kopia lustrzana https://github.com/Dsplib/libdspl-2.0
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dspl/src/dft/fft_create.c modified: dspl/src/dft/fft_free.c modified: dspl/src/dft/fft_krn.c modified: dspl/src/dft/fft_mag.c modified: dspl/src/dft/fft_mag_cmplx.c modified: dspl/src/dft/fft_shift.c modified: dspl/src/dft/fft_shift_cmplx.c modified: dspl/src/dft/fft_subkernel.c modified: dspl/src/dft/fourier_integral_cmplx.c modified: dspl/src/dft/fourier_series_dec.c modified: dspl/src/dft/fourier_series_dec_cmplx.c modified: dspl/src/dft/fourier_series_rec.c modified: dspl/src/dft/goertzel.c modified: dspl/src/dft/goertzel_cmplx.c modified: dspl/src/dft/idft_cmplx.c modified: dspl/src/dft/ifft_cmplx.c deleted: dspl/src/dspl_internal.h modified: dspl/src/filter_design.c modified: dspl/src/filter_design/bilinear.c modified: dspl/src/filter_design/butter_ap.c modified: dspl/src/filter_design/butter_ap_zp.c modified: dspl/src/filter_design/cheby1_ap.c modified: dspl/src/filter_design/cheby1_ap_zp.c modified: dspl/src/filter_design/cheby2_ap.c modified: dspl/src/filter_design/cheby2_ap_wp1.c modified: dspl/src/filter_design/cheby2_ap_zp.c modified: dspl/src/filter_design/ellip_ap.c modified: dspl/src/filter_design/ellip_ap_zp.c new file: dspl/src/filter_design/filter_design.h modified: dspl/src/filter_design/filter_freq_resp.c modified: dspl/src/filter_design/filter_ws1.c modified: dspl/src/filter_design/filter_zp2ab.c modified: dspl/src/filter_design/fir_linphase.c deleted: dspl/src/filter_design/fir_linphase_lpf.c modified: dspl/src/filter_design/freqs.c modified: dspl/src/filter_design/freqs2time.c modified: dspl/src/filter_design/freqs_cmplx.c modified: dspl/src/filter_design/freqz.c modified: dspl/src/filter_design/group_delay.c modified: dspl/src/filter_design/iir.c deleted: dspl/src/filter_design/iir_ap.c modified: dspl/src/filter_design/low2bp.c modified: dspl/src/filter_design/low2bs.c modified: dspl/src/filter_design/low2high.c modified: dspl/src/filter_design/low2low.c modified: dspl/src/filter_design/phase_delay.c modified: dspl/src/filter_design/ratcompos.c renamed: dspl/src/win.c -> dspl/src/filter_design/win.c modified: dspl/src/gnuplot.c new file: dspl/src/gnuplot/gnuplot.h new file: dspl/src/gnuplot/gnuplot_close.c new file: dspl/src/gnuplot/gnuplot_cmd.c new file: dspl/src/gnuplot/gnuplot_create.c new file: dspl/src/gnuplot/gnuplot_open.c modified: dspl/src/inout.c new file: dspl/src/inout/addlog.c new file: dspl/src/inout/dspl_info.c new file: dspl/src/inout/readbin.c new file: dspl/src/inout/verif_data_gen.c new file: dspl/src/inout/verif_str.c new file: dspl/src/inout/verif_str_cmplx.c new file: dspl/src/inout/writebin.c new file: dspl/src/inout/writetxt.c new file: dspl/src/inout/writetxt_3d.c new file: dspl/src/inout/writetxt_3dline.c new file: dspl/src/inout/writetxt_cmplx.c new file: dspl/src/inout/writetxt_cmplx_im.c new file: dspl/src/inout/writetxt_cmplx_re.c new file: dspl/src/inout/writetxt_int.c deleted: dspl/src/math.c modified: dspl/src/math_ellipj/ellip_acd.c modified: dspl/src/math_ellipj/ellip_acd_cmplx.c modified: dspl/src/math_ellipj/ellip_asn.c modified: dspl/src/math_ellipj/ellip_asn_cmplx.c modified: dspl/src/math_ellipj/ellip_cd.c modified: dspl/src/math_ellipj/ellip_cd_cmplx.c modified: dspl/src/math_ellipj/ellip_landen.c modified: dspl/src/math_ellipj/ellip_modulareq.c modified: dspl/src/math_ellipj/ellip_rat.c modified: dspl/src/math_ellipj/ellip_sn.c modified: dspl/src/math_ellipj/ellip_sn_cmplx.c new file: dspl/src/math_matrix.c renamed: dspl/src/blas.h -> dspl/src/math_matrix/blas.h new file: dspl/src/math_matrix/matrix_eig_cmplx.c new file: dspl/src/math_matrix/matrix_eye.c new file: dspl/src/math_matrix/matrix_eye_cmplx.c new file: dspl/src/math_matrix/matrix_mul.c new file: dspl/src/math_matrix/matrix_pinv.c new file: dspl/src/math_matrix/matrix_print.c new file: dspl/src/math_matrix/matrix_print_cmplx.c new file: dspl/src/math_matrix/matrix_svd.c new file: dspl/src/math_matrix/matrix_transpose.c new file: dspl/src/math_matrix/matrix_transpose_cmplx.c new file: dspl/src/math_matrix/matrix_transpose_hermite.c new file: dspl/src/math_matrix/vector_dot.c modified: dspl/src/math_poly/cheby_poly1.c modified: dspl/src/math_poly/cheby_poly2.c modified: dspl/src/math_poly/poly_z2a_cmplx.c modified: dspl/src/math_poly/polyroots.c modified: dspl/src/math_poly/polyval.c modified: dspl/src/math_poly/polyval_cmplx.c new file: dspl/src/math_stat.c new file: dspl/src/math_stat/find_max_abs.c new file: dspl/src/math_stat/histogram.c new file: dspl/src/math_stat/histogram_norm.c new file: dspl/src/math_stat/mean.c new file: dspl/src/math_stat/mean_cmplx.c new file: dspl/src/math_stat/minmax.c new file: dspl/src/math_stat/stat_std.c new file: dspl/src/math_stat/stat_std_cmplx.c renamed: dspl/src/xcorr.c -> dspl/src/math_stat/xcorr.c new file: dspl/src/math_std.c new file: dspl/src/math_std/acos_cmplx.c new file: dspl/src/math_std/asin_cmplx.c new file: dspl/src/math_std/bessel_i0.c new file: dspl/src/math_std/cos_cmplx.c new file: dspl/src/math_std/dmod.c new file: dspl/src/math_std/log_cmplx.c new file: dspl/src/math_std/sin_cmplx.c new file: dspl/src/math_std/sinc.c new file: dspl/src/math_std/sine_int.c new file: dspl/src/math_std/sqrt_cmplx.c new file: dspl/src/math_std/trapint.c renamed: dspl/src/trapint.c -> dspl/src/math_std/trapint_cmplx.c renamed: dspl/src/unwrap.c -> dspl/src/math_std/unwrap.c deleted: dspl/src/matrix.c modified: dspl/src/psd.c new file: dspl/src/psd/psd_bartlett.c new file: dspl/src/psd/psd_bartlett_cmplx.c new file: dspl/src/psd/psd_periodogram.c new file: dspl/src/psd/psd_periodogram_cmplx.c new file: dspl/src/psd/psd_welch.c new file: dspl/src/psd/psd_welch_cmplx.c deleted: dspl/src/randgen.c new file: dspl/src/randomgen.c renamed: dspl/src/mt19937.c -> dspl/src/randomgen/mt19937.c new file: dspl/src/randomgen/mt19937.h new file: dspl/src/randomgen/randb.c new file: dspl/src/randomgen/randb2.c new file: dspl/src/randomgen/randi.c new file: dspl/src/randomgen/randn.c new file: dspl/src/randomgen/randn_cmplx.c new file: dspl/src/randomgen/random_init.c renamed: dspl/src/mt19937.h -> dspl/src/randomgen/randomgen.h new file: dspl/src/randomgen/randu.c new file: dspl/src/randomgen/randu_mrg32k3a.c modified: dspl/src/resampling.c new file: dspl/src/resampling/farrow_lagrange.c new file: dspl/src/resampling/farrow_spline.c modified: dspl/src/signals.c new file: dspl/src/signals/signal_pimp.c new file: dspl/src/signals/signal_saw.c deleted: dspl/src/statistic.c modified: dspl/src/types/cmplx2re.c modified: dspl/src/types/re2cmplx.c deleted: dspl/src/verification.c modified: examples/src/butter_ap_test.c modified: examples/src/iir_test.c new file: examples/src/matrix_eig.c.save new file: examples/src/readbin_test.c new file: examples/src/resampling_block.c modified: include/dspl.c modified: include/dspl.h modified: verification/src/fft_radix2_verification.c modified: verification/src/fft_verification.c modified: verification/src/statistic_verification.c modified: verification/src/writebin_readbin_verification.cmaster 22.01.01
Dsplib
rodzic
945a7fd417
commit
815c56b41b
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@ -1,5 +1,5 @@
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/*
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* Copyright (c) 2015-2020 Sergey Bakhurin
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* Copyright (c) 2015-2022 Sergey Bakhurin
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* Digital Signal Processing Library [http://dsplib.org]
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*
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* This file is part of libdspl-2.0.
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@ -18,6 +18,7 @@
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* along with Foobar. If not, see <http://www.gnu.org/licenses/>.
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*/
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#ifdef WIN_OS
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@ -1,5 +1,5 @@
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/*
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* Copyright (c) 2015-2020 Sergey Bakhurin
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* Copyright (c) 2015-2022 Sergey Bakhurin
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* Digital Signal Processing Library [http://dsplib.org]
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*
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* This file is part of libdspl-2.0.
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@ -1482,7 +1482,8 @@ DECLARE_FUNC(int, re2cmplx, double*
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/*----------------------------------------------------------------------------*/
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DECLARE_FUNC(int, readbin, char* fn
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COMMA void** x
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COMMA int* k
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COMMA int* pn
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COMMA int* pm
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COMMA int* dtype);
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/*----------------------------------------------------------------------------*/
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DECLARE_FUNC(int, signal_pimp, double*
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@ -1587,6 +1588,7 @@ DECLARE_FUNC(int, window, double* w
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COMMA double param);
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/*----------------------------------------------------------------------------*/
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DECLARE_FUNC(int, writebin, void*
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COMMA int
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COMMA int
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COMMA int
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COMMA char*);
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@ -19,6 +19,8 @@ all: $(RELEASE_DIR)/$(LIB_NAME)\
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$(RELEASE_DIR)/$(LIB_NAME): $(DSPL_OBJ_FILES) $(BLAS_LIB_NAME) $(LAPACK_DOUBLE_LIB_NAME) $(LAPACK_COMPLEX_LIB_NAME)
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$(CC) -shared -o $(RELEASE_DIR)/$(LIB_NAME) $(DSPL_OBJ_FILES) -lm -L$(LAPACK_RELEASE_DIR) -llapack_complex -llapack_double -L$(BLAS_RELEASE_DIR) -lblas -lgfortran -lquadmath
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#Compile libdspl obj files from c sources
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$(DSPL_OBJ_DIR)/%.o:$(DSPL_SRC_DIR)/%.c
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$(CC) $(CFLAGS) $< -o $@ -lm
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@ -21,20 +21,24 @@ BLASLIB = bin/libblas.a
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BLAS_OBJ_DIR = obj
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# DSPL src and obj files list
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BLAS_SRC_FILES = $(wildcard src/*.f)
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BLAS_OBJ_FILES = $(addprefix $(BLAS_OBJ_DIR)/,$(notdir $(BLAS_SRC_FILES:.f=.o)))
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BLAS_SRC_FILES = $(wildcard src/*.f)
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BLAS90_SRC_FILES = $(wildcard src/*.f90)
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BLAS_OBJ_FILES = $(addprefix $(BLAS_OBJ_DIR)/,$(notdir $(BLAS_SRC_FILES:.f=.o)))
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BLAS90_OBJ_FILES = $(addprefix $(BLAS_OBJ_DIR)/,$(notdir $(BLAS90_SRC_FILES:.f90=.o)))
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all: $(BLASLIB)
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$(BLASLIB): $(BLAS_OBJ_FILES)
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$(ARCH) $(ARCHFLAGS) $@ $(BLAS_OBJ_FILES)
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$(BLASLIB): $(BLAS_OBJ_FILES) $(BLAS90_OBJ_FILES)
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$(ARCH) $(ARCHFLAGS) $@ $(BLAS_OBJ_FILES) $(BLAS90_OBJ_FILES)
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$(RANLIB) $@
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$(BLAS_OBJ_DIR)/%.o:src/%.f
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$(FORTRAN) $(OPTS) -c $< -o $@
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$(BLAS_OBJ_DIR)/%.o:src/%.f90
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$(FORTRAN) $(OPTS) -c $< -o $@
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clean:
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rm -f $(BLAS_OBJ_DIR)/*.o
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@ -72,8 +72,6 @@
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*> \author Univ. of Colorado Denver
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*> \author NAG Ltd.
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*
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*> \date November 2017
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*
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*> \ingroup complex_blas_level1
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*
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*> \par Further Details:
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@ -88,10 +86,9 @@
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* =====================================================================
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SUBROUTINE CAXPY(N,CA,CX,INCX,CY,INCY)
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*
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* -- Reference BLAS level1 routine (version 3.8.0) --
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* -- Reference BLAS level1 routine --
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* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
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* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
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* November 2017
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*
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* .. Scalar Arguments ..
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COMPLEX CA
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@ -136,4 +133,7 @@
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END IF
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*
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RETURN
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*
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* End of CAXPY
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*
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END
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@ -65,8 +65,6 @@
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*> \author Univ. of Colorado Denver
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*> \author NAG Ltd.
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*
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*> \date November 2017
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*
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*> \ingroup complex_blas_level1
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*
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*> \par Further Details:
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@ -81,10 +79,9 @@
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* =====================================================================
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SUBROUTINE CCOPY(N,CX,INCX,CY,INCY)
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*
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* -- Reference BLAS level1 routine (version 3.8.0) --
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* -- Reference BLAS level1 routine --
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* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
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* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
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* November 2017
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*
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* .. Scalar Arguments ..
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INTEGER INCX,INCY,N
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END DO
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END IF
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RETURN
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*
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* End of CCOPY
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*
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END
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*>
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*> \param[in] CX
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*> \verbatim
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*> CX is REAL array, dimension ( 1 + ( N - 1 )*abs( INCX ) )
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*> CX is COMPLEX array, dimension ( 1 + ( N - 1 )*abs( INCX ) )
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*> \endverbatim
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*>
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*> \param[in] INCX
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*>
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*> \param[in] CY
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*> \verbatim
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*> CY is REAL array, dimension ( 1 + ( N - 1 )*abs( INCY ) )
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*> CY is COMPLEX array, dimension ( 1 + ( N - 1 )*abs( INCY ) )
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*> \endverbatim
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*>
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*> \param[in] INCY
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*> \author Univ. of Colorado Denver
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*> \author NAG Ltd.
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*
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*> \date November 2017
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*
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*> \ingroup complex_blas_level1
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*
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*> \par Further Details:
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* =====================================================================
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COMPLEX FUNCTION CDOTC(N,CX,INCX,CY,INCY)
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*
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* -- Reference BLAS level1 routine (version 3.8.0) --
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* -- Reference BLAS level1 routine --
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* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
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* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
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* November 2017
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*
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* .. Scalar Arguments ..
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INTEGER INCX,INCY,N
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END IF
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CDOTC = CTEMP
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RETURN
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*
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* End of CDOTC
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*
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END
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*>
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*> \param[in] CX
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*> \verbatim
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*> CX is REAL array, dimension ( 1 + ( N - 1 )*abs( INCX ) )
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*> CX is COMPLEX array, dimension ( 1 + ( N - 1 )*abs( INCX ) )
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*> \endverbatim
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*>
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*> \param[in] INCX
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*>
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*> \param[in] CY
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*> \verbatim
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*> CY is REAL array, dimension ( 1 + ( N - 1 )*abs( INCY ) )
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*> CY is COMPLEX array, dimension ( 1 + ( N - 1 )*abs( INCY ) )
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*> \endverbatim
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*>
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*> \param[in] INCY
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*> \author Univ. of Colorado Denver
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*> \author NAG Ltd.
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*
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*> \date November 2017
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*
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*> \ingroup complex_blas_level1
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*
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*> \par Further Details:
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* =====================================================================
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COMPLEX FUNCTION CDOTU(N,CX,INCX,CY,INCY)
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*
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* -- Reference BLAS level1 routine (version 3.8.0) --
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* -- Reference BLAS level1 routine --
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* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
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* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
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* November 2017
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*
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* .. Scalar Arguments ..
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INTEGER INCX,INCY,N
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END IF
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CDOTU = CTEMP
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RETURN
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*
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* End of CDOTU
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*
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END
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*> \author Univ. of Colorado Denver
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*> \author NAG Ltd.
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*
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*> \date December 2016
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*
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*> \ingroup complex_blas_level2
|
||||
*
|
||||
*> \par Further Details:
|
||||
|
|
@ -187,10 +185,9 @@
|
|||
* =====================================================================
|
||||
SUBROUTINE CGBMV(TRANS,M,N,KL,KU,ALPHA,A,LDA,X,INCX,BETA,Y,INCY)
|
||||
*
|
||||
* -- Reference BLAS level2 routine (version 3.7.0) --
|
||||
* -- Reference BLAS level2 routine --
|
||||
* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
|
||||
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
|
||||
* December 2016
|
||||
*
|
||||
* .. Scalar Arguments ..
|
||||
COMPLEX ALPHA,BETA
|
||||
|
|
@ -385,6 +382,6 @@
|
|||
*
|
||||
RETURN
|
||||
*
|
||||
* End of CGBMV .
|
||||
* End of CGBMV
|
||||
*
|
||||
END
|
||||
|
|
|
|||
|
|
@ -166,8 +166,6 @@
|
|||
*> \author Univ. of Colorado Denver
|
||||
*> \author NAG Ltd.
|
||||
*
|
||||
*> \date December 2016
|
||||
*
|
||||
*> \ingroup complex_blas_level3
|
||||
*
|
||||
*> \par Further Details:
|
||||
|
|
@ -187,10 +185,9 @@
|
|||
* =====================================================================
|
||||
SUBROUTINE CGEMM(TRANSA,TRANSB,M,N,K,ALPHA,A,LDA,B,LDB,BETA,C,LDC)
|
||||
*
|
||||
* -- Reference BLAS level3 routine (version 3.7.0) --
|
||||
* -- Reference BLAS level3 routine --
|
||||
* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
|
||||
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
|
||||
* December 2016
|
||||
*
|
||||
* .. Scalar Arguments ..
|
||||
COMPLEX ALPHA,BETA
|
||||
|
|
@ -215,7 +212,7 @@
|
|||
* ..
|
||||
* .. Local Scalars ..
|
||||
COMPLEX TEMP
|
||||
INTEGER I,INFO,J,L,NCOLA,NROWA,NROWB
|
||||
INTEGER I,INFO,J,L,NROWA,NROWB
|
||||
LOGICAL CONJA,CONJB,NOTA,NOTB
|
||||
* ..
|
||||
* .. Parameters ..
|
||||
|
|
@ -228,8 +225,7 @@
|
|||
* Set NOTA and NOTB as true if A and B respectively are not
|
||||
* conjugated or transposed, set CONJA and CONJB as true if A and
|
||||
* B respectively are to be transposed but not conjugated and set
|
||||
* NROWA, NCOLA and NROWB as the number of rows and columns of A
|
||||
* and the number of rows of B respectively.
|
||||
* NROWA and NROWB as the number of rows of A and B respectively.
|
||||
*
|
||||
NOTA = LSAME(TRANSA,'N')
|
||||
NOTB = LSAME(TRANSB,'N')
|
||||
|
|
@ -237,10 +233,8 @@
|
|||
CONJB = LSAME(TRANSB,'C')
|
||||
IF (NOTA) THEN
|
||||
NROWA = M
|
||||
NCOLA = K
|
||||
ELSE
|
||||
NROWA = K
|
||||
NCOLA = M
|
||||
END IF
|
||||
IF (NOTB) THEN
|
||||
NROWB = K
|
||||
|
|
@ -478,6 +472,6 @@
|
|||
*
|
||||
RETURN
|
||||
*
|
||||
* End of CGEMM .
|
||||
* End of CGEMM
|
||||
*
|
||||
END
|
||||
|
|
|
|||
|
|
@ -136,8 +136,6 @@
|
|||
*> \author Univ. of Colorado Denver
|
||||
*> \author NAG Ltd.
|
||||
*
|
||||
*> \date December 2016
|
||||
*
|
||||
*> \ingroup complex_blas_level2
|
||||
*
|
||||
*> \par Further Details:
|
||||
|
|
@ -158,10 +156,9 @@
|
|||
* =====================================================================
|
||||
SUBROUTINE CGEMV(TRANS,M,N,ALPHA,A,LDA,X,INCX,BETA,Y,INCY)
|
||||
*
|
||||
* -- Reference BLAS level2 routine (version 3.7.0) --
|
||||
* -- Reference BLAS level2 routine --
|
||||
* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
|
||||
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
|
||||
* December 2016
|
||||
*
|
||||
* .. Scalar Arguments ..
|
||||
COMPLEX ALPHA,BETA
|
||||
|
|
@ -345,6 +342,6 @@
|
|||
*
|
||||
RETURN
|
||||
*
|
||||
* End of CGEMV .
|
||||
* End of CGEMV
|
||||
*
|
||||
END
|
||||
|
|
|
|||
|
|
@ -109,8 +109,6 @@
|
|||
*> \author Univ. of Colorado Denver
|
||||
*> \author NAG Ltd.
|
||||
*
|
||||
*> \date December 2016
|
||||
*
|
||||
*> \ingroup complex_blas_level2
|
||||
*
|
||||
*> \par Further Details:
|
||||
|
|
@ -130,10 +128,9 @@
|
|||
* =====================================================================
|
||||
SUBROUTINE CGERC(M,N,ALPHA,X,INCX,Y,INCY,A,LDA)
|
||||
*
|
||||
* -- Reference BLAS level2 routine (version 3.7.0) --
|
||||
* -- Reference BLAS level2 routine --
|
||||
* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
|
||||
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
|
||||
* December 2016
|
||||
*
|
||||
* .. Scalar Arguments ..
|
||||
COMPLEX ALPHA
|
||||
|
|
@ -222,6 +219,6 @@
|
|||
*
|
||||
RETURN
|
||||
*
|
||||
* End of CGERC .
|
||||
* End of CGERC
|
||||
*
|
||||
END
|
||||
|
|
|
|||
|
|
@ -109,8 +109,6 @@
|
|||
*> \author Univ. of Colorado Denver
|
||||
*> \author NAG Ltd.
|
||||
*
|
||||
*> \date December 2016
|
||||
*
|
||||
*> \ingroup complex_blas_level2
|
||||
*
|
||||
*> \par Further Details:
|
||||
|
|
@ -130,10 +128,9 @@
|
|||
* =====================================================================
|
||||
SUBROUTINE CGERU(M,N,ALPHA,X,INCX,Y,INCY,A,LDA)
|
||||
*
|
||||
* -- Reference BLAS level2 routine (version 3.7.0) --
|
||||
* -- Reference BLAS level2 routine --
|
||||
* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
|
||||
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
|
||||
* December 2016
|
||||
*
|
||||
* .. Scalar Arguments ..
|
||||
COMPLEX ALPHA
|
||||
|
|
@ -222,6 +219,6 @@
|
|||
*
|
||||
RETURN
|
||||
*
|
||||
* End of CGERU .
|
||||
* End of CGERU
|
||||
*
|
||||
END
|
||||
|
|
|
|||
|
|
@ -165,8 +165,6 @@
|
|||
*> \author Univ. of Colorado Denver
|
||||
*> \author NAG Ltd.
|
||||
*
|
||||
*> \date December 2016
|
||||
*
|
||||
*> \ingroup complex_blas_level2
|
||||
*
|
||||
*> \par Further Details:
|
||||
|
|
@ -187,10 +185,9 @@
|
|||
* =====================================================================
|
||||
SUBROUTINE CHBMV(UPLO,N,K,ALPHA,A,LDA,X,INCX,BETA,Y,INCY)
|
||||
*
|
||||
* -- Reference BLAS level2 routine (version 3.7.0) --
|
||||
* -- Reference BLAS level2 routine --
|
||||
* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
|
||||
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
|
||||
* December 2016
|
||||
*
|
||||
* .. Scalar Arguments ..
|
||||
COMPLEX ALPHA,BETA
|
||||
|
|
@ -375,6 +372,6 @@
|
|||
*
|
||||
RETURN
|
||||
*
|
||||
* End of CHBMV .
|
||||
* End of CHBMV
|
||||
*
|
||||
END
|
||||
|
|
|
|||
|
|
@ -170,8 +170,6 @@
|
|||
*> \author Univ. of Colorado Denver
|
||||
*> \author NAG Ltd.
|
||||
*
|
||||
*> \date December 2016
|
||||
*
|
||||
*> \ingroup complex_blas_level3
|
||||
*
|
||||
*> \par Further Details:
|
||||
|
|
@ -191,10 +189,9 @@
|
|||
* =====================================================================
|
||||
SUBROUTINE CHEMM(SIDE,UPLO,M,N,ALPHA,A,LDA,B,LDB,BETA,C,LDC)
|
||||
*
|
||||
* -- Reference BLAS level3 routine (version 3.7.0) --
|
||||
* -- Reference BLAS level3 routine --
|
||||
* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
|
||||
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
|
||||
* December 2016
|
||||
*
|
||||
* .. Scalar Arguments ..
|
||||
COMPLEX ALPHA,BETA
|
||||
|
|
@ -366,6 +363,6 @@
|
|||
*
|
||||
RETURN
|
||||
*
|
||||
* End of CHEMM .
|
||||
* End of CHEMM
|
||||
*
|
||||
END
|
||||
|
|
|
|||
|
|
@ -132,8 +132,6 @@
|
|||
*> \author Univ. of Colorado Denver
|
||||
*> \author NAG Ltd.
|
||||
*
|
||||
*> \date December 2016
|
||||
*
|
||||
*> \ingroup complex_blas_level2
|
||||
*
|
||||
*> \par Further Details:
|
||||
|
|
@ -154,10 +152,9 @@
|
|||
* =====================================================================
|
||||
SUBROUTINE CHEMV(UPLO,N,ALPHA,A,LDA,X,INCX,BETA,Y,INCY)
|
||||
*
|
||||
* -- Reference BLAS level2 routine (version 3.7.0) --
|
||||
* -- Reference BLAS level2 routine --
|
||||
* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
|
||||
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
|
||||
* December 2016
|
||||
*
|
||||
* .. Scalar Arguments ..
|
||||
COMPLEX ALPHA,BETA
|
||||
|
|
@ -332,6 +329,6 @@
|
|||
*
|
||||
RETURN
|
||||
*
|
||||
* End of CHEMV .
|
||||
* End of CHEMV
|
||||
*
|
||||
END
|
||||
|
|
|
|||
|
|
@ -114,8 +114,6 @@
|
|||
*> \author Univ. of Colorado Denver
|
||||
*> \author NAG Ltd.
|
||||
*
|
||||
*> \date December 2016
|
||||
*
|
||||
*> \ingroup complex_blas_level2
|
||||
*
|
||||
*> \par Further Details:
|
||||
|
|
@ -135,10 +133,9 @@
|
|||
* =====================================================================
|
||||
SUBROUTINE CHER(UPLO,N,ALPHA,X,INCX,A,LDA)
|
||||
*
|
||||
* -- Reference BLAS level2 routine (version 3.7.0) --
|
||||
* -- Reference BLAS level2 routine --
|
||||
* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
|
||||
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
|
||||
* December 2016
|
||||
*
|
||||
* .. Scalar Arguments ..
|
||||
REAL ALPHA
|
||||
|
|
@ -273,6 +270,6 @@
|
|||
*
|
||||
RETURN
|
||||
*
|
||||
* End of CHER .
|
||||
* End of CHER
|
||||
*
|
||||
END
|
||||
|
|
|
|||
|
|
@ -129,8 +129,6 @@
|
|||
*> \author Univ. of Colorado Denver
|
||||
*> \author NAG Ltd.
|
||||
*
|
||||
*> \date December 2016
|
||||
*
|
||||
*> \ingroup complex_blas_level2
|
||||
*
|
||||
*> \par Further Details:
|
||||
|
|
@ -150,10 +148,9 @@
|
|||
* =====================================================================
|
||||
SUBROUTINE CHER2(UPLO,N,ALPHA,X,INCX,Y,INCY,A,LDA)
|
||||
*
|
||||
* -- Reference BLAS level2 routine (version 3.7.0) --
|
||||
* -- Reference BLAS level2 routine --
|
||||
* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
|
||||
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
|
||||
* December 2016
|
||||
*
|
||||
* .. Scalar Arguments ..
|
||||
COMPLEX ALPHA
|
||||
|
|
@ -312,6 +309,6 @@
|
|||
*
|
||||
RETURN
|
||||
*
|
||||
* End of CHER2 .
|
||||
* End of CHER2
|
||||
*
|
||||
END
|
||||
|
|
|
|||
|
|
@ -173,8 +173,6 @@
|
|||
*> \author Univ. of Colorado Denver
|
||||
*> \author NAG Ltd.
|
||||
*
|
||||
*> \date December 2016
|
||||
*
|
||||
*> \ingroup complex_blas_level3
|
||||
*
|
||||
*> \par Further Details:
|
||||
|
|
@ -197,10 +195,9 @@
|
|||
* =====================================================================
|
||||
SUBROUTINE CHER2K(UPLO,TRANS,N,K,ALPHA,A,LDA,B,LDB,BETA,C,LDC)
|
||||
*
|
||||
* -- Reference BLAS level3 routine (version 3.7.0) --
|
||||
* -- Reference BLAS level3 routine --
|
||||
* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
|
||||
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
|
||||
* December 2016
|
||||
*
|
||||
* .. Scalar Arguments ..
|
||||
COMPLEX ALPHA
|
||||
|
|
@ -437,6 +434,6 @@
|
|||
*
|
||||
RETURN
|
||||
*
|
||||
* End of CHER2K.
|
||||
* End of CHER2K
|
||||
*
|
||||
END
|
||||
|
|
|
|||
|
|
@ -149,8 +149,6 @@
|
|||
*> \author Univ. of Colorado Denver
|
||||
*> \author NAG Ltd.
|
||||
*
|
||||
*> \date December 2016
|
||||
*
|
||||
*> \ingroup complex_blas_level3
|
||||
*
|
||||
*> \par Further Details:
|
||||
|
|
@ -173,10 +171,9 @@
|
|||
* =====================================================================
|
||||
SUBROUTINE CHERK(UPLO,TRANS,N,K,ALPHA,A,LDA,BETA,C,LDC)
|
||||
*
|
||||
* -- Reference BLAS level3 routine (version 3.7.0) --
|
||||
* -- Reference BLAS level3 routine --
|
||||
* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
|
||||
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
|
||||
* December 2016
|
||||
*
|
||||
* .. Scalar Arguments ..
|
||||
REAL ALPHA,BETA
|
||||
|
|
@ -391,6 +388,6 @@
|
|||
*
|
||||
RETURN
|
||||
*
|
||||
* End of CHERK .
|
||||
* End of CHERK
|
||||
*
|
||||
END
|
||||
|
|
|
|||
|
|
@ -127,8 +127,6 @@
|
|||
*> \author Univ. of Colorado Denver
|
||||
*> \author NAG Ltd.
|
||||
*
|
||||
*> \date December 2016
|
||||
*
|
||||
*> \ingroup complex_blas_level2
|
||||
*
|
||||
*> \par Further Details:
|
||||
|
|
@ -149,10 +147,9 @@
|
|||
* =====================================================================
|
||||
SUBROUTINE CHPMV(UPLO,N,ALPHA,AP,X,INCX,BETA,Y,INCY)
|
||||
*
|
||||
* -- Reference BLAS level2 routine (version 3.7.0) --
|
||||
* -- Reference BLAS level2 routine --
|
||||
* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
|
||||
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
|
||||
* December 2016
|
||||
*
|
||||
* .. Scalar Arguments ..
|
||||
COMPLEX ALPHA,BETA
|
||||
|
|
@ -333,6 +330,6 @@
|
|||
*
|
||||
RETURN
|
||||
*
|
||||
* End of CHPMV .
|
||||
* End of CHPMV
|
||||
*
|
||||
END
|
||||
|
|
|
|||
|
|
@ -109,8 +109,6 @@
|
|||
*> \author Univ. of Colorado Denver
|
||||
*> \author NAG Ltd.
|
||||
*
|
||||
*> \date December 2016
|
||||
*
|
||||
*> \ingroup complex_blas_level2
|
||||
*
|
||||
*> \par Further Details:
|
||||
|
|
@ -130,10 +128,9 @@
|
|||
* =====================================================================
|
||||
SUBROUTINE CHPR(UPLO,N,ALPHA,X,INCX,AP)
|
||||
*
|
||||
* -- Reference BLAS level2 routine (version 3.7.0) --
|
||||
* -- Reference BLAS level2 routine --
|
||||
* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
|
||||
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
|
||||
* December 2016
|
||||
*
|
||||
* .. Scalar Arguments ..
|
||||
REAL ALPHA
|
||||
|
|
@ -274,6 +271,6 @@
|
|||
*
|
||||
RETURN
|
||||
*
|
||||
* End of CHPR .
|
||||
* End of CHPR
|
||||
*
|
||||
END
|
||||
|
|
|
|||
|
|
@ -124,8 +124,6 @@
|
|||
*> \author Univ. of Colorado Denver
|
||||
*> \author NAG Ltd.
|
||||
*
|
||||
*> \date December 2016
|
||||
*
|
||||
*> \ingroup complex_blas_level2
|
||||
*
|
||||
*> \par Further Details:
|
||||
|
|
@ -145,10 +143,9 @@
|
|||
* =====================================================================
|
||||
SUBROUTINE CHPR2(UPLO,N,ALPHA,X,INCX,Y,INCY,AP)
|
||||
*
|
||||
* -- Reference BLAS level2 routine (version 3.7.0) --
|
||||
* -- Reference BLAS level2 routine --
|
||||
* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
|
||||
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
|
||||
* December 2016
|
||||
*
|
||||
* .. Scalar Arguments ..
|
||||
COMPLEX ALPHA
|
||||
|
|
@ -313,6 +310,6 @@
|
|||
*
|
||||
RETURN
|
||||
*
|
||||
* End of CHPR2 .
|
||||
* End of CHPR2
|
||||
*
|
||||
END
|
||||
|
|
|
|||
|
|
@ -1,97 +0,0 @@
|
|||
*> \brief \b CROTG
|
||||
*
|
||||
* =========== DOCUMENTATION ===========
|
||||
*
|
||||
* Online html documentation available at
|
||||
* http://www.netlib.org/lapack/explore-html/
|
||||
*
|
||||
* Definition:
|
||||
* ===========
|
||||
*
|
||||
* SUBROUTINE CROTG(CA,CB,C,S)
|
||||
*
|
||||
* .. Scalar Arguments ..
|
||||
* COMPLEX CA,CB,S
|
||||
* REAL C
|
||||
* ..
|
||||
*
|
||||
*
|
||||
*> \par Purpose:
|
||||
* =============
|
||||
*>
|
||||
*> \verbatim
|
||||
*>
|
||||
*> CROTG determines a complex Givens rotation.
|
||||
*> \endverbatim
|
||||
*
|
||||
* Arguments:
|
||||
* ==========
|
||||
*
|
||||
*> \param[in] CA
|
||||
*> \verbatim
|
||||
*> CA is COMPLEX
|
||||
*> \endverbatim
|
||||
*>
|
||||
*> \param[in] CB
|
||||
*> \verbatim
|
||||
*> CB is COMPLEX
|
||||
*> \endverbatim
|
||||
*>
|
||||
*> \param[out] C
|
||||
*> \verbatim
|
||||
*> C is REAL
|
||||
*> \endverbatim
|
||||
*>
|
||||
*> \param[out] S
|
||||
*> \verbatim
|
||||
*> S is COMPLEX
|
||||
*> \endverbatim
|
||||
*
|
||||
* Authors:
|
||||
* ========
|
||||
*
|
||||
*> \author Univ. of Tennessee
|
||||
*> \author Univ. of California Berkeley
|
||||
*> \author Univ. of Colorado Denver
|
||||
*> \author NAG Ltd.
|
||||
*
|
||||
*> \date November 2017
|
||||
*
|
||||
*> \ingroup complex_blas_level1
|
||||
*
|
||||
* =====================================================================
|
||||
SUBROUTINE CROTG(CA,CB,C,S)
|
||||
*
|
||||
* -- Reference BLAS level1 routine (version 3.8.0) --
|
||||
* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
|
||||
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
|
||||
* November 2017
|
||||
*
|
||||
* .. Scalar Arguments ..
|
||||
COMPLEX CA,CB,S
|
||||
REAL C
|
||||
* ..
|
||||
*
|
||||
* =====================================================================
|
||||
*
|
||||
* .. Local Scalars ..
|
||||
COMPLEX ALPHA
|
||||
REAL NORM,SCALE
|
||||
* ..
|
||||
* .. Intrinsic Functions ..
|
||||
INTRINSIC CABS,CONJG,SQRT
|
||||
* ..
|
||||
IF (CABS(CA).EQ.0.) THEN
|
||||
C = 0.
|
||||
S = (1.,0.)
|
||||
CA = CB
|
||||
ELSE
|
||||
SCALE = CABS(CA) + CABS(CB)
|
||||
NORM = SCALE*SQRT((CABS(CA/SCALE))**2+ (CABS(CB/SCALE))**2)
|
||||
ALPHA = CA/CABS(CA)
|
||||
C = CABS(CA)/NORM
|
||||
S = ALPHA*CONJG(CB)/NORM
|
||||
CA = ALPHA*NORM
|
||||
END IF
|
||||
RETURN
|
||||
END
|
||||
|
|
@ -0,0 +1,229 @@
|
|||
!> \brief \b CROTG
|
||||
!
|
||||
! =========== DOCUMENTATION ===========
|
||||
!
|
||||
! Online html documentation available at
|
||||
! http://www.netlib.org/lapack/explore-html/
|
||||
!
|
||||
! Definition:
|
||||
! ===========
|
||||
!
|
||||
! CROTG constructs a plane rotation
|
||||
! [ c s ] [ a ] = [ r ]
|
||||
! [ -conjg(s) c ] [ b ] [ 0 ]
|
||||
! where c is real, s ic complex, and c**2 + conjg(s)*s = 1.
|
||||
!
|
||||
!> \par Purpose:
|
||||
! =============
|
||||
!>
|
||||
!> \verbatim
|
||||
!>
|
||||
!> The computation uses the formulas
|
||||
!> |x| = sqrt( Re(x)**2 + Im(x)**2 )
|
||||
!> sgn(x) = x / |x| if x /= 0
|
||||
!> = 1 if x = 0
|
||||
!> c = |a| / sqrt(|a|**2 + |b|**2)
|
||||
!> s = sgn(a) * conjg(b) / sqrt(|a|**2 + |b|**2)
|
||||
!> When a and b are real and r /= 0, the formulas simplify to
|
||||
!> r = sgn(a)*sqrt(|a|**2 + |b|**2)
|
||||
!> c = a / r
|
||||
!> s = b / r
|
||||
!> the same as in CROTG when |a| > |b|. When |b| >= |a|, the
|
||||
!> sign of c and s will be different from those computed by CROTG
|
||||
!> if the signs of a and b are not the same.
|
||||
!>
|
||||
!> \endverbatim
|
||||
!
|
||||
! Arguments:
|
||||
! ==========
|
||||
!
|
||||
!> \param[in,out] A
|
||||
!> \verbatim
|
||||
!> A is COMPLEX
|
||||
!> On entry, the scalar a.
|
||||
!> On exit, the scalar r.
|
||||
!> \endverbatim
|
||||
!>
|
||||
!> \param[in] B
|
||||
!> \verbatim
|
||||
!> B is COMPLEX
|
||||
!> The scalar b.
|
||||
!> \endverbatim
|
||||
!>
|
||||
!> \param[out] C
|
||||
!> \verbatim
|
||||
!> C is REAL
|
||||
!> The scalar c.
|
||||
!> \endverbatim
|
||||
!>
|
||||
!> \param[out] S
|
||||
!> \verbatim
|
||||
!> S is REAL
|
||||
!> The scalar s.
|
||||
!> \endverbatim
|
||||
!
|
||||
! Authors:
|
||||
! ========
|
||||
!
|
||||
!> \author Edward Anderson, Lockheed Martin
|
||||
!
|
||||
!> \par Contributors:
|
||||
! ==================
|
||||
!>
|
||||
!> Weslley Pereira, University of Colorado Denver, USA
|
||||
!
|
||||
!> \ingroup single_blas_level1
|
||||
!
|
||||
!> \par Further Details:
|
||||
! =====================
|
||||
!>
|
||||
!> \verbatim
|
||||
!>
|
||||
!> Anderson E. (2017)
|
||||
!> Algorithm 978: Safe Scaling in the Level 1 BLAS
|
||||
!> ACM Trans Math Softw 44:1--28
|
||||
!> https://doi.org/10.1145/3061665
|
||||
!>
|
||||
!> \endverbatim
|
||||
!
|
||||
! =====================================================================
|
||||
subroutine CROTG( a, b, c, s )
|
||||
integer, parameter :: wp = kind(1.e0)
|
||||
!
|
||||
! -- Reference BLAS level1 routine --
|
||||
! -- Reference BLAS is a software package provided by Univ. of Tennessee, --
|
||||
! -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
|
||||
!
|
||||
! .. Constants ..
|
||||
real(wp), parameter :: zero = 0.0_wp
|
||||
real(wp), parameter :: one = 1.0_wp
|
||||
complex(wp), parameter :: czero = 0.0_wp
|
||||
! ..
|
||||
! .. Scaling constants ..
|
||||
real(wp), parameter :: safmin = real(radix(0._wp),wp)**max( &
|
||||
minexponent(0._wp)-1, &
|
||||
1-maxexponent(0._wp) &
|
||||
)
|
||||
real(wp), parameter :: safmax = real(radix(0._wp),wp)**max( &
|
||||
1-minexponent(0._wp), &
|
||||
maxexponent(0._wp)-1 &
|
||||
)
|
||||
real(wp), parameter :: rtmin = sqrt( real(radix(0._wp),wp)**max( &
|
||||
minexponent(0._wp)-1, &
|
||||
1-maxexponent(0._wp) &
|
||||
) / epsilon(0._wp) )
|
||||
real(wp), parameter :: rtmax = sqrt( real(radix(0._wp),wp)**max( &
|
||||
1-minexponent(0._wp), &
|
||||
maxexponent(0._wp)-1 &
|
||||
) * epsilon(0._wp) )
|
||||
! ..
|
||||
! .. Scalar Arguments ..
|
||||
real(wp) :: c
|
||||
complex(wp) :: a, b, s
|
||||
! ..
|
||||
! .. Local Scalars ..
|
||||
real(wp) :: d, f1, f2, g1, g2, h2, p, u, uu, v, vv, w
|
||||
complex(wp) :: f, fs, g, gs, r, t
|
||||
! ..
|
||||
! .. Intrinsic Functions ..
|
||||
intrinsic :: abs, aimag, conjg, max, min, real, sqrt
|
||||
! ..
|
||||
! .. Statement Functions ..
|
||||
real(wp) :: ABSSQ
|
||||
! ..
|
||||
! .. Statement Function definitions ..
|
||||
ABSSQ( t ) = real( t )**2 + aimag( t )**2
|
||||
! ..
|
||||
! .. Executable Statements ..
|
||||
!
|
||||
f = a
|
||||
g = b
|
||||
if( g == czero ) then
|
||||
c = one
|
||||
s = czero
|
||||
r = f
|
||||
else if( f == czero ) then
|
||||
c = zero
|
||||
g1 = max( abs(real(g)), abs(aimag(g)) )
|
||||
if( g1 > rtmin .and. g1 < rtmax ) then
|
||||
!
|
||||
! Use unscaled algorithm
|
||||
!
|
||||
g2 = ABSSQ( g )
|
||||
d = sqrt( g2 )
|
||||
s = conjg( g ) / d
|
||||
r = d
|
||||
else
|
||||
!
|
||||
! Use scaled algorithm
|
||||
!
|
||||
u = min( safmax, max( safmin, g1 ) )
|
||||
uu = one / u
|
||||
gs = g*uu
|
||||
g2 = ABSSQ( gs )
|
||||
d = sqrt( g2 )
|
||||
s = conjg( gs ) / d
|
||||
r = d*u
|
||||
end if
|
||||
else
|
||||
f1 = max( abs(real(f)), abs(aimag(f)) )
|
||||
g1 = max( abs(real(g)), abs(aimag(g)) )
|
||||
if( f1 > rtmin .and. f1 < rtmax .and. &
|
||||
g1 > rtmin .and. g1 < rtmax ) then
|
||||
!
|
||||
! Use unscaled algorithm
|
||||
!
|
||||
f2 = ABSSQ( f )
|
||||
g2 = ABSSQ( g )
|
||||
h2 = f2 + g2
|
||||
if( f2 > rtmin .and. h2 < rtmax ) then
|
||||
d = sqrt( f2*h2 )
|
||||
else
|
||||
d = sqrt( f2 )*sqrt( h2 )
|
||||
end if
|
||||
p = 1 / d
|
||||
c = f2*p
|
||||
s = conjg( g )*( f*p )
|
||||
r = f*( h2*p )
|
||||
else
|
||||
!
|
||||
! Use scaled algorithm
|
||||
!
|
||||
u = min( safmax, max( safmin, f1, g1 ) )
|
||||
uu = one / u
|
||||
gs = g*uu
|
||||
g2 = ABSSQ( gs )
|
||||
if( f1*uu < rtmin ) then
|
||||
!
|
||||
! f is not well-scaled when scaled by g1.
|
||||
! Use a different scaling for f.
|
||||
!
|
||||
v = min( safmax, max( safmin, f1 ) )
|
||||
vv = one / v
|
||||
w = v * uu
|
||||
fs = f*vv
|
||||
f2 = ABSSQ( fs )
|
||||
h2 = f2*w**2 + g2
|
||||
else
|
||||
!
|
||||
! Otherwise use the same scaling for f and g.
|
||||
!
|
||||
w = one
|
||||
fs = f*uu
|
||||
f2 = ABSSQ( fs )
|
||||
h2 = f2 + g2
|
||||
end if
|
||||
if( f2 > rtmin .and. h2 < rtmax ) then
|
||||
d = sqrt( f2*h2 )
|
||||
else
|
||||
d = sqrt( f2 )*sqrt( h2 )
|
||||
end if
|
||||
p = 1 / d
|
||||
c = ( f2*p )*w
|
||||
s = conjg( gs )*( fs*p )
|
||||
r = ( fs*( h2*p ) )*u
|
||||
end if
|
||||
end if
|
||||
a = r
|
||||
return
|
||||
end subroutine
|
||||
|
|
@ -61,8 +61,6 @@
|
|||
*> \author Univ. of Colorado Denver
|
||||
*> \author NAG Ltd.
|
||||
*
|
||||
*> \date November 2017
|
||||
*
|
||||
*> \ingroup complex_blas_level1
|
||||
*
|
||||
*> \par Further Details:
|
||||
|
|
@ -78,10 +76,9 @@
|
|||
* =====================================================================
|
||||
SUBROUTINE CSCAL(N,CA,CX,INCX)
|
||||
*
|
||||
* -- Reference BLAS level1 routine (version 3.8.0) --
|
||||
* -- Reference BLAS level1 routine --
|
||||
* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
|
||||
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
|
||||
* November 2017
|
||||
*
|
||||
* .. Scalar Arguments ..
|
||||
COMPLEX CA
|
||||
|
|
@ -114,4 +111,7 @@
|
|||
END DO
|
||||
END IF
|
||||
RETURN
|
||||
*
|
||||
* End of CSCAL
|
||||
*
|
||||
END
|
||||
|
|
|
|||
|
|
@ -91,17 +91,14 @@
|
|||
*> \author Univ. of Colorado Denver
|
||||
*> \author NAG Ltd.
|
||||
*
|
||||
*> \date December 2016
|
||||
*
|
||||
*> \ingroup complex_blas_level1
|
||||
*
|
||||
* =====================================================================
|
||||
SUBROUTINE CSROT( N, CX, INCX, CY, INCY, C, S )
|
||||
*
|
||||
* -- Reference BLAS level1 routine (version 3.7.0) --
|
||||
* -- Reference BLAS level1 routine --
|
||||
* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
|
||||
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
|
||||
* December 2016
|
||||
*
|
||||
* .. Scalar Arguments ..
|
||||
INTEGER INCX, INCY, N
|
||||
|
|
@ -150,4 +147,7 @@
|
|||
END DO
|
||||
END IF
|
||||
RETURN
|
||||
*
|
||||
* End of CSROT
|
||||
*
|
||||
END
|
||||
|
|
|
|||
|
|
@ -61,8 +61,6 @@
|
|||
*> \author Univ. of Colorado Denver
|
||||
*> \author NAG Ltd.
|
||||
*
|
||||
*> \date November 2017
|
||||
*
|
||||
*> \ingroup complex_blas_level1
|
||||
*
|
||||
*> \par Further Details:
|
||||
|
|
@ -78,10 +76,9 @@
|
|||
* =====================================================================
|
||||
SUBROUTINE CSSCAL(N,SA,CX,INCX)
|
||||
*
|
||||
* -- Reference BLAS level1 routine (version 3.8.0) --
|
||||
* -- Reference BLAS level1 routine --
|
||||
* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
|
||||
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
|
||||
* November 2017
|
||||
*
|
||||
* .. Scalar Arguments ..
|
||||
REAL SA
|
||||
|
|
@ -117,4 +114,7 @@
|
|||
END DO
|
||||
END IF
|
||||
RETURN
|
||||
*
|
||||
* End of CSSCAL
|
||||
*
|
||||
END
|
||||
|
|
|
|||
|
|
@ -65,8 +65,6 @@
|
|||
*> \author Univ. of Colorado Denver
|
||||
*> \author NAG Ltd.
|
||||
*
|
||||
*> \date November 2017
|
||||
*
|
||||
*> \ingroup complex_blas_level1
|
||||
*
|
||||
*> \par Further Details:
|
||||
|
|
@ -81,10 +79,9 @@
|
|||
* =====================================================================
|
||||
SUBROUTINE CSWAP(N,CX,INCX,CY,INCY)
|
||||
*
|
||||
* -- Reference BLAS level1 routine (version 3.8.0) --
|
||||
* -- Reference BLAS level1 routine --
|
||||
* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
|
||||
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
|
||||
* November 2017
|
||||
*
|
||||
* .. Scalar Arguments ..
|
||||
INTEGER INCX,INCY,N
|
||||
|
|
@ -126,4 +123,7 @@
|
|||
END DO
|
||||
END IF
|
||||
RETURN
|
||||
*
|
||||
* End of CSWAP
|
||||
*
|
||||
END
|
||||
|
|
|
|||
|
|
@ -168,8 +168,6 @@
|
|||
*> \author Univ. of Colorado Denver
|
||||
*> \author NAG Ltd.
|
||||
*
|
||||
*> \date December 2016
|
||||
*
|
||||
*> \ingroup complex_blas_level3
|
||||
*
|
||||
*> \par Further Details:
|
||||
|
|
@ -189,10 +187,9 @@
|
|||
* =====================================================================
|
||||
SUBROUTINE CSYMM(SIDE,UPLO,M,N,ALPHA,A,LDA,B,LDB,BETA,C,LDC)
|
||||
*
|
||||
* -- Reference BLAS level3 routine (version 3.7.0) --
|
||||
* -- Reference BLAS level3 routine --
|
||||
* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
|
||||
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
|
||||
* December 2016
|
||||
*
|
||||
* .. Scalar Arguments ..
|
||||
COMPLEX ALPHA,BETA
|
||||
|
|
@ -364,6 +361,6 @@
|
|||
*
|
||||
RETURN
|
||||
*
|
||||
* End of CSYMM .
|
||||
* End of CSYMM
|
||||
*
|
||||
END
|
||||
|
|
|
|||
|
|
@ -167,8 +167,6 @@
|
|||
*> \author Univ. of Colorado Denver
|
||||
*> \author NAG Ltd.
|
||||
*
|
||||
*> \date December 2016
|
||||
*
|
||||
*> \ingroup complex_blas_level3
|
||||
*
|
||||
*> \par Further Details:
|
||||
|
|
@ -188,10 +186,9 @@
|
|||
* =====================================================================
|
||||
SUBROUTINE CSYR2K(UPLO,TRANS,N,K,ALPHA,A,LDA,B,LDB,BETA,C,LDC)
|
||||
*
|
||||
* -- Reference BLAS level3 routine (version 3.7.0) --
|
||||
* -- Reference BLAS level3 routine --
|
||||
* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
|
||||
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
|
||||
* December 2016
|
||||
*
|
||||
* .. Scalar Arguments ..
|
||||
COMPLEX ALPHA,BETA
|
||||
|
|
@ -391,6 +388,6 @@
|
|||
*
|
||||
RETURN
|
||||
*
|
||||
* End of CSYR2K.
|
||||
* End of CSYR2K
|
||||
*
|
||||
END
|
||||
|
|
|
|||
|
|
@ -146,8 +146,6 @@
|
|||
*> \author Univ. of Colorado Denver
|
||||
*> \author NAG Ltd.
|
||||
*
|
||||
*> \date December 2016
|
||||
*
|
||||
*> \ingroup complex_blas_level3
|
||||
*
|
||||
*> \par Further Details:
|
||||
|
|
@ -167,10 +165,9 @@
|
|||
* =====================================================================
|
||||
SUBROUTINE CSYRK(UPLO,TRANS,N,K,ALPHA,A,LDA,BETA,C,LDC)
|
||||
*
|
||||
* -- Reference BLAS level3 routine (version 3.7.0) --
|
||||
* -- Reference BLAS level3 routine --
|
||||
* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
|
||||
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
|
||||
* December 2016
|
||||
*
|
||||
* .. Scalar Arguments ..
|
||||
COMPLEX ALPHA,BETA
|
||||
|
|
@ -358,6 +355,6 @@
|
|||
*
|
||||
RETURN
|
||||
*
|
||||
* End of CSYRK .
|
||||
* End of CSYRK
|
||||
*
|
||||
END
|
||||
|
|
|
|||
|
|
@ -164,8 +164,6 @@
|
|||
*> \author Univ. of Colorado Denver
|
||||
*> \author NAG Ltd.
|
||||
*
|
||||
*> \date December 2016
|
||||
*
|
||||
*> \ingroup complex_blas_level2
|
||||
*
|
||||
*> \par Further Details:
|
||||
|
|
@ -186,10 +184,9 @@
|
|||
* =====================================================================
|
||||
SUBROUTINE CTBMV(UPLO,TRANS,DIAG,N,K,A,LDA,X,INCX)
|
||||
*
|
||||
* -- Reference BLAS level2 routine (version 3.7.0) --
|
||||
* -- Reference BLAS level2 routine --
|
||||
* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
|
||||
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
|
||||
* December 2016
|
||||
*
|
||||
* .. Scalar Arguments ..
|
||||
INTEGER INCX,K,LDA,N
|
||||
|
|
@ -424,6 +421,6 @@
|
|||
*
|
||||
RETURN
|
||||
*
|
||||
* End of CTBMV .
|
||||
* End of CTBMV
|
||||
*
|
||||
END
|
||||
|
|
|
|||
|
|
@ -168,8 +168,6 @@
|
|||
*> \author Univ. of Colorado Denver
|
||||
*> \author NAG Ltd.
|
||||
*
|
||||
*> \date December 2016
|
||||
*
|
||||
*> \ingroup complex_blas_level2
|
||||
*
|
||||
*> \par Further Details:
|
||||
|
|
@ -189,10 +187,9 @@
|
|||
* =====================================================================
|
||||
SUBROUTINE CTBSV(UPLO,TRANS,DIAG,N,K,A,LDA,X,INCX)
|
||||
*
|
||||
* -- Reference BLAS level2 routine (version 3.7.0) --
|
||||
* -- Reference BLAS level2 routine --
|
||||
* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
|
||||
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
|
||||
* December 2016
|
||||
*
|
||||
* .. Scalar Arguments ..
|
||||
INTEGER INCX,K,LDA,N
|
||||
|
|
@ -427,6 +424,6 @@
|
|||
*
|
||||
RETURN
|
||||
*
|
||||
* End of CTBSV .
|
||||
* End of CTBSV
|
||||
*
|
||||
END
|
||||
|
|
|
|||
|
|
@ -120,8 +120,6 @@
|
|||
*> \author Univ. of Colorado Denver
|
||||
*> \author NAG Ltd.
|
||||
*
|
||||
*> \date December 2016
|
||||
*
|
||||
*> \ingroup complex_blas_level2
|
||||
*
|
||||
*> \par Further Details:
|
||||
|
|
@ -142,10 +140,9 @@
|
|||
* =====================================================================
|
||||
SUBROUTINE CTPMV(UPLO,TRANS,DIAG,N,AP,X,INCX)
|
||||
*
|
||||
* -- Reference BLAS level2 routine (version 3.7.0) --
|
||||
* -- Reference BLAS level2 routine --
|
||||
* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
|
||||
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
|
||||
* December 2016
|
||||
*
|
||||
* .. Scalar Arguments ..
|
||||
INTEGER INCX,N
|
||||
|
|
@ -383,6 +380,6 @@
|
|||
*
|
||||
RETURN
|
||||
*
|
||||
* End of CTPMV .
|
||||
* End of CTPMV
|
||||
*
|
||||
END
|
||||
|
|
|
|||
|
|
@ -123,8 +123,6 @@
|
|||
*> \author Univ. of Colorado Denver
|
||||
*> \author NAG Ltd.
|
||||
*
|
||||
*> \date December 2016
|
||||
*
|
||||
*> \ingroup complex_blas_level2
|
||||
*
|
||||
*> \par Further Details:
|
||||
|
|
@ -144,10 +142,9 @@
|
|||
* =====================================================================
|
||||
SUBROUTINE CTPSV(UPLO,TRANS,DIAG,N,AP,X,INCX)
|
||||
*
|
||||
* -- Reference BLAS level2 routine (version 3.7.0) --
|
||||
* -- Reference BLAS level2 routine --
|
||||
* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
|
||||
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
|
||||
* December 2016
|
||||
*
|
||||
* .. Scalar Arguments ..
|
||||
INTEGER INCX,N
|
||||
|
|
@ -385,6 +382,6 @@
|
|||
*
|
||||
RETURN
|
||||
*
|
||||
* End of CTPSV .
|
||||
* End of CTPSV
|
||||
*
|
||||
END
|
||||
|
|
|
|||
|
|
@ -156,8 +156,6 @@
|
|||
*> \author Univ. of Colorado Denver
|
||||
*> \author NAG Ltd.
|
||||
*
|
||||
*> \date December 2016
|
||||
*
|
||||
*> \ingroup complex_blas_level3
|
||||
*
|
||||
*> \par Further Details:
|
||||
|
|
@ -177,10 +175,9 @@
|
|||
* =====================================================================
|
||||
SUBROUTINE CTRMM(SIDE,UPLO,TRANSA,DIAG,M,N,ALPHA,A,LDA,B,LDB)
|
||||
*
|
||||
* -- Reference BLAS level3 routine (version 3.7.0) --
|
||||
* -- Reference BLAS level3 routine --
|
||||
* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
|
||||
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
|
||||
* December 2016
|
||||
*
|
||||
* .. Scalar Arguments ..
|
||||
COMPLEX ALPHA
|
||||
|
|
@ -447,6 +444,6 @@
|
|||
*
|
||||
RETURN
|
||||
*
|
||||
* End of CTRMM .
|
||||
* End of CTRMM
|
||||
*
|
||||
END
|
||||
|
|
|
|||
|
|
@ -125,8 +125,6 @@
|
|||
*> \author Univ. of Colorado Denver
|
||||
*> \author NAG Ltd.
|
||||
*
|
||||
*> \date December 2016
|
||||
*
|
||||
*> \ingroup complex_blas_level2
|
||||
*
|
||||
*> \par Further Details:
|
||||
|
|
@ -147,10 +145,9 @@
|
|||
* =====================================================================
|
||||
SUBROUTINE CTRMV(UPLO,TRANS,DIAG,N,A,LDA,X,INCX)
|
||||
*
|
||||
* -- Reference BLAS level2 routine (version 3.7.0) --
|
||||
* -- Reference BLAS level2 routine --
|
||||
* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
|
||||
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
|
||||
* December 2016
|
||||
*
|
||||
* .. Scalar Arguments ..
|
||||
INTEGER INCX,LDA,N
|
||||
|
|
@ -368,6 +365,6 @@
|
|||
*
|
||||
RETURN
|
||||
*
|
||||
* End of CTRMV .
|
||||
* End of CTRMV
|
||||
*
|
||||
END
|
||||
|
|
|
|||
|
|
@ -159,8 +159,6 @@
|
|||
*> \author Univ. of Colorado Denver
|
||||
*> \author NAG Ltd.
|
||||
*
|
||||
*> \date December 2016
|
||||
*
|
||||
*> \ingroup complex_blas_level3
|
||||
*
|
||||
*> \par Further Details:
|
||||
|
|
@ -180,10 +178,9 @@
|
|||
* =====================================================================
|
||||
SUBROUTINE CTRSM(SIDE,UPLO,TRANSA,DIAG,M,N,ALPHA,A,LDA,B,LDB)
|
||||
*
|
||||
* -- Reference BLAS level3 routine (version 3.7.0) --
|
||||
* -- Reference BLAS level3 routine --
|
||||
* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
|
||||
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
|
||||
* December 2016
|
||||
*
|
||||
* .. Scalar Arguments ..
|
||||
COMPLEX ALPHA
|
||||
|
|
@ -472,6 +469,6 @@
|
|||
*
|
||||
RETURN
|
||||
*
|
||||
* End of CTRSM .
|
||||
* End of CTRSM
|
||||
*
|
||||
END
|
||||
|
|
|
|||
|
|
@ -128,8 +128,6 @@
|
|||
*> \author Univ. of Colorado Denver
|
||||
*> \author NAG Ltd.
|
||||
*
|
||||
*> \date December 2016
|
||||
*
|
||||
*> \ingroup complex_blas_level2
|
||||
*
|
||||
*> \par Further Details:
|
||||
|
|
@ -149,10 +147,9 @@
|
|||
* =====================================================================
|
||||
SUBROUTINE CTRSV(UPLO,TRANS,DIAG,N,A,LDA,X,INCX)
|
||||
*
|
||||
* -- Reference BLAS level2 routine (version 3.7.0) --
|
||||
* -- Reference BLAS level2 routine --
|
||||
* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
|
||||
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
|
||||
* December 2016
|
||||
*
|
||||
* .. Scalar Arguments ..
|
||||
INTEGER INCX,LDA,N
|
||||
|
|
@ -370,6 +367,6 @@
|
|||
*
|
||||
RETURN
|
||||
*
|
||||
* End of CTRSV .
|
||||
* End of CTRSV
|
||||
*
|
||||
END
|
||||
|
|
|
|||
|
|
@ -54,8 +54,6 @@
|
|||
*> \author Univ. of Colorado Denver
|
||||
*> \author NAG Ltd.
|
||||
*
|
||||
*> \date November 2017
|
||||
*
|
||||
*> \ingroup double_blas_level1
|
||||
*
|
||||
*> \par Further Details:
|
||||
|
|
@ -71,10 +69,9 @@
|
|||
* =====================================================================
|
||||
DOUBLE PRECISION FUNCTION DASUM(N,DX,INCX)
|
||||
*
|
||||
* -- Reference BLAS level1 routine (version 3.8.0) --
|
||||
* -- Reference BLAS level1 routine --
|
||||
* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
|
||||
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
|
||||
* November 2017
|
||||
*
|
||||
* .. Scalar Arguments ..
|
||||
INTEGER INCX,N
|
||||
|
|
@ -128,4 +125,7 @@
|
|||
END IF
|
||||
DASUM = DTEMP
|
||||
RETURN
|
||||
*
|
||||
* End of DASUM
|
||||
*
|
||||
END
|
||||
|
|
|
|||
|
|
@ -73,8 +73,6 @@
|
|||
*> \author Univ. of Colorado Denver
|
||||
*> \author NAG Ltd.
|
||||
*
|
||||
*> \date November 2017
|
||||
*
|
||||
*> \ingroup double_blas_level1
|
||||
*
|
||||
*> \par Further Details:
|
||||
|
|
@ -89,10 +87,9 @@
|
|||
* =====================================================================
|
||||
SUBROUTINE DAXPY(N,DA,DX,INCX,DY,INCY)
|
||||
*
|
||||
* -- Reference BLAS level1 routine (version 3.8.0) --
|
||||
* -- Reference BLAS level1 routine --
|
||||
* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
|
||||
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
|
||||
* November 2017
|
||||
*
|
||||
* .. Scalar Arguments ..
|
||||
DOUBLE PRECISION DA
|
||||
|
|
@ -149,4 +146,7 @@
|
|||
END DO
|
||||
END IF
|
||||
RETURN
|
||||
*
|
||||
* End of DAXPY
|
||||
*
|
||||
END
|
||||
|
|
|
|||
|
|
@ -40,17 +40,14 @@
|
|||
*> \author Univ. of Colorado Denver
|
||||
*> \author NAG Ltd.
|
||||
*
|
||||
*> \date November 2017
|
||||
*
|
||||
*> \ingroup double_blas_level1
|
||||
*
|
||||
* =====================================================================
|
||||
DOUBLE PRECISION FUNCTION DCABS1(Z)
|
||||
*
|
||||
* -- Reference BLAS level1 routine (version 3.8.0) --
|
||||
* -- Reference BLAS level1 routine --
|
||||
* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
|
||||
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
|
||||
* November 2017
|
||||
*
|
||||
* .. Scalar Arguments ..
|
||||
COMPLEX*16 Z
|
||||
|
|
@ -63,4 +60,7 @@
|
|||
*
|
||||
DCABS1 = ABS(DBLE(Z)) + ABS(DIMAG(Z))
|
||||
RETURN
|
||||
*
|
||||
* End of DCABS1
|
||||
*
|
||||
END
|
||||
|
|
|
|||
|
|
@ -66,8 +66,6 @@
|
|||
*> \author Univ. of Colorado Denver
|
||||
*> \author NAG Ltd.
|
||||
*
|
||||
*> \date November 2017
|
||||
*
|
||||
*> \ingroup double_blas_level1
|
||||
*
|
||||
*> \par Further Details:
|
||||
|
|
@ -82,10 +80,9 @@
|
|||
* =====================================================================
|
||||
SUBROUTINE DCOPY(N,DX,INCX,DY,INCY)
|
||||
*
|
||||
* -- Reference BLAS level1 routine (version 3.8.0) --
|
||||
* -- Reference BLAS level1 routine --
|
||||
* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
|
||||
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
|
||||
* November 2017
|
||||
*
|
||||
* .. Scalar Arguments ..
|
||||
INTEGER INCX,INCY,N
|
||||
|
|
@ -143,4 +140,7 @@
|
|||
END DO
|
||||
END IF
|
||||
RETURN
|
||||
*
|
||||
* End of DCOPY
|
||||
*
|
||||
END
|
||||
|
|
|
|||
|
|
@ -66,8 +66,6 @@
|
|||
*> \author Univ. of Colorado Denver
|
||||
*> \author NAG Ltd.
|
||||
*
|
||||
*> \date November 2017
|
||||
*
|
||||
*> \ingroup double_blas_level1
|
||||
*
|
||||
*> \par Further Details:
|
||||
|
|
@ -82,10 +80,9 @@
|
|||
* =====================================================================
|
||||
DOUBLE PRECISION FUNCTION DDOT(N,DX,INCX,DY,INCY)
|
||||
*
|
||||
* -- Reference BLAS level1 routine (version 3.8.0) --
|
||||
* -- Reference BLAS level1 routine --
|
||||
* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
|
||||
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
|
||||
* November 2017
|
||||
*
|
||||
* .. Scalar Arguments ..
|
||||
INTEGER INCX,INCY,N
|
||||
|
|
@ -145,4 +142,7 @@
|
|||
END IF
|
||||
DDOT = DTEMP
|
||||
RETURN
|
||||
*
|
||||
* End of DDOT
|
||||
*
|
||||
END
|
||||
|
|
|
|||
|
|
@ -163,8 +163,6 @@
|
|||
*> \author Univ. of Colorado Denver
|
||||
*> \author NAG Ltd.
|
||||
*
|
||||
*> \date December 2016
|
||||
*
|
||||
*> \ingroup double_blas_level2
|
||||
*
|
||||
*> \par Further Details:
|
||||
|
|
@ -185,10 +183,9 @@
|
|||
* =====================================================================
|
||||
SUBROUTINE DGBMV(TRANS,M,N,KL,KU,ALPHA,A,LDA,X,INCX,BETA,Y,INCY)
|
||||
*
|
||||
* -- Reference BLAS level2 routine (version 3.7.0) --
|
||||
* -- Reference BLAS level2 routine --
|
||||
* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
|
||||
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
|
||||
* December 2016
|
||||
*
|
||||
* .. Scalar Arguments ..
|
||||
DOUBLE PRECISION ALPHA,BETA
|
||||
|
|
@ -365,6 +362,6 @@
|
|||
*
|
||||
RETURN
|
||||
*
|
||||
* End of DGBMV .
|
||||
* End of DGBMV
|
||||
*
|
||||
END
|
||||
|
|
|
|||
|
|
@ -166,8 +166,6 @@
|
|||
*> \author Univ. of Colorado Denver
|
||||
*> \author NAG Ltd.
|
||||
*
|
||||
*> \date December 2016
|
||||
*
|
||||
*> \ingroup double_blas_level3
|
||||
*
|
||||
*> \par Further Details:
|
||||
|
|
@ -187,10 +185,9 @@
|
|||
* =====================================================================
|
||||
SUBROUTINE DGEMM(TRANSA,TRANSB,M,N,K,ALPHA,A,LDA,B,LDB,BETA,C,LDC)
|
||||
*
|
||||
* -- Reference BLAS level3 routine (version 3.7.0) --
|
||||
* -- Reference BLAS level3 routine --
|
||||
* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
|
||||
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
|
||||
* December 2016
|
||||
*
|
||||
* .. Scalar Arguments ..
|
||||
DOUBLE PRECISION ALPHA,BETA
|
||||
|
|
@ -215,7 +212,7 @@
|
|||
* ..
|
||||
* .. Local Scalars ..
|
||||
DOUBLE PRECISION TEMP
|
||||
INTEGER I,INFO,J,L,NCOLA,NROWA,NROWB
|
||||
INTEGER I,INFO,J,L,NROWA,NROWB
|
||||
LOGICAL NOTA,NOTB
|
||||
* ..
|
||||
* .. Parameters ..
|
||||
|
|
@ -224,17 +221,15 @@
|
|||
* ..
|
||||
*
|
||||
* Set NOTA and NOTB as true if A and B respectively are not
|
||||
* transposed and set NROWA, NCOLA and NROWB as the number of rows
|
||||
* and columns of A and the number of rows of B respectively.
|
||||
* transposed and set NROWA and NROWB as the number of rows of A
|
||||
* and B respectively.
|
||||
*
|
||||
NOTA = LSAME(TRANSA,'N')
|
||||
NOTB = LSAME(TRANSB,'N')
|
||||
IF (NOTA) THEN
|
||||
NROWA = M
|
||||
NCOLA = K
|
||||
ELSE
|
||||
NROWA = K
|
||||
NCOLA = M
|
||||
END IF
|
||||
IF (NOTB) THEN
|
||||
NROWB = K
|
||||
|
|
@ -379,6 +374,6 @@
|
|||
*
|
||||
RETURN
|
||||
*
|
||||
* End of DGEMM .
|
||||
* End of DGEMM
|
||||
*
|
||||
END
|
||||
|
|
|
|||
|
|
@ -134,8 +134,6 @@
|
|||
*> \author Univ. of Colorado Denver
|
||||
*> \author NAG Ltd.
|
||||
*
|
||||
*> \date December 2016
|
||||
*
|
||||
*> \ingroup double_blas_level2
|
||||
*
|
||||
*> \par Further Details:
|
||||
|
|
@ -156,10 +154,9 @@
|
|||
* =====================================================================
|
||||
SUBROUTINE DGEMV(TRANS,M,N,ALPHA,A,LDA,X,INCX,BETA,Y,INCY)
|
||||
*
|
||||
* -- Reference BLAS level2 routine (version 3.7.0) --
|
||||
* -- Reference BLAS level2 routine --
|
||||
* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
|
||||
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
|
||||
* December 2016
|
||||
*
|
||||
* .. Scalar Arguments ..
|
||||
DOUBLE PRECISION ALPHA,BETA
|
||||
|
|
@ -325,6 +322,6 @@
|
|||
*
|
||||
RETURN
|
||||
*
|
||||
* End of DGEMV .
|
||||
* End of DGEMV
|
||||
*
|
||||
END
|
||||
|
|
|
|||
|
|
@ -109,8 +109,6 @@
|
|||
*> \author Univ. of Colorado Denver
|
||||
*> \author NAG Ltd.
|
||||
*
|
||||
*> \date December 2016
|
||||
*
|
||||
*> \ingroup double_blas_level2
|
||||
*
|
||||
*> \par Further Details:
|
||||
|
|
@ -130,10 +128,9 @@
|
|||
* =====================================================================
|
||||
SUBROUTINE DGER(M,N,ALPHA,X,INCX,Y,INCY,A,LDA)
|
||||
*
|
||||
* -- Reference BLAS level2 routine (version 3.7.0) --
|
||||
* -- Reference BLAS level2 routine --
|
||||
* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
|
||||
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
|
||||
* December 2016
|
||||
*
|
||||
* .. Scalar Arguments ..
|
||||
DOUBLE PRECISION ALPHA
|
||||
|
|
@ -222,6 +219,6 @@
|
|||
*
|
||||
RETURN
|
||||
*
|
||||
* End of DGER .
|
||||
* End of DGER
|
||||
*
|
||||
END
|
||||
|
|
|
|||
|
|
@ -1,132 +0,0 @@
|
|||
*> \brief \b DNRM2
|
||||
*
|
||||
* =========== DOCUMENTATION ===========
|
||||
*
|
||||
* Online html documentation available at
|
||||
* http://www.netlib.org/lapack/explore-html/
|
||||
*
|
||||
* Definition:
|
||||
* ===========
|
||||
*
|
||||
* DOUBLE PRECISION FUNCTION DNRM2(N,X,INCX)
|
||||
*
|
||||
* .. Scalar Arguments ..
|
||||
* INTEGER INCX,N
|
||||
* ..
|
||||
* .. Array Arguments ..
|
||||
* DOUBLE PRECISION X(*)
|
||||
* ..
|
||||
*
|
||||
*
|
||||
*> \par Purpose:
|
||||
* =============
|
||||
*>
|
||||
*> \verbatim
|
||||
*>
|
||||
*> DNRM2 returns the euclidean norm of a vector via the function
|
||||
*> name, so that
|
||||
*>
|
||||
*> DNRM2 := sqrt( x'*x )
|
||||
*> \endverbatim
|
||||
*
|
||||
* Arguments:
|
||||
* ==========
|
||||
*
|
||||
*> \param[in] N
|
||||
*> \verbatim
|
||||
*> N is INTEGER
|
||||
*> number of elements in input vector(s)
|
||||
*> \endverbatim
|
||||
*>
|
||||
*> \param[in] X
|
||||
*> \verbatim
|
||||
*> X is DOUBLE PRECISION array, dimension ( 1 + ( N - 1 )*abs( INCX ) )
|
||||
*> \endverbatim
|
||||
*>
|
||||
*> \param[in] INCX
|
||||
*> \verbatim
|
||||
*> INCX is INTEGER
|
||||
*> storage spacing between elements of DX
|
||||
*> \endverbatim
|
||||
*
|
||||
* Authors:
|
||||
* ========
|
||||
*
|
||||
*> \author Univ. of Tennessee
|
||||
*> \author Univ. of California Berkeley
|
||||
*> \author Univ. of Colorado Denver
|
||||
*> \author NAG Ltd.
|
||||
*
|
||||
*> \date November 2017
|
||||
*
|
||||
*> \ingroup double_blas_level1
|
||||
*
|
||||
*> \par Further Details:
|
||||
* =====================
|
||||
*>
|
||||
*> \verbatim
|
||||
*>
|
||||
*> -- This version written on 25-October-1982.
|
||||
*> Modified on 14-October-1993 to inline the call to DLASSQ.
|
||||
*> Sven Hammarling, Nag Ltd.
|
||||
*> \endverbatim
|
||||
*>
|
||||
* =====================================================================
|
||||
DOUBLE PRECISION FUNCTION DNRM2(N,X,INCX)
|
||||
*
|
||||
* -- Reference BLAS level1 routine (version 3.8.0) --
|
||||
* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
|
||||
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
|
||||
* November 2017
|
||||
*
|
||||
* .. Scalar Arguments ..
|
||||
INTEGER INCX,N
|
||||
* ..
|
||||
* .. Array Arguments ..
|
||||
DOUBLE PRECISION X(*)
|
||||
* ..
|
||||
*
|
||||
* =====================================================================
|
||||
*
|
||||
* .. Parameters ..
|
||||
DOUBLE PRECISION ONE,ZERO
|
||||
PARAMETER (ONE=1.0D+0,ZERO=0.0D+0)
|
||||
* ..
|
||||
* .. Local Scalars ..
|
||||
DOUBLE PRECISION ABSXI,NORM,SCALE,SSQ
|
||||
INTEGER IX
|
||||
* ..
|
||||
* .. Intrinsic Functions ..
|
||||
INTRINSIC ABS,SQRT
|
||||
* ..
|
||||
IF (N.LT.1 .OR. INCX.LT.1) THEN
|
||||
NORM = ZERO
|
||||
ELSE IF (N.EQ.1) THEN
|
||||
NORM = ABS(X(1))
|
||||
ELSE
|
||||
SCALE = ZERO
|
||||
SSQ = ONE
|
||||
* The following loop is equivalent to this call to the LAPACK
|
||||
* auxiliary routine:
|
||||
* CALL DLASSQ( N, X, INCX, SCALE, SSQ )
|
||||
*
|
||||
DO 10 IX = 1,1 + (N-1)*INCX,INCX
|
||||
IF (X(IX).NE.ZERO) THEN
|
||||
ABSXI = ABS(X(IX))
|
||||
IF (SCALE.LT.ABSXI) THEN
|
||||
SSQ = ONE + SSQ* (SCALE/ABSXI)**2
|
||||
SCALE = ABSXI
|
||||
ELSE
|
||||
SSQ = SSQ + (ABSXI/SCALE)**2
|
||||
END IF
|
||||
END IF
|
||||
10 CONTINUE
|
||||
NORM = SCALE*SQRT(SSQ)
|
||||
END IF
|
||||
*
|
||||
DNRM2 = NORM
|
||||
RETURN
|
||||
*
|
||||
* End of DNRM2.
|
||||
*
|
||||
END
|
||||
|
|
@ -0,0 +1,199 @@
|
|||
!> \brief \b DNRM2
|
||||
!
|
||||
! =========== DOCUMENTATION ===========
|
||||
!
|
||||
! Online html documentation available at
|
||||
! http://www.netlib.org/lapack/explore-html/
|
||||
!
|
||||
! Definition:
|
||||
! ===========
|
||||
!
|
||||
! DOUBLE PRECISION FUNCTION DNRM2(N,X,INCX)
|
||||
!
|
||||
! .. Scalar Arguments ..
|
||||
! INTEGER INCX,N
|
||||
! ..
|
||||
! .. Array Arguments ..
|
||||
! DOUBLE PRECISION X(*)
|
||||
! ..
|
||||
!
|
||||
!
|
||||
!> \par Purpose:
|
||||
! =============
|
||||
!>
|
||||
!> \verbatim
|
||||
!>
|
||||
!> DNRM2 returns the euclidean norm of a vector via the function
|
||||
!> name, so that
|
||||
!>
|
||||
!> DNRM2 := sqrt( x'*x )
|
||||
!> \endverbatim
|
||||
!
|
||||
! Arguments:
|
||||
! ==========
|
||||
!
|
||||
!> \param[in] N
|
||||
!> \verbatim
|
||||
!> N is INTEGER
|
||||
!> number of elements in input vector(s)
|
||||
!> \endverbatim
|
||||
!>
|
||||
!> \param[in] X
|
||||
!> \verbatim
|
||||
!> X is DOUBLE PRECISION array, dimension ( 1 + ( N - 1 )*abs( INCX ) )
|
||||
!> \endverbatim
|
||||
!>
|
||||
!> \param[in] INCX
|
||||
!> \verbatim
|
||||
!> INCX is INTEGER, storage spacing between elements of X
|
||||
!> If INCX > 0, X(1+(i-1)*INCX) = x(i) for 1 <= i <= n
|
||||
!> If INCX < 0, X(1-(n-i)*INCX) = x(i) for 1 <= i <= n
|
||||
!> If INCX = 0, x isn't a vector so there is no need to call
|
||||
!> this subroutine. If you call it anyway, it will count x(1)
|
||||
!> in the vector norm N times.
|
||||
!> \endverbatim
|
||||
!
|
||||
! Authors:
|
||||
! ========
|
||||
!
|
||||
!> \author Edward Anderson, Lockheed Martin
|
||||
!
|
||||
!> \date August 2016
|
||||
!
|
||||
!> \ingroup single_blas_level1
|
||||
!
|
||||
!> \par Contributors:
|
||||
! ==================
|
||||
!>
|
||||
!> Weslley Pereira, University of Colorado Denver, USA
|
||||
!
|
||||
!> \par Further Details:
|
||||
! =====================
|
||||
!>
|
||||
!> \verbatim
|
||||
!>
|
||||
!> Anderson E. (2017)
|
||||
!> Algorithm 978: Safe Scaling in the Level 1 BLAS
|
||||
!> ACM Trans Math Softw 44:1--28
|
||||
!> https://doi.org/10.1145/3061665
|
||||
!>
|
||||
!> Blue, James L. (1978)
|
||||
!> A Portable Fortran Program to Find the Euclidean Norm of a Vector
|
||||
!> ACM Trans Math Softw 4:15--23
|
||||
!> https://doi.org/10.1145/355769.355771
|
||||
!>
|
||||
!> \endverbatim
|
||||
!>
|
||||
! =====================================================================
|
||||
function DNRM2( n, x, incx )
|
||||
integer, parameter :: wp = kind(1.d0)
|
||||
real(wp) :: DNRM2
|
||||
!
|
||||
! -- Reference BLAS level1 routine (version 3.9.1) --
|
||||
! -- Reference BLAS is a software package provided by Univ. of Tennessee, --
|
||||
! -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
|
||||
! March 2021
|
||||
!
|
||||
! .. Constants ..
|
||||
real(wp), parameter :: zero = 0.0_wp
|
||||
real(wp), parameter :: one = 1.0_wp
|
||||
real(wp), parameter :: maxN = huge(0.0_wp)
|
||||
! ..
|
||||
! .. Blue's ccaling constants ..
|
||||
real(wp), parameter :: tsml = real(radix(0._wp), wp)**ceiling( &
|
||||
(minexponent(0._wp) - 1) * 0.5_wp)
|
||||
real(wp), parameter :: tbig = real(radix(0._wp), wp)**floor( &
|
||||
(maxexponent(0._wp) - digits(0._wp) + 1) * 0.5_wp)
|
||||
real(wp), parameter :: ssml = real(radix(0._wp), wp)**( - floor( &
|
||||
(minexponent(0._wp) - 1) * 0.5_wp))
|
||||
real(wp), parameter :: sbig = real(radix(0._wp), wp)**( - ceiling( &
|
||||
(maxexponent(0._wp) - digits(0._wp) + 1) * 0.5_wp))
|
||||
! ..
|
||||
! .. Scalar Arguments ..
|
||||
integer :: incx, n
|
||||
! ..
|
||||
! .. Array Arguments ..
|
||||
real(wp) :: x(*)
|
||||
! ..
|
||||
! .. Local Scalars ..
|
||||
integer :: i, ix
|
||||
logical :: notbig
|
||||
real(wp) :: abig, amed, asml, ax, scl, sumsq, ymax, ymin
|
||||
!
|
||||
! Quick return if possible
|
||||
!
|
||||
DNRM2 = zero
|
||||
if( n <= 0 ) return
|
||||
!
|
||||
scl = one
|
||||
sumsq = zero
|
||||
!
|
||||
! Compute the sum of squares in 3 accumulators:
|
||||
! abig -- sums of squares scaled down to avoid overflow
|
||||
! asml -- sums of squares scaled up to avoid underflow
|
||||
! amed -- sums of squares that do not require scaling
|
||||
! The thresholds and multipliers are
|
||||
! tbig -- values bigger than this are scaled down by sbig
|
||||
! tsml -- values smaller than this are scaled up by ssml
|
||||
!
|
||||
notbig = .true.
|
||||
asml = zero
|
||||
amed = zero
|
||||
abig = zero
|
||||
ix = 1
|
||||
if( incx < 0 ) ix = 1 - (n-1)*incx
|
||||
do i = 1, n
|
||||
ax = abs(x(ix))
|
||||
if (ax > tbig) then
|
||||
abig = abig + (ax*sbig)**2
|
||||
notbig = .false.
|
||||
else if (ax < tsml) then
|
||||
if (notbig) asml = asml + (ax*ssml)**2
|
||||
else
|
||||
amed = amed + ax**2
|
||||
end if
|
||||
ix = ix + incx
|
||||
end do
|
||||
!
|
||||
! Combine abig and amed or amed and asml if more than one
|
||||
! accumulator was used.
|
||||
!
|
||||
if (abig > zero) then
|
||||
!
|
||||
! Combine abig and amed if abig > 0.
|
||||
!
|
||||
if ( (amed > zero) .or. (amed > maxN) .or. (amed /= amed) ) then
|
||||
abig = abig + (amed*sbig)*sbig
|
||||
end if
|
||||
scl = one / sbig
|
||||
sumsq = abig
|
||||
else if (asml > zero) then
|
||||
!
|
||||
! Combine amed and asml if asml > 0.
|
||||
!
|
||||
if ( (amed > zero) .or. (amed > maxN) .or. (amed /= amed) ) then
|
||||
amed = sqrt(amed)
|
||||
asml = sqrt(asml) / ssml
|
||||
if (asml > amed) then
|
||||
ymin = amed
|
||||
ymax = asml
|
||||
else
|
||||
ymin = asml
|
||||
ymax = amed
|
||||
end if
|
||||
scl = one
|
||||
sumsq = ymax**2*( one + (ymin/ymax)**2 )
|
||||
else
|
||||
scl = one / ssml
|
||||
sumsq = asml
|
||||
end if
|
||||
else
|
||||
!
|
||||
! Otherwise all values are mid-range
|
||||
!
|
||||
scl = one
|
||||
sumsq = amed
|
||||
end if
|
||||
DNRM2 = scl*sqrt( sumsq )
|
||||
return
|
||||
end function
|
||||
|
|
@ -76,8 +76,6 @@
|
|||
*> \author Univ. of Colorado Denver
|
||||
*> \author NAG Ltd.
|
||||
*
|
||||
*> \date November 2017
|
||||
*
|
||||
*> \ingroup double_blas_level1
|
||||
*
|
||||
*> \par Further Details:
|
||||
|
|
@ -92,10 +90,9 @@
|
|||
* =====================================================================
|
||||
SUBROUTINE DROT(N,DX,INCX,DY,INCY,C,S)
|
||||
*
|
||||
* -- Reference BLAS level1 routine (version 3.8.0) --
|
||||
* -- Reference BLAS level1 routine --
|
||||
* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
|
||||
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
|
||||
* November 2017
|
||||
*
|
||||
* .. Scalar Arguments ..
|
||||
DOUBLE PRECISION C,S
|
||||
|
|
@ -139,4 +136,7 @@
|
|||
END DO
|
||||
END IF
|
||||
RETURN
|
||||
*
|
||||
* End of DROT
|
||||
*
|
||||
END
|
||||
|
|
|
|||
|
|
@ -1,109 +0,0 @@
|
|||
*> \brief \b DROTG
|
||||
*
|
||||
* =========== DOCUMENTATION ===========
|
||||
*
|
||||
* Online html documentation available at
|
||||
* http://www.netlib.org/lapack/explore-html/
|
||||
*
|
||||
* Definition:
|
||||
* ===========
|
||||
*
|
||||
* SUBROUTINE DROTG(DA,DB,C,S)
|
||||
*
|
||||
* .. Scalar Arguments ..
|
||||
* DOUBLE PRECISION C,DA,DB,S
|
||||
* ..
|
||||
*
|
||||
*
|
||||
*> \par Purpose:
|
||||
* =============
|
||||
*>
|
||||
*> \verbatim
|
||||
*>
|
||||
*> DROTG construct givens plane rotation.
|
||||
*> \endverbatim
|
||||
*
|
||||
* Arguments:
|
||||
* ==========
|
||||
*
|
||||
*> \param[in] DA
|
||||
*> \verbatim
|
||||
*> DA is DOUBLE PRECISION
|
||||
*> \endverbatim
|
||||
*>
|
||||
*> \param[in] DB
|
||||
*> \verbatim
|
||||
*> DB is DOUBLE PRECISION
|
||||
*> \endverbatim
|
||||
*>
|
||||
*> \param[out] C
|
||||
*> \verbatim
|
||||
*> C is DOUBLE PRECISION
|
||||
*> \endverbatim
|
||||
*>
|
||||
*> \param[out] S
|
||||
*> \verbatim
|
||||
*> S is DOUBLE PRECISION
|
||||
*> \endverbatim
|
||||
*
|
||||
* Authors:
|
||||
* ========
|
||||
*
|
||||
*> \author Univ. of Tennessee
|
||||
*> \author Univ. of California Berkeley
|
||||
*> \author Univ. of Colorado Denver
|
||||
*> \author NAG Ltd.
|
||||
*
|
||||
*> \date November 2017
|
||||
*
|
||||
*> \ingroup double_blas_level1
|
||||
*
|
||||
*> \par Further Details:
|
||||
* =====================
|
||||
*>
|
||||
*> \verbatim
|
||||
*>
|
||||
*> jack dongarra, linpack, 3/11/78.
|
||||
*> \endverbatim
|
||||
*>
|
||||
* =====================================================================
|
||||
SUBROUTINE DROTG(DA,DB,C,S)
|
||||
*
|
||||
* -- Reference BLAS level1 routine (version 3.8.0) --
|
||||
* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
|
||||
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
|
||||
* November 2017
|
||||
*
|
||||
* .. Scalar Arguments ..
|
||||
DOUBLE PRECISION C,DA,DB,S
|
||||
* ..
|
||||
*
|
||||
* =====================================================================
|
||||
*
|
||||
* .. Local Scalars ..
|
||||
DOUBLE PRECISION R,ROE,SCALE,Z
|
||||
* ..
|
||||
* .. Intrinsic Functions ..
|
||||
INTRINSIC DABS,DSIGN,DSQRT
|
||||
* ..
|
||||
ROE = DB
|
||||
IF (DABS(DA).GT.DABS(DB)) ROE = DA
|
||||
SCALE = DABS(DA) + DABS(DB)
|
||||
IF (SCALE.EQ.0.0d0) THEN
|
||||
C = 1.0d0
|
||||
S = 0.0d0
|
||||
R = 0.0d0
|
||||
Z = 0.0d0
|
||||
ELSE
|
||||
R = SCALE*DSQRT((DA/SCALE)**2+ (DB/SCALE)**2)
|
||||
R = DSIGN(1.0d0,ROE)*R
|
||||
C = DA/R
|
||||
S = DB/R
|
||||
Z = 1.0d0
|
||||
IF (DABS(DA).GT.DABS(DB)) Z = S
|
||||
IF (DABS(DB).GE.DABS(DA) .AND. C.NE.0.0d0) Z = 1.0d0/C
|
||||
END IF
|
||||
DA = R
|
||||
DB = Z
|
||||
RETURN
|
||||
END
|
||||
|
|
@ -0,0 +1,151 @@
|
|||
!> \brief \b DROTG
|
||||
!
|
||||
! =========== DOCUMENTATION ===========
|
||||
!
|
||||
! Online html documentation available at
|
||||
! http://www.netlib.org/lapack/explore-html/
|
||||
!
|
||||
! Definition:
|
||||
! ===========
|
||||
!
|
||||
! DROTG constructs a plane rotation
|
||||
! [ c s ] [ a ] = [ r ]
|
||||
! [ -s c ] [ b ] [ 0 ]
|
||||
! satisfying c**2 + s**2 = 1.
|
||||
!
|
||||
!> \par Purpose:
|
||||
! =============
|
||||
!>
|
||||
!> \verbatim
|
||||
!>
|
||||
!> The computation uses the formulas
|
||||
!> sigma = sgn(a) if |a| > |b|
|
||||
!> = sgn(b) if |b| >= |a|
|
||||
!> r = sigma*sqrt( a**2 + b**2 )
|
||||
!> c = 1; s = 0 if r = 0
|
||||
!> c = a/r; s = b/r if r != 0
|
||||
!> The subroutine also computes
|
||||
!> z = s if |a| > |b|,
|
||||
!> = 1/c if |b| >= |a| and c != 0
|
||||
!> = 1 if c = 0
|
||||
!> This allows c and s to be reconstructed from z as follows:
|
||||
!> If z = 1, set c = 0, s = 1.
|
||||
!> If |z| < 1, set c = sqrt(1 - z**2) and s = z.
|
||||
!> If |z| > 1, set c = 1/z and s = sqrt( 1 - c**2).
|
||||
!>
|
||||
!> \endverbatim
|
||||
!
|
||||
! Arguments:
|
||||
! ==========
|
||||
!
|
||||
!> \param[in,out] A
|
||||
!> \verbatim
|
||||
!> A is DOUBLE PRECISION
|
||||
!> On entry, the scalar a.
|
||||
!> On exit, the scalar r.
|
||||
!> \endverbatim
|
||||
!>
|
||||
!> \param[in,out] B
|
||||
!> \verbatim
|
||||
!> B is DOUBLE PRECISION
|
||||
!> On entry, the scalar b.
|
||||
!> On exit, the scalar z.
|
||||
!> \endverbatim
|
||||
!>
|
||||
!> \param[out] C
|
||||
!> \verbatim
|
||||
!> C is DOUBLE PRECISION
|
||||
!> The scalar c.
|
||||
!> \endverbatim
|
||||
!>
|
||||
!> \param[out] S
|
||||
!> \verbatim
|
||||
!> S is DOUBLE PRECISION
|
||||
!> The scalar s.
|
||||
!> \endverbatim
|
||||
!
|
||||
! Authors:
|
||||
! ========
|
||||
!
|
||||
!> \author Edward Anderson, Lockheed Martin
|
||||
!
|
||||
!> \par Contributors:
|
||||
! ==================
|
||||
!>
|
||||
!> Weslley Pereira, University of Colorado Denver, USA
|
||||
!
|
||||
!> \ingroup single_blas_level1
|
||||
!
|
||||
!> \par Further Details:
|
||||
! =====================
|
||||
!>
|
||||
!> \verbatim
|
||||
!>
|
||||
!> Anderson E. (2017)
|
||||
!> Algorithm 978: Safe Scaling in the Level 1 BLAS
|
||||
!> ACM Trans Math Softw 44:1--28
|
||||
!> https://doi.org/10.1145/3061665
|
||||
!>
|
||||
!> \endverbatim
|
||||
!
|
||||
! =====================================================================
|
||||
subroutine DROTG( a, b, c, s )
|
||||
integer, parameter :: wp = kind(1.d0)
|
||||
!
|
||||
! -- Reference BLAS level1 routine --
|
||||
! -- Reference BLAS is a software package provided by Univ. of Tennessee, --
|
||||
! -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
|
||||
!
|
||||
! .. Constants ..
|
||||
real(wp), parameter :: zero = 0.0_wp
|
||||
real(wp), parameter :: one = 1.0_wp
|
||||
! ..
|
||||
! .. Scaling constants ..
|
||||
real(wp), parameter :: safmin = real(radix(0._wp),wp)**max( &
|
||||
minexponent(0._wp)-1, &
|
||||
1-maxexponent(0._wp) &
|
||||
)
|
||||
real(wp), parameter :: safmax = real(radix(0._wp),wp)**max( &
|
||||
1-minexponent(0._wp), &
|
||||
maxexponent(0._wp)-1 &
|
||||
)
|
||||
! ..
|
||||
! .. Scalar Arguments ..
|
||||
real(wp) :: a, b, c, s
|
||||
! ..
|
||||
! .. Local Scalars ..
|
||||
real(wp) :: anorm, bnorm, scl, sigma, r, z
|
||||
! ..
|
||||
anorm = abs(a)
|
||||
bnorm = abs(b)
|
||||
if( bnorm == zero ) then
|
||||
c = one
|
||||
s = zero
|
||||
b = zero
|
||||
else if( anorm == zero ) then
|
||||
c = zero
|
||||
s = one
|
||||
a = b
|
||||
b = one
|
||||
else
|
||||
scl = min( safmax, max( safmin, anorm, bnorm ) )
|
||||
if( anorm > bnorm ) then
|
||||
sigma = sign(one,a)
|
||||
else
|
||||
sigma = sign(one,b)
|
||||
end if
|
||||
r = sigma*( scl*sqrt((a/scl)**2 + (b/scl)**2) )
|
||||
c = a/r
|
||||
s = b/r
|
||||
if( anorm > bnorm ) then
|
||||
z = s
|
||||
else if( c /= zero ) then
|
||||
z = one/c
|
||||
else
|
||||
z = one
|
||||
end if
|
||||
a = r
|
||||
b = z
|
||||
end if
|
||||
return
|
||||
end subroutine
|
||||
|
|
@ -89,17 +89,14 @@
|
|||
*> \author Univ. of Colorado Denver
|
||||
*> \author NAG Ltd.
|
||||
*
|
||||
*> \date November 2017
|
||||
*
|
||||
*> \ingroup double_blas_level1
|
||||
*
|
||||
* =====================================================================
|
||||
SUBROUTINE DROTM(N,DX,INCX,DY,INCY,DPARAM)
|
||||
*
|
||||
* -- Reference BLAS level1 routine (version 3.8.0) --
|
||||
* -- Reference BLAS level1 routine --
|
||||
* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
|
||||
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
|
||||
* November 2017
|
||||
*
|
||||
* .. Scalar Arguments ..
|
||||
INTEGER INCX,INCY,N
|
||||
|
|
@ -197,4 +194,7 @@
|
|||
END IF
|
||||
END IF
|
||||
RETURN
|
||||
*
|
||||
* End of DROTM
|
||||
*
|
||||
END
|
||||
|
|
|
|||
|
|
@ -83,17 +83,14 @@
|
|||
*> \author Univ. of Colorado Denver
|
||||
*> \author NAG Ltd.
|
||||
*
|
||||
*> \date November 2017
|
||||
*
|
||||
*> \ingroup double_blas_level1
|
||||
*
|
||||
* =====================================================================
|
||||
SUBROUTINE DROTMG(DD1,DD2,DX1,DY1,DPARAM)
|
||||
*
|
||||
* -- Reference BLAS level1 routine (version 3.8.0) --
|
||||
* -- Reference BLAS level1 routine --
|
||||
* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
|
||||
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
|
||||
* November 2017
|
||||
*
|
||||
* .. Scalar Arguments ..
|
||||
DOUBLE PRECISION DD1,DD2,DX1,DY1
|
||||
|
|
@ -152,6 +149,19 @@
|
|||
DD1 = DD1/DU
|
||||
DD2 = DD2/DU
|
||||
DX1 = DX1*DU
|
||||
ELSE
|
||||
* This code path if here for safety. We do not expect this
|
||||
* condition to ever hold except in edge cases with rounding
|
||||
* errors. See DOI: 10.1145/355841.355847
|
||||
DFLAG = -ONE
|
||||
DH11 = ZERO
|
||||
DH12 = ZERO
|
||||
DH21 = ZERO
|
||||
DH22 = ZERO
|
||||
*
|
||||
DD1 = ZERO
|
||||
DD2 = ZERO
|
||||
DX1 = ZERO
|
||||
END IF
|
||||
ELSE
|
||||
|
||||
|
|
@ -244,8 +254,7 @@
|
|||
|
||||
DPARAM(1) = DFLAG
|
||||
RETURN
|
||||
*
|
||||
* End of DROTMG
|
||||
*
|
||||
END
|
||||
|
||||
|
||||
|
||||
|
||||
|
|
|
|||
|
|
@ -162,8 +162,6 @@
|
|||
*> \author Univ. of Colorado Denver
|
||||
*> \author NAG Ltd.
|
||||
*
|
||||
*> \date December 2016
|
||||
*
|
||||
*> \ingroup double_blas_level2
|
||||
*
|
||||
*> \par Further Details:
|
||||
|
|
@ -184,10 +182,9 @@
|
|||
* =====================================================================
|
||||
SUBROUTINE DSBMV(UPLO,N,K,ALPHA,A,LDA,X,INCX,BETA,Y,INCY)
|
||||
*
|
||||
* -- Reference BLAS level2 routine (version 3.7.0) --
|
||||
* -- Reference BLAS level2 routine --
|
||||
* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
|
||||
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
|
||||
* December 2016
|
||||
*
|
||||
* .. Scalar Arguments ..
|
||||
DOUBLE PRECISION ALPHA,BETA
|
||||
|
|
@ -370,6 +367,6 @@
|
|||
*
|
||||
RETURN
|
||||
*
|
||||
* End of DSBMV .
|
||||
* End of DSBMV
|
||||
*
|
||||
END
|
||||
|
|
|
|||
|
|
@ -62,8 +62,6 @@
|
|||
*> \author Univ. of Colorado Denver
|
||||
*> \author NAG Ltd.
|
||||
*
|
||||
*> \date November 2017
|
||||
*
|
||||
*> \ingroup double_blas_level1
|
||||
*
|
||||
*> \par Further Details:
|
||||
|
|
@ -79,10 +77,9 @@
|
|||
* =====================================================================
|
||||
SUBROUTINE DSCAL(N,DA,DX,INCX)
|
||||
*
|
||||
* -- Reference BLAS level1 routine (version 3.8.0) --
|
||||
* -- Reference BLAS level1 routine --
|
||||
* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
|
||||
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
|
||||
* November 2017
|
||||
*
|
||||
* .. Scalar Arguments ..
|
||||
DOUBLE PRECISION DA
|
||||
|
|
@ -133,4 +130,7 @@
|
|||
END DO
|
||||
END IF
|
||||
RETURN
|
||||
*
|
||||
* End of DSCAL
|
||||
*
|
||||
END
|
||||
|
|
|
|||
|
|
@ -84,8 +84,6 @@
|
|||
*> \author Univ. of Colorado Denver
|
||||
*> \author NAG Ltd.
|
||||
*
|
||||
*> \date December 2016
|
||||
*
|
||||
*> \ingroup double_blas_level1
|
||||
*
|
||||
*> \par Further Details:
|
||||
|
|
@ -119,10 +117,9 @@
|
|||
* =====================================================================
|
||||
DOUBLE PRECISION FUNCTION DSDOT(N,SX,INCX,SY,INCY)
|
||||
*
|
||||
* -- Reference BLAS level1 routine (version 3.7.0) --
|
||||
* -- Reference BLAS level1 routine --
|
||||
* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
|
||||
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
|
||||
* December 2016
|
||||
*
|
||||
* .. Scalar Arguments ..
|
||||
INTEGER INCX,INCY,N
|
||||
|
|
@ -169,4 +166,7 @@
|
|||
END DO
|
||||
END IF
|
||||
RETURN
|
||||
*
|
||||
* End of DSDOT
|
||||
*
|
||||
END
|
||||
|
|
|
|||
|
|
@ -125,8 +125,6 @@
|
|||
*> \author Univ. of Colorado Denver
|
||||
*> \author NAG Ltd.
|
||||
*
|
||||
*> \date December 2016
|
||||
*
|
||||
*> \ingroup double_blas_level2
|
||||
*
|
||||
*> \par Further Details:
|
||||
|
|
@ -147,10 +145,9 @@
|
|||
* =====================================================================
|
||||
SUBROUTINE DSPMV(UPLO,N,ALPHA,AP,X,INCX,BETA,Y,INCY)
|
||||
*
|
||||
* -- Reference BLAS level2 routine (version 3.7.0) --
|
||||
* -- Reference BLAS level2 routine --
|
||||
* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
|
||||
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
|
||||
* December 2016
|
||||
*
|
||||
* .. Scalar Arguments ..
|
||||
DOUBLE PRECISION ALPHA,BETA
|
||||
|
|
@ -326,6 +323,6 @@
|
|||
*
|
||||
RETURN
|
||||
*
|
||||
* End of DSPMV .
|
||||
* End of DSPMV
|
||||
*
|
||||
END
|
||||
|
|
|
|||
|
|
@ -106,8 +106,6 @@
|
|||
*> \author Univ. of Colorado Denver
|
||||
*> \author NAG Ltd.
|
||||
*
|
||||
*> \date December 2016
|
||||
*
|
||||
*> \ingroup double_blas_level2
|
||||
*
|
||||
*> \par Further Details:
|
||||
|
|
@ -127,10 +125,9 @@
|
|||
* =====================================================================
|
||||
SUBROUTINE DSPR(UPLO,N,ALPHA,X,INCX,AP)
|
||||
*
|
||||
* -- Reference BLAS level2 routine (version 3.7.0) --
|
||||
* -- Reference BLAS level2 routine --
|
||||
* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
|
||||
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
|
||||
* December 2016
|
||||
*
|
||||
* .. Scalar Arguments ..
|
||||
DOUBLE PRECISION ALPHA
|
||||
|
|
@ -256,6 +253,6 @@
|
|||
*
|
||||
RETURN
|
||||
*
|
||||
* End of DSPR .
|
||||
* End of DSPR
|
||||
*
|
||||
END
|
||||
|
|
|
|||
|
|
@ -121,8 +121,6 @@
|
|||
*> \author Univ. of Colorado Denver
|
||||
*> \author NAG Ltd.
|
||||
*
|
||||
*> \date December 2016
|
||||
*
|
||||
*> \ingroup double_blas_level2
|
||||
*
|
||||
*> \par Further Details:
|
||||
|
|
@ -142,10 +140,9 @@
|
|||
* =====================================================================
|
||||
SUBROUTINE DSPR2(UPLO,N,ALPHA,X,INCX,Y,INCY,AP)
|
||||
*
|
||||
* -- Reference BLAS level2 routine (version 3.7.0) --
|
||||
* -- Reference BLAS level2 routine --
|
||||
* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
|
||||
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
|
||||
* December 2016
|
||||
*
|
||||
* .. Scalar Arguments ..
|
||||
DOUBLE PRECISION ALPHA
|
||||
|
|
@ -291,6 +288,6 @@
|
|||
*
|
||||
RETURN
|
||||
*
|
||||
* End of DSPR2 .
|
||||
* End of DSPR2
|
||||
*
|
||||
END
|
||||
|
|
|
|||
|
|
@ -66,8 +66,6 @@
|
|||
*> \author Univ. of Colorado Denver
|
||||
*> \author NAG Ltd.
|
||||
*
|
||||
*> \date November 2017
|
||||
*
|
||||
*> \ingroup double_blas_level1
|
||||
*
|
||||
*> \par Further Details:
|
||||
|
|
@ -82,10 +80,9 @@
|
|||
* =====================================================================
|
||||
SUBROUTINE DSWAP(N,DX,INCX,DY,INCY)
|
||||
*
|
||||
* -- Reference BLAS level1 routine (version 3.8.0) --
|
||||
* -- Reference BLAS level1 routine --
|
||||
* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
|
||||
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
|
||||
* November 2017
|
||||
*
|
||||
* .. Scalar Arguments ..
|
||||
INTEGER INCX,INCY,N
|
||||
|
|
@ -150,4 +147,7 @@
|
|||
END DO
|
||||
END IF
|
||||
RETURN
|
||||
*
|
||||
* End of DSWAP
|
||||
*
|
||||
END
|
||||
|
|
|
|||
|
|
@ -168,8 +168,6 @@
|
|||
*> \author Univ. of Colorado Denver
|
||||
*> \author NAG Ltd.
|
||||
*
|
||||
*> \date December 2016
|
||||
*
|
||||
*> \ingroup double_blas_level3
|
||||
*
|
||||
*> \par Further Details:
|
||||
|
|
@ -189,10 +187,9 @@
|
|||
* =====================================================================
|
||||
SUBROUTINE DSYMM(SIDE,UPLO,M,N,ALPHA,A,LDA,B,LDB,BETA,C,LDC)
|
||||
*
|
||||
* -- Reference BLAS level3 routine (version 3.7.0) --
|
||||
* -- Reference BLAS level3 routine --
|
||||
* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
|
||||
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
|
||||
* December 2016
|
||||
*
|
||||
* .. Scalar Arguments ..
|
||||
DOUBLE PRECISION ALPHA,BETA
|
||||
|
|
@ -362,6 +359,6 @@
|
|||
*
|
||||
RETURN
|
||||
*
|
||||
* End of DSYMM .
|
||||
* End of DSYMM
|
||||
*
|
||||
END
|
||||
|
|
|
|||
|
|
@ -130,8 +130,6 @@
|
|||
*> \author Univ. of Colorado Denver
|
||||
*> \author NAG Ltd.
|
||||
*
|
||||
*> \date December 2016
|
||||
*
|
||||
*> \ingroup double_blas_level2
|
||||
*
|
||||
*> \par Further Details:
|
||||
|
|
@ -152,10 +150,9 @@
|
|||
* =====================================================================
|
||||
SUBROUTINE DSYMV(UPLO,N,ALPHA,A,LDA,X,INCX,BETA,Y,INCY)
|
||||
*
|
||||
* -- Reference BLAS level2 routine (version 3.7.0) --
|
||||
* -- Reference BLAS level2 routine --
|
||||
* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
|
||||
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
|
||||
* December 2016
|
||||
*
|
||||
* .. Scalar Arguments ..
|
||||
DOUBLE PRECISION ALPHA,BETA
|
||||
|
|
@ -328,6 +325,6 @@
|
|||
*
|
||||
RETURN
|
||||
*
|
||||
* End of DSYMV .
|
||||
* End of DSYMV
|
||||
*
|
||||
END
|
||||
|
|
|
|||
|
|
@ -111,8 +111,6 @@
|
|||
*> \author Univ. of Colorado Denver
|
||||
*> \author NAG Ltd.
|
||||
*
|
||||
*> \date December 2016
|
||||
*
|
||||
*> \ingroup double_blas_level2
|
||||
*
|
||||
*> \par Further Details:
|
||||
|
|
@ -132,10 +130,9 @@
|
|||
* =====================================================================
|
||||
SUBROUTINE DSYR(UPLO,N,ALPHA,X,INCX,A,LDA)
|
||||
*
|
||||
* -- Reference BLAS level2 routine (version 3.7.0) --
|
||||
* -- Reference BLAS level2 routine --
|
||||
* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
|
||||
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
|
||||
* December 2016
|
||||
*
|
||||
* .. Scalar Arguments ..
|
||||
DOUBLE PRECISION ALPHA
|
||||
|
|
@ -258,6 +255,6 @@
|
|||
*
|
||||
RETURN
|
||||
*
|
||||
* End of DSYR .
|
||||
* End of DSYR
|
||||
*
|
||||
END
|
||||
|
|
|
|||
|
|
@ -126,8 +126,6 @@
|
|||
*> \author Univ. of Colorado Denver
|
||||
*> \author NAG Ltd.
|
||||
*
|
||||
*> \date December 2016
|
||||
*
|
||||
*> \ingroup double_blas_level2
|
||||
*
|
||||
*> \par Further Details:
|
||||
|
|
@ -147,10 +145,9 @@
|
|||
* =====================================================================
|
||||
SUBROUTINE DSYR2(UPLO,N,ALPHA,X,INCX,Y,INCY,A,LDA)
|
||||
*
|
||||
* -- Reference BLAS level2 routine (version 3.7.0) --
|
||||
* -- Reference BLAS level2 routine --
|
||||
* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
|
||||
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
|
||||
* December 2016
|
||||
*
|
||||
* .. Scalar Arguments ..
|
||||
DOUBLE PRECISION ALPHA
|
||||
|
|
@ -293,6 +290,6 @@
|
|||
*
|
||||
RETURN
|
||||
*
|
||||
* End of DSYR2 .
|
||||
* End of DSYR2
|
||||
*
|
||||
END
|
||||
|
|
|
|||
|
|
@ -170,8 +170,6 @@
|
|||
*> \author Univ. of Colorado Denver
|
||||
*> \author NAG Ltd.
|
||||
*
|
||||
*> \date December 2016
|
||||
*
|
||||
*> \ingroup double_blas_level3
|
||||
*
|
||||
*> \par Further Details:
|
||||
|
|
@ -192,10 +190,9 @@
|
|||
* =====================================================================
|
||||
SUBROUTINE DSYR2K(UPLO,TRANS,N,K,ALPHA,A,LDA,B,LDB,BETA,C,LDC)
|
||||
*
|
||||
* -- Reference BLAS level3 routine (version 3.7.0) --
|
||||
* -- Reference BLAS level3 routine --
|
||||
* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
|
||||
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
|
||||
* December 2016
|
||||
*
|
||||
* .. Scalar Arguments ..
|
||||
DOUBLE PRECISION ALPHA,BETA
|
||||
|
|
@ -394,6 +391,6 @@
|
|||
*
|
||||
RETURN
|
||||
*
|
||||
* End of DSYR2K.
|
||||
* End of DSYR2K
|
||||
*
|
||||
END
|
||||
|
|
|
|||
|
|
@ -148,8 +148,6 @@
|
|||
*> \author Univ. of Colorado Denver
|
||||
*> \author NAG Ltd.
|
||||
*
|
||||
*> \date December 2016
|
||||
*
|
||||
*> \ingroup double_blas_level3
|
||||
*
|
||||
*> \par Further Details:
|
||||
|
|
@ -169,10 +167,9 @@
|
|||
* =====================================================================
|
||||
SUBROUTINE DSYRK(UPLO,TRANS,N,K,ALPHA,A,LDA,BETA,C,LDC)
|
||||
*
|
||||
* -- Reference BLAS level3 routine (version 3.7.0) --
|
||||
* -- Reference BLAS level3 routine --
|
||||
* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
|
||||
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
|
||||
* December 2016
|
||||
*
|
||||
* .. Scalar Arguments ..
|
||||
DOUBLE PRECISION ALPHA,BETA
|
||||
|
|
@ -359,6 +356,6 @@
|
|||
*
|
||||
RETURN
|
||||
*
|
||||
* End of DSYRK .
|
||||
* End of DSYRK
|
||||
*
|
||||
END
|
||||
|
|
|
|||
|
|
@ -164,8 +164,6 @@
|
|||
*> \author Univ. of Colorado Denver
|
||||
*> \author NAG Ltd.
|
||||
*
|
||||
*> \date December 2016
|
||||
*
|
||||
*> \ingroup double_blas_level2
|
||||
*
|
||||
*> \par Further Details:
|
||||
|
|
@ -186,10 +184,9 @@
|
|||
* =====================================================================
|
||||
SUBROUTINE DTBMV(UPLO,TRANS,DIAG,N,K,A,LDA,X,INCX)
|
||||
*
|
||||
* -- Reference BLAS level2 routine (version 3.7.0) --
|
||||
* -- Reference BLAS level2 routine --
|
||||
* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
|
||||
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
|
||||
* December 2016
|
||||
*
|
||||
* .. Scalar Arguments ..
|
||||
INTEGER INCX,K,LDA,N
|
||||
|
|
@ -393,6 +390,6 @@
|
|||
*
|
||||
RETURN
|
||||
*
|
||||
* End of DTBMV .
|
||||
* End of DTBMV
|
||||
*
|
||||
END
|
||||
|
|
|
|||
|
|
@ -168,8 +168,6 @@
|
|||
*> \author Univ. of Colorado Denver
|
||||
*> \author NAG Ltd.
|
||||
*
|
||||
*> \date December 2016
|
||||
*
|
||||
*> \ingroup double_blas_level2
|
||||
*
|
||||
*> \par Further Details:
|
||||
|
|
@ -189,10 +187,9 @@
|
|||
* =====================================================================
|
||||
SUBROUTINE DTBSV(UPLO,TRANS,DIAG,N,K,A,LDA,X,INCX)
|
||||
*
|
||||
* -- Reference BLAS level2 routine (version 3.7.0) --
|
||||
* -- Reference BLAS level2 routine --
|
||||
* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
|
||||
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
|
||||
* December 2016
|
||||
*
|
||||
* .. Scalar Arguments ..
|
||||
INTEGER INCX,K,LDA,N
|
||||
|
|
@ -396,6 +393,6 @@
|
|||
*
|
||||
RETURN
|
||||
*
|
||||
* End of DTBSV .
|
||||
* End of DTBSV
|
||||
*
|
||||
END
|
||||
|
|
|
|||
|
|
@ -120,8 +120,6 @@
|
|||
*> \author Univ. of Colorado Denver
|
||||
*> \author NAG Ltd.
|
||||
*
|
||||
*> \date December 2016
|
||||
*
|
||||
*> \ingroup double_blas_level2
|
||||
*
|
||||
*> \par Further Details:
|
||||
|
|
@ -142,10 +140,9 @@
|
|||
* =====================================================================
|
||||
SUBROUTINE DTPMV(UPLO,TRANS,DIAG,N,AP,X,INCX)
|
||||
*
|
||||
* -- Reference BLAS level2 routine (version 3.7.0) --
|
||||
* -- Reference BLAS level2 routine --
|
||||
* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
|
||||
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
|
||||
* December 2016
|
||||
*
|
||||
* .. Scalar Arguments ..
|
||||
INTEGER INCX,N
|
||||
|
|
@ -347,6 +344,6 @@
|
|||
*
|
||||
RETURN
|
||||
*
|
||||
* End of DTPMV .
|
||||
* End of DTPMV
|
||||
*
|
||||
END
|
||||
|
|
|
|||
|
|
@ -123,8 +123,6 @@
|
|||
*> \author Univ. of Colorado Denver
|
||||
*> \author NAG Ltd.
|
||||
*
|
||||
*> \date December 2016
|
||||
*
|
||||
*> \ingroup double_blas_level2
|
||||
*
|
||||
*> \par Further Details:
|
||||
|
|
@ -144,10 +142,9 @@
|
|||
* =====================================================================
|
||||
SUBROUTINE DTPSV(UPLO,TRANS,DIAG,N,AP,X,INCX)
|
||||
*
|
||||
* -- Reference BLAS level2 routine (version 3.7.0) --
|
||||
* -- Reference BLAS level2 routine --
|
||||
* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
|
||||
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
|
||||
* December 2016
|
||||
*
|
||||
* .. Scalar Arguments ..
|
||||
INTEGER INCX,N
|
||||
|
|
@ -349,6 +346,6 @@
|
|||
*
|
||||
RETURN
|
||||
*
|
||||
* End of DTPSV .
|
||||
* End of DTPSV
|
||||
*
|
||||
END
|
||||
|
|
|
|||
|
|
@ -156,8 +156,6 @@
|
|||
*> \author Univ. of Colorado Denver
|
||||
*> \author NAG Ltd.
|
||||
*
|
||||
*> \date December 2016
|
||||
*
|
||||
*> \ingroup double_blas_level3
|
||||
*
|
||||
*> \par Further Details:
|
||||
|
|
@ -177,10 +175,9 @@
|
|||
* =====================================================================
|
||||
SUBROUTINE DTRMM(SIDE,UPLO,TRANSA,DIAG,M,N,ALPHA,A,LDA,B,LDB)
|
||||
*
|
||||
* -- Reference BLAS level3 routine (version 3.7.0) --
|
||||
* -- Reference BLAS level3 routine --
|
||||
* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
|
||||
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
|
||||
* December 2016
|
||||
*
|
||||
* .. Scalar Arguments ..
|
||||
DOUBLE PRECISION ALPHA
|
||||
|
|
@ -410,6 +407,6 @@
|
|||
*
|
||||
RETURN
|
||||
*
|
||||
* End of DTRMM .
|
||||
* End of DTRMM
|
||||
*
|
||||
END
|
||||
|
|
|
|||
|
|
@ -125,8 +125,6 @@
|
|||
*> \author Univ. of Colorado Denver
|
||||
*> \author NAG Ltd.
|
||||
*
|
||||
*> \date December 2016
|
||||
*
|
||||
*> \ingroup double_blas_level2
|
||||
*
|
||||
*> \par Further Details:
|
||||
|
|
@ -147,10 +145,9 @@
|
|||
* =====================================================================
|
||||
SUBROUTINE DTRMV(UPLO,TRANS,DIAG,N,A,LDA,X,INCX)
|
||||
*
|
||||
* -- Reference BLAS level2 routine (version 3.7.0) --
|
||||
* -- Reference BLAS level2 routine --
|
||||
* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
|
||||
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
|
||||
* December 2016
|
||||
*
|
||||
* .. Scalar Arguments ..
|
||||
INTEGER INCX,LDA,N
|
||||
|
|
@ -337,6 +334,6 @@
|
|||
*
|
||||
RETURN
|
||||
*
|
||||
* End of DTRMV .
|
||||
* End of DTRMV
|
||||
*
|
||||
END
|
||||
|
|
|
|||
|
|
@ -159,8 +159,6 @@
|
|||
*> \author Univ. of Colorado Denver
|
||||
*> \author NAG Ltd.
|
||||
*
|
||||
*> \date December 2016
|
||||
*
|
||||
*> \ingroup double_blas_level3
|
||||
*
|
||||
*> \par Further Details:
|
||||
|
|
@ -181,10 +179,9 @@
|
|||
* =====================================================================
|
||||
SUBROUTINE DTRSM(SIDE,UPLO,TRANSA,DIAG,M,N,ALPHA,A,LDA,B,LDB)
|
||||
*
|
||||
* -- Reference BLAS level3 routine (version 3.7.0) --
|
||||
* -- Reference BLAS level3 routine --
|
||||
* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
|
||||
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
|
||||
* December 2016
|
||||
*
|
||||
* .. Scalar Arguments ..
|
||||
DOUBLE PRECISION ALPHA
|
||||
|
|
@ -438,6 +435,6 @@
|
|||
*
|
||||
RETURN
|
||||
*
|
||||
* End of DTRSM .
|
||||
* End of DTRSM
|
||||
*
|
||||
END
|
||||
|
|
|
|||
|
|
@ -136,17 +136,14 @@
|
|||
*> \author Univ. of Colorado Denver
|
||||
*> \author NAG Ltd.
|
||||
*
|
||||
*> \date December 2016
|
||||
*
|
||||
*> \ingroup double_blas_level1
|
||||
*
|
||||
* =====================================================================
|
||||
SUBROUTINE DTRSV(UPLO,TRANS,DIAG,N,A,LDA,X,INCX)
|
||||
*
|
||||
* -- Reference BLAS level1 routine (version 3.7.0) --
|
||||
* -- Reference BLAS level1 routine --
|
||||
* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
|
||||
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
|
||||
* December 2016
|
||||
*
|
||||
* .. Scalar Arguments ..
|
||||
INTEGER INCX,LDA,N
|
||||
|
|
@ -333,6 +330,6 @@
|
|||
*
|
||||
RETURN
|
||||
*
|
||||
* End of DTRSV .
|
||||
* End of DTRSV
|
||||
*
|
||||
END
|
||||
|
|
|
|||
|
|
@ -24,7 +24,7 @@
|
|||
*> \verbatim
|
||||
*>
|
||||
*> DZASUM takes the sum of the (|Re(.)| + |Im(.)|)'s of a complex vector and
|
||||
*> returns a single precision result.
|
||||
*> returns a double precision result.
|
||||
*> \endverbatim
|
||||
*
|
||||
* Arguments:
|
||||
|
|
@ -55,8 +55,6 @@
|
|||
*> \author Univ. of Colorado Denver
|
||||
*> \author NAG Ltd.
|
||||
*
|
||||
*> \date November 2017
|
||||
*
|
||||
*> \ingroup double_blas_level1
|
||||
*
|
||||
*> \par Further Details:
|
||||
|
|
@ -72,10 +70,9 @@
|
|||
* =====================================================================
|
||||
DOUBLE PRECISION FUNCTION DZASUM(N,ZX,INCX)
|
||||
*
|
||||
* -- Reference BLAS level1 routine (version 3.8.0) --
|
||||
* -- Reference BLAS level1 routine --
|
||||
* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
|
||||
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
|
||||
* November 2017
|
||||
*
|
||||
* .. Scalar Arguments ..
|
||||
INTEGER INCX,N
|
||||
|
|
@ -115,4 +112,7 @@
|
|||
END IF
|
||||
DZASUM = STEMP
|
||||
RETURN
|
||||
*
|
||||
* End of DZASUM
|
||||
*
|
||||
END
|
||||
|
|
|
|||
|
|
@ -1,140 +0,0 @@
|
|||
*> \brief \b DZNRM2
|
||||
*
|
||||
* =========== DOCUMENTATION ===========
|
||||
*
|
||||
* Online html documentation available at
|
||||
* http://www.netlib.org/lapack/explore-html/
|
||||
*
|
||||
* Definition:
|
||||
* ===========
|
||||
*
|
||||
* DOUBLE PRECISION FUNCTION DZNRM2(N,X,INCX)
|
||||
*
|
||||
* .. Scalar Arguments ..
|
||||
* INTEGER INCX,N
|
||||
* ..
|
||||
* .. Array Arguments ..
|
||||
* COMPLEX*16 X(*)
|
||||
* ..
|
||||
*
|
||||
*
|
||||
*> \par Purpose:
|
||||
* =============
|
||||
*>
|
||||
*> \verbatim
|
||||
*>
|
||||
*> DZNRM2 returns the euclidean norm of a vector via the function
|
||||
*> name, so that
|
||||
*>
|
||||
*> DZNRM2 := sqrt( x**H*x )
|
||||
*> \endverbatim
|
||||
*
|
||||
* Arguments:
|
||||
* ==========
|
||||
*
|
||||
*> \param[in] N
|
||||
*> \verbatim
|
||||
*> N is INTEGER
|
||||
*> number of elements in input vector(s)
|
||||
*> \endverbatim
|
||||
*>
|
||||
*> \param[in] X
|
||||
*> \verbatim
|
||||
*> X is COMPLEX*16 array, dimension (N)
|
||||
*> complex vector with N elements
|
||||
*> \endverbatim
|
||||
*>
|
||||
*> \param[in] INCX
|
||||
*> \verbatim
|
||||
*> INCX is INTEGER
|
||||
*> storage spacing between elements of X
|
||||
*> \endverbatim
|
||||
*
|
||||
* Authors:
|
||||
* ========
|
||||
*
|
||||
*> \author Univ. of Tennessee
|
||||
*> \author Univ. of California Berkeley
|
||||
*> \author Univ. of Colorado Denver
|
||||
*> \author NAG Ltd.
|
||||
*
|
||||
*> \date November 2017
|
||||
*
|
||||
*> \ingroup double_blas_level1
|
||||
*
|
||||
*> \par Further Details:
|
||||
* =====================
|
||||
*>
|
||||
*> \verbatim
|
||||
*>
|
||||
*> -- This version written on 25-October-1982.
|
||||
*> Modified on 14-October-1993 to inline the call to ZLASSQ.
|
||||
*> Sven Hammarling, Nag Ltd.
|
||||
*> \endverbatim
|
||||
*>
|
||||
* =====================================================================
|
||||
DOUBLE PRECISION FUNCTION DZNRM2(N,X,INCX)
|
||||
*
|
||||
* -- Reference BLAS level1 routine (version 3.8.0) --
|
||||
* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
|
||||
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
|
||||
* November 2017
|
||||
*
|
||||
* .. Scalar Arguments ..
|
||||
INTEGER INCX,N
|
||||
* ..
|
||||
* .. Array Arguments ..
|
||||
COMPLEX*16 X(*)
|
||||
* ..
|
||||
*
|
||||
* =====================================================================
|
||||
*
|
||||
* .. Parameters ..
|
||||
DOUBLE PRECISION ONE,ZERO
|
||||
PARAMETER (ONE=1.0D+0,ZERO=0.0D+0)
|
||||
* ..
|
||||
* .. Local Scalars ..
|
||||
DOUBLE PRECISION NORM,SCALE,SSQ,TEMP
|
||||
INTEGER IX
|
||||
* ..
|
||||
* .. Intrinsic Functions ..
|
||||
INTRINSIC ABS,DBLE,DIMAG,SQRT
|
||||
* ..
|
||||
IF (N.LT.1 .OR. INCX.LT.1) THEN
|
||||
NORM = ZERO
|
||||
ELSE
|
||||
SCALE = ZERO
|
||||
SSQ = ONE
|
||||
* The following loop is equivalent to this call to the LAPACK
|
||||
* auxiliary routine:
|
||||
* CALL ZLASSQ( N, X, INCX, SCALE, SSQ )
|
||||
*
|
||||
DO 10 IX = 1,1 + (N-1)*INCX,INCX
|
||||
IF (DBLE(X(IX)).NE.ZERO) THEN
|
||||
TEMP = ABS(DBLE(X(IX)))
|
||||
IF (SCALE.LT.TEMP) THEN
|
||||
SSQ = ONE + SSQ* (SCALE/TEMP)**2
|
||||
SCALE = TEMP
|
||||
ELSE
|
||||
SSQ = SSQ + (TEMP/SCALE)**2
|
||||
END IF
|
||||
END IF
|
||||
IF (DIMAG(X(IX)).NE.ZERO) THEN
|
||||
TEMP = ABS(DIMAG(X(IX)))
|
||||
IF (SCALE.LT.TEMP) THEN
|
||||
SSQ = ONE + SSQ* (SCALE/TEMP)**2
|
||||
SCALE = TEMP
|
||||
ELSE
|
||||
SSQ = SSQ + (TEMP/SCALE)**2
|
||||
END IF
|
||||
END IF
|
||||
10 CONTINUE
|
||||
NORM = SCALE*SQRT(SSQ)
|
||||
END IF
|
||||
*
|
||||
DZNRM2 = NORM
|
||||
RETURN
|
||||
*
|
||||
* End of DZNRM2.
|
||||
*
|
||||
END
|
||||
|
|
@ -0,0 +1,209 @@
|
|||
!> \brief \b DZNRM2
|
||||
!
|
||||
! =========== DOCUMENTATION ===========
|
||||
!
|
||||
! Online html documentation available at
|
||||
! http://www.netlib.org/lapack/explore-html/
|
||||
!
|
||||
! Definition:
|
||||
! ===========
|
||||
!
|
||||
! DOUBLE PRECISION FUNCTION DZNRM2(N,X,INCX)
|
||||
!
|
||||
! .. Scalar Arguments ..
|
||||
! INTEGER INCX,N
|
||||
! ..
|
||||
! .. Array Arguments ..
|
||||
! DOUBLE COMPLEX X(*)
|
||||
! ..
|
||||
!
|
||||
!
|
||||
!> \par Purpose:
|
||||
! =============
|
||||
!>
|
||||
!> \verbatim
|
||||
!>
|
||||
!> DZNRM2 returns the euclidean norm of a vector via the function
|
||||
!> name, so that
|
||||
!>
|
||||
!> DZNRM2 := sqrt( x**H*x )
|
||||
!> \endverbatim
|
||||
!
|
||||
! Arguments:
|
||||
! ==========
|
||||
!
|
||||
!> \param[in] N
|
||||
!> \verbatim
|
||||
!> N is INTEGER
|
||||
!> number of elements in input vector(s)
|
||||
!> \endverbatim
|
||||
!>
|
||||
!> \param[in] X
|
||||
!> \verbatim
|
||||
!> X is COMPLEX*16 array, dimension (N)
|
||||
!> complex vector with N elements
|
||||
!> \endverbatim
|
||||
!>
|
||||
!> \param[in] INCX
|
||||
!> \verbatim
|
||||
!> INCX is INTEGER, storage spacing between elements of X
|
||||
!> If INCX > 0, X(1+(i-1)*INCX) = x(i) for 1 <= i <= n
|
||||
!> If INCX < 0, X(1-(n-i)*INCX) = x(i) for 1 <= i <= n
|
||||
!> If INCX = 0, x isn't a vector so there is no need to call
|
||||
!> this subroutine. If you call it anyway, it will count x(1)
|
||||
!> in the vector norm N times.
|
||||
!> \endverbatim
|
||||
!
|
||||
! Authors:
|
||||
! ========
|
||||
!
|
||||
!> \author Edward Anderson, Lockheed Martin
|
||||
!
|
||||
!> \date August 2016
|
||||
!
|
||||
!> \ingroup single_blas_level1
|
||||
!
|
||||
!> \par Contributors:
|
||||
! ==================
|
||||
!>
|
||||
!> Weslley Pereira, University of Colorado Denver, USA
|
||||
!
|
||||
!> \par Further Details:
|
||||
! =====================
|
||||
!>
|
||||
!> \verbatim
|
||||
!>
|
||||
!> Anderson E. (2017)
|
||||
!> Algorithm 978: Safe Scaling in the Level 1 BLAS
|
||||
!> ACM Trans Math Softw 44:1--28
|
||||
!> https://doi.org/10.1145/3061665
|
||||
!>
|
||||
!> Blue, James L. (1978)
|
||||
!> A Portable Fortran Program to Find the Euclidean Norm of a Vector
|
||||
!> ACM Trans Math Softw 4:15--23
|
||||
!> https://doi.org/10.1145/355769.355771
|
||||
!>
|
||||
!> \endverbatim
|
||||
!>
|
||||
! =====================================================================
|
||||
function DZNRM2( n, x, incx )
|
||||
integer, parameter :: wp = kind(1.d0)
|
||||
real(wp) :: DZNRM2
|
||||
!
|
||||
! -- Reference BLAS level1 routine (version 3.9.1) --
|
||||
! -- Reference BLAS is a software package provided by Univ. of Tennessee, --
|
||||
! -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
|
||||
! March 2021
|
||||
!
|
||||
! .. Constants ..
|
||||
real(wp), parameter :: zero = 0.0_wp
|
||||
real(wp), parameter :: one = 1.0_wp
|
||||
real(wp), parameter :: maxN = huge(0.0_wp)
|
||||
! ..
|
||||
! .. Blue's ccaling constants ..
|
||||
real(wp), parameter :: tsml = real(radix(0._wp), wp)**ceiling( &
|
||||
(minexponent(0._wp) - 1) * 0.5_wp)
|
||||
real(wp), parameter :: tbig = real(radix(0._wp), wp)**floor( &
|
||||
(maxexponent(0._wp) - digits(0._wp) + 1) * 0.5_wp)
|
||||
real(wp), parameter :: ssml = real(radix(0._wp), wp)**( - floor( &
|
||||
(minexponent(0._wp) - 1) * 0.5_wp))
|
||||
real(wp), parameter :: sbig = real(radix(0._wp), wp)**( - ceiling( &
|
||||
(maxexponent(0._wp) - digits(0._wp) + 1) * 0.5_wp))
|
||||
! ..
|
||||
! .. Scalar Arguments ..
|
||||
integer :: incx, n
|
||||
! ..
|
||||
! .. Array Arguments ..
|
||||
complex(wp) :: x(*)
|
||||
! ..
|
||||
! .. Local Scalars ..
|
||||
integer :: i, ix
|
||||
logical :: notbig
|
||||
real(wp) :: abig, amed, asml, ax, scl, sumsq, ymax, ymin
|
||||
!
|
||||
! Quick return if possible
|
||||
!
|
||||
DZNRM2 = zero
|
||||
if( n <= 0 ) return
|
||||
!
|
||||
scl = one
|
||||
sumsq = zero
|
||||
!
|
||||
! Compute the sum of squares in 3 accumulators:
|
||||
! abig -- sums of squares scaled down to avoid overflow
|
||||
! asml -- sums of squares scaled up to avoid underflow
|
||||
! amed -- sums of squares that do not require scaling
|
||||
! The thresholds and multipliers are
|
||||
! tbig -- values bigger than this are scaled down by sbig
|
||||
! tsml -- values smaller than this are scaled up by ssml
|
||||
!
|
||||
notbig = .true.
|
||||
asml = zero
|
||||
amed = zero
|
||||
abig = zero
|
||||
ix = 1
|
||||
if( incx < 0 ) ix = 1 - (n-1)*incx
|
||||
do i = 1, n
|
||||
ax = abs(real(x(ix)))
|
||||
if (ax > tbig) then
|
||||
abig = abig + (ax*sbig)**2
|
||||
notbig = .false.
|
||||
else if (ax < tsml) then
|
||||
if (notbig) asml = asml + (ax*ssml)**2
|
||||
else
|
||||
amed = amed + ax**2
|
||||
end if
|
||||
ax = abs(aimag(x(ix)))
|
||||
if (ax > tbig) then
|
||||
abig = abig + (ax*sbig)**2
|
||||
notbig = .false.
|
||||
else if (ax < tsml) then
|
||||
if (notbig) asml = asml + (ax*ssml)**2
|
||||
else
|
||||
amed = amed + ax**2
|
||||
end if
|
||||
ix = ix + incx
|
||||
end do
|
||||
!
|
||||
! Combine abig and amed or amed and asml if more than one
|
||||
! accumulator was used.
|
||||
!
|
||||
if (abig > zero) then
|
||||
!
|
||||
! Combine abig and amed if abig > 0.
|
||||
!
|
||||
if ( (amed > zero) .or. (amed > maxN) .or. (amed /= amed) ) then
|
||||
abig = abig + (amed*sbig)*sbig
|
||||
end if
|
||||
scl = one / sbig
|
||||
sumsq = abig
|
||||
else if (asml > zero) then
|
||||
!
|
||||
! Combine amed and asml if asml > 0.
|
||||
!
|
||||
if ( (amed > zero) .or. (amed > maxN) .or. (amed /= amed) ) then
|
||||
amed = sqrt(amed)
|
||||
asml = sqrt(asml) / ssml
|
||||
if (asml > amed) then
|
||||
ymin = amed
|
||||
ymax = asml
|
||||
else
|
||||
ymin = asml
|
||||
ymax = amed
|
||||
end if
|
||||
scl = one
|
||||
sumsq = ymax**2*( one + (ymin/ymax)**2 )
|
||||
else
|
||||
scl = one / ssml
|
||||
sumsq = asml
|
||||
end if
|
||||
else
|
||||
!
|
||||
! Otherwise all values are mid-range
|
||||
!
|
||||
scl = one
|
||||
sumsq = amed
|
||||
end if
|
||||
DZNRM2 = scl*sqrt( sumsq )
|
||||
return
|
||||
end function
|
||||
|
|
@ -43,7 +43,7 @@
|
|||
*> \param[in] INCX
|
||||
*> \verbatim
|
||||
*> INCX is INTEGER
|
||||
*> storage spacing between elements of SX
|
||||
*> storage spacing between elements of CX
|
||||
*> \endverbatim
|
||||
*
|
||||
* Authors:
|
||||
|
|
@ -54,8 +54,6 @@
|
|||
*> \author Univ. of Colorado Denver
|
||||
*> \author NAG Ltd.
|
||||
*
|
||||
*> \date November 2017
|
||||
*
|
||||
*> \ingroup aux_blas
|
||||
*
|
||||
*> \par Further Details:
|
||||
|
|
@ -71,10 +69,9 @@
|
|||
* =====================================================================
|
||||
INTEGER FUNCTION ICAMAX(N,CX,INCX)
|
||||
*
|
||||
* -- Reference BLAS level1 routine (version 3.8.0) --
|
||||
* -- Reference BLAS level1 routine --
|
||||
* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
|
||||
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
|
||||
* November 2017
|
||||
*
|
||||
* .. Scalar Arguments ..
|
||||
INTEGER INCX,N
|
||||
|
|
@ -124,4 +121,7 @@
|
|||
END DO
|
||||
END IF
|
||||
RETURN
|
||||
*
|
||||
* End of ICAMAX
|
||||
*
|
||||
END
|
||||
|
|
|
|||
|
|
@ -43,7 +43,7 @@
|
|||
*> \param[in] INCX
|
||||
*> \verbatim
|
||||
*> INCX is INTEGER
|
||||
*> storage spacing between elements of SX
|
||||
*> storage spacing between elements of DX
|
||||
*> \endverbatim
|
||||
*
|
||||
* Authors:
|
||||
|
|
@ -54,8 +54,6 @@
|
|||
*> \author Univ. of Colorado Denver
|
||||
*> \author NAG Ltd.
|
||||
*
|
||||
*> \date November 2017
|
||||
*
|
||||
*> \ingroup aux_blas
|
||||
*
|
||||
*> \par Further Details:
|
||||
|
|
@ -71,10 +69,9 @@
|
|||
* =====================================================================
|
||||
INTEGER FUNCTION IDAMAX(N,DX,INCX)
|
||||
*
|
||||
* -- Reference BLAS level1 routine (version 3.8.0) --
|
||||
* -- Reference BLAS level1 routine --
|
||||
* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
|
||||
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
|
||||
* November 2017
|
||||
*
|
||||
* .. Scalar Arguments ..
|
||||
INTEGER INCX,N
|
||||
|
|
@ -123,4 +120,7 @@
|
|||
END DO
|
||||
END IF
|
||||
RETURN
|
||||
*
|
||||
* End of IDAMAX
|
||||
*
|
||||
END
|
||||
|
|
|
|||
|
|
@ -54,8 +54,6 @@
|
|||
*> \author Univ. of Colorado Denver
|
||||
*> \author NAG Ltd.
|
||||
*
|
||||
*> \date November 2017
|
||||
*
|
||||
*> \ingroup aux_blas
|
||||
*
|
||||
*> \par Further Details:
|
||||
|
|
@ -71,10 +69,9 @@
|
|||
* =====================================================================
|
||||
INTEGER FUNCTION ISAMAX(N,SX,INCX)
|
||||
*
|
||||
* -- Reference BLAS level1 routine (version 3.8.0) --
|
||||
* -- Reference BLAS level1 routine --
|
||||
* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
|
||||
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
|
||||
* November 2017
|
||||
*
|
||||
* .. Scalar Arguments ..
|
||||
INTEGER INCX,N
|
||||
|
|
@ -123,4 +120,7 @@
|
|||
END DO
|
||||
END IF
|
||||
RETURN
|
||||
*
|
||||
* End of ISAMAX
|
||||
*
|
||||
END
|
||||
|
|
|
|||
|
|
@ -43,7 +43,7 @@
|
|||
*> \param[in] INCX
|
||||
*> \verbatim
|
||||
*> INCX is INTEGER
|
||||
*> storage spacing between elements of SX
|
||||
*> storage spacing between elements of ZX
|
||||
*> \endverbatim
|
||||
*
|
||||
* Authors:
|
||||
|
|
@ -54,8 +54,6 @@
|
|||
*> \author Univ. of Colorado Denver
|
||||
*> \author NAG Ltd.
|
||||
*
|
||||
*> \date November 2017
|
||||
*
|
||||
*> \ingroup aux_blas
|
||||
*
|
||||
*> \par Further Details:
|
||||
|
|
@ -71,10 +69,9 @@
|
|||
* =====================================================================
|
||||
INTEGER FUNCTION IZAMAX(N,ZX,INCX)
|
||||
*
|
||||
* -- Reference BLAS level1 routine (version 3.8.0) --
|
||||
* -- Reference BLAS level1 routine --
|
||||
* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
|
||||
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
|
||||
* November 2017
|
||||
*
|
||||
* .. Scalar Arguments ..
|
||||
INTEGER INCX,N
|
||||
|
|
@ -124,4 +121,7 @@
|
|||
END DO
|
||||
END IF
|
||||
RETURN
|
||||
*
|
||||
* End of IZAMAX
|
||||
*
|
||||
END
|
||||
|
|
|
|||
|
|
@ -46,17 +46,14 @@
|
|||
*> \author Univ. of Colorado Denver
|
||||
*> \author NAG Ltd.
|
||||
*
|
||||
*> \date December 2016
|
||||
*
|
||||
*> \ingroup aux_blas
|
||||
*
|
||||
* =====================================================================
|
||||
LOGICAL FUNCTION LSAME(CA,CB)
|
||||
*
|
||||
* -- Reference BLAS level1 routine (version 3.1) --
|
||||
* -- Reference BLAS level1 routine --
|
||||
* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
|
||||
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
|
||||
* December 2016
|
||||
*
|
||||
* .. Scalar Arguments ..
|
||||
CHARACTER CA,CB
|
||||
|
|
|
|||
|
|
@ -55,8 +55,6 @@
|
|||
*> \author Univ. of Colorado Denver
|
||||
*> \author NAG Ltd.
|
||||
*
|
||||
*> \date November 2017
|
||||
*
|
||||
*> \ingroup single_blas_level1
|
||||
*
|
||||
*> \par Further Details:
|
||||
|
|
@ -72,10 +70,9 @@
|
|||
* =====================================================================
|
||||
REAL FUNCTION SASUM(N,SX,INCX)
|
||||
*
|
||||
* -- Reference BLAS level1 routine (version 3.8.0) --
|
||||
* -- Reference BLAS level1 routine --
|
||||
* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
|
||||
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
|
||||
* November 2017
|
||||
*
|
||||
* .. Scalar Arguments ..
|
||||
INTEGER INCX,N
|
||||
|
|
@ -129,4 +126,7 @@
|
|||
END IF
|
||||
SASUM = STEMP
|
||||
RETURN
|
||||
*
|
||||
* End of SASUM
|
||||
*
|
||||
END
|
||||
|
|
|
|||
|
|
@ -73,8 +73,6 @@
|
|||
*> \author Univ. of Colorado Denver
|
||||
*> \author NAG Ltd.
|
||||
*
|
||||
*> \date November 2017
|
||||
*
|
||||
*> \ingroup single_blas_level1
|
||||
*
|
||||
*> \par Further Details:
|
||||
|
|
@ -89,10 +87,9 @@
|
|||
* =====================================================================
|
||||
SUBROUTINE SAXPY(N,SA,SX,INCX,SY,INCY)
|
||||
*
|
||||
* -- Reference BLAS level1 routine (version 3.8.0) --
|
||||
* -- Reference BLAS level1 routine --
|
||||
* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
|
||||
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
|
||||
* November 2017
|
||||
*
|
||||
* .. Scalar Arguments ..
|
||||
REAL SA
|
||||
|
|
@ -149,4 +146,7 @@
|
|||
END DO
|
||||
END IF
|
||||
RETURN
|
||||
*
|
||||
* End of SAXPY
|
||||
*
|
||||
END
|
||||
|
|
|
|||
|
|
@ -39,17 +39,14 @@
|
|||
*> \author Univ. of Colorado Denver
|
||||
*> \author NAG Ltd.
|
||||
*
|
||||
*> \date November 2017
|
||||
*
|
||||
*> \ingroup single_blas_level1
|
||||
*
|
||||
* =====================================================================
|
||||
REAL FUNCTION SCABS1(Z)
|
||||
*
|
||||
* -- Reference BLAS level1 routine (version 3.8.0) --
|
||||
* -- Reference BLAS level1 routine --
|
||||
* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
|
||||
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
|
||||
* November 2017
|
||||
*
|
||||
* .. Scalar Arguments ..
|
||||
COMPLEX Z
|
||||
|
|
@ -62,4 +59,7 @@
|
|||
* ..
|
||||
SCABS1 = ABS(REAL(Z)) + ABS(AIMAG(Z))
|
||||
RETURN
|
||||
*
|
||||
* End of SCABS1
|
||||
*
|
||||
END
|
||||
|
|
|
|||
|
|
@ -55,8 +55,6 @@
|
|||
*> \author Univ. of Colorado Denver
|
||||
*> \author NAG Ltd.
|
||||
*
|
||||
*> \date November 2017
|
||||
*
|
||||
*> \ingroup single_blas_level1
|
||||
*
|
||||
*> \par Further Details:
|
||||
|
|
@ -72,10 +70,9 @@
|
|||
* =====================================================================
|
||||
REAL FUNCTION SCASUM(N,CX,INCX)
|
||||
*
|
||||
* -- Reference BLAS level1 routine (version 3.8.0) --
|
||||
* -- Reference BLAS level1 routine --
|
||||
* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
|
||||
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
|
||||
* November 2017
|
||||
*
|
||||
* .. Scalar Arguments ..
|
||||
INTEGER INCX,N
|
||||
|
|
@ -114,4 +111,7 @@
|
|||
END IF
|
||||
SCASUM = STEMP
|
||||
RETURN
|
||||
*
|
||||
* End of SCASUM
|
||||
*
|
||||
END
|
||||
|
|
|
|||
|
|
@ -1,140 +0,0 @@
|
|||
*> \brief \b SCNRM2
|
||||
*
|
||||
* =========== DOCUMENTATION ===========
|
||||
*
|
||||
* Online html documentation available at
|
||||
* http://www.netlib.org/lapack/explore-html/
|
||||
*
|
||||
* Definition:
|
||||
* ===========
|
||||
*
|
||||
* REAL FUNCTION SCNRM2(N,X,INCX)
|
||||
*
|
||||
* .. Scalar Arguments ..
|
||||
* INTEGER INCX,N
|
||||
* ..
|
||||
* .. Array Arguments ..
|
||||
* COMPLEX X(*)
|
||||
* ..
|
||||
*
|
||||
*
|
||||
*> \par Purpose:
|
||||
* =============
|
||||
*>
|
||||
*> \verbatim
|
||||
*>
|
||||
*> SCNRM2 returns the euclidean norm of a vector via the function
|
||||
*> name, so that
|
||||
*>
|
||||
*> SCNRM2 := sqrt( x**H*x )
|
||||
*> \endverbatim
|
||||
*
|
||||
* Arguments:
|
||||
* ==========
|
||||
*
|
||||
*> \param[in] N
|
||||
*> \verbatim
|
||||
*> N is INTEGER
|
||||
*> number of elements in input vector(s)
|
||||
*> \endverbatim
|
||||
*>
|
||||
*> \param[in] X
|
||||
*> \verbatim
|
||||
*> X is COMPLEX array, dimension (N)
|
||||
*> complex vector with N elements
|
||||
*> \endverbatim
|
||||
*>
|
||||
*> \param[in] INCX
|
||||
*> \verbatim
|
||||
*> INCX is INTEGER
|
||||
*> storage spacing between elements of X
|
||||
*> \endverbatim
|
||||
*
|
||||
* Authors:
|
||||
* ========
|
||||
*
|
||||
*> \author Univ. of Tennessee
|
||||
*> \author Univ. of California Berkeley
|
||||
*> \author Univ. of Colorado Denver
|
||||
*> \author NAG Ltd.
|
||||
*
|
||||
*> \date November 2017
|
||||
*
|
||||
*> \ingroup single_blas_level1
|
||||
*
|
||||
*> \par Further Details:
|
||||
* =====================
|
||||
*>
|
||||
*> \verbatim
|
||||
*>
|
||||
*> -- This version written on 25-October-1982.
|
||||
*> Modified on 14-October-1993 to inline the call to CLASSQ.
|
||||
*> Sven Hammarling, Nag Ltd.
|
||||
*> \endverbatim
|
||||
*>
|
||||
* =====================================================================
|
||||
REAL FUNCTION SCNRM2(N,X,INCX)
|
||||
*
|
||||
* -- Reference BLAS level1 routine (version 3.8.0) --
|
||||
* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
|
||||
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
|
||||
* November 2017
|
||||
*
|
||||
* .. Scalar Arguments ..
|
||||
INTEGER INCX,N
|
||||
* ..
|
||||
* .. Array Arguments ..
|
||||
COMPLEX X(*)
|
||||
* ..
|
||||
*
|
||||
* =====================================================================
|
||||
*
|
||||
* .. Parameters ..
|
||||
REAL ONE,ZERO
|
||||
PARAMETER (ONE=1.0E+0,ZERO=0.0E+0)
|
||||
* ..
|
||||
* .. Local Scalars ..
|
||||
REAL NORM,SCALE,SSQ,TEMP
|
||||
INTEGER IX
|
||||
* ..
|
||||
* .. Intrinsic Functions ..
|
||||
INTRINSIC ABS,AIMAG,REAL,SQRT
|
||||
* ..
|
||||
IF (N.LT.1 .OR. INCX.LT.1) THEN
|
||||
NORM = ZERO
|
||||
ELSE
|
||||
SCALE = ZERO
|
||||
SSQ = ONE
|
||||
* The following loop is equivalent to this call to the LAPACK
|
||||
* auxiliary routine:
|
||||
* CALL CLASSQ( N, X, INCX, SCALE, SSQ )
|
||||
*
|
||||
DO 10 IX = 1,1 + (N-1)*INCX,INCX
|
||||
IF (REAL(X(IX)).NE.ZERO) THEN
|
||||
TEMP = ABS(REAL(X(IX)))
|
||||
IF (SCALE.LT.TEMP) THEN
|
||||
SSQ = ONE + SSQ* (SCALE/TEMP)**2
|
||||
SCALE = TEMP
|
||||
ELSE
|
||||
SSQ = SSQ + (TEMP/SCALE)**2
|
||||
END IF
|
||||
END IF
|
||||
IF (AIMAG(X(IX)).NE.ZERO) THEN
|
||||
TEMP = ABS(AIMAG(X(IX)))
|
||||
IF (SCALE.LT.TEMP) THEN
|
||||
SSQ = ONE + SSQ* (SCALE/TEMP)**2
|
||||
SCALE = TEMP
|
||||
ELSE
|
||||
SSQ = SSQ + (TEMP/SCALE)**2
|
||||
END IF
|
||||
END IF
|
||||
10 CONTINUE
|
||||
NORM = SCALE*SQRT(SSQ)
|
||||
END IF
|
||||
*
|
||||
SCNRM2 = NORM
|
||||
RETURN
|
||||
*
|
||||
* End of SCNRM2.
|
||||
*
|
||||
END
|
||||
|
|
@ -0,0 +1,209 @@
|
|||
!> \brief \b SCNRM2
|
||||
!
|
||||
! =========== DOCUMENTATION ===========
|
||||
!
|
||||
! Online html documentation available at
|
||||
! http://www.netlib.org/lapack/explore-html/
|
||||
!
|
||||
! Definition:
|
||||
! ===========
|
||||
!
|
||||
! REAL FUNCTION SCNRM2(N,X,INCX)
|
||||
!
|
||||
! .. Scalar Arguments ..
|
||||
! INTEGER INCX,N
|
||||
! ..
|
||||
! .. Array Arguments ..
|
||||
! COMPLEX X(*)
|
||||
! ..
|
||||
!
|
||||
!
|
||||
!> \par Purpose:
|
||||
! =============
|
||||
!>
|
||||
!> \verbatim
|
||||
!>
|
||||
!> SCNRM2 returns the euclidean norm of a vector via the function
|
||||
!> name, so that
|
||||
!>
|
||||
!> SCNRM2 := sqrt( x**H*x )
|
||||
!> \endverbatim
|
||||
!
|
||||
! Arguments:
|
||||
! ==========
|
||||
!
|
||||
!> \param[in] N
|
||||
!> \verbatim
|
||||
!> N is INTEGER
|
||||
!> number of elements in input vector(s)
|
||||
!> \endverbatim
|
||||
!>
|
||||
!> \param[in] X
|
||||
!> \verbatim
|
||||
!> X is COMPLEX array, dimension (N)
|
||||
!> complex vector with N elements
|
||||
!> \endverbatim
|
||||
!>
|
||||
!> \param[in] INCX
|
||||
!> \verbatim
|
||||
!> INCX is INTEGER, storage spacing between elements of X
|
||||
!> If INCX > 0, X(1+(i-1)*INCX) = x(i) for 1 <= i <= n
|
||||
!> If INCX < 0, X(1-(n-i)*INCX) = x(i) for 1 <= i <= n
|
||||
!> If INCX = 0, x isn't a vector so there is no need to call
|
||||
!> this subroutine. If you call it anyway, it will count x(1)
|
||||
!> in the vector norm N times.
|
||||
!> \endverbatim
|
||||
!
|
||||
! Authors:
|
||||
! ========
|
||||
!
|
||||
!> \author Edward Anderson, Lockheed Martin
|
||||
!
|
||||
!> \date August 2016
|
||||
!
|
||||
!> \ingroup single_blas_level1
|
||||
!
|
||||
!> \par Contributors:
|
||||
! ==================
|
||||
!>
|
||||
!> Weslley Pereira, University of Colorado Denver, USA
|
||||
!
|
||||
!> \par Further Details:
|
||||
! =====================
|
||||
!>
|
||||
!> \verbatim
|
||||
!>
|
||||
!> Anderson E. (2017)
|
||||
!> Algorithm 978: Safe Scaling in the Level 1 BLAS
|
||||
!> ACM Trans Math Softw 44:1--28
|
||||
!> https://doi.org/10.1145/3061665
|
||||
!>
|
||||
!> Blue, James L. (1978)
|
||||
!> A Portable Fortran Program to Find the Euclidean Norm of a Vector
|
||||
!> ACM Trans Math Softw 4:15--23
|
||||
!> https://doi.org/10.1145/355769.355771
|
||||
!>
|
||||
!> \endverbatim
|
||||
!>
|
||||
! =====================================================================
|
||||
function SCNRM2( n, x, incx )
|
||||
integer, parameter :: wp = kind(1.e0)
|
||||
real(wp) :: SCNRM2
|
||||
!
|
||||
! -- Reference BLAS level1 routine (version 3.9.1) --
|
||||
! -- Reference BLAS is a software package provided by Univ. of Tennessee, --
|
||||
! -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
|
||||
! March 2021
|
||||
!
|
||||
! .. Constants ..
|
||||
real(wp), parameter :: zero = 0.0_wp
|
||||
real(wp), parameter :: one = 1.0_wp
|
||||
real(wp), parameter :: maxN = huge(0.0_wp)
|
||||
! ..
|
||||
! .. Blue's ccaling constants ..
|
||||
real(wp), parameter :: tsml = real(radix(0._wp), wp)**ceiling( &
|
||||
(minexponent(0._wp) - 1) * 0.5_wp)
|
||||
real(wp), parameter :: tbig = real(radix(0._wp), wp)**floor( &
|
||||
(maxexponent(0._wp) - digits(0._wp) + 1) * 0.5_wp)
|
||||
real(wp), parameter :: ssml = real(radix(0._wp), wp)**( - floor( &
|
||||
(minexponent(0._wp) - 1) * 0.5_wp))
|
||||
real(wp), parameter :: sbig = real(radix(0._wp), wp)**( - ceiling( &
|
||||
(maxexponent(0._wp) - digits(0._wp) + 1) * 0.5_wp))
|
||||
! ..
|
||||
! .. Scalar Arguments ..
|
||||
integer :: incx, n
|
||||
! ..
|
||||
! .. Array Arguments ..
|
||||
complex(wp) :: x(*)
|
||||
! ..
|
||||
! .. Local Scalars ..
|
||||
integer :: i, ix
|
||||
logical :: notbig
|
||||
real(wp) :: abig, amed, asml, ax, scl, sumsq, ymax, ymin
|
||||
!
|
||||
! Quick return if possible
|
||||
!
|
||||
SCNRM2 = zero
|
||||
if( n <= 0 ) return
|
||||
!
|
||||
scl = one
|
||||
sumsq = zero
|
||||
!
|
||||
! Compute the sum of squares in 3 accumulators:
|
||||
! abig -- sums of squares scaled down to avoid overflow
|
||||
! asml -- sums of squares scaled up to avoid underflow
|
||||
! amed -- sums of squares that do not require scaling
|
||||
! The thresholds and multipliers are
|
||||
! tbig -- values bigger than this are scaled down by sbig
|
||||
! tsml -- values smaller than this are scaled up by ssml
|
||||
!
|
||||
notbig = .true.
|
||||
asml = zero
|
||||
amed = zero
|
||||
abig = zero
|
||||
ix = 1
|
||||
if( incx < 0 ) ix = 1 - (n-1)*incx
|
||||
do i = 1, n
|
||||
ax = abs(real(x(ix)))
|
||||
if (ax > tbig) then
|
||||
abig = abig + (ax*sbig)**2
|
||||
notbig = .false.
|
||||
else if (ax < tsml) then
|
||||
if (notbig) asml = asml + (ax*ssml)**2
|
||||
else
|
||||
amed = amed + ax**2
|
||||
end if
|
||||
ax = abs(aimag(x(ix)))
|
||||
if (ax > tbig) then
|
||||
abig = abig + (ax*sbig)**2
|
||||
notbig = .false.
|
||||
else if (ax < tsml) then
|
||||
if (notbig) asml = asml + (ax*ssml)**2
|
||||
else
|
||||
amed = amed + ax**2
|
||||
end if
|
||||
ix = ix + incx
|
||||
end do
|
||||
!
|
||||
! Combine abig and amed or amed and asml if more than one
|
||||
! accumulator was used.
|
||||
!
|
||||
if (abig > zero) then
|
||||
!
|
||||
! Combine abig and amed if abig > 0.
|
||||
!
|
||||
if ( (amed > zero) .or. (amed > maxN) .or. (amed /= amed) ) then
|
||||
abig = abig + (amed*sbig)*sbig
|
||||
end if
|
||||
scl = one / sbig
|
||||
sumsq = abig
|
||||
else if (asml > zero) then
|
||||
!
|
||||
! Combine amed and asml if asml > 0.
|
||||
!
|
||||
if ( (amed > zero) .or. (amed > maxN) .or. (amed /= amed) ) then
|
||||
amed = sqrt(amed)
|
||||
asml = sqrt(asml) / ssml
|
||||
if (asml > amed) then
|
||||
ymin = amed
|
||||
ymax = asml
|
||||
else
|
||||
ymin = asml
|
||||
ymax = amed
|
||||
end if
|
||||
scl = one
|
||||
sumsq = ymax**2*( one + (ymin/ymax)**2 )
|
||||
else
|
||||
scl = one / ssml
|
||||
sumsq = asml
|
||||
end if
|
||||
else
|
||||
!
|
||||
! Otherwise all values are mid-range
|
||||
!
|
||||
scl = one
|
||||
sumsq = amed
|
||||
end if
|
||||
SCNRM2 = scl*sqrt( sumsq )
|
||||
return
|
||||
end function
|
||||
|
|
@ -66,8 +66,6 @@
|
|||
*> \author Univ. of Colorado Denver
|
||||
*> \author NAG Ltd.
|
||||
*
|
||||
*> \date November 2017
|
||||
*
|
||||
*> \ingroup single_blas_level1
|
||||
*
|
||||
*> \par Further Details:
|
||||
|
|
@ -82,10 +80,9 @@
|
|||
* =====================================================================
|
||||
SUBROUTINE SCOPY(N,SX,INCX,SY,INCY)
|
||||
*
|
||||
* -- Reference BLAS level1 routine (version 3.8.0) --
|
||||
* -- Reference BLAS level1 routine --
|
||||
* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
|
||||
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
|
||||
* November 2017
|
||||
*
|
||||
* .. Scalar Arguments ..
|
||||
INTEGER INCX,INCY,N
|
||||
|
|
@ -143,4 +140,7 @@
|
|||
END DO
|
||||
END IF
|
||||
RETURN
|
||||
*
|
||||
* End of SCOPY
|
||||
*
|
||||
END
|
||||
|
|
|
|||
|
|
@ -66,8 +66,6 @@
|
|||
*> \author Univ. of Colorado Denver
|
||||
*> \author NAG Ltd.
|
||||
*
|
||||
*> \date November 2017
|
||||
*
|
||||
*> \ingroup single_blas_level1
|
||||
*
|
||||
*> \par Further Details:
|
||||
|
|
@ -82,10 +80,9 @@
|
|||
* =====================================================================
|
||||
REAL FUNCTION SDOT(N,SX,INCX,SY,INCY)
|
||||
*
|
||||
* -- Reference BLAS level1 routine (version 3.8.0) --
|
||||
* -- Reference BLAS level1 routine --
|
||||
* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
|
||||
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
|
||||
* November 2017
|
||||
*
|
||||
* .. Scalar Arguments ..
|
||||
INTEGER INCX,INCY,N
|
||||
|
|
@ -145,4 +142,7 @@
|
|||
END IF
|
||||
SDOT = STEMP
|
||||
RETURN
|
||||
*
|
||||
* End of SDOT
|
||||
*
|
||||
END
|
||||
|
|
|
|||
|
|
@ -23,13 +23,13 @@
|
|||
*>
|
||||
*> \verbatim
|
||||
*>
|
||||
* Compute the inner product of two vectors with extended
|
||||
* precision accumulation.
|
||||
*
|
||||
* Returns S.P. result with dot product accumulated in D.P.
|
||||
* SDSDOT = SB + sum for I = 0 to N-1 of SX(LX+I*INCX)*SY(LY+I*INCY),
|
||||
* where LX = 1 if INCX .GE. 0, else LX = 1+(1-N)*INCX, and LY is
|
||||
* defined in a similar way using INCY.
|
||||
*> Compute the inner product of two vectors with extended
|
||||
*> precision accumulation.
|
||||
*>
|
||||
*> Returns S.P. result with dot product accumulated in D.P.
|
||||
*> SDSDOT = SB + sum for I = 0 to N-1 of SX(LX+I*INCX)*SY(LY+I*INCY),
|
||||
*> where LX = 1 if INCX .GE. 0, else LX = 1+(1-N)*INCX, and LY is
|
||||
*> defined in a similar way using INCY.
|
||||
*> \endverbatim
|
||||
*
|
||||
* Arguments:
|
||||
|
|
@ -77,7 +77,12 @@
|
|||
*> \author Lawson, C. L., (JPL), Hanson, R. J., (SNLA),
|
||||
*> \author Kincaid, D. R., (U. of Texas), Krogh, F. T., (JPL)
|
||||
*
|
||||
*> \ingroup complex_blas_level1
|
||||
*> \author Univ. of Tennessee
|
||||
*> \author Univ. of California Berkeley
|
||||
*> \author Univ. of Colorado Denver
|
||||
*> \author NAG Ltd.
|
||||
*
|
||||
*> \ingroup single_blas_level1
|
||||
*
|
||||
*> \par Further Details:
|
||||
* =====================
|
||||
|
|
@ -102,72 +107,13 @@
|
|||
*> 920501 Reformatted the REFERENCES section. (WRB)
|
||||
*> 070118 Reformat to LAPACK coding style
|
||||
*> \endverbatim
|
||||
*
|
||||
* =====================================================================
|
||||
*
|
||||
* .. Local Scalars ..
|
||||
* DOUBLE PRECISION DSDOT
|
||||
* INTEGER I,KX,KY,NS
|
||||
* ..
|
||||
* .. Intrinsic Functions ..
|
||||
* INTRINSIC DBLE
|
||||
* ..
|
||||
* DSDOT = SB
|
||||
* IF (N.LE.0) THEN
|
||||
* SDSDOT = DSDOT
|
||||
* RETURN
|
||||
* END IF
|
||||
* IF (INCX.EQ.INCY .AND. INCX.GT.0) THEN
|
||||
*
|
||||
* Code for equal and positive increments.
|
||||
*
|
||||
* NS = N*INCX
|
||||
* DO I = 1,NS,INCX
|
||||
* DSDOT = DSDOT + DBLE(SX(I))*DBLE(SY(I))
|
||||
* END DO
|
||||
* ELSE
|
||||
*
|
||||
* Code for unequal or nonpositive increments.
|
||||
*
|
||||
* KX = 1
|
||||
* KY = 1
|
||||
* IF (INCX.LT.0) KX = 1 + (1-N)*INCX
|
||||
* IF (INCY.LT.0) KY = 1 + (1-N)*INCY
|
||||
* DO I = 1,N
|
||||
* DSDOT = DSDOT + DBLE(SX(KX))*DBLE(SY(KY))
|
||||
* KX = KX + INCX
|
||||
* KY = KY + INCY
|
||||
* END DO
|
||||
* END IF
|
||||
* SDSDOT = DSDOT
|
||||
* RETURN
|
||||
* END
|
||||
*
|
||||
*> \par Purpose:
|
||||
* =============
|
||||
*>
|
||||
*> \verbatim
|
||||
*> \endverbatim
|
||||
*
|
||||
* Authors:
|
||||
* ========
|
||||
*
|
||||
*> \author Univ. of Tennessee
|
||||
*> \author Univ. of California Berkeley
|
||||
*> \author Univ. of Colorado Denver
|
||||
*> \author NAG Ltd.
|
||||
*
|
||||
*> \date November 2017
|
||||
*
|
||||
*> \ingroup single_blas_level1
|
||||
*
|
||||
* =====================================================================
|
||||
REAL FUNCTION SDSDOT(N,SB,SX,INCX,SY,INCY)
|
||||
*
|
||||
* -- Reference BLAS level1 routine (version 3.8.0) --
|
||||
* -- Reference BLAS level1 routine --
|
||||
* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
|
||||
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
|
||||
* November 2017
|
||||
*
|
||||
* .. Scalar Arguments ..
|
||||
REAL SB
|
||||
|
|
@ -175,71 +121,6 @@
|
|||
* ..
|
||||
* .. Array Arguments ..
|
||||
REAL SX(*),SY(*)
|
||||
* ..
|
||||
*
|
||||
* PURPOSE
|
||||
* =======
|
||||
*
|
||||
* Compute the inner product of two vectors with extended
|
||||
* precision accumulation.
|
||||
*
|
||||
* Returns S.P. result with dot product accumulated in D.P.
|
||||
* SDSDOT = SB + sum for I = 0 to N-1 of SX(LX+I*INCX)*SY(LY+I*INCY),
|
||||
* where LX = 1 if INCX .GE. 0, else LX = 1+(1-N)*INCX, and LY is
|
||||
* defined in a similar way using INCY.
|
||||
*
|
||||
* AUTHOR
|
||||
* ======
|
||||
* Lawson, C. L., (JPL), Hanson, R. J., (SNLA),
|
||||
* Kincaid, D. R., (U. of Texas), Krogh, F. T., (JPL)
|
||||
*
|
||||
* ARGUMENTS
|
||||
* =========
|
||||
*
|
||||
* N (input) INTEGER
|
||||
* number of elements in input vector(s)
|
||||
*
|
||||
* SB (input) REAL
|
||||
* single precision scalar to be added to inner product
|
||||
*
|
||||
* SX (input) REAL array, dimension (N)
|
||||
* single precision vector with N elements
|
||||
*
|
||||
* INCX (input) INTEGER
|
||||
* storage spacing between elements of SX
|
||||
*
|
||||
* SY (input) REAL array, dimension (N)
|
||||
* single precision vector with N elements
|
||||
*
|
||||
* INCY (input) INTEGER
|
||||
* storage spacing between elements of SY
|
||||
*
|
||||
* SDSDOT (output) REAL
|
||||
* single precision dot product (SB if N .LE. 0)
|
||||
*
|
||||
* Further Details
|
||||
* ===============
|
||||
*
|
||||
* REFERENCES
|
||||
*
|
||||
* C. L. Lawson, R. J. Hanson, D. R. Kincaid and F. T.
|
||||
* Krogh, Basic linear algebra subprograms for Fortran
|
||||
* usage, Algorithm No. 539, Transactions on Mathematical
|
||||
* Software 5, 3 (September 1979), pp. 308-323.
|
||||
*
|
||||
* REVISION HISTORY (YYMMDD)
|
||||
*
|
||||
* 791001 DATE WRITTEN
|
||||
* 890531 Changed all specific intrinsics to generic. (WRB)
|
||||
* 890831 Modified array declarations. (WRB)
|
||||
* 890831 REVISION DATE from Version 3.2
|
||||
* 891214 Prologue converted to Version 4.0 format. (BAB)
|
||||
* 920310 Corrected definition of LX in DESCRIPTION. (WRB)
|
||||
* 920501 Reformatted the REFERENCES section. (WRB)
|
||||
* 070118 Reformat to LAPACK coding style
|
||||
*
|
||||
* =====================================================================
|
||||
*
|
||||
* .. Local Scalars ..
|
||||
DOUBLE PRECISION DSDOT
|
||||
INTEGER I,KX,KY,NS
|
||||
|
|
@ -276,4 +157,7 @@
|
|||
END IF
|
||||
SDSDOT = DSDOT
|
||||
RETURN
|
||||
*
|
||||
* End of SDSDOT
|
||||
*
|
||||
END
|
||||
|
|
|
|||
|
|
@ -163,8 +163,6 @@
|
|||
*> \author Univ. of Colorado Denver
|
||||
*> \author NAG Ltd.
|
||||
*
|
||||
*> \date December 2016
|
||||
*
|
||||
*> \ingroup single_blas_level2
|
||||
*
|
||||
*> \par Further Details:
|
||||
|
|
@ -185,10 +183,9 @@
|
|||
* =====================================================================
|
||||
SUBROUTINE SGBMV(TRANS,M,N,KL,KU,ALPHA,A,LDA,X,INCX,BETA,Y,INCY)
|
||||
*
|
||||
* -- Reference BLAS level2 routine (version 3.7.0) --
|
||||
* -- Reference BLAS level2 routine --
|
||||
* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
|
||||
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
|
||||
* December 2016
|
||||
*
|
||||
* .. Scalar Arguments ..
|
||||
REAL ALPHA,BETA
|
||||
|
|
@ -365,6 +362,6 @@
|
|||
*
|
||||
RETURN
|
||||
*
|
||||
* End of SGBMV .
|
||||
* End of SGBMV
|
||||
*
|
||||
END
|
||||
|
|
|
|||
|
|
@ -166,8 +166,6 @@
|
|||
*> \author Univ. of Colorado Denver
|
||||
*> \author NAG Ltd.
|
||||
*
|
||||
*> \date December 2016
|
||||
*
|
||||
*> \ingroup single_blas_level3
|
||||
*
|
||||
*> \par Further Details:
|
||||
|
|
@ -187,10 +185,9 @@
|
|||
* =====================================================================
|
||||
SUBROUTINE SGEMM(TRANSA,TRANSB,M,N,K,ALPHA,A,LDA,B,LDB,BETA,C,LDC)
|
||||
*
|
||||
* -- Reference BLAS level3 routine (version 3.7.0) --
|
||||
* -- Reference BLAS level3 routine --
|
||||
* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
|
||||
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
|
||||
* December 2016
|
||||
*
|
||||
* .. Scalar Arguments ..
|
||||
REAL ALPHA,BETA
|
||||
|
|
@ -215,7 +212,7 @@
|
|||
* ..
|
||||
* .. Local Scalars ..
|
||||
REAL TEMP
|
||||
INTEGER I,INFO,J,L,NCOLA,NROWA,NROWB
|
||||
INTEGER I,INFO,J,L,NROWA,NROWB
|
||||
LOGICAL NOTA,NOTB
|
||||
* ..
|
||||
* .. Parameters ..
|
||||
|
|
@ -224,17 +221,15 @@
|
|||
* ..
|
||||
*
|
||||
* Set NOTA and NOTB as true if A and B respectively are not
|
||||
* transposed and set NROWA, NCOLA and NROWB as the number of rows
|
||||
* and columns of A and the number of rows of B respectively.
|
||||
* transposed and set NROWA and NROWB as the number of rows of A
|
||||
* and B respectively.
|
||||
*
|
||||
NOTA = LSAME(TRANSA,'N')
|
||||
NOTB = LSAME(TRANSB,'N')
|
||||
IF (NOTA) THEN
|
||||
NROWA = M
|
||||
NCOLA = K
|
||||
ELSE
|
||||
NROWA = K
|
||||
NCOLA = M
|
||||
END IF
|
||||
IF (NOTB) THEN
|
||||
NROWB = K
|
||||
|
|
@ -379,6 +374,6 @@
|
|||
*
|
||||
RETURN
|
||||
*
|
||||
* End of SGEMM .
|
||||
* End of SGEMM
|
||||
*
|
||||
END
|
||||
|
|
|
|||
|
|
@ -134,8 +134,6 @@
|
|||
*> \author Univ. of Colorado Denver
|
||||
*> \author NAG Ltd.
|
||||
*
|
||||
*> \date December 2016
|
||||
*
|
||||
*> \ingroup single_blas_level2
|
||||
*
|
||||
*> \par Further Details:
|
||||
|
|
@ -156,10 +154,9 @@
|
|||
* =====================================================================
|
||||
SUBROUTINE SGEMV(TRANS,M,N,ALPHA,A,LDA,X,INCX,BETA,Y,INCY)
|
||||
*
|
||||
* -- Reference BLAS level2 routine (version 3.7.0) --
|
||||
* -- Reference BLAS level2 routine --
|
||||
* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
|
||||
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
|
||||
* December 2016
|
||||
*
|
||||
* .. Scalar Arguments ..
|
||||
REAL ALPHA,BETA
|
||||
|
|
@ -325,6 +322,6 @@
|
|||
*
|
||||
RETURN
|
||||
*
|
||||
* End of SGEMV .
|
||||
* End of SGEMV
|
||||
*
|
||||
END
|
||||
|
|
|
|||
|
|
@ -109,8 +109,6 @@
|
|||
*> \author Univ. of Colorado Denver
|
||||
*> \author NAG Ltd.
|
||||
*
|
||||
*> \date December 2016
|
||||
*
|
||||
*> \ingroup single_blas_level2
|
||||
*
|
||||
*> \par Further Details:
|
||||
|
|
@ -130,10 +128,9 @@
|
|||
* =====================================================================
|
||||
SUBROUTINE SGER(M,N,ALPHA,X,INCX,Y,INCY,A,LDA)
|
||||
*
|
||||
* -- Reference BLAS level2 routine (version 3.7.0) --
|
||||
* -- Reference BLAS level2 routine --
|
||||
* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
|
||||
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
|
||||
* December 2016
|
||||
*
|
||||
* .. Scalar Arguments ..
|
||||
REAL ALPHA
|
||||
|
|
@ -222,6 +219,6 @@
|
|||
*
|
||||
RETURN
|
||||
*
|
||||
* End of SGER .
|
||||
* End of SGER
|
||||
*
|
||||
END
|
||||
|
|
|
|||
|
|
@ -1,132 +0,0 @@
|
|||
*> \brief \b SNRM2
|
||||
*
|
||||
* =========== DOCUMENTATION ===========
|
||||
*
|
||||
* Online html documentation available at
|
||||
* http://www.netlib.org/lapack/explore-html/
|
||||
*
|
||||
* Definition:
|
||||
* ===========
|
||||
*
|
||||
* REAL FUNCTION SNRM2(N,X,INCX)
|
||||
*
|
||||
* .. Scalar Arguments ..
|
||||
* INTEGER INCX,N
|
||||
* ..
|
||||
* .. Array Arguments ..
|
||||
* REAL X(*)
|
||||
* ..
|
||||
*
|
||||
*
|
||||
*> \par Purpose:
|
||||
* =============
|
||||
*>
|
||||
*> \verbatim
|
||||
*>
|
||||
*> SNRM2 returns the euclidean norm of a vector via the function
|
||||
*> name, so that
|
||||
*>
|
||||
*> SNRM2 := sqrt( x'*x ).
|
||||
*> \endverbatim
|
||||
*
|
||||
* Arguments:
|
||||
* ==========
|
||||
*
|
||||
*> \param[in] N
|
||||
*> \verbatim
|
||||
*> N is INTEGER
|
||||
*> number of elements in input vector(s)
|
||||
*> \endverbatim
|
||||
*>
|
||||
*> \param[in] X
|
||||
*> \verbatim
|
||||
*> X is REAL array, dimension ( 1 + ( N - 1 )*abs( INCX ) )
|
||||
*> \endverbatim
|
||||
*>
|
||||
*> \param[in] INCX
|
||||
*> \verbatim
|
||||
*> INCX is INTEGER
|
||||
*> storage spacing between elements of SX
|
||||
*> \endverbatim
|
||||
*
|
||||
* Authors:
|
||||
* ========
|
||||
*
|
||||
*> \author Univ. of Tennessee
|
||||
*> \author Univ. of California Berkeley
|
||||
*> \author Univ. of Colorado Denver
|
||||
*> \author NAG Ltd.
|
||||
*
|
||||
*> \date November 2017
|
||||
*
|
||||
*> \ingroup single_blas_level1
|
||||
*
|
||||
*> \par Further Details:
|
||||
* =====================
|
||||
*>
|
||||
*> \verbatim
|
||||
*>
|
||||
*> -- This version written on 25-October-1982.
|
||||
*> Modified on 14-October-1993 to inline the call to SLASSQ.
|
||||
*> Sven Hammarling, Nag Ltd.
|
||||
*> \endverbatim
|
||||
*>
|
||||
* =====================================================================
|
||||
REAL FUNCTION SNRM2(N,X,INCX)
|
||||
*
|
||||
* -- Reference BLAS level1 routine (version 3.8.0) --
|
||||
* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
|
||||
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
|
||||
* November 2017
|
||||
*
|
||||
* .. Scalar Arguments ..
|
||||
INTEGER INCX,N
|
||||
* ..
|
||||
* .. Array Arguments ..
|
||||
REAL X(*)
|
||||
* ..
|
||||
*
|
||||
* =====================================================================
|
||||
*
|
||||
* .. Parameters ..
|
||||
REAL ONE,ZERO
|
||||
PARAMETER (ONE=1.0E+0,ZERO=0.0E+0)
|
||||
* ..
|
||||
* .. Local Scalars ..
|
||||
REAL ABSXI,NORM,SCALE,SSQ
|
||||
INTEGER IX
|
||||
* ..
|
||||
* .. Intrinsic Functions ..
|
||||
INTRINSIC ABS,SQRT
|
||||
* ..
|
||||
IF (N.LT.1 .OR. INCX.LT.1) THEN
|
||||
NORM = ZERO
|
||||
ELSE IF (N.EQ.1) THEN
|
||||
NORM = ABS(X(1))
|
||||
ELSE
|
||||
SCALE = ZERO
|
||||
SSQ = ONE
|
||||
* The following loop is equivalent to this call to the LAPACK
|
||||
* auxiliary routine:
|
||||
* CALL SLASSQ( N, X, INCX, SCALE, SSQ )
|
||||
*
|
||||
DO 10 IX = 1,1 + (N-1)*INCX,INCX
|
||||
IF (X(IX).NE.ZERO) THEN
|
||||
ABSXI = ABS(X(IX))
|
||||
IF (SCALE.LT.ABSXI) THEN
|
||||
SSQ = ONE + SSQ* (SCALE/ABSXI)**2
|
||||
SCALE = ABSXI
|
||||
ELSE
|
||||
SSQ = SSQ + (ABSXI/SCALE)**2
|
||||
END IF
|
||||
END IF
|
||||
10 CONTINUE
|
||||
NORM = SCALE*SQRT(SSQ)
|
||||
END IF
|
||||
*
|
||||
SNRM2 = NORM
|
||||
RETURN
|
||||
*
|
||||
* End of SNRM2.
|
||||
*
|
||||
END
|
||||
|
|
@ -0,0 +1,199 @@
|
|||
!> \brief \b SNRM2
|
||||
!
|
||||
! =========== DOCUMENTATION ===========
|
||||
!
|
||||
! Online html documentation available at
|
||||
! http://www.netlib.org/lapack/explore-html/
|
||||
!
|
||||
! Definition:
|
||||
! ===========
|
||||
!
|
||||
! REAL FUNCTION SNRM2(N,X,INCX)
|
||||
!
|
||||
! .. Scalar Arguments ..
|
||||
! INTEGER INCX,N
|
||||
! ..
|
||||
! .. Array Arguments ..
|
||||
! REAL X(*)
|
||||
! ..
|
||||
!
|
||||
!
|
||||
!> \par Purpose:
|
||||
! =============
|
||||
!>
|
||||
!> \verbatim
|
||||
!>
|
||||
!> SNRM2 returns the euclidean norm of a vector via the function
|
||||
!> name, so that
|
||||
!>
|
||||
!> SNRM2 := sqrt( x'*x ).
|
||||
!> \endverbatim
|
||||
!
|
||||
! Arguments:
|
||||
! ==========
|
||||
!
|
||||
!> \param[in] N
|
||||
!> \verbatim
|
||||
!> N is INTEGER
|
||||
!> number of elements in input vector(s)
|
||||
!> \endverbatim
|
||||
!>
|
||||
!> \param[in] X
|
||||
!> \verbatim
|
||||
!> X is REAL array, dimension ( 1 + ( N - 1 )*abs( INCX ) )
|
||||
!> \endverbatim
|
||||
!>
|
||||
!> \param[in] INCX
|
||||
!> \verbatim
|
||||
!> INCX is INTEGER, storage spacing between elements of X
|
||||
!> If INCX > 0, X(1+(i-1)*INCX) = x(i) for 1 <= i <= n
|
||||
!> If INCX < 0, X(1-(n-i)*INCX) = x(i) for 1 <= i <= n
|
||||
!> If INCX = 0, x isn't a vector so there is no need to call
|
||||
!> this subroutine. If you call it anyway, it will count x(1)
|
||||
!> in the vector norm N times.
|
||||
!> \endverbatim
|
||||
!
|
||||
! Authors:
|
||||
! ========
|
||||
!
|
||||
!> \author Edward Anderson, Lockheed Martin
|
||||
!
|
||||
!> \date August 2016
|
||||
!
|
||||
!> \ingroup single_blas_level1
|
||||
!
|
||||
!> \par Contributors:
|
||||
! ==================
|
||||
!>
|
||||
!> Weslley Pereira, University of Colorado Denver, USA
|
||||
!
|
||||
!> \par Further Details:
|
||||
! =====================
|
||||
!>
|
||||
!> \verbatim
|
||||
!>
|
||||
!> Anderson E. (2017)
|
||||
!> Algorithm 978: Safe Scaling in the Level 1 BLAS
|
||||
!> ACM Trans Math Softw 44:1--28
|
||||
!> https://doi.org/10.1145/3061665
|
||||
!>
|
||||
!> Blue, James L. (1978)
|
||||
!> A Portable Fortran Program to Find the Euclidean Norm of a Vector
|
||||
!> ACM Trans Math Softw 4:15--23
|
||||
!> https://doi.org/10.1145/355769.355771
|
||||
!>
|
||||
!> \endverbatim
|
||||
!>
|
||||
! =====================================================================
|
||||
function SNRM2( n, x, incx )
|
||||
integer, parameter :: wp = kind(1.e0)
|
||||
real(wp) :: SNRM2
|
||||
!
|
||||
! -- Reference BLAS level1 routine (version 3.9.1) --
|
||||
! -- Reference BLAS is a software package provided by Univ. of Tennessee, --
|
||||
! -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
|
||||
! March 2021
|
||||
!
|
||||
! .. Constants ..
|
||||
real(wp), parameter :: zero = 0.0_wp
|
||||
real(wp), parameter :: one = 1.0_wp
|
||||
real(wp), parameter :: maxN = huge(0.0_wp)
|
||||
! ..
|
||||
! .. Blue's ccaling constants ..
|
||||
real(wp), parameter :: tsml = real(radix(0._wp), wp)**ceiling( &
|
||||
(minexponent(0._wp) - 1) * 0.5_wp)
|
||||
real(wp), parameter :: tbig = real(radix(0._wp), wp)**floor( &
|
||||
(maxexponent(0._wp) - digits(0._wp) + 1) * 0.5_wp)
|
||||
real(wp), parameter :: ssml = real(radix(0._wp), wp)**( - floor( &
|
||||
(minexponent(0._wp) - 1) * 0.5_wp))
|
||||
real(wp), parameter :: sbig = real(radix(0._wp), wp)**( - ceiling( &
|
||||
(maxexponent(0._wp) - digits(0._wp) + 1) * 0.5_wp))
|
||||
! ..
|
||||
! .. Scalar Arguments ..
|
||||
integer :: incx, n
|
||||
! ..
|
||||
! .. Array Arguments ..
|
||||
real(wp) :: x(*)
|
||||
! ..
|
||||
! .. Local Scalars ..
|
||||
integer :: i, ix
|
||||
logical :: notbig
|
||||
real(wp) :: abig, amed, asml, ax, scl, sumsq, ymax, ymin
|
||||
!
|
||||
! Quick return if possible
|
||||
!
|
||||
SNRM2 = zero
|
||||
if( n <= 0 ) return
|
||||
!
|
||||
scl = one
|
||||
sumsq = zero
|
||||
!
|
||||
! Compute the sum of squares in 3 accumulators:
|
||||
! abig -- sums of squares scaled down to avoid overflow
|
||||
! asml -- sums of squares scaled up to avoid underflow
|
||||
! amed -- sums of squares that do not require scaling
|
||||
! The thresholds and multipliers are
|
||||
! tbig -- values bigger than this are scaled down by sbig
|
||||
! tsml -- values smaller than this are scaled up by ssml
|
||||
!
|
||||
notbig = .true.
|
||||
asml = zero
|
||||
amed = zero
|
||||
abig = zero
|
||||
ix = 1
|
||||
if( incx < 0 ) ix = 1 - (n-1)*incx
|
||||
do i = 1, n
|
||||
ax = abs(x(ix))
|
||||
if (ax > tbig) then
|
||||
abig = abig + (ax*sbig)**2
|
||||
notbig = .false.
|
||||
else if (ax < tsml) then
|
||||
if (notbig) asml = asml + (ax*ssml)**2
|
||||
else
|
||||
amed = amed + ax**2
|
||||
end if
|
||||
ix = ix + incx
|
||||
end do
|
||||
!
|
||||
! Combine abig and amed or amed and asml if more than one
|
||||
! accumulator was used.
|
||||
!
|
||||
if (abig > zero) then
|
||||
!
|
||||
! Combine abig and amed if abig > 0.
|
||||
!
|
||||
if ( (amed > zero) .or. (amed > maxN) .or. (amed /= amed) ) then
|
||||
abig = abig + (amed*sbig)*sbig
|
||||
end if
|
||||
scl = one / sbig
|
||||
sumsq = abig
|
||||
else if (asml > zero) then
|
||||
!
|
||||
! Combine amed and asml if asml > 0.
|
||||
!
|
||||
if ( (amed > zero) .or. (amed > maxN) .or. (amed /= amed) ) then
|
||||
amed = sqrt(amed)
|
||||
asml = sqrt(asml) / ssml
|
||||
if (asml > amed) then
|
||||
ymin = amed
|
||||
ymax = asml
|
||||
else
|
||||
ymin = asml
|
||||
ymax = amed
|
||||
end if
|
||||
scl = one
|
||||
sumsq = ymax**2*( one + (ymin/ymax)**2 )
|
||||
else
|
||||
scl = one / ssml
|
||||
sumsq = asml
|
||||
end if
|
||||
else
|
||||
!
|
||||
! Otherwise all values are mid-range
|
||||
!
|
||||
scl = one
|
||||
sumsq = amed
|
||||
end if
|
||||
SNRM2 = scl*sqrt( sumsq )
|
||||
return
|
||||
end function
|
||||
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