.TH "real" 3 "Wed Mar 8 2017" "Version 3.7.0" "LAPACK" \" -*- nroff -*- .ad l .nh .SH NAME real \- .SS "Functions" .in +1c .ti -1c .RI "real function \fBsasum\fP (\fBN\fP, SX, INCX)" .br .RI "\fI\fBSASUM\fP \fP" .ti -1c .RI "subroutine \fBsaxpy\fP (\fBN\fP, SA, SX, INCX, SY, INCY)" .br .RI "\fI\fBSAXPY\fP \fP" .ti -1c .RI "real function \fBscabs1\fP (Z)" .br .RI "\fI\fBSCABS1\fP \fP" .ti -1c .RI "real function \fBscasum\fP (\fBN\fP, CX, INCX)" .br .RI "\fI\fBSCASUM\fP \fP" .ti -1c .RI "real function \fBscnrm2\fP (\fBN\fP, X, INCX)" .br .RI "\fI\fBSCNRM2\fP \fP" .ti -1c .RI "subroutine \fBscopy\fP (\fBN\fP, SX, INCX, SY, INCY)" .br .RI "\fI\fBSCOPY\fP \fP" .ti -1c .RI "real function \fBsdot\fP (\fBN\fP, SX, INCX, SY, INCY)" .br .RI "\fI\fBSDOT\fP \fP" .ti -1c .RI "real function \fBsdsdot\fP (\fBN\fP, SB, SX, INCX, SY, INCY)" .br .RI "\fI\fBSDSDOT\fP \fP" .ti -1c .RI "real function \fBsnrm2\fP (\fBN\fP, X, INCX)" .br .RI "\fI\fBSNRM2\fP \fP" .ti -1c .RI "subroutine \fBsrot\fP (\fBN\fP, SX, INCX, SY, INCY, C, S)" .br .RI "\fI\fBSROT\fP \fP" .ti -1c .RI "subroutine \fBsrotg\fP (SA, SB, C, S)" .br .RI "\fI\fBSROTG\fP \fP" .ti -1c .RI "subroutine \fBsrotm\fP (\fBN\fP, SX, INCX, SY, INCY, SPARAM)" .br .RI "\fI\fBSROTM\fP \fP" .ti -1c .RI "subroutine \fBsrotmg\fP (SD1, SD2, SX1, SY1, SPARAM)" .br .RI "\fI\fBSROTMG\fP \fP" .ti -1c .RI "subroutine \fBsscal\fP (\fBN\fP, SA, SX, INCX)" .br .RI "\fI\fBSSCAL\fP \fP" .ti -1c .RI "subroutine \fBsswap\fP (\fBN\fP, SX, INCX, SY, INCY)" .br .RI "\fI\fBSSWAP\fP \fP" .in -1c .SH "Detailed Description" .PP This is the group of real LEVEL 1 BLAS routines\&. .SH "Function Documentation" .PP .SS "real function sasum (integerN, real, dimension(*)SX, integerINCX)" .PP \fBSASUM\fP .PP \fBPurpose: \fP .RS 4 .PP .nf SASUM takes the sum of the absolute values. uses unrolled loops for increment equal to one. .fi .PP .RE .PP \fBAuthor:\fP .RS 4 Univ\&. of Tennessee .PP Univ\&. of California Berkeley .PP Univ\&. of Colorado Denver .PP NAG Ltd\&. .RE .PP \fBDate:\fP .RS 4 December 2016 .RE .PP \fBFurther Details: \fP .RS 4 .PP .nf jack dongarra, linpack, 3/11/78. modified 3/93 to return if incx .le. 0. modified 12/3/93, array(1) declarations changed to array(*) .fi .PP .RE .PP .SS "subroutine saxpy (integerN, realSA, real, dimension(*)SX, integerINCX, real, dimension(*)SY, integerINCY)" .PP \fBSAXPY\fP .PP \fBPurpose: \fP .RS 4 .PP .nf SAXPY constant times a vector plus a vector. uses unrolled loops for increments equal to one. .fi .PP .RE .PP \fBAuthor:\fP .RS 4 Univ\&. of Tennessee .PP Univ\&. of California Berkeley .PP Univ\&. of Colorado Denver .PP NAG Ltd\&. .RE .PP \fBDate:\fP .RS 4 December 2016 .RE .PP \fBFurther Details: \fP .RS 4 .PP .nf jack dongarra, linpack, 3/11/78. modified 12/3/93, array(1) declarations changed to array(*) .fi .PP .RE .PP .SS "real function scabs1 (complexZ)" .PP \fBSCABS1\fP .PP \fBPurpose: \fP .RS 4 .PP .nf SCABS1 computes |Re(.)| + |Im(.)| of a complex number .fi .PP .RE .PP \fBAuthor:\fP .RS 4 Univ\&. of Tennessee .PP Univ\&. of California Berkeley .PP Univ\&. of Colorado Denver .PP NAG Ltd\&. .RE .PP \fBDate:\fP .RS 4 December 2016 .RE .PP .SS "real function scasum (integerN, complex, dimension(*)CX, integerINCX)" .PP \fBSCASUM\fP .PP \fBPurpose: \fP .RS 4 .PP .nf SCASUM takes the sum of the (|Re(.)| + |Im(.)|)'s of a complex vector and returns a single precision result. .fi .PP .RE .PP \fBAuthor:\fP .RS 4 Univ\&. of Tennessee .PP Univ\&. of California Berkeley .PP Univ\&. of Colorado Denver .PP NAG Ltd\&. .RE .PP \fBDate:\fP .RS 4 December 2016 .RE .PP \fBFurther Details: \fP .RS 4 .PP .nf jack dongarra, linpack, 3/11/78. modified 3/93 to return if incx .le. 0. modified 12/3/93, array(1) declarations changed to array(*) .fi .PP .RE .PP .SS "real function scnrm2 (integerN, complex, dimension(*)X, integerINCX)" .PP \fBSCNRM2\fP .PP \fBPurpose: \fP .RS 4 .PP .nf SCNRM2 returns the euclidean norm of a vector via the function name, so that SCNRM2 := sqrt( x**H*x ) .fi .PP .RE .PP \fBAuthor:\fP .RS 4 Univ\&. of Tennessee .PP Univ\&. of California Berkeley .PP Univ\&. of Colorado Denver .PP NAG Ltd\&. .RE .PP \fBDate:\fP .RS 4 December 2016 .RE .PP \fBFurther Details: \fP .RS 4 .PP .nf -- This version written on 25-October-1982. Modified on 14-October-1993 to inline the call to CLASSQ. Sven Hammarling, Nag Ltd. .fi .PP .RE .PP .SS "subroutine scopy (integerN, real, dimension(*)SX, integerINCX, real, dimension(*)SY, integerINCY)" .PP \fBSCOPY\fP .PP \fBPurpose: \fP .RS 4 .PP .nf SCOPY copies a vector, x, to a vector, y. uses unrolled loops for increments equal to 1. .fi .PP .RE .PP \fBAuthor:\fP .RS 4 Univ\&. of Tennessee .PP Univ\&. of California Berkeley .PP Univ\&. of Colorado Denver .PP NAG Ltd\&. .RE .PP \fBDate:\fP .RS 4 December 2016 .RE .PP \fBFurther Details: \fP .RS 4 .PP .nf jack dongarra, linpack, 3/11/78. modified 12/3/93, array(1) declarations changed to array(*) .fi .PP .RE .PP .SS "real function sdot (integerN, real, dimension(*)SX, integerINCX, real, dimension(*)SY, integerINCY)" .PP \fBSDOT\fP .PP \fBPurpose: \fP .RS 4 .PP .nf SDOT forms the dot product of two vectors. uses unrolled loops for increments equal to one. .fi .PP .RE .PP \fBAuthor:\fP .RS 4 Univ\&. of Tennessee .PP Univ\&. of California Berkeley .PP Univ\&. of Colorado Denver .PP NAG Ltd\&. .RE .PP \fBDate:\fP .RS 4 December 2016 .RE .PP \fBFurther Details: \fP .RS 4 .PP .nf jack dongarra, linpack, 3/11/78. modified 12/3/93, array(1) declarations changed to array(*) .fi .PP .RE .PP .SS "real function sdsdot (integerN, realSB, real, dimension(*)SX, integerINCX, real, dimension(*)SY, integerINCY)" .PP \fBSDSDOT\fP .PP \fBPurpose: \fP .RS 4 .PP .nf .fi .PP .RE .PP \fBAuthor:\fP .RS 4 Univ\&. of Tennessee .PP Univ\&. of California Berkeley .PP Univ\&. of Colorado Denver .PP NAG Ltd\&. .RE .PP \fBDate:\fP .RS 4 December 2016 .RE .PP .SS "real function snrm2 (integerN, real, dimension(*)X, integerINCX)" .PP \fBSNRM2\fP .PP \fBPurpose: \fP .RS 4 .PP .nf SNRM2 returns the euclidean norm of a vector via the function name, so that SNRM2 := sqrt( x'*x ). .fi .PP .RE .PP \fBAuthor:\fP .RS 4 Univ\&. of Tennessee .PP Univ\&. of California Berkeley .PP Univ\&. of Colorado Denver .PP NAG Ltd\&. .RE .PP \fBDate:\fP .RS 4 December 2016 .RE .PP \fBFurther Details: \fP .RS 4 .PP .nf -- This version written on 25-October-1982. Modified on 14-October-1993 to inline the call to SLASSQ. Sven Hammarling, Nag Ltd. .fi .PP .RE .PP .SS "subroutine srot (integerN, real, dimension(*)SX, integerINCX, real, dimension(*)SY, integerINCY, realC, realS)" .PP \fBSROT\fP .PP \fBPurpose: \fP .RS 4 .PP .nf applies a plane rotation. .fi .PP .RE .PP \fBAuthor:\fP .RS 4 Univ\&. of Tennessee .PP Univ\&. of California Berkeley .PP Univ\&. of Colorado Denver .PP NAG Ltd\&. .RE .PP \fBDate:\fP .RS 4 December 2016 .RE .PP \fBFurther Details: \fP .RS 4 .PP .nf jack dongarra, linpack, 3/11/78. modified 12/3/93, array(1) declarations changed to array(*) .fi .PP .RE .PP .SS "subroutine srotg (realSA, realSB, realC, realS)" .PP \fBSROTG\fP .PP \fBPurpose: \fP .RS 4 .PP .nf SROTG construct givens plane rotation. .fi .PP .RE .PP \fBAuthor:\fP .RS 4 Univ\&. of Tennessee .PP Univ\&. of California Berkeley .PP Univ\&. of Colorado Denver .PP NAG Ltd\&. .RE .PP \fBDate:\fP .RS 4 December 2016 .RE .PP \fBFurther Details: \fP .RS 4 .PP .nf jack dongarra, linpack, 3/11/78. .fi .PP .RE .PP .SS "subroutine srotm (integerN, real, dimension(*)SX, integerINCX, real, dimension(*)SY, integerINCY, real, dimension(5)SPARAM)" .PP \fBSROTM\fP .PP \fBPurpose: \fP .RS 4 .PP .nf APPLY THE MODIFIED GIVENS TRANSFORMATION, H, TO THE 2 BY N MATRIX (SX**T) , WHERE **T INDICATES TRANSPOSE. THE ELEMENTS OF SX ARE IN (SX**T) SX(LX+I*INCX), I = 0 TO N-1, WHERE LX = 1 IF INCX .GE. 0, ELSE LX = (-INCX)*N, AND SIMILARLY FOR SY USING USING LY AND INCY. WITH SPARAM(1)=SFLAG, H HAS ONE OF THE FOLLOWING FORMS.. SFLAG=-1.E0 SFLAG=0.E0 SFLAG=1.E0 SFLAG=-2.E0 (SH11 SH12) (1.E0 SH12) (SH11 1.E0) (1.E0 0.E0) H=( ) ( ) ( ) ( ) (SH21 SH22), (SH21 1.E0), (-1.E0 SH22), (0.E0 1.E0). SEE SROTMG FOR A DESCRIPTION OF DATA STORAGE IN SPARAM. .fi .PP .RE .PP \fBParameters:\fP .RS 4 \fIN\fP .PP .nf N is INTEGER number of elements in input vector(s) .fi .PP .br \fISX\fP .PP .nf SX is REAL array, dimension N double precision vector with N elements .fi .PP .br \fIINCX\fP .PP .nf INCX is INTEGER storage spacing between elements of SX .fi .PP .br \fISY\fP .PP .nf SY is REAL array, dimension N double precision vector with N elements .fi .PP .br \fIINCY\fP .PP .nf INCY is INTEGER storage spacing between elements of SY .fi .PP .br \fISPARAM\fP .PP .nf SPARAM is REAL array, dimension 5 SPARAM(1)=SFLAG SPARAM(2)=SH11 SPARAM(3)=SH21 SPARAM(4)=SH12 SPARAM(5)=SH22 .fi .PP .RE .PP \fBAuthor:\fP .RS 4 Univ\&. of Tennessee .PP Univ\&. of California Berkeley .PP Univ\&. of Colorado Denver .PP NAG Ltd\&. .RE .PP \fBDate:\fP .RS 4 December 2016 .RE .PP .SS "subroutine srotmg (realSD1, realSD2, realSX1, realSY1, real, dimension(5)SPARAM)" .PP \fBSROTMG\fP .PP \fBPurpose: \fP .RS 4 .PP .nf CONSTRUCT THE MODIFIED GIVENS TRANSFORMATION MATRIX H WHICH ZEROS THE SECOND COMPONENT OF THE 2-VECTOR (SQRT(SD1)*SX1,SQRT(SD2)*> SY2)**T. WITH SPARAM(1)=SFLAG, H HAS ONE OF THE FOLLOWING FORMS.. SFLAG=-1.E0 SFLAG=0.E0 SFLAG=1.E0 SFLAG=-2.E0 (SH11 SH12) (1.E0 SH12) (SH11 1.E0) (1.E0 0.E0) H=( ) ( ) ( ) ( ) (SH21 SH22), (SH21 1.E0), (-1.E0 SH22), (0.E0 1.E0). LOCATIONS 2-4 OF SPARAM CONTAIN SH11,SH21,SH12, AND SH22 RESPECTIVELY. (VALUES OF 1.E0, -1.E0, OR 0.E0 IMPLIED BY THE VALUE OF SPARAM(1) ARE NOT STORED IN SPARAM.) THE VALUES OF GAMSQ AND RGAMSQ SET IN THE DATA STATEMENT MAY BE INEXACT. THIS IS OK AS THEY ARE ONLY USED FOR TESTING THE SIZE OF SD1 AND SD2. ALL ACTUAL SCALING OF DATA IS DONE USING GAM. .fi .PP .RE .PP \fBParameters:\fP .RS 4 \fISD1\fP .PP .nf SD1 is REAL .fi .PP .br \fISD2\fP .PP .nf SD2 is REAL .fi .PP .br \fISX1\fP .PP .nf SX1 is REAL .fi .PP .br \fISY1\fP .PP .nf SY1 is REAL .fi .PP .br \fISPARAM\fP .PP .nf SPARAM is REAL array, dimension 5 SPARAM(1)=SFLAG SPARAM(2)=SH11 SPARAM(3)=SH21 SPARAM(4)=SH12 SPARAM(5)=SH22 .fi .PP .RE .PP \fBAuthor:\fP .RS 4 Univ\&. of Tennessee .PP Univ\&. of California Berkeley .PP Univ\&. of Colorado Denver .PP NAG Ltd\&. .RE .PP \fBDate:\fP .RS 4 December 2016 .RE .PP .SS "subroutine sscal (integerN, realSA, real, dimension(*)SX, integerINCX)" .PP \fBSSCAL\fP .PP \fBPurpose: \fP .RS 4 .PP .nf scales a vector by a constant. uses unrolled loops for increment equal to 1. .fi .PP .RE .PP \fBAuthor:\fP .RS 4 Univ\&. of Tennessee .PP Univ\&. of California Berkeley .PP Univ\&. of Colorado Denver .PP NAG Ltd\&. .RE .PP \fBDate:\fP .RS 4 December 2016 .RE .PP \fBFurther Details: \fP .RS 4 .PP .nf jack dongarra, linpack, 3/11/78. modified 3/93 to return if incx .le. 0. modified 12/3/93, array(1) declarations changed to array(*) .fi .PP .RE .PP .SS "subroutine sswap (integerN, real, dimension(*)SX, integerINCX, real, dimension(*)SY, integerINCY)" .PP \fBSSWAP\fP .PP \fBPurpose: \fP .RS 4 .PP .nf interchanges two vectors. uses unrolled loops for increments equal to 1. .fi .PP .RE .PP \fBAuthor:\fP .RS 4 Univ\&. of Tennessee .PP Univ\&. of California Berkeley .PP Univ\&. of Colorado Denver .PP NAG Ltd\&. .RE .PP \fBDate:\fP .RS 4 December 2016 .RE .PP \fBFurther Details: \fP .RS 4 .PP .nf jack dongarra, linpack, 3/11/78. modified 12/3/93, array(1) declarations changed to array(*) .fi .PP .RE .PP .SH "Author" .PP Generated automatically by Doxygen for LAPACK from the source code\&.