,7 +452,7 @@
IF( LNOTIDENT ) THEN IF( LNOTIDENT ) THEN
* *
* col2_(2) Compute W2: = (V1**H) * W2 = (A1**H) * W2, * col2_(2) Compute W2: = (V1**H) * W2 = (A1**H) * W2,
* V1 is not an identy matrix, but unit lower-triangular
* V1 is not an identity matrix, but unit lower-triangular
* V1 stored in A1 (diagonal ones are not stored). * V1 stored in A1 (diagonal ones are not stored).
* *
* *


+ 1
- 1
lapack-netlib/SRC/clatdf.f View File

@@ -227,7 +227,7 @@
BM = RHS( J ) - CONE BM = RHS( J ) - CONE
SPLUS = ONE SPLUS = ONE
* *
* Lockahead for L- part RHS(1:N-1) = +-1
* Look-ahead for L- part RHS(1:N-1) = +-1
* SPLUS and SMIN computed more efficiently than in BSOLVE[1]. * SPLUS and SMIN computed more efficiently than in BSOLVE[1].
* *
SPLUS = SPLUS + REAL( CDOTC( N-J, Z( J+1, J ), 1, Z( J+1, SPLUS = SPLUS + REAL( CDOTC( N-J, Z( J+1, J ), 1, Z( J+1,


+ 1
- 1
lapack-netlib/SRC/clatrs3.f View File

@@ -577,7 +577,7 @@
* Prepare the linear update to be executed with GEMM. * Prepare the linear update to be executed with GEMM.
* For each column, compute a consistent scaling, a * For each column, compute a consistent scaling, a
* scaling factor to survive the linear update, and * scaling factor to survive the linear update, and
* rescale the column segments, if necesssary. Then
* rescale the column segments, if necessary. Then
* the linear update is safely executed. * the linear update is safely executed.
* *
DO KK = 1, K2-K1 DO KK = 1, K2-K1


+ 5
- 5
lapack-netlib/SRC/csyconvf.f View File

@@ -39,7 +39,7 @@
*> CSYTRF provided on entry in parameter A into the factorization *> CSYTRF provided on entry in parameter A into the factorization
*> output format used in CSYTRF_RK (or CSYTRF_BK) that is stored *> output format used in CSYTRF_RK (or CSYTRF_BK) that is stored
*> on exit in parameters A and E. It also converts in place details of *> on exit in parameters A and E. It also converts in place details of
*> the intechanges stored in IPIV from the format used in CSYTRF into
*> the interchanges stored in IPIV from the format used in CSYTRF into
*> the format used in CSYTRF_RK (or CSYTRF_BK). *> the format used in CSYTRF_RK (or CSYTRF_BK).
*> *>
*> If parameter WAY = 'R': *> If parameter WAY = 'R':
@@ -48,7 +48,7 @@
*> (or CSYTRF_BK) provided on entry in parameters A and E into *> (or CSYTRF_BK) provided on entry in parameters A and E into
*> the factorization output format used in CSYTRF that is stored *> the factorization output format used in CSYTRF that is stored
*> on exit in parameter A. It also converts in place details of *> on exit in parameter A. It also converts in place details of
*> the intechanges stored in IPIV from the format used in CSYTRF_RK
*> the interchanges stored in IPIV from the format used in CSYTRF_RK
*> (or CSYTRF_BK) into the format used in CSYTRF. *> (or CSYTRF_BK) into the format used in CSYTRF.
*> *>
*> CSYCONVF can also convert in Hermitian matrix case, i.e. between *> CSYCONVF can also convert in Hermitian matrix case, i.e. between
@@ -325,7 +325,7 @@
END IF END IF
* *
* Convert IPIV * Convert IPIV
* There is no interchnge of rows i and and IPIV(i),
* There is no interchange of rows i and and IPIV(i),
* so this should be reflected in IPIV format for * so this should be reflected in IPIV format for
* *SYTRF_RK ( or *SYTRF_BK) * *SYTRF_RK ( or *SYTRF_BK)
* *
@@ -469,7 +469,7 @@
END IF END IF
* *
* Convert IPIV * Convert IPIV
* There is no interchnge of rows i and and IPIV(i),
* There is no interchange of rows i and and IPIV(i),
* so this should be reflected in IPIV format for * so this should be reflected in IPIV format for
* *SYTRF_RK ( or *SYTRF_BK) * *SYTRF_RK ( or *SYTRF_BK)
* *
@@ -535,7 +535,7 @@
* *
* Revert VALUE * Revert VALUE
* Assign subdiagonal entries of D from array E to * Assign subdiagonal entries of D from array E to
* subgiagonal entries of A.
* subdiagonal entries of A.
* *
I = 1 I = 1
DO WHILE ( I.LE.N-1 ) DO WHILE ( I.LE.N-1 )


+ 1
- 1
lapack-netlib/SRC/csyconvf_rook.f View File

@@ -520,7 +520,7 @@
* *
* Revert VALUE * Revert VALUE
* Assign subdiagonal entries of D from array E to * Assign subdiagonal entries of D from array E to
* subgiagonal entries of A.
* subdiagonal entries of A.
* *
I = 1 I = 1
DO WHILE ( I.LE.N-1 ) DO WHILE ( I.LE.N-1 )


+ 1
- 1
lapack-netlib/SRC/csysv_aa_2stage.f View File

@@ -87,7 +87,7 @@
*> triangular part of the matrix A, and the strictly upper *> triangular part of the matrix A, and the strictly upper
*> triangular part of A is not referenced. *> triangular part of A is not referenced.
*> *>
*> On exit, L is stored below (or above) the subdiaonal blocks,
*> On exit, L is stored below (or above) the subdiagonal blocks,
*> when UPLO is 'L' (or 'U'). *> when UPLO is 'L' (or 'U').
*> \endverbatim *> \endverbatim
*> *>


+ 1
- 1
lapack-netlib/SRC/csytrf_aa.f View File

@@ -74,7 +74,7 @@
*> *>
*> On exit, the tridiagonal matrix is stored in the diagonals *> On exit, the tridiagonal matrix is stored in the diagonals
*> and the subdiagonals of A just below (or above) the diagonals, *> and the subdiagonals of A just below (or above) the diagonals,
*> and L is stored below (or above) the subdiaonals, when UPLO
*> and L is stored below (or above) the subdiagonals, when UPLO
*> is 'L' (or 'U'). *> is 'L' (or 'U').
*> \endverbatim *> \endverbatim
*> *>


+ 1
- 1
lapack-netlib/SRC/csytrf_aa_2stage.f View File

@@ -75,7 +75,7 @@
*> triangular part of the matrix A, and the strictly upper *> triangular part of the matrix A, and the strictly upper
*> triangular part of A is not referenced. *> triangular part of A is not referenced.
*> *>
*> On exit, L is stored below (or above) the subdiaonal blocks,
*> On exit, L is stored below (or above) the subdiagonal blocks,
*> when UPLO is 'L' (or 'U'). *> when UPLO is 'L' (or 'U').
*> \endverbatim *> \endverbatim
*> *>


+ 1
- 1
lapack-netlib/SRC/ctrexc.f View File

@@ -40,7 +40,7 @@
*> *>
*> The Schur form T is reordered by a unitary similarity transformation *> The Schur form T is reordered by a unitary similarity transformation
*> Z**H*T*Z, and optionally the matrix Q of Schur vectors is updated by *> Z**H*T*Z, and optionally the matrix Q of Schur vectors is updated by
*> postmultplying it with Z.
*> postmultiplying it with Z.
*> \endverbatim *> \endverbatim
* *
* Arguments: * Arguments:


+ 1
- 1
lapack-netlib/SRC/cunbdb1.f View File

@@ -37,7 +37,7 @@
*>\verbatim *>\verbatim
*> *>
*> CUNBDB1 simultaneously bidiagonalizes the blocks of a tall and skinny *> CUNBDB1 simultaneously bidiagonalizes the blocks of a tall and skinny
*> matrix X with orthonomal columns:
*> matrix X with orthonormal columns:
*> *>
*> [ B11 ] *> [ B11 ]
*> [ X11 ] [ P1 | ] [ 0 ] *> [ X11 ] [ P1 | ] [ 0 ]


+ 1
- 1
lapack-netlib/SRC/cunbdb2.f View File

@@ -37,7 +37,7 @@
*>\verbatim *>\verbatim
*> *>
*> CUNBDB2 simultaneously bidiagonalizes the blocks of a tall and skinny *> CUNBDB2 simultaneously bidiagonalizes the blocks of a tall and skinny
*> matrix X with orthonomal columns:
*> matrix X with orthonormal columns:
*> *>
*> [ B11 ] *> [ B11 ]
*> [ X11 ] [ P1 | ] [ 0 ] *> [ X11 ] [ P1 | ] [ 0 ]


+ 1
- 1
lapack-netlib/SRC/cunbdb3.f View File

@@ -37,7 +37,7 @@
*>\verbatim *>\verbatim
*> *>
*> CUNBDB3 simultaneously bidiagonalizes the blocks of a tall and skinny *> CUNBDB3 simultaneously bidiagonalizes the blocks of a tall and skinny
*> matrix X with orthonomal columns:
*> matrix X with orthonormal columns:
*> *>
*> [ B11 ] *> [ B11 ]
*> [ X11 ] [ P1 | ] [ 0 ] *> [ X11 ] [ P1 | ] [ 0 ]


+ 1
- 1
lapack-netlib/SRC/cunbdb4.f View File

@@ -38,7 +38,7 @@
*>\verbatim *>\verbatim
*> *>
*> CUNBDB4 simultaneously bidiagonalizes the blocks of a tall and skinny *> CUNBDB4 simultaneously bidiagonalizes the blocks of a tall and skinny
*> matrix X with orthonomal columns:
*> matrix X with orthonormal columns:
*> *>
*> [ B11 ] *> [ B11 ]
*> [ X11 ] [ P1 | ] [ 0 ] *> [ X11 ] [ P1 | ] [ 0 ]


+ 1
- 1
lapack-netlib/SRC/dbdsvdx.f View File

@@ -45,7 +45,7 @@
*> *>
*> Given an upper bidiagonal B with diagonal D = [ d_1 d_2 ... d_N ] *> Given an upper bidiagonal B with diagonal D = [ d_1 d_2 ... d_N ]
*> and superdiagonal E = [ e_1 e_2 ... e_N-1 ], DBDSVDX computes the *> and superdiagonal E = [ e_1 e_2 ... e_N-1 ], DBDSVDX computes the
*> singular value decompositon of B through the eigenvalues and
*> singular value decomposition of B through the eigenvalues and
*> eigenvectors of the N*2-by-N*2 tridiagonal matrix *> eigenvectors of the N*2-by-N*2 tridiagonal matrix
*> *>
*> | 0 d_1 | *> | 0 d_1 |


+ 1
- 1
lapack-netlib/SRC/dgejsv.f View File

@@ -253,7 +253,7 @@
*> If JOBV = 'V', 'J' then V contains on exit the N-by-N matrix of *> If JOBV = 'V', 'J' then V contains on exit the N-by-N matrix of
*> the right singular vectors; *> the right singular vectors;
*> If JOBV = 'W', AND (JOBU = 'U' AND JOBT = 'T' AND M = N), *> If JOBV = 'W', AND (JOBU = 'U' AND JOBT = 'T' AND M = N),
*> then V is used as workspace if the pprocedure
*> then V is used as workspace if the procedure
*> replaces A with A^t. In that case, [U] is computed *> replaces A with A^t. In that case, [U] is computed
*> in V as right singular vectors of A^t and then *> in V as right singular vectors of A^t and then
*> copied back to the U array. This 'W' option is just *> copied back to the U array. This 'W' option is just


+ 1
- 1
lapack-netlib/SRC/dgesvdq.f View File

@@ -365,7 +365,7 @@
*> an optimal implementation would do all necessary scaling before calling *> an optimal implementation would do all necessary scaling before calling
*> CGESVD and the scaling in CGESVD can be switched off. *> CGESVD and the scaling in CGESVD can be switched off.
*> 3. Other comments related to code optimization are given in comments in the *> 3. Other comments related to code optimization are given in comments in the
*> code, enlosed in [[double brackets]].
*> code, enclosed in [[double brackets]].
*> \endverbatim *> \endverbatim
* *
*> \par Bugs, examples and comments *> \par Bugs, examples and comments


+ 2
- 2
lapack-netlib/SRC/dgsvj0.f View File

@@ -52,10 +52,10 @@
*> Specifies whether the output from this procedure is used *> Specifies whether the output from this procedure is used
*> to compute the matrix V: *> to compute the matrix V:
*> = 'V': the product of the Jacobi rotations is accumulated *> = 'V': the product of the Jacobi rotations is accumulated
*> by postmulyiplying the N-by-N array V.
*> by postmultiplying the N-by-N array V.
*> (See the description of V.) *> (See the description of V.)
*> = 'A': the product of the Jacobi rotations is accumulated *> = 'A': the product of the Jacobi rotations is accumulated
*> by postmulyiplying the MV-by-N array V.
*> by postmultiplying the MV-by-N array V.
*> (See the descriptions of MV and V.) *> (See the descriptions of MV and V.)
*> = 'N': the Jacobi rotations are not accumulated. *> = 'N': the Jacobi rotations are not accumulated.
*> \endverbatim *> \endverbatim


+ 2
- 2
lapack-netlib/SRC/dgsvj1.f View File

@@ -75,10 +75,10 @@
*> Specifies whether the output from this procedure is used *> Specifies whether the output from this procedure is used
*> to compute the matrix V: *> to compute the matrix V:
*> = 'V': the product of the Jacobi rotations is accumulated *> = 'V': the product of the Jacobi rotations is accumulated
*> by postmulyiplying the N-by-N array V.
*> by postmultiplying the N-by-N array V.
*> (See the description of V.) *> (See the description of V.)
*> = 'A': the product of the Jacobi rotations is accumulated *> = 'A': the product of the Jacobi rotations is accumulated
*> by postmulyiplying the MV-by-N array V.
*> by postmultiplying the MV-by-N array V.
*> (See the descriptions of MV and V.) *> (See the descriptions of MV and V.)
*> = 'N': the Jacobi rotations are not accumulated. *> = 'N': the Jacobi rotations are not accumulated.
*> \endverbatim *> \endverbatim


+ 1
- 1
lapack-netlib/SRC/dla_gbrfsx_extended.f View File

@@ -645,7 +645,7 @@
PREVNORMDX = NORMDX PREVNORMDX = NORMDX
PREV_DZ_Z = DZ_Z PREV_DZ_Z = DZ_Z
* *
* Update soluton.
* Update solution.
* *
IF (Y_PREC_STATE .LT. EXTRA_Y) THEN IF (Y_PREC_STATE .LT. EXTRA_Y) THEN
CALL DAXPY( N, 1.0D+0, DY, 1, Y(1,J), 1 ) CALL DAXPY( N, 1.0D+0, DY, 1, Y(1,J), 1 )


+ 1
- 1
lapack-netlib/SRC/dla_gerfsx_extended.f View File

@@ -625,7 +625,7 @@
PREVNORMDX = NORMDX PREVNORMDX = NORMDX
PREV_DZ_Z = DZ_Z PREV_DZ_Z = DZ_Z
* *
* Update soluton.
* Update solution.
* *
IF ( Y_PREC_STATE .LT. EXTRA_Y ) THEN IF ( Y_PREC_STATE .LT. EXTRA_Y ) THEN
CALL DAXPY( N, 1.0D+0, DY, 1, Y( 1, J ), 1 ) CALL DAXPY( N, 1.0D+0, DY, 1, Y( 1, J ), 1 )


+ 1
- 1
lapack-netlib/SRC/dla_porfsx_extended.f View File

@@ -617,7 +617,7 @@
PREVNORMDX = NORMDX PREVNORMDX = NORMDX
PREV_DZ_Z = DZ_Z PREV_DZ_Z = DZ_Z
* *
* Update soluton.
* Update solution.
* *
IF (Y_PREC_STATE .LT. EXTRA_Y) THEN IF (Y_PREC_STATE .LT. EXTRA_Y) THEN
CALL DAXPY( N, 1.0D+0, DY, 1, Y(1,J), 1 ) CALL DAXPY( N, 1.0D+0, DY, 1, Y(1,J), 1 )


+ 1
- 1
lapack-netlib/SRC/dla_syrfsx_extended.f View File

@@ -647,7 +647,7 @@
PREVNORMDX = NORMDX PREVNORMDX = NORMDX
PREV_DZ_Z = DZ_Z PREV_DZ_Z = DZ_Z
* *
* Update soluton.
* Update solution.
* *
IF (Y_PREC_STATE .LT. EXTRA_Y) THEN IF (Y_PREC_STATE .LT. EXTRA_Y) THEN
CALL DAXPY( N, 1.0D+0, DY, 1, Y(1,J), 1 ) CALL DAXPY( N, 1.0D+0, DY, 1, Y(1,J), 1 )


+ 3
- 4
lapack-netlib/SRC/dlaqz0.f View File

@@ -102,7 +102,7 @@
*> Anal., 29(2006), pp. 199--227. *> Anal., 29(2006), pp. 199--227.
*> *>
*> Ref: T. Steel, D. Camps, K. Meerbergen, R. Vandebril "A multishift, *> Ref: T. Steel, D. Camps, K. Meerbergen, R. Vandebril "A multishift,
*> multipole rational QZ method with agressive early deflation"
*> multipole rational QZ method with aggressive early deflation"
*> \endverbatim *> \endverbatim
* *
* Arguments: * Arguments:
@@ -332,7 +332,7 @@
CHARACTER :: JBCMPZ*3 CHARACTER :: JBCMPZ*3


* External Functions * External Functions
EXTERNAL :: XERBLA, DHGEQZ, DLASET, DLAQZ3, DLAQZ4, DLABAD,
EXTERNAL :: XERBLA, DHGEQZ, DLASET, DLAQZ3, DLAQZ4,
$ DLARTG, DROT $ DLARTG, DROT
DOUBLE PRECISION, EXTERNAL :: DLAMCH, DLANHS DOUBLE PRECISION, EXTERNAL :: DLAMCH, DLANHS
LOGICAL, EXTERNAL :: LSAME LOGICAL, EXTERNAL :: LSAME
@@ -482,7 +482,6 @@
* Get machine constants * Get machine constants
SAFMIN = DLAMCH( 'SAFE MINIMUM' ) SAFMIN = DLAMCH( 'SAFE MINIMUM' )
SAFMAX = ONE/SAFMIN SAFMAX = ONE/SAFMIN
CALL DLABAD( SAFMIN, SAFMAX )
ULP = DLAMCH( 'PRECISION' ) ULP = DLAMCH( 'PRECISION' )
SMLNUM = SAFMIN*( DBLE( N )/ULP ) SMLNUM = SAFMIN*( DBLE( N )/ULP )


@@ -567,7 +566,7 @@
DO WHILE ( K.GE.ISTART2 ) DO WHILE ( K.GE.ISTART2 )


IF( ABS( B( K, K ) ) .LT. BTOL ) THEN IF( ABS( B( K, K ) ) .LT. BTOL ) THEN
* A diagonal element of B is negligable, move it
* A diagonal element of B is negligible, move it
* to the top and deflate it * to the top and deflate it
DO K2 = K, ISTART2+1, -1 DO K2 = K, ISTART2+1, -1


+ 1
- 1
lapack-netlib/SRC/dlarfb_gett.f View File

@@ -451,7 +451,7 @@
IF( LNOTIDENT ) THEN IF( LNOTIDENT ) THEN
* *
* col2_(2) Compute W2: = (V1**T) * W2 = (A1**T) * W2, * col2_(2) Compute W2: = (V1**T) * W2 = (A1**T) * W2,
* V1 is not an identy matrix, but unit lower-triangular
* V1 is not an identity matrix, but unit lower-triangular
* V1 stored in A1 (diagonal ones are not stored). * V1 stored in A1 (diagonal ones are not stored).
* *
* *


+ 1
- 1
lapack-netlib/SRC/dlatrs3.f View File

@@ -574,7 +574,7 @@
* Prepare the linear update to be executed with GEMM. * Prepare the linear update to be executed with GEMM.
* For each column, compute a consistent scaling, a * For each column, compute a consistent scaling, a
* scaling factor to survive the linear update, and * scaling factor to survive the linear update, and
* rescale the column segments, if necesssary. Then
* rescale the column segments, if necessary. Then
* the linear update is safely executed. * the linear update is safely executed.
* *
DO KK = 1, K2-K1 DO KK = 1, K2-K1


+ 1
- 1
lapack-netlib/SRC/dorbdb1.f View File

@@ -37,7 +37,7 @@
*>\verbatim *>\verbatim
*> *>
*> DORBDB1 simultaneously bidiagonalizes the blocks of a tall and skinny *> DORBDB1 simultaneously bidiagonalizes the blocks of a tall and skinny
*> matrix X with orthonomal columns:
*> matrix X with orthonormal columns:
*> *>
*> [ B11 ] *> [ B11 ]
*> [ X11 ] [ P1 | ] [ 0 ] *> [ X11 ] [ P1 | ] [ 0 ]


+ 1
- 1
lapack-netlib/SRC/dorbdb2.f View File

@@ -37,7 +37,7 @@
*>\verbatim *>\verbatim
*> *>
*> DORBDB2 simultaneously bidiagonalizes the blocks of a tall and skinny *> DORBDB2 simultaneously bidiagonalizes the blocks of a tall and skinny
*> matrix X with orthonomal columns:
*> matrix X with orthonormal columns:
*> *>
*> [ B11 ] *> [ B11 ]
*> [ X11 ] [ P1 | ] [ 0 ] *> [ X11 ] [ P1 | ] [ 0 ]


+ 1
- 1
lapack-netlib/SRC/dorbdb3.f View File

@@ -37,7 +37,7 @@
*>\verbatim *>\verbatim
*> *>
*> DORBDB3 simultaneously bidiagonalizes the blocks of a tall and skinny *> DORBDB3 simultaneously bidiagonalizes the blocks of a tall and skinny
*> matrix X with orthonomal columns:
*> matrix X with orthonormal columns:
*> *>
*> [ B11 ] *> [ B11 ]
*> [ X11 ] [ P1 | ] [ 0 ] *> [ X11 ] [ P1 | ] [ 0 ]


+ 1
- 1
lapack-netlib/SRC/dorbdb4.f View File

@@ -38,7 +38,7 @@
*>\verbatim *>\verbatim
*> *>
*> DORBDB4 simultaneously bidiagonalizes the blocks of a tall and skinny *> DORBDB4 simultaneously bidiagonalizes the blocks of a tall and skinny
*> matrix X with orthonomal columns:
*> matrix X with orthonormal columns:
*> *>
*> [ B11 ] *> [ B11 ]
*> [ X11 ] [ P1 | ] [ 0 ] *> [ X11 ] [ P1 | ] [ 0 ]


+ 5
- 5
lapack-netlib/SRC/dsyconvf.f View File

@@ -39,7 +39,7 @@
*> DSYTRF provided on entry in parameter A into the factorization *> DSYTRF provided on entry in parameter A into the factorization
*> output format used in DSYTRF_RK (or DSYTRF_BK) that is stored *> output format used in DSYTRF_RK (or DSYTRF_BK) that is stored
*> on exit in parameters A and E. It also converts in place details of *> on exit in parameters A and E. It also converts in place details of
*> the intechanges stored in IPIV from the format used in DSYTRF into
*> the interchanges stored in IPIV from the format used in DSYTRF into
*> the format used in DSYTRF_RK (or DSYTRF_BK). *> the format used in DSYTRF_RK (or DSYTRF_BK).
*> *>
*> If parameter WAY = 'R': *> If parameter WAY = 'R':
@@ -48,7 +48,7 @@
*> (or DSYTRF_BK) provided on entry in parameters A and E into *> (or DSYTRF_BK) provided on entry in parameters A and E into
*> the factorization output format used in DSYTRF that is stored *> the factorization output format used in DSYTRF that is stored
*> on exit in parameter A. It also converts in place details of *> on exit in parameter A. It also converts in place details of
*> the intechanges stored in IPIV from the format used in DSYTRF_RK
*> the interchanges stored in IPIV from the format used in DSYTRF_RK
*> (or DSYTRF_BK) into the format used in DSYTRF. *> (or DSYTRF_BK) into the format used in DSYTRF.
*> \endverbatim *> \endverbatim
* *
@@ -322,7 +322,7 @@
END IF END IF
* *
* Convert IPIV * Convert IPIV
* There is no interchnge of rows i and and IPIV(i),
* There is no interchange of rows i and and IPIV(i),
* so this should be reflected in IPIV format for * so this should be reflected in IPIV format for
* *SYTRF_RK ( or *SYTRF_BK) * *SYTRF_RK ( or *SYTRF_BK)
* *
@@ -466,7 +466,7 @@
END IF END IF
* *
* Convert IPIV * Convert IPIV
* There is no interchnge of rows i and and IPIV(i),
* There is no interchange of rows i and and IPIV(i),
* so this should be reflected in IPIV format for * so this should be reflected in IPIV format for
* *SYTRF_RK ( or *SYTRF_BK) * *SYTRF_RK ( or *SYTRF_BK)
* *
@@ -532,7 +532,7 @@
* *
* Revert VALUE * Revert VALUE
* Assign subdiagonal entries of D from array E to * Assign subdiagonal entries of D from array E to
* subgiagonal entries of A.
* subdiagonal entries of A.
* *
I = 1 I = 1
DO WHILE ( I.LE.N-1 ) DO WHILE ( I.LE.N-1 )


+ 1
- 1
lapack-netlib/SRC/dsyconvf_rook.f View File

@@ -517,7 +517,7 @@
* *
* Revert VALUE * Revert VALUE
* Assign subdiagonal entries of D from array E to * Assign subdiagonal entries of D from array E to
* subgiagonal entries of A.
* subdiagonal entries of A.
* *
I = 1 I = 1
DO WHILE ( I.LE.N-1 ) DO WHILE ( I.LE.N-1 )


+ 1
- 1
lapack-netlib/SRC/dsysv_aa_2stage.f View File

@@ -89,7 +89,7 @@
*> triangular part of the matrix A, and the strictly upper *> triangular part of the matrix A, and the strictly upper
*> triangular part of A is not referenced. *> triangular part of A is not referenced.
*> *>
*> On exit, L is stored below (or above) the subdiaonal blocks,
*> On exit, L is stored below (or above) the subdiagonal blocks,
*> when UPLO is 'L' (or 'U'). *> when UPLO is 'L' (or 'U').
*> \endverbatim *> \endverbatim
*> *>


+ 1
- 1
lapack-netlib/SRC/dsytrf_aa.f View File

@@ -74,7 +74,7 @@
*> *>
*> On exit, the tridiagonal matrix is stored in the diagonals *> On exit, the tridiagonal matrix is stored in the diagonals
*> and the subdiagonals of A just below (or above) the diagonals, *> and the subdiagonals of A just below (or above) the diagonals,
*> and L is stored below (or above) the subdiaonals, when UPLO
*> and L is stored below (or above) the subdiagonals, when UPLO
*> is 'L' (or 'U'). *> is 'L' (or 'U').
*> \endverbatim *> \endverbatim
*> *>


+ 1
- 1
lapack-netlib/SRC/dsytrf_aa_2stage.f View File

@@ -75,7 +75,7 @@
*> triangular part of the matrix A, and the strictly upper *> triangular part of the matrix A, and the strictly upper
*> triangular part of A is not referenced. *> triangular part of A is not referenced.
*> *>
*> On exit, L is stored below (or above) the subdiaonal blocks,
*> On exit, L is stored below (or above) the subdiagonal blocks,
*> when UPLO is 'L' (or 'U'). *> when UPLO is 'L' (or 'U').
*> \endverbatim *> \endverbatim
*> *>


+ 1
- 1
lapack-netlib/SRC/sbdsvdx.f View File

@@ -45,7 +45,7 @@
*> *>
*> Given an upper bidiagonal B with diagonal D = [ d_1 d_2 ... d_N ] *> Given an upper bidiagonal B with diagonal D = [ d_1 d_2 ... d_N ]
*> and superdiagonal E = [ e_1 e_2 ... e_N-1 ], SBDSVDX computes the *> and superdiagonal E = [ e_1 e_2 ... e_N-1 ], SBDSVDX computes the
*> singular value decompositon of B through the eigenvalues and
*> singular value decomposition of B through the eigenvalues and
*> eigenvectors of the N*2-by-N*2 tridiagonal matrix *> eigenvectors of the N*2-by-N*2 tridiagonal matrix
*> *>
*> | 0 d_1 | *> | 0 d_1 |


+ 1
- 1
lapack-netlib/SRC/sgejsv.f View File

@@ -253,7 +253,7 @@
*> If JOBV = 'V', 'J' then V contains on exit the N-by-N matrix of *> If JOBV = 'V', 'J' then V contains on exit the N-by-N matrix of
*> the right singular vectors; *> the right singular vectors;
*> If JOBV = 'W', AND (JOBU = 'U' AND JOBT = 'T' AND M = N), *> If JOBV = 'W', AND (JOBU = 'U' AND JOBT = 'T' AND M = N),
*> then V is used as workspace if the pprocedure
*> then V is used as workspace if the procedure
*> replaces A with A^t. In that case, [U] is computed *> replaces A with A^t. In that case, [U] is computed
*> in V as right singular vectors of A^t and then *> in V as right singular vectors of A^t and then
*> copied back to the U array. This 'W' option is just *> copied back to the U array. This 'W' option is just


+ 1
- 1
lapack-netlib/SRC/sgesvdq.f View File

@@ -365,7 +365,7 @@
*> an optimal implementation would do all necessary scaling before calling *> an optimal implementation would do all necessary scaling before calling
*> CGESVD and the scaling in CGESVD can be switched off. *> CGESVD and the scaling in CGESVD can be switched off.
*> 3. Other comments related to code optimization are given in comments in the *> 3. Other comments related to code optimization are given in comments in the
*> code, enlosed in [[double brackets]].
*> code, enclosed in [[double brackets]].
*> \endverbatim *> \endverbatim
* *
*> \par Bugs, examples and comments *> \par Bugs, examples and comments


+ 2
- 2
lapack-netlib/SRC/sgsvj0.f View File

@@ -52,10 +52,10 @@
*> Specifies whether the output from this procedure is used *> Specifies whether the output from this procedure is used
*> to compute the matrix V: *> to compute the matrix V:
*> = 'V': the product of the Jacobi rotations is accumulated *> = 'V': the product of the Jacobi rotations is accumulated
*> by postmulyiplying the N-by-N array V.
*> by postmultiplying the N-by-N array V.
*> (See the description of V.) *> (See the description of V.)
*> = 'A': the product of the Jacobi rotations is accumulated *> = 'A': the product of the Jacobi rotations is accumulated
*> by postmulyiplying the MV-by-N array V.
*> by postmultiplying the MV-by-N array V.
*> (See the descriptions of MV and V.) *> (See the descriptions of MV and V.)
*> = 'N': the Jacobi rotations are not accumulated. *> = 'N': the Jacobi rotations are not accumulated.
*> \endverbatim *> \endverbatim


+ 2
- 2
lapack-netlib/SRC/sgsvj1.f View File

@@ -75,10 +75,10 @@
*> Specifies whether the output from this procedure is used *> Specifies whether the output from this procedure is used
*> to compute the matrix V: *> to compute the matrix V:
*> = 'V': the product of the Jacobi rotations is accumulated *> = 'V': the product of the Jacobi rotations is accumulated
*> by postmulyiplying the N-by-N array V.
*> by postmultiplying the N-by-N array V.
*> (See the description of V.) *> (See the description of V.)
*> = 'A': the product of the Jacobi rotations is accumulated *> = 'A': the product of the Jacobi rotations is accumulated
*> by postmulyiplying the MV-by-N array V.
*> by postmultiplying the MV-by-N array V.
*> (See the descriptions of MV and V.) *> (See the descriptions of MV and V.)
*> = 'N': the Jacobi rotations are not accumulated. *> = 'N': the Jacobi rotations are not accumulated.
*> \endverbatim *> \endverbatim


+ 1
- 1
lapack-netlib/SRC/sla_gbrfsx_extended.f View File

@@ -644,7 +644,7 @@
PREVNORMDX = NORMDX PREVNORMDX = NORMDX
PREV_DZ_Z = DZ_Z PREV_DZ_Z = DZ_Z
* *
* Update soluton.
* Update solution.
* *
IF (Y_PREC_STATE .LT. EXTRA_Y) THEN IF (Y_PREC_STATE .LT. EXTRA_Y) THEN
CALL SAXPY( N, 1.0, DY, 1, Y(1,J), 1 ) CALL SAXPY( N, 1.0, DY, 1, Y(1,J), 1 )


+ 1
- 1
lapack-netlib/SRC/sla_gerfsx_extended.f View File

@@ -628,7 +628,7 @@
PREVNORMDX = NORMDX PREVNORMDX = NORMDX
PREV_DZ_Z = DZ_Z PREV_DZ_Z = DZ_Z
* *
* Update soluton.
* Update solution.
* *
IF ( Y_PREC_STATE .LT. EXTRA_Y ) THEN IF ( Y_PREC_STATE .LT. EXTRA_Y ) THEN
CALL SAXPY( N, 1.0, DY, 1, Y( 1, J ), 1 ) CALL SAXPY( N, 1.0, DY, 1, Y( 1, J ), 1 )


+ 1
- 1
lapack-netlib/SRC/sla_porfsx_extended.f View File

@@ -617,7 +617,7 @@
PREVNORMDX = NORMDX PREVNORMDX = NORMDX
PREV_DZ_Z = DZ_Z PREV_DZ_Z = DZ_Z
* *
* Update soluton.
* Update solution.
* *
IF (Y_PREC_STATE .LT. EXTRA_Y) THEN IF (Y_PREC_STATE .LT. EXTRA_Y) THEN
CALL SAXPY( N, 1.0, DY, 1, Y(1,J), 1 ) CALL SAXPY( N, 1.0, DY, 1, Y(1,J), 1 )


+ 1
- 1
lapack-netlib/SRC/sla_syrfsx_extended.f View File

@@ -647,7 +647,7 @@
PREVNORMDX = NORMDX PREVNORMDX = NORMDX
PREV_DZ_Z = DZ_Z PREV_DZ_Z = DZ_Z
* *
* Update soluton.
* Update solution.
* *
IF (Y_PREC_STATE .LT. EXTRA_Y) THEN IF (Y_PREC_STATE .LT. EXTRA_Y) THEN
CALL SAXPY( N, 1.0, DY, 1, Y(1,J), 1 ) CALL SAXPY( N, 1.0, DY, 1, Y(1,J), 1 )


+ 3
- 4
lapack-netlib/SRC/slaqz0.f View File

@@ -100,7 +100,7 @@
*> Anal., 29(2006), pp. 199--227. *> Anal., 29(2006), pp. 199--227.
*> *>
*> Ref: T. Steel, D. Camps, K. Meerbergen, R. Vandebril "A multishift, *> Ref: T. Steel, D. Camps, K. Meerbergen, R. Vandebril "A multishift,
*> multipole rational QZ method with agressive early deflation"
*> multipole rational QZ method with aggressive early deflation"
*> \endverbatim *> \endverbatim
* *
* Arguments: * Arguments:
@@ -329,7 +329,7 @@
CHARACTER :: JBCMPZ*3 CHARACTER :: JBCMPZ*3


* External Functions * External Functions
EXTERNAL :: XERBLA, SHGEQZ, SLAQZ3, SLAQZ4, SLASET, SLABAD,
EXTERNAL :: XERBLA, SHGEQZ, SLAQZ3, SLAQZ4, SLASET,
$ SLARTG, SROT $ SLARTG, SROT
REAL, EXTERNAL :: SLAMCH, SLANHS REAL, EXTERNAL :: SLAMCH, SLANHS
LOGICAL, EXTERNAL :: LSAME LOGICAL, EXTERNAL :: LSAME
@@ -479,7 +479,6 @@
* Get machine constants * Get machine constants
SAFMIN = SLAMCH( 'SAFE MINIMUM' ) SAFMIN = SLAMCH( 'SAFE MINIMUM' )
SAFMAX = ONE/SAFMIN SAFMAX = ONE/SAFMIN
CALL SLABAD( SAFMIN, SAFMAX )
ULP = SLAMCH( 'PRECISION' ) ULP = SLAMCH( 'PRECISION' )
SMLNUM = SAFMIN*( REAL( N )/ULP ) SMLNUM = SAFMIN*( REAL( N )/ULP )


@@ -564,7 +563,7 @@
DO WHILE ( K.GE.ISTART2 ) DO WHILE ( K.GE.ISTART2 )


IF( ABS( B( K, K ) ) .LT. BTOL ) THEN IF( ABS( B( K, K ) ) .LT. BTOL ) THEN
* A diagonal element of B is negligable, move it
* A diagonal element of B is negligible, move it
* to the top and deflate it * to the top and deflate it
DO K2 = K, ISTART2+1, -1 DO K2 = K, ISTART2+1, -1


+ 1
- 1
lapack-netlib/SRC/slarfb_gett.f View File

@@ -451,7 +451,7 @@
IF( LNOTIDENT ) THEN IF( LNOTIDENT ) THEN
* *
* col2_(2) Compute W2: = (V1**T) * W2 = (A1**T) * W2, * col2_(2) Compute W2: = (V1**T) * W2 = (A1**T) * W2,
* V1 is not an identy matrix, but unit lower-triangular
* V1 is not an identity matrix, but unit lower-triangular
* V1 stored in A1 (diagonal ones are not stored). * V1 stored in A1 (diagonal ones are not stored).
* *
* *


+ 1
- 1
lapack-netlib/SRC/slatrs3.f View File

@@ -574,7 +574,7 @@
* Prepare the linear update to be executed with GEMM. * Prepare the linear update to be executed with GEMM.
* For each column, compute a consistent scaling, a * For each column, compute a consistent scaling, a
* scaling factor to survive the linear update, and * scaling factor to survive the linear update, and
* rescale the column segments, if necesssary. Then
* rescale the column segments, if necessary. Then
* the linear update is safely executed. * the linear update is safely executed.
* *
DO KK = 1, K2-K1 DO KK = 1, K2-K1


+ 1
- 1
lapack-netlib/SRC/sorbdb1.f View File

@@ -37,7 +37,7 @@
*>\verbatim *>\verbatim
*> *>
*> SORBDB1 simultaneously bidiagonalizes the blocks of a tall and skinny *> SORBDB1 simultaneously bidiagonalizes the blocks of a tall and skinny
*> matrix X with orthonomal columns:
*> matrix X with orthonormal columns:
*> *>
*> [ B11 ] *> [ B11 ]
*> [ X11 ] [ P1 | ] [ 0 ] *> [ X11 ] [ P1 | ] [ 0 ]


+ 1
- 1
lapack-netlib/SRC/sorbdb2.f View File

@@ -37,7 +37,7 @@
*>\verbatim *>\verbatim
*> *>
*> SORBDB2 simultaneously bidiagonalizes the blocks of a tall and skinny *> SORBDB2 simultaneously bidiagonalizes the blocks of a tall and skinny
*> matrix X with orthonomal columns:
*> matrix X with orthonormal columns:
*> *>
*> [ B11 ] *> [ B11 ]
*> [ X11 ] [ P1 | ] [ 0 ] *> [ X11 ] [ P1 | ] [ 0 ]


+ 1
- 1
lapack-netlib/SRC/sorbdb3.f View File

@@ -37,7 +37,7 @@
*>\verbatim *>\verbatim
*> *>
*> SORBDB3 simultaneously bidiagonalizes the blocks of a tall and skinny *> SORBDB3 simultaneously bidiagonalizes the blocks of a tall and skinny
*> matrix X with orthonomal columns:
*> matrix X with orthonormal columns:
*> *>
*> [ B11 ] *> [ B11 ]
*> [ X11 ] [ P1 | ] [ 0 ] *> [ X11 ] [ P1 | ] [ 0 ]


+ 1
- 1
lapack-netlib/SRC/sorbdb4.f View File

@@ -38,7 +38,7 @@
*>\verbatim *>\verbatim
*> *>
*> SORBDB4 simultaneously bidiagonalizes the blocks of a tall and skinny *> SORBDB4 simultaneously bidiagonalizes the blocks of a tall and skinny
*> matrix X with orthonomal columns:
*> matrix X with orthonormal columns:
*> *>
*> [ B11 ] *> [ B11 ]
*> [ X11 ] [ P1 | ] [ 0 ] *> [ X11 ] [ P1 | ] [ 0 ]


+ 5
- 5
lapack-netlib/SRC/ssyconvf.f View File

@@ -39,7 +39,7 @@
*> SSYTRF provided on entry in parameter A into the factorization *> SSYTRF provided on entry in parameter A into the factorization
*> output format used in SSYTRF_RK (or SSYTRF_BK) that is stored *> output format used in SSYTRF_RK (or SSYTRF_BK) that is stored
*> on exit in parameters A and E. It also converts in place details of *> on exit in parameters A and E. It also converts in place details of
*> the intechanges stored in IPIV from the format used in SSYTRF into
*> the interchanges stored in IPIV from the format used in SSYTRF into
*> the format used in SSYTRF_RK (or SSYTRF_BK). *> the format used in SSYTRF_RK (or SSYTRF_BK).
*> *>
*> If parameter WAY = 'R': *> If parameter WAY = 'R':
@@ -48,7 +48,7 @@
*> (or SSYTRF_BK) provided on entry in parameters A and E into *> (or SSYTRF_BK) provided on entry in parameters A and E into
*> the factorization output format used in SSYTRF that is stored *> the factorization output format used in SSYTRF that is stored
*> on exit in parameter A. It also converts in place details of *> on exit in parameter A. It also converts in place details of
*> the intechanges stored in IPIV from the format used in SSYTRF_RK
*> the interchanges stored in IPIV from the format used in SSYTRF_RK
*> (or SSYTRF_BK) into the format used in SSYTRF. *> (or SSYTRF_BK) into the format used in SSYTRF.
*> \endverbatim *> \endverbatim
* *
@@ -322,7 +322,7 @@
END IF END IF
* *
* Convert IPIV * Convert IPIV
* There is no interchnge of rows i and and IPIV(i),
* There is no interchange of rows i and and IPIV(i),
* so this should be reflected in IPIV format for * so this should be reflected in IPIV format for
* *SYTRF_RK ( or *SYTRF_BK) * *SYTRF_RK ( or *SYTRF_BK)
* *
@@ -466,7 +466,7 @@
END IF END IF
* *
* Convert IPIV * Convert IPIV
* There is no interchnge of rows i and and IPIV(i),
* There is no interchange of rows i and and IPIV(i),
* so this should be reflected in IPIV format for * so this should be reflected in IPIV format for
* *SYTRF_RK ( or *SYTRF_BK) * *SYTRF_RK ( or *SYTRF_BK)
* *
@@ -532,7 +532,7 @@
* *
* Revert VALUE * Revert VALUE
* Assign subdiagonal entries of D from array E to * Assign subdiagonal entries of D from array E to
* subgiagonal entries of A.
* subdiagonal entries of A.
* *
I = 1 I = 1
DO WHILE ( I.LE.N-1 ) DO WHILE ( I.LE.N-1 )


+ 1
- 1
lapack-netlib/SRC/ssyconvf_rook.f View File

@@ -517,7 +517,7 @@
* *
* Revert VALUE * Revert VALUE
* Assign subdiagonal entries of D from array E to * Assign subdiagonal entries of D from array E to
* subgiagonal entries of A.
* subdiagonal entries of A.
* *
I = 1 I = 1
DO WHILE ( I.LE.N-1 ) DO WHILE ( I.LE.N-1 )


+ 1
- 1
lapack-netlib/SRC/ssysv_aa_2stage.f View File

@@ -88,7 +88,7 @@
*> triangular part of the matrix A, and the strictly upper *> triangular part of the matrix A, and the strictly upper
*> triangular part of A is not referenced. *> triangular part of A is not referenced.
*> *>
*> On exit, L is stored below (or above) the subdiaonal blocks,
*> On exit, L is stored below (or above) the subdiagonal blocks,
*> when UPLO is 'L' (or 'U'). *> when UPLO is 'L' (or 'U').
*> \endverbatim *> \endverbatim
*> *>


+ 1
- 1
lapack-netlib/SRC/ssytrf_aa.f View File

@@ -74,7 +74,7 @@
*> *>
*> On exit, the tridiagonal matrix is stored in the diagonals *> On exit, the tridiagonal matrix is stored in the diagonals
*> and the subdiagonals of A just below (or above) the diagonals, *> and the subdiagonals of A just below (or above) the diagonals,
*> and L is stored below (or above) the subdiaonals, when UPLO
*> and L is stored below (or above) the subdiagonals, when UPLO
*> is 'L' (or 'U'). *> is 'L' (or 'U').
*> \endverbatim *> \endverbatim
*> *>


+ 1
- 1
lapack-netlib/SRC/ssytrf_aa_2stage.f View File

@@ -75,7 +75,7 @@
*> triangular part of the matrix A, and the strictly upper *> triangular part of the matrix A, and the strictly upper
*> triangular part of A is not referenced. *> triangular part of A is not referenced.
*> *>
*> On exit, L is stored below (or above) the subdiaonal blocks,
*> On exit, L is stored below (or above) the subdiagonal blocks,
*> when UPLO is 'L' (or 'U'). *> when UPLO is 'L' (or 'U').
*> \endverbatim *> \endverbatim
*> *>


+ 1
- 1
lapack-netlib/SRC/zgejsv.f View File

@@ -252,7 +252,7 @@
*> If JOBV = 'V', 'J' then V contains on exit the N-by-N matrix of *> If JOBV = 'V', 'J' then V contains on exit the N-by-N matrix of
*> the right singular vectors; *> the right singular vectors;
*> If JOBV = 'W', AND (JOBU = 'U' AND JOBT = 'T' AND M = N), *> If JOBV = 'W', AND (JOBU = 'U' AND JOBT = 'T' AND M = N),
*> then V is used as workspace if the pprocedure
*> then V is used as workspace if the procedure
*> replaces A with A^*. In that case, [U] is computed *> replaces A with A^*. In that case, [U] is computed
*> in V as right singular vectors of A^* and then *> in V as right singular vectors of A^* and then
*> copied back to the U array. This 'W' option is just *> copied back to the U array. This 'W' option is just


+ 1
- 1
lapack-netlib/SRC/zgesvdq.f View File

@@ -363,7 +363,7 @@
*> an optimal implementation would do all necessary scaling before calling *> an optimal implementation would do all necessary scaling before calling
*> CGESVD and the scaling in CGESVD can be switched off. *> CGESVD and the scaling in CGESVD can be switched off.
*> 3. Other comments related to code optimization are given in comments in the *> 3. Other comments related to code optimization are given in comments in the
*> code, enlosed in [[double brackets]].
*> code, enclosed in [[double brackets]].
*> \endverbatim *> \endverbatim
* *
*> \par Bugs, examples and comments *> \par Bugs, examples and comments


+ 2
- 2
lapack-netlib/SRC/zgsvj0.f View File

@@ -52,10 +52,10 @@
*> Specifies whether the output from this procedure is used *> Specifies whether the output from this procedure is used
*> to compute the matrix V: *> to compute the matrix V:
*> = 'V': the product of the Jacobi rotations is accumulated *> = 'V': the product of the Jacobi rotations is accumulated
*> by postmulyiplying the N-by-N array V.
*> by postmultiplying the N-by-N array V.
*> (See the description of V.) *> (See the description of V.)
*> = 'A': the product of the Jacobi rotations is accumulated *> = 'A': the product of the Jacobi rotations is accumulated
*> by postmulyiplying the MV-by-N array V.
*> by postmultiplying the MV-by-N array V.
*> (See the descriptions of MV and V.) *> (See the descriptions of MV and V.)
*> = 'N': the Jacobi rotations are not accumulated. *> = 'N': the Jacobi rotations are not accumulated.
*> \endverbatim *> \endverbatim


+ 2
- 2
lapack-netlib/SRC/zgsvj1.f View File

@@ -75,10 +75,10 @@
*> Specifies whether the output from this procedure is used *> Specifies whether the output from this procedure is used
*> to compute the matrix V: *> to compute the matrix V:
*> = 'V': the product of the Jacobi rotations is accumulated *> = 'V': the product of the Jacobi rotations is accumulated
*> by postmulyiplying the N-by-N array V.
*> by postmultiplying the N-by-N array V.
*> (See the description of V.) *> (See the description of V.)
*> = 'A': the product of the Jacobi rotations is accumulated *> = 'A': the product of the Jacobi rotations is accumulated
*> by postmulyiplying the MV-by-N array V.
*> by postmultiplying the MV-by-N array V.
*> (See the descriptions of MV and V.) *> (See the descriptions of MV and V.)
*> = 'N': the Jacobi rotations are not accumulated. *> = 'N': the Jacobi rotations are not accumulated.
*> \endverbatim *> \endverbatim


+ 1
- 1
lapack-netlib/SRC/zhesv_aa_2stage.f View File

@@ -88,7 +88,7 @@
*> triangular part of the matrix A, and the strictly upper *> triangular part of the matrix A, and the strictly upper
*> triangular part of A is not referenced. *> triangular part of A is not referenced.
*> *>
*> On exit, L is stored below (or above) the subdiaonal blocks,
*> On exit, L is stored below (or above) the subdiagonal blocks,
*> when UPLO is 'L' (or 'U'). *> when UPLO is 'L' (or 'U').
*> \endverbatim *> \endverbatim
*> *>


+ 4
- 4
lapack-netlib/SRC/zhetf2_rk.f View File

@@ -480,7 +480,7 @@
A( J, K ) = DCONJG( A( P, J ) ) A( J, K ) = DCONJG( A( P, J ) )
A( P, J ) = T A( P, J ) = T
14 CONTINUE 14 CONTINUE
* (3) Swap and conjugate corner elements at row-col interserction
* (3) Swap and conjugate corner elements at row-col intersection
A( P, K ) = DCONJG( A( P, K ) ) A( P, K ) = DCONJG( A( P, K ) )
* (4) Swap diagonal elements at row-col intersection * (4) Swap diagonal elements at row-col intersection
R1 = DBLE( A( K, K ) ) R1 = DBLE( A( K, K ) )
@@ -508,7 +508,7 @@
A( J, KK ) = DCONJG( A( KP, J ) ) A( J, KK ) = DCONJG( A( KP, J ) )
A( KP, J ) = T A( KP, J ) = T
15 CONTINUE 15 CONTINUE
* (3) Swap and conjugate corner elements at row-col interserction
* (3) Swap and conjugate corner elements at row-col intersection
A( KP, KK ) = DCONJG( A( KP, KK ) ) A( KP, KK ) = DCONJG( A( KP, KK ) )
* (4) Swap diagonal elements at row-col intersection * (4) Swap diagonal elements at row-col intersection
R1 = DBLE( A( KK, KK ) ) R1 = DBLE( A( KK, KK ) )
@@ -834,7 +834,7 @@
A( J, K ) = DCONJG( A( P, J ) ) A( J, K ) = DCONJG( A( P, J ) )
A( P, J ) = T A( P, J ) = T
44 CONTINUE 44 CONTINUE
* (3) Swap and conjugate corner elements at row-col interserction
* (3) Swap and conjugate corner elements at row-col intersection
A( P, K ) = DCONJG( A( P, K ) ) A( P, K ) = DCONJG( A( P, K ) )
* (4) Swap diagonal elements at row-col intersection * (4) Swap diagonal elements at row-col intersection
R1 = DBLE( A( K, K ) ) R1 = DBLE( A( K, K ) )
@@ -862,7 +862,7 @@
A( J, KK ) = DCONJG( A( KP, J ) ) A( J, KK ) = DCONJG( A( KP, J ) )
A( KP, J ) = T A( KP, J ) = T
45 CONTINUE 45 CONTINUE
* (3) Swap and conjugate corner elements at row-col interserction
* (3) Swap and conjugate corner elements at row-col intersection
A( KP, KK ) = DCONJG( A( KP, KK ) ) A( KP, KK ) = DCONJG( A( KP, KK ) )
* (4) Swap diagonal elements at row-col intersection * (4) Swap diagonal elements at row-col intersection
R1 = DBLE( A( KK, KK ) ) R1 = DBLE( A( KK, KK ) )


+ 4
- 4
lapack-netlib/SRC/zhetf2_rook.f View File

@@ -420,7 +420,7 @@
A( J, K ) = DCONJG( A( P, J ) ) A( J, K ) = DCONJG( A( P, J ) )
A( P, J ) = T A( P, J ) = T
14 CONTINUE 14 CONTINUE
* (3) Swap and conjugate corner elements at row-col interserction
* (3) Swap and conjugate corner elements at row-col intersection
A( P, K ) = DCONJG( A( P, K ) ) A( P, K ) = DCONJG( A( P, K ) )
* (4) Swap diagonal elements at row-col intersection * (4) Swap diagonal elements at row-col intersection
R1 = DBLE( A( K, K ) ) R1 = DBLE( A( K, K ) )
@@ -441,7 +441,7 @@
A( J, KK ) = DCONJG( A( KP, J ) ) A( J, KK ) = DCONJG( A( KP, J ) )
A( KP, J ) = T A( KP, J ) = T
15 CONTINUE 15 CONTINUE
* (3) Swap and conjugate corner elements at row-col interserction
* (3) Swap and conjugate corner elements at row-col intersection
A( KP, KK ) = DCONJG( A( KP, KK ) ) A( KP, KK ) = DCONJG( A( KP, KK ) )
* (4) Swap diagonal elements at row-col intersection * (4) Swap diagonal elements at row-col intersection
R1 = DBLE( A( KK, KK ) ) R1 = DBLE( A( KK, KK ) )
@@ -733,7 +733,7 @@
A( J, K ) = DCONJG( A( P, J ) ) A( J, K ) = DCONJG( A( P, J ) )
A( P, J ) = T A( P, J ) = T
44 CONTINUE 44 CONTINUE
* (3) Swap and conjugate corner elements at row-col interserction
* (3) Swap and conjugate corner elements at row-col intersection
A( P, K ) = DCONJG( A( P, K ) ) A( P, K ) = DCONJG( A( P, K ) )
* (4) Swap diagonal elements at row-col intersection * (4) Swap diagonal elements at row-col intersection
R1 = DBLE( A( K, K ) ) R1 = DBLE( A( K, K ) )
@@ -754,7 +754,7 @@
A( J, KK ) = DCONJG( A( KP, J ) ) A( J, KK ) = DCONJG( A( KP, J ) )
A( KP, J ) = T A( KP, J ) = T
45 CONTINUE 45 CONTINUE
* (3) Swap and conjugate corner elements at row-col interserction
* (3) Swap and conjugate corner elements at row-col intersection
A( KP, KK ) = DCONJG( A( KP, KK ) ) A( KP, KK ) = DCONJG( A( KP, KK ) )
* (4) Swap diagonal elements at row-col intersection * (4) Swap diagonal elements at row-col intersection
R1 = DBLE( A( KK, KK ) ) R1 = DBLE( A( KK, KK ) )


+ 1
- 1
lapack-netlib/SRC/zhetrf_aa.f View File

@@ -74,7 +74,7 @@
*> *>
*> On exit, the tridiagonal matrix is stored in the diagonals *> On exit, the tridiagonal matrix is stored in the diagonals
*> and the subdiagonals of A just below (or above) the diagonals, *> and the subdiagonals of A just below (or above) the diagonals,
*> and L is stored below (or above) the subdiaonals, when UPLO
*> and L is stored below (or above) the subdiagonals, when UPLO
*> is 'L' (or 'U'). *> is 'L' (or 'U').
*> \endverbatim *> \endverbatim
*> *>


+ 1
- 1
lapack-netlib/SRC/zhetrf_aa_2stage.f View File

@@ -75,7 +75,7 @@
*> triangular part of the matrix A, and the strictly upper *> triangular part of the matrix A, and the strictly upper
*> triangular part of A is not referenced. *> triangular part of A is not referenced.
*> *>
*> On exit, L is stored below (or above) the subdiaonal blocks,
*> On exit, L is stored below (or above) the subdiagonal blocks,
*> when UPLO is 'L' (or 'U'). *> when UPLO is 'L' (or 'U').
*> \endverbatim *> \endverbatim
*> *>


+ 1
- 1
lapack-netlib/SRC/zla_gbrfsx_extended.f View File

@@ -651,7 +651,7 @@
PREVNORMDX = NORMDX PREVNORMDX = NORMDX
PREV_DZ_Z = DZ_Z PREV_DZ_Z = DZ_Z
* *
* Update soluton.
* Update solution.
* *
IF ( Y_PREC_STATE .LT. EXTRA_Y ) THEN IF ( Y_PREC_STATE .LT. EXTRA_Y ) THEN
CALL ZAXPY( N, (1.0D+0,0.0D+0), DY, 1, Y(1,J), 1 ) CALL ZAXPY( N, (1.0D+0,0.0D+0), DY, 1, Y(1,J), 1 )


+ 1
- 1
lapack-netlib/SRC/zla_gerfsx_extended.f View File

@@ -636,7 +636,7 @@
PREVNORMDX = NORMDX PREVNORMDX = NORMDX
PREV_DZ_Z = DZ_Z PREV_DZ_Z = DZ_Z
* *
* Update soluton.
* Update solution.
* *
IF ( Y_PREC_STATE .LT. EXTRA_Y ) THEN IF ( Y_PREC_STATE .LT. EXTRA_Y ) THEN
CALL ZAXPY( N, (1.0D+0,0.0D+0), DY, 1, Y(1,J), 1 ) CALL ZAXPY( N, (1.0D+0,0.0D+0), DY, 1, Y(1,J), 1 )


+ 1
- 1
lapack-netlib/SRC/zla_herfsx_extended.f View File

@@ -655,7 +655,7 @@
PREVNORMDX = NORMDX PREVNORMDX = NORMDX
PREV_DZ_Z = DZ_Z PREV_DZ_Z = DZ_Z
* *
* Update soluton.
* Update solution.
* *
IF ( Y_PREC_STATE .LT. EXTRA_Y ) THEN IF ( Y_PREC_STATE .LT. EXTRA_Y ) THEN
CALL ZAXPY( N, DCMPLX(1.0D+0), DY, 1, Y(1,J), 1 ) CALL ZAXPY( N, DCMPLX(1.0D+0), DY, 1, Y(1,J), 1 )


+ 1
- 1
lapack-netlib/SRC/zla_porfsx_extended.f View File

@@ -626,7 +626,7 @@
PREVNORMDX = NORMDX PREVNORMDX = NORMDX
PREV_DZ_Z = DZ_Z PREV_DZ_Z = DZ_Z
* *
* Update soluton.
* Update solution.
* *
IF (Y_PREC_STATE .LT. EXTRA_Y) THEN IF (Y_PREC_STATE .LT. EXTRA_Y) THEN
CALL ZAXPY( N, DCMPLX(1.0D+0), DY, 1, Y(1,J), 1 ) CALL ZAXPY( N, DCMPLX(1.0D+0), DY, 1, Y(1,J), 1 )


+ 1
- 1
lapack-netlib/SRC/zla_syrfsx_extended.f View File

@@ -655,7 +655,7 @@
PREVNORMDX = NORMDX PREVNORMDX = NORMDX
PREV_DZ_Z = DZ_Z PREV_DZ_Z = DZ_Z
* *
* Update soluton.
* Update solution.
* *
IF ( Y_PREC_STATE .LT. EXTRA_Y ) THEN IF ( Y_PREC_STATE .LT. EXTRA_Y ) THEN
CALL ZAXPY( N, DCMPLX(1.0D+0), DY, 1, Y(1,J), 1 ) CALL ZAXPY( N, DCMPLX(1.0D+0), DY, 1, Y(1,J), 1 )


+ 1
- 1
lapack-netlib/SRC/zlaed7.f View File

@@ -363,7 +363,7 @@
RETURN RETURN
END IF END IF
* *
* Prepare the INDXQ sorting premutation.
* Prepare the INDXQ sorting permutation.
* *
N1 = K N1 = K
N2 = N - K N2 = N - K


+ 3
- 4
lapack-netlib/SRC/zlaqz0.f View File

@@ -89,7 +89,7 @@
*> Anal., 29(2006), pp. 199--227. *> Anal., 29(2006), pp. 199--227.
*> *>
*> Ref: T. Steel, D. Camps, K. Meerbergen, R. Vandebril "A multishift, *> Ref: T. Steel, D. Camps, K. Meerbergen, R. Vandebril "A multishift,
*> multipole rational QZ method with agressive early deflation"
*> multipole rational QZ method with aggressive early deflation"
*> \endverbatim *> \endverbatim
* *
* Arguments: * Arguments:
@@ -312,7 +312,7 @@
CHARACTER :: JBCMPZ*3 CHARACTER :: JBCMPZ*3


* External Functions * External Functions
EXTERNAL :: XERBLA, ZHGEQZ, ZLAQZ2, ZLAQZ3, ZLASET, DLABAD,
EXTERNAL :: XERBLA, ZHGEQZ, ZLAQZ2, ZLAQZ3, ZLASET,
$ ZLARTG, ZROT $ ZLARTG, ZROT
DOUBLE PRECISION, EXTERNAL :: DLAMCH, ZLANHS DOUBLE PRECISION, EXTERNAL :: DLAMCH, ZLANHS
LOGICAL, EXTERNAL :: LSAME LOGICAL, EXTERNAL :: LSAME
@@ -464,7 +464,6 @@
* Get machine constants * Get machine constants
SAFMIN = DLAMCH( 'SAFE MINIMUM' ) SAFMIN = DLAMCH( 'SAFE MINIMUM' )
SAFMAX = ONE/SAFMIN SAFMAX = ONE/SAFMIN
CALL DLABAD( SAFMIN, SAFMAX )
ULP = DLAMCH( 'PRECISION' ) ULP = DLAMCH( 'PRECISION' )
SMLNUM = SAFMIN*( DBLE( N )/ULP ) SMLNUM = SAFMIN*( DBLE( N )/ULP )


@@ -535,7 +534,7 @@
DO WHILE ( K.GE.ISTART2 ) DO WHILE ( K.GE.ISTART2 )


IF( ABS( B( K, K ) ) .LT. BTOL ) THEN IF( ABS( B( K, K ) ) .LT. BTOL ) THEN
* A diagonal element of B is negligable, move it
* A diagonal element of B is negligible, move it
* to the top and deflate it * to the top and deflate it
DO K2 = K, ISTART2+1, -1 DO K2 = K, ISTART2+1, -1


+ 1
- 1
lapack-netlib/SRC/zlarfb_gett.f View File

@@ -452,7 +452,7 @@
IF( LNOTIDENT ) THEN IF( LNOTIDENT ) THEN
* *
* col2_(2) Compute W2: = (V1**H) * W2 = (A1**H) * W2, * col2_(2) Compute W2: = (V1**H) * W2 = (A1**H) * W2,
* V1 is not an identy matrix, but unit lower-triangular
* V1 is not an identity matrix, but unit lower-triangular
* V1 stored in A1 (diagonal ones are not stored). * V1 stored in A1 (diagonal ones are not stored).
* *
* *


+ 1
- 1
lapack-netlib/SRC/zlatdf.f View File

@@ -227,7 +227,7 @@
BM = RHS( J ) - CONE BM = RHS( J ) - CONE
SPLUS = ONE SPLUS = ONE
* *
* Lockahead for L- part RHS(1:N-1) = +-1
* Look-ahead for L- part RHS(1:N-1) = +-1
* SPLUS and SMIN computed more efficiently than in BSOLVE[1]. * SPLUS and SMIN computed more efficiently than in BSOLVE[1].
* *
SPLUS = SPLUS + DBLE( ZDOTC( N-J, Z( J+1, J ), 1, Z( J+1, SPLUS = SPLUS + DBLE( ZDOTC( N-J, Z( J+1, J ), 1, Z( J+1,


+ 1
- 1
lapack-netlib/SRC/zlatrs3.f View File

@@ -577,7 +577,7 @@
* Prepare the linear update to be executed with GEMM. * Prepare the linear update to be executed with GEMM.
* For each column, compute a consistent scaling, a * For each column, compute a consistent scaling, a
* scaling factor to survive the linear update, and * scaling factor to survive the linear update, and
* rescale the column segments, if necesssary. Then
* rescale the column segments, if necessary. Then
* the linear update is safely executed. * the linear update is safely executed.
* *
DO KK = 1, K2 - K1 DO KK = 1, K2 - K1


+ 5
- 5
lapack-netlib/SRC/zsyconvf.f View File

@@ -39,7 +39,7 @@
*> ZSYTRF provided on entry in parameter A into the factorization *> ZSYTRF provided on entry in parameter A into the factorization
*> output format used in ZSYTRF_RK (or ZSYTRF_BK) that is stored *> output format used in ZSYTRF_RK (or ZSYTRF_BK) that is stored
*> on exit in parameters A and E. It also converts in place details of *> on exit in parameters A and E. It also converts in place details of
*> the intechanges stored in IPIV from the format used in ZSYTRF into
*> the interchanges stored in IPIV from the format used in ZSYTRF into
*> the format used in ZSYTRF_RK (or ZSYTRF_BK). *> the format used in ZSYTRF_RK (or ZSYTRF_BK).
*> *>
*> If parameter WAY = 'R': *> If parameter WAY = 'R':
@@ -48,7 +48,7 @@
*> (or ZSYTRF_BK) provided on entry in parameters A and E into *> (or ZSYTRF_BK) provided on entry in parameters A and E into
*> the factorization output format used in ZSYTRF that is stored *> the factorization output format used in ZSYTRF that is stored
*> on exit in parameter A. It also converts in place details of *> on exit in parameter A. It also converts in place details of
*> the intechanges stored in IPIV from the format used in ZSYTRF_RK
*> the interchanges stored in IPIV from the format used in ZSYTRF_RK
*> (or ZSYTRF_BK) into the format used in ZSYTRF. *> (or ZSYTRF_BK) into the format used in ZSYTRF.
*> *>
*> ZSYCONVF can also convert in Hermitian matrix case, i.e. between *> ZSYCONVF can also convert in Hermitian matrix case, i.e. between
@@ -325,7 +325,7 @@
END IF END IF
* *
* Convert IPIV * Convert IPIV
* There is no interchnge of rows i and and IPIV(i),
* There is no interchange of rows i and and IPIV(i),
* so this should be reflected in IPIV format for * so this should be reflected in IPIV format for
* *SYTRF_RK ( or *SYTRF_BK) * *SYTRF_RK ( or *SYTRF_BK)
* *
@@ -469,7 +469,7 @@
END IF END IF
* *
* Convert IPIV * Convert IPIV
* There is no interchnge of rows i and and IPIV(i),
* There is no interchange of rows i and and IPIV(i),
* so this should be reflected in IPIV format for * so this should be reflected in IPIV format for
* *SYTRF_RK ( or *SYTRF_BK) * *SYTRF_RK ( or *SYTRF_BK)
* *
@@ -535,7 +535,7 @@
* *
* Revert VALUE * Revert VALUE
* Assign subdiagonal entries of D from array E to * Assign subdiagonal entries of D from array E to
* subgiagonal entries of A.
* subdiagonal entries of A.
* *
I = 1 I = 1
DO WHILE ( I.LE.N-1 ) DO WHILE ( I.LE.N-1 )


+ 1
- 1
lapack-netlib/SRC/zsyconvf_rook.f View File

@@ -520,7 +520,7 @@
* *
* Revert VALUE * Revert VALUE
* Assign subdiagonal entries of D from array E to * Assign subdiagonal entries of D from array E to
* subgiagonal entries of A.
* subdiagonal entries of A.
* *
I = 1 I = 1
DO WHILE ( I.LE.N-1 ) DO WHILE ( I.LE.N-1 )


+ 1
- 1
lapack-netlib/SRC/zsysv_aa_2stage.f View File

@@ -87,7 +87,7 @@
*> triangular part of the matrix A, and the strictly upper *> triangular part of the matrix A, and the strictly upper
*> triangular part of A is not referenced. *> triangular part of A is not referenced.
*> *>
*> On exit, L is stored below (or above) the subdiaonal blocks,
*> On exit, L is stored below (or above) the subdiagonal blocks,
*> when UPLO is 'L' (or 'U'). *> when UPLO is 'L' (or 'U').
*> \endverbatim *> \endverbatim
*> *>


+ 1
- 1
lapack-netlib/SRC/zsytrf_aa.f View File

@@ -74,7 +74,7 @@
*> *>
*> On exit, the tridiagonal matrix is stored in the diagonals *> On exit, the tridiagonal matrix is stored in the diagonals
*> and the subdiagonals of A just below (or above) the diagonals, *> and the subdiagonals of A just below (or above) the diagonals,
*> and L is stored below (or above) the subdiaonals, when UPLO
*> and L is stored below (or above) the subdiagonals, when UPLO
*> is 'L' (or 'U'). *> is 'L' (or 'U').
*> \endverbatim *> \endverbatim
*> *>


+ 1
- 1
lapack-netlib/SRC/zsytrf_aa_2stage.f View File

@@ -75,7 +75,7 @@
*> triangular part of the matrix A, and the strictly upper *> triangular part of the matrix A, and the strictly upper
*> triangular part of A is not referenced. *> triangular part of A is not referenced.
*> *>
*> On exit, L is stored below (or above) the subdiaonal blocks,
*> On exit, L is stored below (or above) the subdiagonal blocks,
*> when UPLO is 'L' (or 'U'). *> when UPLO is 'L' (or 'U').
*> \endverbatim *> \endverbatim
*> *>


+ 1
- 1
lapack-netlib/SRC/ztrexc.f View File

@@ -40,7 +40,7 @@
*> *>
*> The Schur form T is reordered by a unitary similarity transformation *> The Schur form T is reordered by a unitary similarity transformation
*> Z**H*T*Z, and optionally the matrix Q of Schur vectors is updated by *> Z**H*T*Z, and optionally the matrix Q of Schur vectors is updated by
*> postmultplying it with Z.
*> postmultiplying it with Z.
*> \endverbatim *> \endverbatim
* *
* Arguments: * Arguments:


+ 1
- 1
lapack-netlib/SRC/zunbdb1.f View File

@@ -37,7 +37,7 @@
*>\verbatim *>\verbatim
*> *>
*> ZUNBDB1 simultaneously bidiagonalizes the blocks of a tall and skinny *> ZUNBDB1 simultaneously bidiagonalizes the blocks of a tall and skinny
*> matrix X with orthonomal columns:
*> matrix X with orthonormal columns:
*> *>
*> [ B11 ] *> [ B11 ]
*> [ X11 ] [ P1 | ] [ 0 ] *> [ X11 ] [ P1 | ] [ 0 ]


+ 1
- 1
lapack-netlib/SRC/zunbdb2.f View File

@@ -37,7 +37,7 @@
*>\verbatim *>\verbatim
*> *>
*> ZUNBDB2 simultaneously bidiagonalizes the blocks of a tall and skinny *> ZUNBDB2 simultaneously bidiagonalizes the blocks of a tall and skinny
*> matrix X with orthonomal columns:
*> matrix X with orthonormal columns:
*> *>
*> [ B11 ] *> [ B11 ]
*> [ X11 ] [ P1 | ] [ 0 ] *> [ X11 ] [ P1 | ] [ 0 ]


+ 1
- 1
lapack-netlib/SRC/zunbdb3.f View File

@@ -37,7 +37,7 @@
*>\verbatim *>\verbatim
*> *>
*> ZUNBDB3 simultaneously bidiagonalizes the blocks of a tall and skinny *> ZUNBDB3 simultaneously bidiagonalizes the blocks of a tall and skinny
*> matrix X with orthonomal columns:
*> matrix X with orthonormal columns:
*> *>
*> [ B11 ] *> [ B11 ]
*> [ X11 ] [ P1 | ] [ 0 ] *> [ X11 ] [ P1 | ] [ 0 ]


+ 1
- 1
lapack-netlib/SRC/zunbdb4.f View File

@@ -38,7 +38,7 @@
*>\verbatim *>\verbatim
*> *>
*> ZUNBDB4 simultaneously bidiagonalizes the blocks of a tall and skinny *> ZUNBDB4 simultaneously bidiagonalizes the blocks of a tall and skinny
*> matrix X with orthonomal columns:
*> matrix X with orthonormal columns:
*> *>
*> [ B11 ] *> [ B11 ]
*> [ X11 ] [ P1 | ] [ 0 ] *> [ X11 ] [ P1 | ] [ 0 ]


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