From 827843bbbdb5a27019d7d679f371a3a69053c762 Mon Sep 17 00:00:00 2001 From: Gael Guennebaud Date: Wed, 12 Jun 2013 10:12:50 +0200 Subject: Complete the lapack interface to make it complete enough for suitesparse QR. --- lapack/CMakeLists.txt | 18 +++-- lapack/clacgv.f | 116 ++++++++++++++++++++++++++++++ lapack/cladiv.f | 97 +++++++++++++++++++++++++ lapack/dladiv.f | 128 +++++++++++++++++++++++++++++++++ lapack/dlamch.f | 189 +++++++++++++++++++++++++++++++++++++++++++++++++ lapack/dlapy2.f | 104 +++++++++++++++++++++++++++ lapack/dlapy3.f | 111 +++++++++++++++++++++++++++++ lapack/ilaclc.f | 118 +++++++++++++++++++++++++++++++ lapack/ilaclr.f | 121 +++++++++++++++++++++++++++++++ lapack/iladlc.f | 118 +++++++++++++++++++++++++++++++ lapack/iladlr.f | 121 +++++++++++++++++++++++++++++++ lapack/ilaslc.f | 118 +++++++++++++++++++++++++++++++ lapack/ilaslr.f | 121 +++++++++++++++++++++++++++++++ lapack/ilazlc.f | 118 +++++++++++++++++++++++++++++++ lapack/ilazlr.f | 121 +++++++++++++++++++++++++++++++ lapack/sladiv.f | 128 +++++++++++++++++++++++++++++++++ lapack/slamch.f | 192 ++++++++++++++++++++++++++++++++++++++++++++++++++ lapack/slapy2.f | 104 +++++++++++++++++++++++++++ lapack/slapy3.f | 111 +++++++++++++++++++++++++++++ lapack/zlacgv.f | 116 ++++++++++++++++++++++++++++++ lapack/zladiv.f | 97 +++++++++++++++++++++++++ 21 files changed, 2462 insertions(+), 5 deletions(-) create mode 100644 lapack/clacgv.f create mode 100644 lapack/cladiv.f create mode 100644 lapack/dladiv.f create mode 100644 lapack/dlamch.f create mode 100644 lapack/dlapy2.f create mode 100644 lapack/dlapy3.f create mode 100644 lapack/ilaclc.f create mode 100644 lapack/ilaclr.f create mode 100644 lapack/iladlc.f create mode 100644 lapack/iladlr.f create mode 100644 lapack/ilaslc.f create mode 100644 lapack/ilaslr.f create mode 100644 lapack/ilazlc.f create mode 100644 lapack/ilazlr.f create mode 100644 lapack/sladiv.f create mode 100644 lapack/slamch.f create mode 100644 lapack/slapy2.f create mode 100644 lapack/slapy3.f create mode 100644 lapack/zlacgv.f create mode 100644 lapack/zladiv.f (limited to 'lapack') diff --git a/lapack/CMakeLists.txt b/lapack/CMakeLists.txt index 174e77d8d..296e05838 100644 --- a/lapack/CMakeLists.txt +++ b/lapack/CMakeLists.txt @@ -18,11 +18,17 @@ single.cpp double.cpp complex_single.cpp complex_double.cpp ../blas/xerbla.cpp if(EIGEN_Fortran_COMPILER_WORKS) -set(EigenLapack_SRCS -slarft.f dlarft.f clarft.f zlarft.f -slarfb.f dlarfb.f clarfb.f zlarfb.f -slarfg.f dlarfg.f clarfg.f zlarfg.f -slarf.f dlarf.f clarf.f zlarf.f +set(EigenLapack_SRCS ${EigenLapack_SRCS} + slarft.f dlarft.f clarft.f zlarft.f + slarfb.f dlarfb.f clarfb.f zlarfb.f + slarfg.f dlarfg.f clarfg.f zlarfg.f + slarf.f dlarf.f clarf.f zlarf.f + sladiv.f dladiv.f cladiv.f zladiv.f + ilaslr.f iladlr.f ilaclr.f ilazlr.f + ilaslc.f iladlc.f ilaclc.f ilazlc.f + dlapy2.f dlapy3.f slapy2.f slapy3.f + clacgv.f zlacgv.f + slamch.f dlamch.f ) get_filename_component(eigen_full_path_to_reference_to_reference_lapack "./reference/" ABSOLUTE) @@ -364,6 +370,8 @@ endif(EIGEN_Fortran_COMPILER_WORKS) add_library(eigen_lapack_static ${EigenLapack_SRCS}) add_library(eigen_lapack SHARED ${EigenLapack_SRCS}) +target_link_libraries(eigen_lapack eigen_blas) + if(EIGEN_STANDARD_LIBRARIES_TO_LINK_TO) target_link_libraries(eigen_lapack_static ${EIGEN_STANDARD_LIBRARIES_TO_LINK_TO}) target_link_libraries(eigen_lapack ${EIGEN_STANDARD_LIBRARIES_TO_LINK_TO}) diff --git a/lapack/clacgv.f b/lapack/clacgv.f new file mode 100644 index 000000000..359eb07f3 --- /dev/null +++ b/lapack/clacgv.f @@ -0,0 +1,116 @@ +*> \brief \b CLACGV +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +*> \htmlonly +*> Download CLACGV + dependencies +*> +*> [TGZ] +*> +*> [ZIP] +*> +*> [TXT] +*> \endhtmlonly +* +* Definition: +* =========== +* +* SUBROUTINE CLACGV( N, X, INCX ) +* +* .. Scalar Arguments .. +* INTEGER INCX, N +* .. +* .. Array Arguments .. +* COMPLEX X( * ) +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> CLACGV conjugates a complex vector of length N. +*> \endverbatim +* +* Arguments: +* ========== +* +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> The length of the vector X. N >= 0. +*> \endverbatim +*> +*> \param[in,out] X +*> \verbatim +*> X is COMPLEX array, dimension +*> (1+(N-1)*abs(INCX)) +*> On entry, the vector of length N to be conjugated. +*> On exit, X is overwritten with conjg(X). +*> \endverbatim +*> +*> \param[in] INCX +*> \verbatim +*> INCX is INTEGER +*> The spacing between successive elements of X. +*> \endverbatim +* +* Authors: +* ======== +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup complexOTHERauxiliary +* +* ===================================================================== + SUBROUTINE CLACGV( N, X, INCX ) +* +* -- LAPACK auxiliary routine (version 3.4.0) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 +* +* .. Scalar Arguments .. + INTEGER INCX, N +* .. +* .. Array Arguments .. + COMPLEX X( * ) +* .. +* +* ===================================================================== +* +* .. Local Scalars .. + INTEGER I, IOFF +* .. +* .. Intrinsic Functions .. + INTRINSIC CONJG +* .. +* .. Executable Statements .. +* + IF( INCX.EQ.1 ) THEN + DO 10 I = 1, N + X( I ) = CONJG( X( I ) ) + 10 CONTINUE + ELSE + IOFF = 1 + IF( INCX.LT.0 ) + $ IOFF = 1 - ( N-1 )*INCX + DO 20 I = 1, N + X( IOFF ) = CONJG( X( IOFF ) ) + IOFF = IOFF + INCX + 20 CONTINUE + END IF + RETURN +* +* End of CLACGV +* + END diff --git a/lapack/cladiv.f b/lapack/cladiv.f new file mode 100644 index 000000000..2807ac5fc --- /dev/null +++ b/lapack/cladiv.f @@ -0,0 +1,97 @@ +*> \brief \b CLADIV +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +*> \htmlonly +*> Download CLADIV + dependencies +*> +*> [TGZ] +*> +*> [ZIP] +*> +*> [TXT] +*> \endhtmlonly +* +* Definition: +* =========== +* +* COMPLEX FUNCTION CLADIV( X, Y ) +* +* .. Scalar Arguments .. +* COMPLEX X, Y +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> CLADIV := X / Y, where X and Y are complex. The computation of X / Y +*> will not overflow on an intermediary step unless the results +*> overflows. +*> \endverbatim +* +* Arguments: +* ========== +* +*> \param[in] X +*> \verbatim +*> X is COMPLEX +*> \endverbatim +*> +*> \param[in] Y +*> \verbatim +*> Y is COMPLEX +*> The complex scalars X and Y. +*> \endverbatim +* +* Authors: +* ======== +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup complexOTHERauxiliary +* +* ===================================================================== + COMPLEX FUNCTION CLADIV( X, Y ) +* +* -- LAPACK auxiliary routine (version 3.4.0) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 +* +* .. Scalar Arguments .. + COMPLEX X, Y +* .. +* +* ===================================================================== +* +* .. Local Scalars .. + REAL ZI, ZR +* .. +* .. External Subroutines .. + EXTERNAL SLADIV +* .. +* .. Intrinsic Functions .. + INTRINSIC AIMAG, CMPLX, REAL +* .. +* .. Executable Statements .. +* + CALL SLADIV( REAL( X ), AIMAG( X ), REAL( Y ), AIMAG( Y ), ZR, + $ ZI ) + CLADIV = CMPLX( ZR, ZI ) +* + RETURN +* +* End of CLADIV +* + END diff --git a/lapack/dladiv.f b/lapack/dladiv.f new file mode 100644 index 000000000..090a90654 --- /dev/null +++ b/lapack/dladiv.f @@ -0,0 +1,128 @@ +*> \brief \b DLADIV +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +*> \htmlonly +*> Download DLADIV + dependencies +*> +*> [TGZ] +*> +*> [ZIP] +*> +*> [TXT] +*> \endhtmlonly +* +* Definition: +* =========== +* +* SUBROUTINE DLADIV( A, B, C, D, P, Q ) +* +* .. Scalar Arguments .. +* DOUBLE PRECISION A, B, C, D, P, Q +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> DLADIV performs complex division in real arithmetic +*> +*> a + i*b +*> p + i*q = --------- +*> c + i*d +*> +*> The algorithm is due to Robert L. Smith and can be found +*> in D. Knuth, The art of Computer Programming, Vol.2, p.195 +*> \endverbatim +* +* Arguments: +* ========== +* +*> \param[in] A +*> \verbatim +*> A is DOUBLE PRECISION +*> \endverbatim +*> +*> \param[in] B +*> \verbatim +*> B is DOUBLE PRECISION +*> \endverbatim +*> +*> \param[in] C +*> \verbatim +*> C is DOUBLE PRECISION +*> \endverbatim +*> +*> \param[in] D +*> \verbatim +*> D is DOUBLE PRECISION +*> The scalars a, b, c, and d in the above expression. +*> \endverbatim +*> +*> \param[out] P +*> \verbatim +*> P is DOUBLE PRECISION +*> \endverbatim +*> +*> \param[out] Q +*> \verbatim +*> Q is DOUBLE PRECISION +*> The scalars p and q in the above expression. +*> \endverbatim +* +* Authors: +* ======== +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup auxOTHERauxiliary +* +* ===================================================================== + SUBROUTINE DLADIV( A, B, C, D, P, Q ) +* +* -- LAPACK auxiliary routine (version 3.4.0) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 +* +* .. Scalar Arguments .. + DOUBLE PRECISION A, B, C, D, P, Q +* .. +* +* ===================================================================== +* +* .. Local Scalars .. + DOUBLE PRECISION E, F +* .. +* .. Intrinsic Functions .. + INTRINSIC ABS +* .. +* .. Executable Statements .. +* + IF( ABS( D ).LT.ABS( C ) ) THEN + E = D / C + F = C + D*E + P = ( A+B*E ) / F + Q = ( B-A*E ) / F + ELSE + E = C / D + F = D + C*E + P = ( B+A*E ) / F + Q = ( -A+B*E ) / F + END IF +* + RETURN +* +* End of DLADIV +* + END diff --git a/lapack/dlamch.f b/lapack/dlamch.f new file mode 100644 index 000000000..eb307e5e1 --- /dev/null +++ b/lapack/dlamch.f @@ -0,0 +1,189 @@ +*> \brief \b DLAMCH +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +* Definition: +* =========== +* +* DOUBLE PRECISION FUNCTION DLAMCH( CMACH ) +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> DLAMCH determines double precision machine parameters. +*> \endverbatim +* +* Arguments: +* ========== +* +*> \param[in] CMACH +*> \verbatim +*> Specifies the value to be returned by DLAMCH: +*> = 'E' or 'e', DLAMCH := eps +*> = 'S' or 's , DLAMCH := sfmin +*> = 'B' or 'b', DLAMCH := base +*> = 'P' or 'p', DLAMCH := eps*base +*> = 'N' or 'n', DLAMCH := t +*> = 'R' or 'r', DLAMCH := rnd +*> = 'M' or 'm', DLAMCH := emin +*> = 'U' or 'u', DLAMCH := rmin +*> = 'L' or 'l', DLAMCH := emax +*> = 'O' or 'o', DLAMCH := rmax +*> where +*> eps = relative machine precision +*> sfmin = safe minimum, such that 1/sfmin does not overflow +*> base = base of the machine +*> prec = eps*base +*> t = number of (base) digits in the mantissa +*> rnd = 1.0 when rounding occurs in addition, 0.0 otherwise +*> emin = minimum exponent before (gradual) underflow +*> rmin = underflow threshold - base**(emin-1) +*> emax = largest exponent before overflow +*> rmax = overflow threshold - (base**emax)*(1-eps) +*> \endverbatim +* +* Authors: +* ======== +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup auxOTHERauxiliary +* +* ===================================================================== + DOUBLE PRECISION FUNCTION DLAMCH( CMACH ) +* +* -- LAPACK auxiliary routine (version 3.4.0) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 +* +* .. Scalar Arguments .. + CHARACTER CMACH +* .. +* +* ===================================================================== +* +* .. Parameters .. + DOUBLE PRECISION ONE, ZERO + PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) +* .. +* .. Local Scalars .. + DOUBLE PRECISION RND, EPS, SFMIN, SMALL, RMACH +* .. +* .. External Functions .. + LOGICAL LSAME + EXTERNAL LSAME +* .. +* .. Intrinsic Functions .. + INTRINSIC DIGITS, EPSILON, HUGE, MAXEXPONENT, + $ MINEXPONENT, RADIX, TINY +* .. +* .. Executable Statements .. +* +* +* Assume rounding, not chopping. Always. +* + RND = ONE +* + IF( ONE.EQ.RND ) THEN + EPS = EPSILON(ZERO) * 0.5 + ELSE + EPS = EPSILON(ZERO) + END IF +* + IF( LSAME( CMACH, 'E' ) ) THEN + RMACH = EPS + ELSE IF( LSAME( CMACH, 'S' ) ) THEN + SFMIN = TINY(ZERO) + SMALL = ONE / HUGE(ZERO) + IF( SMALL.GE.SFMIN ) THEN +* +* Use SMALL plus a bit, to avoid the possibility of rounding +* causing overflow when computing 1/sfmin. +* + SFMIN = SMALL*( ONE+EPS ) + END IF + RMACH = SFMIN + ELSE IF( LSAME( CMACH, 'B' ) ) THEN + RMACH = RADIX(ZERO) + ELSE IF( LSAME( CMACH, 'P' ) ) THEN + RMACH = EPS * RADIX(ZERO) + ELSE IF( LSAME( CMACH, 'N' ) ) THEN + RMACH = DIGITS(ZERO) + ELSE IF( LSAME( CMACH, 'R' ) ) THEN + RMACH = RND + ELSE IF( LSAME( CMACH, 'M' ) ) THEN + RMACH = MINEXPONENT(ZERO) + ELSE IF( LSAME( CMACH, 'U' ) ) THEN + RMACH = tiny(zero) + ELSE IF( LSAME( CMACH, 'L' ) ) THEN + RMACH = MAXEXPONENT(ZERO) + ELSE IF( LSAME( CMACH, 'O' ) ) THEN + RMACH = HUGE(ZERO) + ELSE + RMACH = ZERO + END IF +* + DLAMCH = RMACH + RETURN +* +* End of DLAMCH +* + END +************************************************************************ +*> \brief \b DLAMC3 +*> \details +*> \b Purpose: +*> \verbatim +*> DLAMC3 is intended to force A and B to be stored prior to doing +*> the addition of A and B , for use in situations where optimizers +*> might hold one of these in a register. +*> \endverbatim +*> \author LAPACK is a software package provided by Univ. of Tennessee, Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd.. +*> \date November 2011 +*> \ingroup auxOTHERauxiliary +*> +*> \param[in] A +*> \verbatim +*> A is a DOUBLE PRECISION +*> \endverbatim +*> +*> \param[in] B +*> \verbatim +*> B is a DOUBLE PRECISION +*> The values A and B. +*> \endverbatim +*> + DOUBLE PRECISION FUNCTION DLAMC3( A, B ) +* +* -- LAPACK auxiliary routine (version 3.4.0) -- +* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. +* November 2010 +* +* .. Scalar Arguments .. + DOUBLE PRECISION A, B +* .. +* ===================================================================== +* +* .. Executable Statements .. +* + DLAMC3 = A + B +* + RETURN +* +* End of DLAMC3 +* + END +* +************************************************************************ diff --git a/lapack/dlapy2.f b/lapack/dlapy2.f new file mode 100644 index 000000000..e6a62bf4a --- /dev/null +++ b/lapack/dlapy2.f @@ -0,0 +1,104 @@ +*> \brief \b DLAPY2 +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +*> \htmlonly +*> Download DLAPY2 + dependencies +*> +*> [TGZ] +*> +*> [ZIP] +*> +*> [TXT] +*> \endhtmlonly +* +* Definition: +* =========== +* +* DOUBLE PRECISION FUNCTION DLAPY2( X, Y ) +* +* .. Scalar Arguments .. +* DOUBLE PRECISION X, Y +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> DLAPY2 returns sqrt(x**2+y**2), taking care not to cause unnecessary +*> overflow. +*> \endverbatim +* +* Arguments: +* ========== +* +*> \param[in] X +*> \verbatim +*> X is DOUBLE PRECISION +*> \endverbatim +*> +*> \param[in] Y +*> \verbatim +*> Y is DOUBLE PRECISION +*> X and Y specify the values x and y. +*> \endverbatim +* +* Authors: +* ======== +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup auxOTHERauxiliary +* +* ===================================================================== + DOUBLE PRECISION FUNCTION DLAPY2( X, Y ) +* +* -- LAPACK auxiliary routine (version 3.4.0) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 +* +* .. Scalar Arguments .. + DOUBLE PRECISION X, Y +* .. +* +* ===================================================================== +* +* .. Parameters .. + DOUBLE PRECISION ZERO + PARAMETER ( ZERO = 0.0D0 ) + DOUBLE PRECISION ONE + PARAMETER ( ONE = 1.0D0 ) +* .. +* .. Local Scalars .. + DOUBLE PRECISION W, XABS, YABS, Z +* .. +* .. Intrinsic Functions .. + INTRINSIC ABS, MAX, MIN, SQRT +* .. +* .. Executable Statements .. +* + XABS = ABS( X ) + YABS = ABS( Y ) + W = MAX( XABS, YABS ) + Z = MIN( XABS, YABS ) + IF( Z.EQ.ZERO ) THEN + DLAPY2 = W + ELSE + DLAPY2 = W*SQRT( ONE+( Z / W )**2 ) + END IF + RETURN +* +* End of DLAPY2 +* + END diff --git a/lapack/dlapy3.f b/lapack/dlapy3.f new file mode 100644 index 000000000..ae9844f80 --- /dev/null +++ b/lapack/dlapy3.f @@ -0,0 +1,111 @@ +*> \brief \b DLAPY3 +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +*> \htmlonly +*> Download DLAPY3 + dependencies +*> +*> [TGZ] +*> +*> [ZIP] +*> +*> [TXT] +*> \endhtmlonly +* +* Definition: +* =========== +* +* DOUBLE PRECISION FUNCTION DLAPY3( X, Y, Z ) +* +* .. Scalar Arguments .. +* DOUBLE PRECISION X, Y, Z +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> DLAPY3 returns sqrt(x**2+y**2+z**2), taking care not to cause +*> unnecessary overflow. +*> \endverbatim +* +* Arguments: +* ========== +* +*> \param[in] X +*> \verbatim +*> X is DOUBLE PRECISION +*> \endverbatim +*> +*> \param[in] Y +*> \verbatim +*> Y is DOUBLE PRECISION +*> \endverbatim +*> +*> \param[in] Z +*> \verbatim +*> Z is DOUBLE PRECISION +*> X, Y and Z specify the values x, y and z. +*> \endverbatim +* +* Authors: +* ======== +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup auxOTHERauxiliary +* +* ===================================================================== + DOUBLE PRECISION FUNCTION DLAPY3( X, Y, Z ) +* +* -- LAPACK auxiliary routine (version 3.4.0) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 +* +* .. Scalar Arguments .. + DOUBLE PRECISION X, Y, Z +* .. +* +* ===================================================================== +* +* .. Parameters .. + DOUBLE PRECISION ZERO + PARAMETER ( ZERO = 0.0D0 ) +* .. +* .. Local Scalars .. + DOUBLE PRECISION W, XABS, YABS, ZABS +* .. +* .. Intrinsic Functions .. + INTRINSIC ABS, MAX, SQRT +* .. +* .. Executable Statements .. +* + XABS = ABS( X ) + YABS = ABS( Y ) + ZABS = ABS( Z ) + W = MAX( XABS, YABS, ZABS ) + IF( W.EQ.ZERO ) THEN +* W can be zero for max(0,nan,0) +* adding all three entries together will make sure +* NaN will not disappear. + DLAPY3 = XABS + YABS + ZABS + ELSE + DLAPY3 = W*SQRT( ( XABS / W )**2+( YABS / W )**2+ + $ ( ZABS / W )**2 ) + END IF + RETURN +* +* End of DLAPY3 +* + END diff --git a/lapack/ilaclc.f b/lapack/ilaclc.f new file mode 100644 index 000000000..4ceb61c52 --- /dev/null +++ b/lapack/ilaclc.f @@ -0,0 +1,118 @@ +*> \brief \b ILACLC +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +*> \htmlonly +*> Download ILACLC + dependencies +*> +*> [TGZ] +*> +*> [ZIP] +*> +*> [TXT] +*> \endhtmlonly +* +* Definition: +* =========== +* +* INTEGER FUNCTION ILACLC( M, N, A, LDA ) +* +* .. Scalar Arguments .. +* INTEGER M, N, LDA +* .. +* .. Array Arguments .. +* COMPLEX A( LDA, * ) +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> ILACLC scans A for its last non-zero column. +*> \endverbatim +* +* Arguments: +* ========== +* +*> \param[in] M +*> \verbatim +*> M is INTEGER +*> The number of rows of the matrix A. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> The number of columns of the matrix A. +*> \endverbatim +*> +*> \param[in] A +*> \verbatim +*> A is COMPLEX array, dimension (LDA,N) +*> The m by n matrix A. +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> The leading dimension of the array A. LDA >= max(1,M). +*> \endverbatim +* +* Authors: +* ======== +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup complexOTHERauxiliary +* +* ===================================================================== + INTEGER FUNCTION ILACLC( M, N, A, LDA ) +* +* -- LAPACK auxiliary routine (version 3.4.0) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 +* +* .. Scalar Arguments .. + INTEGER M, N, LDA +* .. +* .. Array Arguments .. + COMPLEX A( LDA, * ) +* .. +* +* ===================================================================== +* +* .. Parameters .. + COMPLEX ZERO + PARAMETER ( ZERO = (0.0E+0, 0.0E+0) ) +* .. +* .. Local Scalars .. + INTEGER I +* .. +* .. Executable Statements .. +* +* Quick test for the common case where one corner is non-zero. + IF( N.EQ.0 ) THEN + ILACLC = N + ELSE IF( A(1, N).NE.ZERO .OR. A(M, N).NE.ZERO ) THEN + ILACLC = N + ELSE +* Now scan each column from the end, returning with the first non-zero. + DO ILACLC = N, 1, -1 + DO I = 1, M + IF( A(I, ILACLC).NE.ZERO ) RETURN + END DO + END DO + END IF + RETURN + END diff --git a/lapack/ilaclr.f b/lapack/ilaclr.f new file mode 100644 index 000000000..d8ab09c55 --- /dev/null +++ b/lapack/ilaclr.f @@ -0,0 +1,121 @@ +*> \brief \b ILACLR +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +*> \htmlonly +*> Download ILACLR + dependencies +*> +*> [TGZ] +*> +*> [ZIP] +*> +*> [TXT] +*> \endhtmlonly +* +* Definition: +* =========== +* +* INTEGER FUNCTION ILACLR( M, N, A, LDA ) +* +* .. Scalar Arguments .. +* INTEGER M, N, LDA +* .. +* .. Array Arguments .. +* COMPLEX A( LDA, * ) +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> ILACLR scans A for its last non-zero row. +*> \endverbatim +* +* Arguments: +* ========== +* +*> \param[in] M +*> \verbatim +*> M is INTEGER +*> The number of rows of the matrix A. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> The number of columns of the matrix A. +*> \endverbatim +*> +*> \param[in] A +*> \verbatim +*> A is array, dimension (LDA,N) +*> The m by n matrix A. +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> The leading dimension of the array A. LDA >= max(1,M). +*> \endverbatim +* +* Authors: +* ======== +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date April 2012 +* +*> \ingroup complexOTHERauxiliary +* +* ===================================================================== + INTEGER FUNCTION ILACLR( M, N, A, LDA ) +* +* -- LAPACK auxiliary routine (version 3.4.1) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* April 2012 +* +* .. Scalar Arguments .. + INTEGER M, N, LDA +* .. +* .. Array Arguments .. + COMPLEX A( LDA, * ) +* .. +* +* ===================================================================== +* +* .. Parameters .. + COMPLEX ZERO + PARAMETER ( ZERO = (0.0E+0, 0.0E+0) ) +* .. +* .. Local Scalars .. + INTEGER I, J +* .. +* .. Executable Statements .. +* +* Quick test for the common case where one corner is non-zero. + IF( M.EQ.0 ) THEN + ILACLR = M + ELSE IF( A(M, 1).NE.ZERO .OR. A(M, N).NE.ZERO ) THEN + ILACLR = M + ELSE +* Scan up each column tracking the last zero row seen. + ILACLR = 0 + DO J = 1, N + I=M + DO WHILE((A(MAX(I,1),J).EQ.ZERO).AND.(I.GE.1)) + I=I-1 + ENDDO + ILACLR = MAX( ILACLR, I ) + END DO + END IF + RETURN + END diff --git a/lapack/iladlc.f b/lapack/iladlc.f new file mode 100644 index 000000000..f84bd833a --- /dev/null +++ b/lapack/iladlc.f @@ -0,0 +1,118 @@ +*> \brief \b ILADLC +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +*> \htmlonly +*> Download ILADLC + dependencies +*> +*> [TGZ] +*> +*> [ZIP] +*> +*> [TXT] +*> \endhtmlonly +* +* Definition: +* =========== +* +* INTEGER FUNCTION ILADLC( M, N, A, LDA ) +* +* .. Scalar Arguments .. +* INTEGER M, N, LDA +* .. +* .. Array Arguments .. +* DOUBLE PRECISION A( LDA, * ) +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> ILADLC scans A for its last non-zero column. +*> \endverbatim +* +* Arguments: +* ========== +* +*> \param[in] M +*> \verbatim +*> M is INTEGER +*> The number of rows of the matrix A. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> The number of columns of the matrix A. +*> \endverbatim +*> +*> \param[in] A +*> \verbatim +*> A is DOUBLE PRECISION array, dimension (LDA,N) +*> The m by n matrix A. +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> The leading dimension of the array A. LDA >= max(1,M). +*> \endverbatim +* +* Authors: +* ======== +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup auxOTHERauxiliary +* +* ===================================================================== + INTEGER FUNCTION ILADLC( M, N, A, LDA ) +* +* -- LAPACK auxiliary routine (version 3.4.0) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 +* +* .. Scalar Arguments .. + INTEGER M, N, LDA +* .. +* .. Array Arguments .. + DOUBLE PRECISION A( LDA, * ) +* .. +* +* ===================================================================== +* +* .. Parameters .. + DOUBLE PRECISION ZERO + PARAMETER ( ZERO = 0.0D+0 ) +* .. +* .. Local Scalars .. + INTEGER I +* .. +* .. Executable Statements .. +* +* Quick test for the common case where one corner is non-zero. + IF( N.EQ.0 ) THEN + ILADLC = N + ELSE IF( A(1, N).NE.ZERO .OR. A(M, N).NE.ZERO ) THEN + ILADLC = N + ELSE +* Now scan each column from the end, returning with the first non-zero. + DO ILADLC = N, 1, -1 + DO I = 1, M + IF( A(I, ILADLC).NE.ZERO ) RETURN + END DO + END DO + END IF + RETURN + END diff --git a/lapack/iladlr.f b/lapack/iladlr.f new file mode 100644 index 000000000..2114c6164 --- /dev/null +++ b/lapack/iladlr.f @@ -0,0 +1,121 @@ +*> \brief \b ILADLR +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +*> \htmlonly +*> Download ILADLR + dependencies +*> +*> [TGZ] +*> +*> [ZIP] +*> +*> [TXT] +*> \endhtmlonly +* +* Definition: +* =========== +* +* INTEGER FUNCTION ILADLR( M, N, A, LDA ) +* +* .. Scalar Arguments .. +* INTEGER M, N, LDA +* .. +* .. Array Arguments .. +* DOUBLE PRECISION A( LDA, * ) +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> ILADLR scans A for its last non-zero row. +*> \endverbatim +* +* Arguments: +* ========== +* +*> \param[in] M +*> \verbatim +*> M is INTEGER +*> The number of rows of the matrix A. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> The number of columns of the matrix A. +*> \endverbatim +*> +*> \param[in] A +*> \verbatim +*> A is DOUBLE PRECISION array, dimension (LDA,N) +*> The m by n matrix A. +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> The leading dimension of the array A. LDA >= max(1,M). +*> \endverbatim +* +* Authors: +* ======== +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date April 2012 +* +*> \ingroup auxOTHERauxiliary +* +* ===================================================================== + INTEGER FUNCTION ILADLR( M, N, A, LDA ) +* +* -- LAPACK auxiliary routine (version 3.4.1) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* April 2012 +* +* .. Scalar Arguments .. + INTEGER M, N, LDA +* .. +* .. Array Arguments .. + DOUBLE PRECISION A( LDA, * ) +* .. +* +* ===================================================================== +* +* .. Parameters .. + DOUBLE PRECISION ZERO + PARAMETER ( ZERO = 0.0D+0 ) +* .. +* .. Local Scalars .. + INTEGER I, J +* .. +* .. Executable Statements .. +* +* Quick test for the common case where one corner is non-zero. + IF( M.EQ.0 ) THEN + ILADLR = M + ELSE IF( A(M, 1).NE.ZERO .OR. A(M, N).NE.ZERO ) THEN + ILADLR = M + ELSE +* Scan up each column tracking the last zero row seen. + ILADLR = 0 + DO J = 1, N + I=M + DO WHILE((A(MAX(I,1),J).EQ.ZERO).AND.(I.GE.1)) + I=I-1 + ENDDO + ILADLR = MAX( ILADLR, I ) + END DO + END IF + RETURN + END diff --git a/lapack/ilaslc.f b/lapack/ilaslc.f new file mode 100644 index 000000000..e3db0f4ae --- /dev/null +++ b/lapack/ilaslc.f @@ -0,0 +1,118 @@ +*> \brief \b ILASLC +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +*> \htmlonly +*> Download ILASLC + dependencies +*> +*> [TGZ] +*> +*> [ZIP] +*> +*> [TXT] +*> \endhtmlonly +* +* Definition: +* =========== +* +* INTEGER FUNCTION ILASLC( M, N, A, LDA ) +* +* .. Scalar Arguments .. +* INTEGER M, N, LDA +* .. +* .. Array Arguments .. +* REAL A( LDA, * ) +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> ILASLC scans A for its last non-zero column. +*> \endverbatim +* +* Arguments: +* ========== +* +*> \param[in] M +*> \verbatim +*> M is INTEGER +*> The number of rows of the matrix A. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> The number of columns of the matrix A. +*> \endverbatim +*> +*> \param[in] A +*> \verbatim +*> A is REAL array, dimension (LDA,N) +*> The m by n matrix A. +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> The leading dimension of the array A. LDA >= max(1,M). +*> \endverbatim +* +* Authors: +* ======== +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup realOTHERauxiliary +* +* ===================================================================== + INTEGER FUNCTION ILASLC( M, N, A, LDA ) +* +* -- LAPACK auxiliary routine (version 3.4.0) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 +* +* .. Scalar Arguments .. + INTEGER M, N, LDA +* .. +* .. Array Arguments .. + REAL A( LDA, * ) +* .. +* +* ===================================================================== +* +* .. Parameters .. + REAL ZERO + PARAMETER ( ZERO = 0.0D+0 ) +* .. +* .. Local Scalars .. + INTEGER I +* .. +* .. Executable Statements .. +* +* Quick test for the common case where one corner is non-zero. + IF( N.EQ.0 ) THEN + ILASLC = N + ELSE IF( A(1, N).NE.ZERO .OR. A(M, N).NE.ZERO ) THEN + ILASLC = N + ELSE +* Now scan each column from the end, returning with the first non-zero. + DO ILASLC = N, 1, -1 + DO I = 1, M + IF( A(I, ILASLC).NE.ZERO ) RETURN + END DO + END DO + END IF + RETURN + END diff --git a/lapack/ilaslr.f b/lapack/ilaslr.f new file mode 100644 index 000000000..48b73f44d --- /dev/null +++ b/lapack/ilaslr.f @@ -0,0 +1,121 @@ +*> \brief \b ILASLR +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +*> \htmlonly +*> Download ILASLR + dependencies +*> +*> [TGZ] +*> +*> [ZIP] +*> +*> [TXT] +*> \endhtmlonly +* +* Definition: +* =========== +* +* INTEGER FUNCTION ILASLR( M, N, A, LDA ) +* +* .. Scalar Arguments .. +* INTEGER M, N, LDA +* .. +* .. Array Arguments .. +* REAL A( LDA, * ) +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> ILASLR scans A for its last non-zero row. +*> \endverbatim +* +* Arguments: +* ========== +* +*> \param[in] M +*> \verbatim +*> M is INTEGER +*> The number of rows of the matrix A. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> The number of columns of the matrix A. +*> \endverbatim +*> +*> \param[in] A +*> \verbatim +*> A is REAL array, dimension (LDA,N) +*> The m by n matrix A. +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> The leading dimension of the array A. LDA >= max(1,M). +*> \endverbatim +* +* Authors: +* ======== +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date April 2012 +* +*> \ingroup realOTHERauxiliary +* +* ===================================================================== + INTEGER FUNCTION ILASLR( M, N, A, LDA ) +* +* -- LAPACK auxiliary routine (version 3.4.1) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* April 2012 +* +* .. Scalar Arguments .. + INTEGER M, N, LDA +* .. +* .. Array Arguments .. + REAL A( LDA, * ) +* .. +* +* ===================================================================== +* +* .. Parameters .. + REAL ZERO + PARAMETER ( ZERO = 0.0E+0 ) +* .. +* .. Local Scalars .. + INTEGER I, J +* .. +* .. Executable Statements .. +* +* Quick test for the common case where one corner is non-zero. + IF( M.EQ.0 ) THEN + ILASLR = M + ELSEIF( A(M, 1).NE.ZERO .OR. A(M, N).NE.ZERO ) THEN + ILASLR = M + ELSE +* Scan up each column tracking the last zero row seen. + ILASLR = 0 + DO J = 1, N + I=M + DO WHILE((A(MAX(I,1),J).EQ.ZERO).AND.(I.GE.1)) + I=I-1 + ENDDO + ILASLR = MAX( ILASLR, I ) + END DO + END IF + RETURN + END diff --git a/lapack/ilazlc.f b/lapack/ilazlc.f new file mode 100644 index 000000000..15b149022 --- /dev/null +++ b/lapack/ilazlc.f @@ -0,0 +1,118 @@ +*> \brief \b ILAZLC +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +*> \htmlonly +*> Download ILAZLC + dependencies +*> +*> [TGZ] +*> +*> [ZIP] +*> +*> [TXT] +*> \endhtmlonly +* +* Definition: +* =========== +* +* INTEGER FUNCTION ILAZLC( M, N, A, LDA ) +* +* .. Scalar Arguments .. +* INTEGER M, N, LDA +* .. +* .. Array Arguments .. +* COMPLEX*16 A( LDA, * ) +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> ILAZLC scans A for its last non-zero column. +*> \endverbatim +* +* Arguments: +* ========== +* +*> \param[in] M +*> \verbatim +*> M is INTEGER +*> The number of rows of the matrix A. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> The number of columns of the matrix A. +*> \endverbatim +*> +*> \param[in] A +*> \verbatim +*> A is COMPLEX*16 array, dimension (LDA,N) +*> The m by n matrix A. +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> The leading dimension of the array A. LDA >= max(1,M). +*> \endverbatim +* +* Authors: +* ======== +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup complex16OTHERauxiliary +* +* ===================================================================== + INTEGER FUNCTION ILAZLC( M, N, A, LDA ) +* +* -- LAPACK auxiliary routine (version 3.4.0) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 +* +* .. Scalar Arguments .. + INTEGER M, N, LDA +* .. +* .. Array Arguments .. + COMPLEX*16 A( LDA, * ) +* .. +* +* ===================================================================== +* +* .. Parameters .. + COMPLEX*16 ZERO + PARAMETER ( ZERO = (0.0D+0, 0.0D+0) ) +* .. +* .. Local Scalars .. + INTEGER I +* .. +* .. Executable Statements .. +* +* Quick test for the common case where one corner is non-zero. + IF( N.EQ.0 ) THEN + ILAZLC = N + ELSE IF( A(1, N).NE.ZERO .OR. A(M, N).NE.ZERO ) THEN + ILAZLC = N + ELSE +* Now scan each column from the end, returning with the first non-zero. + DO ILAZLC = N, 1, -1 + DO I = 1, M + IF( A(I, ILAZLC).NE.ZERO ) RETURN + END DO + END DO + END IF + RETURN + END diff --git a/lapack/ilazlr.f b/lapack/ilazlr.f new file mode 100644 index 000000000..b2ab943ca --- /dev/null +++ b/lapack/ilazlr.f @@ -0,0 +1,121 @@ +*> \brief \b ILAZLR +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +*> \htmlonly +*> Download ILAZLR + dependencies +*> +*> [TGZ] +*> +*> [ZIP] +*> +*> [TXT] +*> \endhtmlonly +* +* Definition: +* =========== +* +* INTEGER FUNCTION ILAZLR( M, N, A, LDA ) +* +* .. Scalar Arguments .. +* INTEGER M, N, LDA +* .. +* .. Array Arguments .. +* COMPLEX*16 A( LDA, * ) +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> ILAZLR scans A for its last non-zero row. +*> \endverbatim +* +* Arguments: +* ========== +* +*> \param[in] M +*> \verbatim +*> M is INTEGER +*> The number of rows of the matrix A. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> The number of columns of the matrix A. +*> \endverbatim +*> +*> \param[in] A +*> \verbatim +*> A is COMPLEX*16 array, dimension (LDA,N) +*> The m by n matrix A. +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> The leading dimension of the array A. LDA >= max(1,M). +*> \endverbatim +* +* Authors: +* ======== +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date April 2012 +* +*> \ingroup complex16OTHERauxiliary +* +* ===================================================================== + INTEGER FUNCTION ILAZLR( M, N, A, LDA ) +* +* -- LAPACK auxiliary routine (version 3.4.1) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* April 2012 +* +* .. Scalar Arguments .. + INTEGER M, N, LDA +* .. +* .. Array Arguments .. + COMPLEX*16 A( LDA, * ) +* .. +* +* ===================================================================== +* +* .. Parameters .. + COMPLEX*16 ZERO + PARAMETER ( ZERO = (0.0D+0, 0.0D+0) ) +* .. +* .. Local Scalars .. + INTEGER I, J +* .. +* .. Executable Statements .. +* +* Quick test for the common case where one corner is non-zero. + IF( M.EQ.0 ) THEN + ILAZLR = M + ELSE IF( A(M, 1).NE.ZERO .OR. A(M, N).NE.ZERO ) THEN + ILAZLR = M + ELSE +* Scan up each column tracking the last zero row seen. + ILAZLR = 0 + DO J = 1, N + I=M + DO WHILE((A(MAX(I,1),J).EQ.ZERO).AND.(I.GE.1)) + I=I-1 + ENDDO + ILAZLR = MAX( ILAZLR, I ) + END DO + END IF + RETURN + END diff --git a/lapack/sladiv.f b/lapack/sladiv.f new file mode 100644 index 000000000..da3afa36b --- /dev/null +++ b/lapack/sladiv.f @@ -0,0 +1,128 @@ +*> \brief \b SLADIV +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +*> \htmlonly +*> Download SLADIV + dependencies +*> +*> [TGZ] +*> +*> [ZIP] +*> +*> [TXT] +*> \endhtmlonly +* +* Definition: +* =========== +* +* SUBROUTINE SLADIV( A, B, C, D, P, Q ) +* +* .. Scalar Arguments .. +* REAL A, B, C, D, P, Q +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> SLADIV performs complex division in real arithmetic +*> +*> a + i*b +*> p + i*q = --------- +*> c + i*d +*> +*> The algorithm is due to Robert L. Smith and can be found +*> in D. Knuth, The art of Computer Programming, Vol.2, p.195 +*> \endverbatim +* +* Arguments: +* ========== +* +*> \param[in] A +*> \verbatim +*> A is REAL +*> \endverbatim +*> +*> \param[in] B +*> \verbatim +*> B is REAL +*> \endverbatim +*> +*> \param[in] C +*> \verbatim +*> C is REAL +*> \endverbatim +*> +*> \param[in] D +*> \verbatim +*> D is REAL +*> The scalars a, b, c, and d in the above expression. +*> \endverbatim +*> +*> \param[out] P +*> \verbatim +*> P is REAL +*> \endverbatim +*> +*> \param[out] Q +*> \verbatim +*> Q is REAL +*> The scalars p and q in the above expression. +*> \endverbatim +* +* Authors: +* ======== +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup auxOTHERauxiliary +* +* ===================================================================== + SUBROUTINE SLADIV( A, B, C, D, P, Q ) +* +* -- LAPACK auxiliary routine (version 3.4.0) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 +* +* .. Scalar Arguments .. + REAL A, B, C, D, P, Q +* .. +* +* ===================================================================== +* +* .. Local Scalars .. + REAL E, F +* .. +* .. Intrinsic Functions .. + INTRINSIC ABS +* .. +* .. Executable Statements .. +* + IF( ABS( D ).LT.ABS( C ) ) THEN + E = D / C + F = C + D*E + P = ( A+B*E ) / F + Q = ( B-A*E ) / F + ELSE + E = C / D + F = D + C*E + P = ( B+A*E ) / F + Q = ( -A+B*E ) / F + END IF +* + RETURN +* +* End of SLADIV +* + END diff --git a/lapack/slamch.f b/lapack/slamch.f new file mode 100644 index 000000000..4bffad0eb --- /dev/null +++ b/lapack/slamch.f @@ -0,0 +1,192 @@ +*> \brief \b SLAMCH +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +* Definition: +* =========== +* +* REAL FUNCTION SLAMCH( CMACH ) +* +* .. Scalar Arguments .. +* CHARACTER CMACH +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> SLAMCH determines single precision machine parameters. +*> \endverbatim +* +* Arguments: +* ========== +* +*> \param[in] CMACH +*> \verbatim +*> Specifies the value to be returned by SLAMCH: +*> = 'E' or 'e', SLAMCH := eps +*> = 'S' or 's , SLAMCH := sfmin +*> = 'B' or 'b', SLAMCH := base +*> = 'P' or 'p', SLAMCH := eps*base +*> = 'N' or 'n', SLAMCH := t +*> = 'R' or 'r', SLAMCH := rnd +*> = 'M' or 'm', SLAMCH := emin +*> = 'U' or 'u', SLAMCH := rmin +*> = 'L' or 'l', SLAMCH := emax +*> = 'O' or 'o', SLAMCH := rmax +*> where +*> eps = relative machine precision +*> sfmin = safe minimum, such that 1/sfmin does not overflow +*> base = base of the machine +*> prec = eps*base +*> t = number of (base) digits in the mantissa +*> rnd = 1.0 when rounding occurs in addition, 0.0 otherwise +*> emin = minimum exponent before (gradual) underflow +*> rmin = underflow threshold - base**(emin-1) +*> emax = largest exponent before overflow +*> rmax = overflow threshold - (base**emax)*(1-eps) +*> \endverbatim +* +* Authors: +* ======== +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup auxOTHERauxiliary +* +* ===================================================================== + REAL FUNCTION SLAMCH( CMACH ) +* +* -- LAPACK auxiliary routine (version 3.4.0) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 +* +* .. Scalar Arguments .. + CHARACTER CMACH +* .. +* +* ===================================================================== +* +* .. Parameters .. + REAL ONE, ZERO + PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 ) +* .. +* .. Local Scalars .. + REAL RND, EPS, SFMIN, SMALL, RMACH +* .. +* .. External Functions .. + LOGICAL LSAME + EXTERNAL LSAME +* .. +* .. Intrinsic Functions .. + INTRINSIC DIGITS, EPSILON, HUGE, MAXEXPONENT, + $ MINEXPONENT, RADIX, TINY +* .. +* .. Executable Statements .. +* +* +* Assume rounding, not chopping. Always. +* + RND = ONE +* + IF( ONE.EQ.RND ) THEN + EPS = EPSILON(ZERO) * 0.5 + ELSE + EPS = EPSILON(ZERO) + END IF +* + IF( LSAME( CMACH, 'E' ) ) THEN + RMACH = EPS + ELSE IF( LSAME( CMACH, 'S' ) ) THEN + SFMIN = TINY(ZERO) + SMALL = ONE / HUGE(ZERO) + IF( SMALL.GE.SFMIN ) THEN +* +* Use SMALL plus a bit, to avoid the possibility of rounding +* causing overflow when computing 1/sfmin. +* + SFMIN = SMALL*( ONE+EPS ) + END IF + RMACH = SFMIN + ELSE IF( LSAME( CMACH, 'B' ) ) THEN + RMACH = RADIX(ZERO) + ELSE IF( LSAME( CMACH, 'P' ) ) THEN + RMACH = EPS * RADIX(ZERO) + ELSE IF( LSAME( CMACH, 'N' ) ) THEN + RMACH = DIGITS(ZERO) + ELSE IF( LSAME( CMACH, 'R' ) ) THEN + RMACH = RND + ELSE IF( LSAME( CMACH, 'M' ) ) THEN + RMACH = MINEXPONENT(ZERO) + ELSE IF( LSAME( CMACH, 'U' ) ) THEN + RMACH = tiny(zero) + ELSE IF( LSAME( CMACH, 'L' ) ) THEN + RMACH = MAXEXPONENT(ZERO) + ELSE IF( LSAME( CMACH, 'O' ) ) THEN + RMACH = HUGE(ZERO) + ELSE + RMACH = ZERO + END IF +* + SLAMCH = RMACH + RETURN +* +* End of SLAMCH +* + END +************************************************************************ +*> \brief \b SLAMC3 +*> \details +*> \b Purpose: +*> \verbatim +*> SLAMC3 is intended to force A and B to be stored prior to doing +*> the addition of A and B , for use in situations where optimizers +*> might hold one of these in a register. +*> \endverbatim +*> \author LAPACK is a software package provided by Univ. of Tennessee, Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd.. +*> \date November 2011 +*> \ingroup auxOTHERauxiliary +*> +*> \param[in] A +*> \verbatim +*> \endverbatim +*> +*> \param[in] B +*> \verbatim +*> The values A and B. +*> \endverbatim +*> +* + REAL FUNCTION SLAMC3( A, B ) +* +* -- LAPACK auxiliary routine (version 3.4.0) -- +* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. +* November 2010 +* +* .. Scalar Arguments .. + REAL A, B +* .. +* ===================================================================== +* +* .. Executable Statements .. +* + SLAMC3 = A + B +* + RETURN +* +* End of SLAMC3 +* + END +* +************************************************************************ diff --git a/lapack/slapy2.f b/lapack/slapy2.f new file mode 100644 index 000000000..1f6b1ca4f --- /dev/null +++ b/lapack/slapy2.f @@ -0,0 +1,104 @@ +*> \brief \b SLAPY2 +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +*> \htmlonly +*> Download SLAPY2 + dependencies +*> +*> [TGZ] +*> +*> [ZIP] +*> +*> [TXT] +*> \endhtmlonly +* +* Definition: +* =========== +* +* REAL FUNCTION SLAPY2( X, Y ) +* +* .. Scalar Arguments .. +* REAL X, Y +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> SLAPY2 returns sqrt(x**2+y**2), taking care not to cause unnecessary +*> overflow. +*> \endverbatim +* +* Arguments: +* ========== +* +*> \param[in] X +*> \verbatim +*> X is REAL +*> \endverbatim +*> +*> \param[in] Y +*> \verbatim +*> Y is REAL +*> X and Y specify the values x and y. +*> \endverbatim +* +* Authors: +* ======== +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup auxOTHERauxiliary +* +* ===================================================================== + REAL FUNCTION SLAPY2( X, Y ) +* +* -- LAPACK auxiliary routine (version 3.4.0) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 +* +* .. Scalar Arguments .. + REAL X, Y +* .. +* +* ===================================================================== +* +* .. Parameters .. + REAL ZERO + PARAMETER ( ZERO = 0.0E0 ) + REAL ONE + PARAMETER ( ONE = 1.0E0 ) +* .. +* .. Local Scalars .. + REAL W, XABS, YABS, Z +* .. +* .. Intrinsic Functions .. + INTRINSIC ABS, MAX, MIN, SQRT +* .. +* .. Executable Statements .. +* + XABS = ABS( X ) + YABS = ABS( Y ) + W = MAX( XABS, YABS ) + Z = MIN( XABS, YABS ) + IF( Z.EQ.ZERO ) THEN + SLAPY2 = W + ELSE + SLAPY2 = W*SQRT( ONE+( Z / W )**2 ) + END IF + RETURN +* +* End of SLAPY2 +* + END diff --git a/lapack/slapy3.f b/lapack/slapy3.f new file mode 100644 index 000000000..aa2f5bfc4 --- /dev/null +++ b/lapack/slapy3.f @@ -0,0 +1,111 @@ +*> \brief \b SLAPY3 +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +*> \htmlonly +*> Download SLAPY3 + dependencies +*> +*> [TGZ] +*> +*> [ZIP] +*> +*> [TXT] +*> \endhtmlonly +* +* Definition: +* =========== +* +* REAL FUNCTION SLAPY3( X, Y, Z ) +* +* .. Scalar Arguments .. +* REAL X, Y, Z +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> SLAPY3 returns sqrt(x**2+y**2+z**2), taking care not to cause +*> unnecessary overflow. +*> \endverbatim +* +* Arguments: +* ========== +* +*> \param[in] X +*> \verbatim +*> X is REAL +*> \endverbatim +*> +*> \param[in] Y +*> \verbatim +*> Y is REAL +*> \endverbatim +*> +*> \param[in] Z +*> \verbatim +*> Z is REAL +*> X, Y and Z specify the values x, y and z. +*> \endverbatim +* +* Authors: +* ======== +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup auxOTHERauxiliary +* +* ===================================================================== + REAL FUNCTION SLAPY3( X, Y, Z ) +* +* -- LAPACK auxiliary routine (version 3.4.0) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 +* +* .. Scalar Arguments .. + REAL X, Y, Z +* .. +* +* ===================================================================== +* +* .. Parameters .. + REAL ZERO + PARAMETER ( ZERO = 0.0E0 ) +* .. +* .. Local Scalars .. + REAL W, XABS, YABS, ZABS +* .. +* .. Intrinsic Functions .. + INTRINSIC ABS, MAX, SQRT +* .. +* .. Executable Statements .. +* + XABS = ABS( X ) + YABS = ABS( Y ) + ZABS = ABS( Z ) + W = MAX( XABS, YABS, ZABS ) + IF( W.EQ.ZERO ) THEN +* W can be zero for max(0,nan,0) +* adding all three entries together will make sure +* NaN will not disappear. + SLAPY3 = XABS + YABS + ZABS + ELSE + SLAPY3 = W*SQRT( ( XABS / W )**2+( YABS / W )**2+ + $ ( ZABS / W )**2 ) + END IF + RETURN +* +* End of SLAPY3 +* + END diff --git a/lapack/zlacgv.f b/lapack/zlacgv.f new file mode 100644 index 000000000..16c2e2ed9 --- /dev/null +++ b/lapack/zlacgv.f @@ -0,0 +1,116 @@ +*> \brief \b ZLACGV +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +*> \htmlonly +*> Download ZLACGV + dependencies +*> +*> [TGZ] +*> +*> [ZIP] +*> +*> [TXT] +*> \endhtmlonly +* +* Definition: +* =========== +* +* SUBROUTINE ZLACGV( N, X, INCX ) +* +* .. Scalar Arguments .. +* INTEGER INCX, N +* .. +* .. Array Arguments .. +* COMPLEX*16 X( * ) +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> ZLACGV conjugates a complex vector of length N. +*> \endverbatim +* +* Arguments: +* ========== +* +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> The length of the vector X. N >= 0. +*> \endverbatim +*> +*> \param[in,out] X +*> \verbatim +*> X is COMPLEX*16 array, dimension +*> (1+(N-1)*abs(INCX)) +*> On entry, the vector of length N to be conjugated. +*> On exit, X is overwritten with conjg(X). +*> \endverbatim +*> +*> \param[in] INCX +*> \verbatim +*> INCX is INTEGER +*> The spacing between successive elements of X. +*> \endverbatim +* +* Authors: +* ======== +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup complex16OTHERauxiliary +* +* ===================================================================== + SUBROUTINE ZLACGV( N, X, INCX ) +* +* -- LAPACK auxiliary routine (version 3.4.0) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 +* +* .. Scalar Arguments .. + INTEGER INCX, N +* .. +* .. Array Arguments .. + COMPLEX*16 X( * ) +* .. +* +* ===================================================================== +* +* .. Local Scalars .. + INTEGER I, IOFF +* .. +* .. Intrinsic Functions .. + INTRINSIC DCONJG +* .. +* .. Executable Statements .. +* + IF( INCX.EQ.1 ) THEN + DO 10 I = 1, N + X( I ) = DCONJG( X( I ) ) + 10 CONTINUE + ELSE + IOFF = 1 + IF( INCX.LT.0 ) + $ IOFF = 1 - ( N-1 )*INCX + DO 20 I = 1, N + X( IOFF ) = DCONJG( X( IOFF ) ) + IOFF = IOFF + INCX + 20 CONTINUE + END IF + RETURN +* +* End of ZLACGV +* + END diff --git a/lapack/zladiv.f b/lapack/zladiv.f new file mode 100644 index 000000000..aa71db14a --- /dev/null +++ b/lapack/zladiv.f @@ -0,0 +1,97 @@ +*> \brief \b ZLADIV +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +*> \htmlonly +*> Download ZLADIV + dependencies +*> +*> [TGZ] +*> +*> [ZIP] +*> +*> [TXT] +*> \endhtmlonly +* +* Definition: +* =========== +* +* COMPLEX*16 FUNCTION ZLADIV( X, Y ) +* +* .. Scalar Arguments .. +* COMPLEX*16 X, Y +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> ZLADIV := X / Y, where X and Y are complex. The computation of X / Y +*> will not overflow on an intermediary step unless the results +*> overflows. +*> \endverbatim +* +* Arguments: +* ========== +* +*> \param[in] X +*> \verbatim +*> X is COMPLEX*16 +*> \endverbatim +*> +*> \param[in] Y +*> \verbatim +*> Y is COMPLEX*16 +*> The complex scalars X and Y. +*> \endverbatim +* +* Authors: +* ======== +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup complex16OTHERauxiliary +* +* ===================================================================== + COMPLEX*16 FUNCTION ZLADIV( X, Y ) +* +* -- LAPACK auxiliary routine (version 3.4.0) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 +* +* .. Scalar Arguments .. + COMPLEX*16 X, Y +* .. +* +* ===================================================================== +* +* .. Local Scalars .. + DOUBLE PRECISION ZI, ZR +* .. +* .. External Subroutines .. + EXTERNAL DLADIV +* .. +* .. Intrinsic Functions .. + INTRINSIC DBLE, DCMPLX, DIMAG +* .. +* .. Executable Statements .. +* + CALL DLADIV( DBLE( X ), DIMAG( X ), DBLE( Y ), DIMAG( Y ), ZR, + $ ZI ) + ZLADIV = DCMPLX( ZR, ZI ) +* + RETURN +* +* End of ZLADIV +* + END -- cgit v1.2.3