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%%EndProlog
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1 pagesetup
10 R f
(Appendix 5)1 469 1 2825 120 t
(BASIC LINEAR ALGEBRA MODULES)3 1691 1 720 360 t
( if the largest element of a vector)7 1316(ISAMAX - index)2 949 2 720 720 t
( of a vector)3 451( 1-norm)1 444(SASUM -)1 577 3 720 840 t
( multiple of one vector to another)6 1337( add)1 294(SAXPY -)1 577 3 720 960 t
( product of two vectors)4 926( dot)1 278(SDOT -)1 577 3 720 1080 t
( a vector)2 343( scale)1 349(SSCAL -)1 577 3 720 1200 t
( two vectors)2 488( interchange)1 615(SSWAP -)1 577 3 720 1320 t
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2 pagesetup
10 R f
(ISAMAX \320 index of the maximum magnitude element of a vector)10 2691 1 1534 120 t
9 B f
(Purpose:)720 480 w
10 R f
( to \256nd the \(\256rst\) component with maximum magnitude.)8 2373(ISAMAX looks through a vector)4 1371 2 1296 480 t
(The integer position of that component in the vector is returned.)10 2555 1 1296 600 t
9 B f
(Type:)720 960 w
10 R f
(Integer function)1 640 1 1296 960 t
9 B f
(Usage:)720 1320 w
10 S f
(<)1296 1320 w
10 R f
(answer)1351 1320 w
10 S f
(>)1633 1320 w
10 R f
(= ISAMAX\(N, X, INCX\))3 1029 1 1713 1320 t
(N)1440 1560 w
14 S f
(\256)1980 1580 w
10 R f
(the number of elements to be compared)6 1580 1 2196 1560 t
(X)1440 1800 w
14 S f
(\256)1980 1820 w
10 R f
(the vector of elements)3 884 1 2196 1800 t
(INCX)1440 2040 w
14 S f
(\256)1980 2060 w
10 R f
(the elements are spaced at intervals of INCX in X:)9 2015 1 2196 2040 t
(X\(1\), X\(1+INCX\), ..., X\(1+\(N)3 1217 1 2196 2160 t
10 S f
(-)3413 2160 w
10 R f
(1\))3468 2160 w
10 S f
(*)3551 2160 w
10 R f
(INCX\))3601 2160 w
10 S f
(<)1440 2400 w
10 R f
(answer)1495 2400 w
10 S f
(>)1777 2400 w
14 S f
(\254)1980 2420 w
10 R f
(M, the position of the \(\256rst\) component of maximum magnitude:)9 2594 1 2196 2400 t
(If INCX = 1,)3 516 1 2484 2520 t
10 S f
(\357)3050 2520 w
10 R f
(X\(M\))3099 2520 w
10 S f
(\357)3326 2520 w
10 R f
(is largest.)1 383 1 3400 2520 t
(In general,)1 426 1 2484 2640 t
10 S f
(\357)2960 2640 w
10 R f
(X\(1 + \(M)2 383 1 3009 2640 t
10 S f
(-)3417 2640 w
10 R f
(1\))3497 2640 w
10 S f
(*)3605 2640 w
10 R f
(INCX\))3680 2640 w
10 S f
(\357)3957 2640 w
10 R f
(is largest.)1 383 1 4031 2640 t
9 B f
(Note 1:)1 278 1 720 3000 t
10 R f
( we can use ISAMAX to deal with the rows)9 1780(Since Fortran stores arrays in column-wise order)6 1964 2 1296 3000 t
(of a 2-dimensional array as in the example below.)8 1993 1 1296 3120 t
9 B f
(Note 2:)1 278 1 720 3480 t
10 R f
(If N=0, ISAMAX=0 is returned.)4 1293 1 1296 3480 t
9 B f
(Error situations:)1 648 1 720 3840 t
10 R f
(\(All errors in this subprogram are fatal \320)7 1666 1 1512 3840 t
(see)1512 3960 w
10 I f
(Error Handling)1 631 1 1664 3960 t
10 R f
(, Framework Chapter\))2 884 1 2295 3960 t
(Number Error)1 1506 1 1800 4200 t
(1 N)1 1108 1 1944 4440 t
10 S f
(<)3077 4440 w
10 R f
(0)3157 4440 w
(2 INCX)1 1280 1 1944 4680 t
10 S f
(\243)3249 4680 w
10 R f
(0)3329 4680 w
9 B f
(Double-precision version:)1 988 1 720 5040 t
10 R f
(IDAMAX with X declared double precision)5 1760 1 1800 5040 t
9 B f
(Complex version:)1 678 1 720 5400 t
10 R f
(ICAMAX with X declared complex)4 1436 1 1473 5400 t
9 B f
(See also:)1 333 1 720 5760 t
10 R f
(SAMAX, ISMAX)1 733 1 1296 5760 t
9 B f
(Author:)720 6120 w
10 R f
(Linda Kaufman)1 629 1 1296 6120 t
9 B f
(Reference:)720 6480 w
10 R f
( J., Kincaid, D. R., and Krogh, F. T., Basic linear algebra subpro-)12 2643(Lawson, C. L., Hanson, R.)4 1074 2 1323 6480 t
(grams for Fortran usage,)3 981 1 1296 6600 t
10 I f
(ACM Trans. Math. Software 5)4 1212 1 2302 6600 t
10 R f
(, 3 \(1979\), 308-323.)3 799 1 3514 6600 t
(Linear Algebra)1 606 1 360 7500 t
(\320 2 \320)2 300 1 2730 7620 t
(ISAMAX)360 7740 w
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3 pagesetup
10 R f
(-- --)1 5544 1 0 120 t
8 R f
(PORT)360 600 w
10 R f
( Algebra)1 346(library Linear)1 4463 2 591 600 t
( ISAMAX)1 4305(February 11, 1993)2 735 2 360 840 t
9 B f
(Example:)720 1320 w
10 R f
( an $m times n$ matrix A, dimensioned \(IA,N\) are permuted)10 2484(In this example the columns of)5 1260 2 1296 1320 t
( the elements of the \256rst row in A.)8 1400(so that the \(1,1\) element of A is the largest in modulus of)12 2344 2 1296 1440 t
(The subroutine SSWAP interchanges two vectors.)5 2003 1 1296 1560 t
8 CW f
(J=ISAMAX\(N,A,IA\))2568 1900 w
(CALL SSWAP\(M,A,1,A\(1,J\),1\))1 1248 1 2568 2000 t
10 R f
(Linear Algebra)1 606 1 4794 7500 t
(\320 3 \320)2 300 1 2730 7620 t
(ISAMAX)5006 7740 w
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4 pagesetup
10 R f
(-- --)1 5544 1 0 120 t
(Linear Algebra)1 606 1 360 600 t
8 R f
(PORT)4903 600 w
10 R f
(library)5134 600 w
( 11, 1993)2 375(ISAMAX February)1 4665 2 360 840 t
(SASUM \320 1-norm of a vector)5 1240 1 2548 1320 t
9 B f
(Purpose:)720 1680 w
10 R f
( sum of the absolute values of a vector: $sum from i=1 to n)13 2401(SASUM computes the)2 904 2 1296 1680 t
10 S f
(\357)4629 1680 w
10 R f
(x sub i \303)3 334 1 4706 1680 t
10 S f
(\357)1296 1800 w
10 R f
($)1345 1800 w
9 B f
(Type:)720 2160 w
10 R f
(Real function)1 541 1 1296 2160 t
9 B f
(Usage:)720 2520 w
10 S f
(<)1296 2520 w
10 R f
(answer)1351 2520 w
10 S f
(>)1633 2520 w
10 R f
(= SASUM\(N, X, INCX\))3 980 1 1713 2520 t
(N)1440 2760 w
14 S f
(\256)1980 2780 w
10 R f
(the number of elements to be summed)6 1526 1 2196 2760 t
(X)1440 3000 w
14 S f
(\256)1980 3020 w
10 R f
(the vector of elements)3 884 1 2196 3000 t
(INCX)1440 3240 w
14 S f
(\256)1980 3260 w
10 R f
(the elements are spaced at intervals of INCX in X:)9 2015 1 2196 3240 t
(X\(1\), X\(1+INCX\), ..., X\(1+\(N)3 1217 1 2196 3360 t
10 S f
(-)3413 3360 w
10 R f
(1\)INCX\))3468 3360 w
10 S f
(<)1440 3600 w
10 R f
(answer)1495 3600 w
10 S f
(>)1777 3600 w
14 S f
(\254)1980 3620 w
10 S f
(\357)2196 3600 w
10 R f
(X\(1\))2270 3600 w
10 S f
(\357)2483 3600 w
10 R f
(+)2557 3600 w
10 S f
(\357)2638 3600 w
10 R f
(X\(1+INCX\))2712 3600 w
10 S f
(\357)3225 3600 w
10 R f
(+ ... +)2 237 1 3299 3600 t
10 S f
(\357)3561 3600 w
10 R f
(X\(1+\(N)3635 3600 w
10 S f
(-)3951 3600 w
10 R f
(1\)INCX\))4006 3600 w
10 S f
(\357)4391 3600 w
9 B f
(Note 1:)1 278 1 720 3960 t
10 R f
( arrays in column-wise order we can use SASUM to deal with the rows)13 2933(Since Fortran stores)2 811 2 1296 3960 t
(of a 2-dimensional array as in the example below.)8 1993 1 1296 4080 t
9 B f
(Note 2:)1 278 1 720 4440 t
10 R f
(If N=0, SASUM=0.0 is returned.)4 1319 1 1296 4440 t
9 B f
(Note 3:)1 278 1 720 4800 t
10 R f
( i=1 to n \()4 427(For complex vectors, SCASUM computes $sum from)6 2194 2 1296 4800 t
10 S f
(\357)3917 4800 w
10 R f
(Re\(x sub i \))3 493 1 3966 4800 t
10 S f
(\357)4459 4800 w
10 R f
(+)4508 4800 w
10 S f
(\357)4564 4800 w
10 R f
(Im\(x sub i)2 427 1 4613 4800 t
(\))1296 4920 w
10 S f
(\357)1329 4920 w
10 R f
(\)$.)1378 4920 w
9 B f
(Note 4:)1 278 1 720 5280 t
10 R f
(No attempt is made to prevent or give warning of under\257ow or over\257ow.)12 2915 1 1296 5280 t
9 B f
(Error situations:)1 648 1 720 5640 t
10 R f
(\(All errors in this subprogram are fatal \320)7 1666 1 1512 5640 t
(see)1512 5760 w
10 I f
(Error Handling)1 631 1 1664 5760 t
10 R f
(, Framework Chapter\))2 884 1 2295 5760 t
(Number Error)1 1506 1 1800 6000 t
(1 N)1 1108 1 1944 6240 t
10 S f
(<)3052 6240 w
10 R f
(0)3107 6240 w
(2 INCX)1 1280 1 1944 6480 t
10 S f
(\243)3224 6480 w
10 R f
(0)3279 6480 w
9 B f
(Double-precision version:)1 988 1 720 6840 t
10 R f
(DASUM with X declared double precision)5 1711 1 1800 6840 t
(Linear Algebra)1 606 1 360 7500 t
(\320 4 \320)2 300 1 2730 7620 t
(SASUM)360 7740 w
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5 pagesetup
10 R f
(-- --)1 5544 1 0 120 t
8 R f
(PORT)360 600 w
10 R f
( Algebra)1 346(library Linear)1 4463 2 591 600 t
( SASUM)1 4305(February 11, 1993)2 735 2 360 840 t
9 B f
(Complex version:)1 678 1 720 1320 t
10 R f
(SCASUM with X declared complex \(see Note 3\).)7 1980 1 1473 1320 t
9 B f
(Author:)720 1680 w
10 R f
(Linda Kaufman)1 629 1 1296 1680 t
9 B f
(Reference:)720 2040 w
10 R f
( J., Kincaid, D. R., and Krogh, F. T., Basic linear algebra subpro-)12 2643(Lawson, C. L., Hanson, R.)4 1074 2 1323 2040 t
( Fortran Usage, Report SAND77-0898, Sandia Laboratories, Albuquerque, New)8 3341(grams for)1 403 2 1296 2160 t
(Mexico 87115, October 1977.)3 1201 1 1296 2280 t
9 B f
(Examples:)720 2640 w
10 R f
( n$ matrix A. The 1-)5 861(The following program fragment computes the 1-norm of an $m times)10 2883 2 1296 2640 t
(norm is de\256ned by $max from 1)6 1288 1 1296 2760 t
10 S f
(<)2584 2760 w
10 R f
(=j)2639 2760 w
10 S f
(<)2723 2760 w
10 R f
(=n sum from i=1 to m)5 882 1 2778 2760 t
10 S f
(\357)3685 2760 w
10 R f
(a sub i,j\303\303)2 380 1 3759 2760 t
10 S f
(\357)4139 2760 w
10 R f
($)4188 2760 w
8 CW f
(ANORM1=0.0)1992 3100 w
(DO 10 J=1,N)2 528 1 1992 3200 t
(ANORMJ = SASUM\(M,A\(1,J\),1\))2 1248 1 2136 3300 t
(IF \(ANORMJ .GT. ANORM1\) ANORM1 = ANORMJ)6 1872 1 2136 3400 t
(10 CONTINUE)1 528 1 1848 3500 t
10 R f
(The next program fragment computes the in\256nity norm of an $m times n$ matrix A, dimen-)15 3744 1 1296 3840 t
( in\256nity norm is de\256ned as $max from 1)8 1683(sioned \(IA,N\). The)2 779 2 1296 3960 t
10 S f
(<)3758 3960 w
10 R f
(=i)3813 3960 w
10 S f
(<)3897 3960 w
10 R f
(=m sum from j=1 to n)5 927 1 3952 3960 t
10 S f
(\357)4913 3960 w
10 R f
(a)4996 3960 w
(sub i,j\303\303)1 311 1 1296 4080 t
10 S f
(\357)1607 4080 w
10 R f
($)1656 4080 w
8 CW f
(ANORM=0.0)2040 4420 w
(DO 10 I=1,M)2 528 1 2040 4520 t
(ANORMI = SASUM\(N,A\(I,1\),IA\))2 1296 1 2184 4620 t
(IF \(ANORMI .GT. ANORM\) ANORM=ANORMI)4 1680 1 2184 4720 t
(10 CONTINUE)1 528 1 1896 4820 t
10 R f
(Linear Algebra)1 606 1 4794 7500 t
(\320 5 \320)2 300 1 2730 7620 t
(SASUM)5055 7740 w
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6 pagesetup
10 R f
(-- --)1 5544 1 0 120 t
(Linear Algebra)1 606 1 360 600 t
8 R f
(PORT)4903 600 w
10 R f
(library)5134 600 w
( 11, 1993)2 375(SASUM February)1 4665 2 360 840 t
(SAXPY \320 add multiple of one vector to another)8 1959 1 2188 1320 t
9 B f
(Purpose:)720 1680 w
10 R f
(SAXPY scales a vector $x$ by a scalar $a$ and adds the result to a vector $y$.)16 3146 1 1296 1680 t
9 B f
(Usage:)720 2040 w
10 R f
(CALL SAXPY \(N, A, X, INCX, Y, INCY\))7 1731 1 1296 2040 t
(N)1440 2280 w
14 S f
(\256)1980 2300 w
10 R f
(the number of affected elements in X and Y)8 1751 1 2196 2280 t
(A)1440 2520 w
14 S f
(\256)1980 2540 w
10 R f
(the scalar variable)2 725 1 2196 2520 t
(X)1440 2760 w
14 S f
(\256)1980 2780 w
10 R f
(the vector which is to be scaled)6 1253 1 2196 2760 t
(INCX)1440 3000 w
14 S f
(\256)1980 3020 w
10 R f
(the elements are spaced at intervals of INCX in X:)9 2015 1 2196 3000 t
(X\(1\), X\(1+INCX\), ..., X\(1+\(N)3 1217 1 2196 3120 t
10 S f
(-)3413 3120 w
10 R f
(1\))3468 3120 w
10 S f
(*)3551 3120 w
10 R f
(INCX\))3601 3120 w
(Y)1440 3360 w
14 S f
(\256)1980 3380 w
10 R f
(the vector which is to be added)6 1242 1 2196 3360 t
14 S f
(\254)1980 3620 w
10 R f
(AX + Y)2 322 1 2196 3600 t
(INCY)1440 3840 w
14 S f
(\256)1980 3860 w
10 R f
(the elements are space at intervals of INCY in Y:)9 1965 1 2196 3840 t
(Y\(1\), Y\(1+INCY\), ..., Y\(1+\(N)3 1217 1 2196 3960 t
10 S f
(-)3413 3960 w
10 R f
(1\))3468 3960 w
10 S f
(*)3551 3960 w
10 R f
(INCY\))3601 3960 w
9 B f
(Note:)720 4320 w
10 R f
(If N=0, no action is performed.)5 1245 1 1296 4320 t
9 B f
(Error situations:)1 648 1 720 4680 t
10 R f
(\(All errors in this subprogram are fatal \320)7 1666 1 1512 4680 t
(see)1512 4800 w
10 I f
(Error Handling)1 631 1 1664 4800 t
10 R f
(, Framework Chapter\))2 884 1 2295 4800 t
(Number Error)1 1506 1 1800 5040 t
(1 N)1 1108 1 1944 5280 t
10 S f
(<)3052 5280 w
10 R f
(0)3107 5280 w
(2 INCX)1 1280 1 1944 5520 t
10 S f
(\243)3224 5520 w
10 R f
(0)3279 5520 w
(3 INCY)1 1280 1 1944 5760 t
10 S f
(\243)3224 5760 w
10 R f
(0)3279 5760 w
9 B f
(Double-precision version:)1 988 1 720 6120 t
10 R f
(DAXPY with X and Y declared double precision)7 1960 1 1783 6120 t
9 B f
(Complex version:)1 678 1 720 6480 t
10 R f
(CAXPY with X and Y declared complex)6 1636 1 1473 6480 t
(Linear Algebra)1 606 1 360 7500 t
(\320 6 \320)2 300 1 2730 7620 t
(SAXPY)360 7740 w
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7 pagesetup
10 R f
(-- --)1 5544 1 0 120 t
8 R f
(PORT)360 600 w
10 R f
( Algebra)1 346(library Linear)1 4463 2 591 600 t
( SAXPY)1 4305(February 11, 1993)2 735 2 360 840 t
9 B f
(See also:)1 333 1 720 1320 t
10 R f
(SSCAL)1296 1320 w
9 B f
(Author:)720 1680 w
10 R f
(Linda Kaufman)1 629 1 1296 1680 t
9 B f
(Reference:)720 2040 w
10 R f
( J., Kincaid, D. R., and Krogh, F. T., Basic linear algebra subpro-)12 2643(Lawson, C. L., Hanson, R.)4 1074 2 1323 2040 t
(grams for Fortran usage,)3 981 1 1296 2160 t
10 I f
(ACM Trans. Math. Software 5)4 1212 1 2302 2160 t
10 R f
(, 3 \(1979\), 308-323.)3 799 1 3514 2160 t
9 B f
(Example:)720 2520 w
10 R f
( times n$ matrix)3 668(The following program fragment forms the product A$x$ where A is an $m)12 3076 2 1296 2520 t
(and puts the result in an array Y:)7 1306 1 1296 2640 t
8 CW f
(DO 10 I=1,M)2 528 1 2136 2980 t
(Y\(I\)=0.0)2280 3080 w
(10 CONTINUE)1 528 1 1992 3180 t
(DO 20 I=1,N)2 528 1 2136 3280 t
(CALL SAXPY\(M,X\(I\),A\(1,I\),1,Y,1\))1 1488 1 2280 3380 t
(20 CONTINUE)1 528 1 1992 3480 t
10 R f
(Matrix by vector multiplication is usually done using inner products as in the example in)14 3744 1 1296 3840 t
( above program fragment can be preferable because)7 2075(SDOT, but on a paged machine using the)7 1669 2 1296 3960 t
( refers to the array)4 762(FORTRAN stores two-dimensional arrays column-wise and this program)7 2982 2 1296 4080 t
(A one column at a time.)5 960 1 1296 4200 t
(Linear Algebra)1 606 1 4794 7500 t
(\320 7 \320)2 300 1 2730 7620 t
(SAXPY)5072 7740 w
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8 pagesetup
10 R f
(-- --)1 5544 1 0 120 t
(Linear Algebra)1 606 1 360 600 t
8 R f
(PORT)4903 600 w
10 R f
(library)5134 600 w
( 11, 1993)2 375(SAXPY February)1 4665 2 360 840 t
(SDOT \320 dot product of two vectors)6 1465 1 2435 1320 t
9 B f
(Purpose:)720 1680 w
10 R f
( from i=1 to n x sub i y)8 931(SDOT determines the inner product of two vectors $x$ and $y$, $sum)11 2813 2 1296 1680 t
(sub i$)1 242 1 1296 1800 t
9 B f
(Type:)720 2160 w
10 R f
(Real function)1 541 1 1296 2160 t
9 B f
(Usage:)720 2520 w
10 S f
(<)1296 2520 w
10 R f
(answer)1351 2520 w
10 S f
(>)1633 2520 w
10 R f
(= SDOT\(N, X, INCX, Y, INCY\))5 1312 1 1713 2520 t
(N)1440 2760 w
14 S f
(\256)1980 2780 w
10 R f
(the number of elements to be summed)6 1526 1 2196 2760 t
(X)1440 3000 w
14 S f
(\256)1980 3020 w
10 R f
(the \256rst vector)2 577 1 2196 3000 t
(INCX)1440 3240 w
14 S f
(\256)1980 3260 w
10 R f
(the elements are spaced at intervals of INCX in X:)9 2015 1 2196 3240 t
(X\(1\), X\(1+INCX\), ..., X\(1+\(N)3 1217 1 2196 3360 t
10 S f
(-)3413 3360 w
10 R f
(1\))3468 3360 w
10 S f
(*)3551 3360 w
10 R f
(INCX\))3601 3360 w
(Y)1440 3600 w
14 S f
(\256)1980 3620 w
10 R f
(the second vector)2 698 1 2196 3600 t
(INCY)1440 3840 w
14 S f
(\256)1980 3860 w
10 R f
(the elements are spaced at intervals of INCY in Y:)9 2015 1 2196 3840 t
(Y\(1\), Y\(1+INCY\), ..., Y\(1+\(N)3 1217 1 2196 3960 t
10 S f
(-)3413 3960 w
10 R f
(1\))3468 3960 w
10 S f
(*)3551 3960 w
10 R f
(INCY\))3601 3960 w
10 S f
(<)1440 4200 w
10 R f
(answer)1495 4200 w
10 S f
(>)1777 4200 w
14 S f
(\254)1980 4220 w
10 R f
(X\(1\))2196 4200 w
10 S f
(*)2384 4200 w
10 R f
(Y\(1\)+X\(1+INCX\))2434 4200 w
10 S f
(*)3166 4200 w
10 R f
(Y\(1+INCY\)+...+)3216 4200 w
(X\(1+\(N)2196 4320 w
10 S f
(-)2512 4320 w
10 R f
(1\))2567 4320 w
10 S f
(*)2650 4320 w
10 R f
(INCX\))2700 4320 w
10 S f
(*)2977 4320 w
10 R f
(Y\(1+\(N)3027 4320 w
10 S f
(-)3343 4320 w
10 R f
(1\))3398 4320 w
10 S f
(*)3481 4320 w
10 R f
(INCY\))3531 4320 w
9 B f
(Note 1:)1 278 1 720 4680 t
10 R f
( can use SDOT to deal with the rows of a)10 1657(Since Fortran stores arrays in column-wise order we)7 2087 2 1296 4680 t
(2-dimensional array as in the example below.)6 1816 1 1296 4800 t
9 B f
(Note 2:)1 278 1 720 5160 t
10 R f
(If N=0, SDOT=0.0 is returned.)4 1235 1 1296 5160 t
9 B f
(Note 3:)1 278 1 720 5520 t
10 R f
(No attempt is made to prevent under\257ow or over\257ow in the subroutine.)11 2847 1 1296 5520 t
(Linear Algebra)1 606 1 360 7500 t
(\320 8 \320)2 300 1 2730 7620 t
(SDOT)360 7740 w
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9 pagesetup
10 R f
(-- --)1 5544 1 0 120 t
8 R f
(PORT)360 600 w
10 R f
( Algebra)1 346(library Linear)1 4463 2 591 600 t
( SDOT)1 4305(February 11, 1993)2 735 2 360 840 t
9 B f
(Error situations:)1 648 1 720 1320 t
10 R f
(\(All errors in this subprogram are fatal \320)7 1666 1 1512 1320 t
(see)1512 1440 w
10 I f
(Error Handling)1 631 1 1664 1440 t
10 R f
(, Framework Chapter\))2 884 1 2295 1440 t
(Number Error)1 1506 1 1800 1680 t
(1 N)1 1108 1 1944 1920 t
10 S f
(<)3052 1920 w
10 R f
(0)3107 1920 w
(2 INCX)1 1280 1 1944 2160 t
10 S f
(\243)3224 2160 w
10 R f
(0)3279 2160 w
(3 INCY)1 1280 1 1944 2400 t
10 S f
(\243)3224 2400 w
10 R f
(0)3279 2400 w
9 B f
(Double-precision version:)1 988 1 720 2760 t
10 R f
(DDOT with X and Y declared double precision)7 1893 1 1783 2760 t
9 B f
(Complex versions:)1 713 1 720 3120 t
10 R f
( complex.)1 403( with X and Y declared)5 968( CDOTC)1 447(CDOTU with X and Y declared complex.)6 1714 4 1508 3120 t
( conjugate of the elements of X)6 1271( the)1 175( bar sub i y sub i$, i.e.)7 904( x)1 131( from i=1 to n)4 568( sum)1 221(CDOTC $=)1 474 7 1296 3240 t
(are used.)1 354 1 1296 3360 t
9 B f
(Author:)720 3720 w
10 R f
(Linda Kaufman)1 629 1 1296 3720 t
9 B f
(Reference:)720 4080 w
10 R f
( J., Kincaid, D. R., and Krogh, F. T., Basic linear algebra subpro-)12 2643(Lawson, C. L., Hanson, R.)4 1074 2 1323 4080 t
(grams for Fortran usage,)3 981 1 1296 4200 t
10 I f
(ACM Trans. Math. Software 5)4 1212 1 2302 4200 t
10 R f
(, 3 \(1979\), 308-323.)3 799 1 3514 4200 t
9 B f
(Example:)720 4560 w
10 R f
( is an $m times n$)5 741(The following program fragment forms the product $A bold x$ where $A$)11 3003 2 1296 4560 t
(matrix dimensioned \(IA,N\), and puts the result in an array Y:)10 2446 1 1296 4680 t
8 CW f
(DO 10 I=1,M)2 528 1 2136 5020 t
(Y\(I\)=SDOT\(N,A\(I,1\),IA,X,1\))2280 5120 w
(10 CONTINUE)1 528 1 1992 5220 t
10 R f
( might re-)2 398(Because of page faults, the execution of this program fragment on certain machines)12 3346 2 1296 5580 t
( program fragment given in the example in SAXPY,)8 2121( The)1 209( amount of time.)3 673(quire an excessive)2 741 4 1296 5700 t
(which accesses the elements of A one column at a time, would be preferable in this case.)16 3542 1 1296 5820 t
(Linear Algebra)1 606 1 4794 7500 t
(\320 9 \320)2 300 1 2730 7620 t
(SDOT)5139 7740 w
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10 pagesetup
10 R f
(-- --)1 5544 1 0 120 t
(Linear Algebra)1 606 1 360 600 t
8 R f
(PORT)4903 600 w
10 R f
(library)5134 600 w
( 11, 1993)2 375(SDOT February)1 4665 2 360 840 t
(SSCAL \320 scale a vector)4 1004 1 2666 1320 t
9 B f
(Purpose:)720 1680 w
10 R f
(SSCAL multiplies a vector $x$ by a scalar A)8 1804 1 1296 1680 t
9 B f
(Usage:)720 2040 w
10 R f
( A, X, INCX\))3 546(CALL SSCAL\(N,)1 753 2 1296 2040 t
(N)1440 2280 w
14 S f
(\256)1980 2300 w
10 R f
(the number of affected elements in X)6 1485 1 2196 2280 t
(A)1440 2520 w
14 S f
(\256)1980 2540 w
10 R f
(the scaling factor)2 687 1 2196 2520 t
(X)1440 2760 w
14 S f
(\256)1980 2780 w
10 R f
(the vector to be scaled)4 892 1 2196 2760 t
14 S f
(\254)1980 3020 w
10 R f
(the scaled vector)2 670 1 2196 3000 t
(INCX)1440 3240 w
14 S f
(\256)1980 3260 w
10 R f
(the elements are spaced at intervals of INCX in X:)9 2015 1 2196 3240 t
(X\(1\), X\(1+INCX\), ..., X\(1+\(N)3 1217 1 2196 3360 t
10 S f
(-)3413 3360 w
10 R f
(1\))3468 3360 w
10 S f
(*)3551 3360 w
10 R f
(INCX\))3601 3360 w
9 B f
(Note 1:)1 278 1 720 3720 t
10 R f
(If N=0, no action is performed.)5 1245 1 1296 3720 t
9 B f
(Note 2:)1 278 1 720 4080 t
10 R f
( the rows of)3 477(Since Fortran stores arrays in column-wise order, we can use SSCAL to deal with)13 3267 2 1296 4080 t
(a 2-dimensional array as in the example below.)7 1885 1 1296 4200 t
9 B f
(Error situations:)1 648 1 720 4560 t
10 R f
(\(All errors in this subprogram are fatal \320)7 1666 1 1512 4560 t
(see)1512 4680 w
10 I f
(Error Handling)1 631 1 1664 4680 t
10 R f
(, Framework Chapter\))2 884 1 2295 4680 t
(Number Error)1 1506 1 1800 4920 t
(1 N)1 1108 1 1944 5160 t
10 S f
(<)3052 5160 w
10 R f
(0)3107 5160 w
(2 INCX)1 1280 1 1944 5400 t
10 S f
(\243)3224 5400 w
10 R f
(0)3279 5400 w
9 B f
(Double-precision version:)1 988 1 720 5760 t
10 R f
(DSCAL with X and A declared double precision)7 1944 1 1800 5760 t
9 B f
(Complex versions:)1 713 1 720 6120 t
10 R f
(CSCAL with X and A declared complex)6 1620 1 1508 6120 t
(CSSCAL with X declared complex and A declared real)8 2212 1 1418 6240 t
9 B f
(See also:)1 333 1 720 6600 t
10 R f
(SAXPY)1296 6600 w
(Linear Algebra)1 606 1 360 7500 t
(\320 10 \320)2 350 1 2705 7620 t
(SSCAL)360 7740 w
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11 pagesetup
10 R f
(-- --)1 5544 1 0 120 t
8 R f
(PORT)360 600 w
10 R f
( Algebra)1 346(library Linear)1 4463 2 591 600 t
( SSCAL)1 4305(February 11, 1993)2 735 2 360 840 t
9 B f
(Author:)720 1320 w
10 R f
(Linda Kaufman)1 629 1 1296 1320 t
9 B f
(Reference:)720 1680 w
10 R f
( J., Kincaid, D. R., and Krogh, F. T., Basic linear algebra subpro-)12 2643(Lawson, C. L., Hanson, R.)4 1074 2 1323 1680 t
(grams for Fortran usage,)3 981 1 1296 1800 t
10 I f
(ACM Trans. Math. Software 5)4 1212 1 2302 1800 t
10 R f
(, 3 \(1979\), 308-323.)3 799 1 3514 1800 t
9 B f
(Example:)720 2160 w
10 R f
( that)1 180(In this example the rows of an $m times n$ matrix A, dimensioned \(IA,N\) are scaled so)16 3564 2 1296 2160 t
( SASUM returns the)3 822( function)1 360( The)1 207(the sum of the modulus of the elements in each row is 1.0.)12 2355 4 1296 2280 t
(sum of the absolute values of the elements of a vector.)10 2171 1 1296 2400 t
8 CW f
(DO 10 J=1,M)2 528 1 2472 2740 t
(SC=1.0/SASUM\(N,A\(J,1\),IA\))2616 2840 w
(CALL SSCAL\(N,SC,A\(J,1\),IA\))1 1248 1 2616 2940 t
(10 CONTINUE)1 528 1 2328 3040 t
10 R f
(Linear Algebra)1 606 1 4794 7500 t
(\320 11 \320)2 350 1 2705 7620 t
(SSCAL)5088 7740 w
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12 pagesetup
10 R f
(-- --)1 5544 1 0 120 t
(Linear Algebra)1 606 1 360 600 t
8 R f
(PORT)4903 600 w
10 R f
(library)5134 600 w
( 11, 1993)2 375(SSCAL February)1 4665 2 360 840 t
(SSWAP \320 interchange two vectors)4 1437 1 2449 1320 t
9 B f
(Purpose:)720 1680 w
10 R f
(SSWAP interchanges two vectors)3 1351 1 1296 1680 t
9 B f
(Usage:)720 2040 w
10 R f
(CALL SSWAP\(N, X, INCX, Y, INCY\))5 1590 1 1296 2040 t
(N)1440 2280 w
14 S f
(\256)1980 2300 w
10 R f
(the number of affected elements in X and Y)8 1751 1 2196 2280 t
(X)1440 2520 w
14 S f
(\256)1980 2540 w
10 R f
(the \256rst vector)2 577 1 2196 2520 t
14 S f
(\254)1980 2780 w
10 R f
(the vector Y)2 493 1 2196 2760 t
(INCX)1440 3000 w
14 S f
(\256)1980 3020 w
10 R f
(the elements are spaced at intervals of INCX in X:)9 2015 1 2196 3000 t
(X\(1\), X\(1+INCX\), ..., X\(1+\(N)3 1217 1 2196 3120 t
10 S f
(-)3413 3120 w
10 R f
(1\)INCX\))3468 3120 w
(Y)1440 3360 w
14 S f
(\256)1980 3380 w
10 R f
(the second vector)2 698 1 2196 3360 t
14 S f
(\254)1980 3620 w
10 R f
(the vector X)2 493 1 2196 3600 t
(INCY)1440 3840 w
14 S f
(\256)1980 3860 w
10 R f
(the elements are spaced at intervals of INCY in Y:)9 2015 1 2196 3840 t
(Y\(1\), Y\(1+INCY\), ..., Y\(1+\(N)3 1217 1 2196 3960 t
10 S f
(-)3413 3960 w
10 R f
(1\)*INCY\))3468 3960 w
9 B f
(Note 1:)1 278 1 720 4320 t
10 R f
(If N=0, no action is performed.)5 1245 1 1296 4320 t
9 B f
(Note 2:)1 278 1 720 4680 t
10 R f
( stores arrays in column-wise order, we can use SSWAP to deal with the rows)14 3198(Since Fortran)1 546 2 1296 4680 t
(of a 2-dimensional array as in the example below.)8 1993 1 1296 4800 t
9 B f
(Error situations:)1 648 1 720 5160 t
10 R f
(\(All errors in this subprogram are fatal \320)7 1666 1 1512 5160 t
(see)1512 5280 w
10 I f
(Error Handling)1 631 1 1664 5280 t
10 R f
(, Framework Chapter\))2 884 1 2295 5280 t
(Number Error)1 1506 1 1800 5520 t
(1 N)1 1108 1 1944 5760 t
10 S f
(<)3052 5760 w
10 R f
(0)3107 5760 w
(2 INCX)1 1280 1 1944 6000 t
10 S f
(\243)3224 6000 w
10 R f
(0)3279 6000 w
(3 INCY)1 1255 1 1944 6240 t
10 S f
(\243)3199 6240 w
10 R f
(0)3254 6240 w
9 B f
(Double-precision version:)1 988 1 720 6600 t
10 R f
(DSWAP with X and Y declared double precision)7 1966 1 1800 6600 t
(Linear Algebra)1 606 1 360 7500 t
(\320 12 \320)2 350 1 2705 7620 t
(SSWAP)360 7740 w
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13 pagesetup
10 R f
(-- --)1 5544 1 0 120 t
8 R f
(PORT)360 600 w
10 R f
( Algebra)1 346(library Linear)1 4463 2 591 600 t
( SSWAP)1 4305(February 11, 1993)2 735 2 360 840 t
9 B f
(Complex version:)1 678 1 720 1320 t
10 R f
(CSWAP with X and Y declared complex)6 1642 1 1473 1320 t
9 B f
(See also:)1 333 1 720 1680 t
10 R f
(MOVExx \(Utility Chapter\))2 1088 1 1296 1680 t
9 B f
(Author:)720 2040 w
10 R f
(Linda Kaufman)1 629 1 1296 2040 t
9 B f
(Reference:)720 2400 w
10 R f
( J., Kincaid, D. R., and Krogh, F. T., Basic linear algebra subpro-)12 2643(Lawson, C. L., Hanson, R.)4 1074 2 1323 2400 t
(grams for Fortran usage,)3 981 1 1296 2520 t
10 I f
(ACM Trans. Math. Software 5)4 1212 1 2302 2520 t
10 R f
(, 3 \(1979\), 308-323.)3 799 1 3514 2520 t
9 B f
(Example:)720 2880 w
10 R f
( \(IA,N\) are permuted so)4 987(In this example the rows of an $m times n$ matrix A, dimensioned)12 2757 2 1296 2880 t
( A is the largest in modulus of the elements in the \256rst column of A.)15 2766(that the \(1,1\) element of)4 978 2 1296 3000 t
( vector having maximum)3 1038(The subroutine ISAMAX computes the index of the element of a)10 2706 2 1296 3120 t
(modulus.)1296 3240 w
8 CW f
(J=ISAMAX\(M,A,1\))2328 3580 w
(CALL SSWAP\(N,A,IA,A\(J,1\),IA\))1 1344 1 2328 3680 t
10 R f
(Linear Algebra)1 606 1 4794 7500 t
(\320 13 \320)2 350 1 2705 7620 t
(SSWAP)5066 7740 w
(-- --)1 5544 1 0 8030 t
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%%Trailer
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%%Pages: 13
%%DocumentFonts: Courier Times-Bold Times-Italic Times-Roman Symbol