diff --git a/books/bookvol10.5.pamphlet b/books/bookvol10.5.pamphlet
index 62240ec..7ef9be3 100644
--- a/books/bookvol10.5.pamphlet
+++ b/books/bookvol10.5.pamphlet
@@ -337,6 +337,38 @@ and may be passed as character strings. They mean:
For real matrices, TRANSx=T and TRANSx=C have the same meaning.
For Hermitian matrices, TRANSx=T is not allowed.
For complex symmetric matrices, TRANSx=H is not allowed.
+
+There were 38 BLAS Level 1 routines defined in \cite{REF-LAW79}. They are
+\begin{itemize}
+\item Dot product SDSDOT, DSDOT, DQ-IDOT DQ-ADOT C-UDOT C-CDOT DDOT SDOT
+\item Constant times a vector plus a vector CAXPY DAXPY SAXPY
+\item Set up Givens rotation DROTG SROTG
+\item Apply rotation DROT SROT
+\item Set up modified Givens rotation DROTMG SROTMG
+\item Apply modified rotation DROTM SROTM
+\item Copy x into y CCOPY DCOPY SCOPY
+\item Sway x and y CSWAP DSWAP SSWAP
+\item 2-norm (Euclidean length) SCNRM2 DNRM2 SNRM2
+\item Sum of absolute values SCASUM DASUM SASUM
+\item Constant times a vector CSSCAL CSCAL DSCAL SSCAL
+\item Index of maximum element ICAMAX IDAMAX ISAMAX
+\end{itemize}
+where
+\begin{itemize}
+\item I Integer
+\item S Single Precision
+\item D Double Precision
+\item C Single Precision Complex
+\item Q extended precision
+\item Z COMPLEX*16
+\end{itemize}
+
+Vector arguments are permitted to have a storage spacing between elements.
+This spacing is specified by an increment parameter. For example, suppose
+a vector $x$ having components $x_i$, $i=1,ldots,N$ is stored in a DOUBLE
+PRECISION array DX() with increment parameter INCX. If $INCX \ge 0$ then
+$x_i$ is stored in $DX(1 + (i-1)*INCX)$. If $INCX < 0$ then $x_i$ is
+stored in $DX(1+ (N-1)*|INCX|)$.
\chapter{Algebra Cover Code}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{package BLAS1 BlasLevelOne}
@@ -348,7 +380,7 @@ For complex symmetric matrices, TRANSx=H is not allowed.
)set message auto off
)clear all
---S 1 of 140
+--S 1 of 148
t1:Complex DoubleFloat := complex(1.0,0)
--R
--R
@@ -356,7 +388,7 @@ t1:Complex DoubleFloat := complex(1.0,0)
--R Type: Complex(DoubleFloat)
--E 1
---S 2 of 140
+--S 2 of 148
dcabs1(t1)
--R
--R
@@ -364,7 +396,7 @@ dcabs1(t1)
--R Type: DoubleFloat
--E 2
---S 3 of 140
+--S 3 of 148
t2:Complex DoubleFloat := complex(1.0,1.0)
--R
--R
@@ -372,7 +404,7 @@ t2:Complex DoubleFloat := complex(1.0,1.0)
--R Type: Complex(DoubleFloat)
--E 3
---S 4 of 140
+--S 4 of 148
dcabs1(t2)
--R
--R
@@ -380,7 +412,7 @@ dcabs1(t2)
--R Type: DoubleFloat
--E 4
---S 5 of 140
+--S 5 of 148
t3:Complex DoubleFloat := complex(1.0,-1.0)
--R
--R
@@ -388,7 +420,7 @@ t3:Complex DoubleFloat := complex(1.0,-1.0)
--R Type: Complex(DoubleFloat)
--E 5
---S 6 of 140
+--S 6 of 148
dcabs1(t3)
--R
--R
@@ -396,7 +428,7 @@ dcabs1(t3)
--R Type: DoubleFloat
--E 6
---S 7 of 140
+--S 7 of 148
t4:Complex DoubleFloat := complex(-1.0,-1.0)
--R
--R
@@ -404,7 +436,7 @@ t4:Complex DoubleFloat := complex(-1.0,-1.0)
--R Type: Complex(DoubleFloat)
--E 7
---S 8 of 140
+--S 8 of 148
dcabs1(t4)
--R
--R
@@ -412,7 +444,7 @@ dcabs1(t4)
--R Type: DoubleFloat
--E 8
---S 9 of 140
+--S 9 of 148
t5:Complex DoubleFloat := complex(-2.0,-2.0)
--R
--R
@@ -420,7 +452,7 @@ t5:Complex DoubleFloat := complex(-2.0,-2.0)
--R Type: Complex(DoubleFloat)
--E 9
---S 10 of 140
+--S 10 of 148
dcabs1(t5)
--R
--R
@@ -430,196 +462,196 @@ dcabs1(t5)
)clear all
---S 11 of 140
+--S 11 of 148
a:PRIMARR(DFLOAT):=[ [1.0,2.0,3.0,4,0,5,0,6,0] ]
--R
--R (1) [1.,2.,3.,4.,0.,5.,0.,6.,0.]
--R Type: PrimitiveArray(DoubleFloat)
--E 11
---S 12 of 140
+--S 12 of 148
dasum(3,a,-1) -- 0.0 neg incx
--R
--R (2) 0.
--R Type: DoubleFloat
--E 12
---S 13 of 140
+--S 13 of 148
dasum(3,a,0) -- 0.0 zero incx
--R
--R (3) 0.
--R Type: DoubleFloat
--E 13
---S 14 of 140
+--S 14 of 148
dasum(-1,a,1) -- 0.0 neg elements
--R
--R (4) 0.
--R Type: DoubleFloat
--E 14
---S 15 of 140
+--S 15 of 148
dasum(0,a,1) -- 0.0 no elements
--R
--R (5) 0.
--R Type: DoubleFloat
--E 15
---S 16 of 140
+--S 16 of 148
dasum(1,a,1) -- 1.0 1.0
--R
--R (6) 1.
--R Type: DoubleFloat
--E 16
---S 17 of 140
+--S 17 of 148
dasum(2,a,1) -- 3.0 1.0+2.0
--R
--R (7) 3.
--R Type: DoubleFloat
--E 17
---S 18 of 140
+--S 18 of 148
dasum(3,a,1) -- 6.0 1.0+2.0+3.0
--R
--R (8) 6.
--R Type: DoubleFloat
--E 18
---S 19 of 140
+--S 19 of 148
dasum(4,a,1) -- 10.0 1.0+2.0+3.0+4.0
--R
--R (9) 10.
--R Type: DoubleFloat
--E 19
---S 20 of 140
+--S 20 of 148
dasum(5,a,1) -- 15.0 1.0+2.0+3.0+4.0+5.0
--R
--R (10) 10.
--R Type: DoubleFloat
--E 20
---S 21 of 140
+--S 21 of 148
dasum(6,a,1) -- 21.0 1.0+2.0+3.0+4.0+5.0+6.0
--R
--R (11) 15.
--R Type: DoubleFloat
--E 21
---S 22 of 140
+--S 22 of 148
dasum(7,a,1) -- 21.0 1.0+2.0+3.0+4.0+5.0+6.0
--R
--R (12) 15.
--R Type: DoubleFloat
--E 22
---S 23 of 140
+--S 23 of 148
dasum(1,a,2) -- 1.0 1.0
--R
--R (13) 1.
--R Type: DoubleFloat
--E 23
---S 24 of 140
+--S 24 of 148
dasum(2,a,2) -- 4.0 1.0+3.0
--R
--R (14) 4.
--R Type: DoubleFloat
--E 24
---S 25 of 140
+--S 25 of 148
dasum(3,a,2) -- 9.0 1.0+3.0+5.0
--R
--R (15) 4.
--R Type: DoubleFloat
--E 25
---S 26 of 140
+--S 26 of 148
dasum(4,a,2) -- 9.0 1.0+3.0+5.0
--R
--R (16) 4.
--R Type: DoubleFloat
--E 26
---S 27 of 140
+--S 27 of 148
dasum(1,a,3) -- 1.0 1.0
--R
--R (17) 1.
--R Type: DoubleFloat
--E 27
---S 28 of 140
+--S 28 of 148
dasum(2,a,3) -- 5.0 1.0+4.0
--R
--R (18) 5.
--R Type: DoubleFloat
--E 28
---S 29 of 140
+--S 29 of 148
dasum(3,a,3) -- 5.0 1.0+4.0
--R
--R (19) 5.
--R Type: DoubleFloat
--E 29
---S 30 of 140
+--S 30 of 148
dasum(1,a,4) -- 1.0 1.0
--R
--R (20) 1.
--R Type: DoubleFloat
--E 30
---S 31 of 140
+--S 31 of 148
dasum(2,a,4) -- 6.0 1.0+5.0
--R
--R (21) 1.
--R Type: DoubleFloat
--E 31
---S 32 of 140
+--S 32 of 148
dasum(3,a,4) -- 6.0 1.0+5.0
--R
--R (22) 1.
--R Type: DoubleFloat
--E 32
---S 33 of 140
+--S 33 of 148
dasum(1,a,5) -- 1.0 1.0
--R
--R (23) 1.
--R Type: DoubleFloat
--E 33
---S 34 of 140
+--S 34 of 148
dasum(2,a,5) -- 7.0 1.0+6.0
--R
--R (24) 6.
--R Type: DoubleFloat
--E 34
---S 35 of 140
+--S 35 of 148
dasum(3,a,5) -- 7.0 1.0+6.0
--R
--R (25) 6.
--R Type: DoubleFloat
--E 35
---S 36 of 140
+--S 36 of 148
dasum(1,a,6) -- 1.0 1.0
--R
--R (26) 1.
--R Type: DoubleFloat
--E 36
---S 37 of 140
+--S 37 of 148
dasum(2,a,6) -- 1.0 1.0
--R
--R (27) 1.
--R Type: DoubleFloat
--E 37
---S 38 of 140
+--S 38 of 148
dasum(1,a,7) -- 1.0 1.0
--R
--R (28) 1.
@@ -628,7 +660,7 @@ dasum(1,a,7) -- 1.0 1.0
)clear all
---S 39 of 140
+--S 39 of 148
a:PRIMARR(DFLOAT):=[ [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0] ]
--R
--R
@@ -636,7 +668,7 @@ a:PRIMARR(DFLOAT):=[ [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0] ]
--R Type: PrimitiveArray(DoubleFloat)
--E 39
---S 40 of 140
+--S 40 of 148
b:PRIMARR(DFLOAT):=[ [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0] ]
--R
--R
@@ -644,7 +676,7 @@ b:PRIMARR(DFLOAT):=[ [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0] ]
--R Type: PrimitiveArray(DoubleFloat)
--E 40
---S 41 of 140
+--S 41 of 148
daxpy(3,2.0,a,1,b,1)
--R
--R
@@ -652,7 +684,7 @@ daxpy(3,2.0,a,1,b,1)
--R Type: PrimitiveArray(DoubleFloat)
--E 41
---S 42 of 140
+--S 42 of 148
b:PRIMARR(DFLOAT):=[ [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0] ]
--R
--R
@@ -660,7 +692,7 @@ b:PRIMARR(DFLOAT):=[ [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0] ]
--R Type: PrimitiveArray(DoubleFloat)
--E 42
---S 43 of 140
+--S 43 of 148
daxpy(7,2.0,a,1,b,1)
--R
--R
@@ -668,7 +700,7 @@ daxpy(7,2.0,a,1,b,1)
--R Type: PrimitiveArray(DoubleFloat)
--E 43
---S 44 of 140
+--S 44 of 148
b:PRIMARR(DFLOAT):=[ [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0] ]
--R
--R
@@ -681,7 +713,7 @@ Note that Axiom properly handles array indexes that are out of bounds.
The BLAS daxpy routine cannot check this condition.
\begin{chunk}{BlasLevelOne.input}
---S 45 of 140
+--S 45 of 148
daxpy(8,2.0,a,1,b,1)
--R
--R
@@ -689,7 +721,7 @@ daxpy(8,2.0,a,1,b,1)
--R Type: PrimitiveArray(DoubleFloat)
--E 45
---S 46 of 140
+--S 46 of 148
b:PRIMARR(DFLOAT):=[ [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0] ]
--R
--R
@@ -697,7 +729,7 @@ b:PRIMARR(DFLOAT):=[ [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0] ]
--R Type: PrimitiveArray(DoubleFloat)
--E 46
---S 47 of 140
+--S 47 of 148
daxpy(3,2.0,a,3,b,3)
--R
--R
@@ -705,7 +737,7 @@ daxpy(3,2.0,a,3,b,3)
--R Type: PrimitiveArray(DoubleFloat)
--E 47
---S 48 of 140
+--S 48 of 148
b:PRIMARR(DFLOAT):=[ [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0] ]
--R
--R
@@ -713,7 +745,7 @@ b:PRIMARR(DFLOAT):=[ [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0] ]
--R Type: PrimitiveArray(DoubleFloat)
--E 48
---S 49 of 140
+--S 49 of 148
daxpy(4,2.0,a,2,b,2)
--R
--R
@@ -721,7 +753,7 @@ daxpy(4,2.0,a,2,b,2)
--R Type: PrimitiveArray(DoubleFloat)
--E 49
---S 50 of 140
+--S 50 of 148
b:PRIMARR(DFLOAT):=[ [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0] ]
--R
--R
@@ -729,7 +761,7 @@ b:PRIMARR(DFLOAT):=[ [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0] ]
--R Type: PrimitiveArray(DoubleFloat)
--E 50
---S 51 of 140
+--S 51 of 148
daxpy(5,2.0,a,2,b,2)
--R
--R
@@ -737,7 +769,7 @@ daxpy(5,2.0,a,2,b,2)
--R Type: PrimitiveArray(DoubleFloat)
--E 51
---S 52 of 140
+--S 52 of 148
b:PRIMARR(DFLOAT):=[ [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0] ]
--R
--R
@@ -745,7 +777,7 @@ b:PRIMARR(DFLOAT):=[ [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0] ]
--R Type: PrimitiveArray(DoubleFloat)
--E 52
---S 53 of 140
+--S 53 of 148
daxpy(3,2.0,a,2,b,2)
--R
--R
@@ -753,7 +785,7 @@ daxpy(3,2.0,a,2,b,2)
--R Type: PrimitiveArray(DoubleFloat)
--E 53
---S 54 of 140
+--S 54 of 148
b:PRIMARR(DFLOAT):=[ [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0] ]
--R
--R
@@ -761,7 +793,7 @@ b:PRIMARR(DFLOAT):=[ [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0] ]
--R Type: PrimitiveArray(DoubleFloat)
--E 54
---S 55 of 140
+--S 55 of 148
daxpy(3,-2.0,a,2,b,2)
--R
--R
@@ -769,7 +801,7 @@ daxpy(3,-2.0,a,2,b,2)
--R Type: PrimitiveArray(DoubleFloat)
--E 55
---S 56 of 140
+--S 56 of 148
a:PRIMARR(DFLOAT):=[ [ 1.0, 2.0, 3.0] ]
--R
--R
@@ -777,7 +809,7 @@ a:PRIMARR(DFLOAT):=[ [ 1.0, 2.0, 3.0] ]
--R Type: PrimitiveArray(DoubleFloat)
--E 56
---S 57 of 140
+--S 57 of 148
b:PRIMARR(DFLOAT):=[ [ 1.0, 2.0, 3.0, 4.0, 5.0] ]
--R
--R
@@ -785,7 +817,7 @@ b:PRIMARR(DFLOAT):=[ [ 1.0, 2.0, 3.0, 4.0, 5.0] ]
--R Type: PrimitiveArray(DoubleFloat)
--E 57
---S 58 of 140
+--S 58 of 148
daxpy(3,-2.0,a,1,b,2)
--R
--R
@@ -793,7 +825,7 @@ daxpy(3,-2.0,a,1,b,2)
--R Type: PrimitiveArray(DoubleFloat)
--E 58
---S 59 of 140
+--S 59 of 148
b:PRIMARR(DFLOAT):=[ [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0] ]
--R
--R
@@ -801,7 +833,7 @@ b:PRIMARR(DFLOAT):=[ [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0] ]
--R Type: PrimitiveArray(DoubleFloat)
--E 59
---S 60 of 140
+--S 60 of 148
daxpy(3,0.0,a,1,b,2)
--R
--R
@@ -811,7 +843,7 @@ daxpy(3,0.0,a,1,b,2)
)clear all
---S 61 of 140
+--S 61 of 148
a:PRIMARR(DFLOAT):=[ [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0] ]
--R
--R
@@ -819,7 +851,7 @@ a:PRIMARR(DFLOAT):=[ [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0] ]
--R Type: PrimitiveArray(DoubleFloat)
--E 61
---S 62 of 140
+--S 62 of 148
b:PRIMARR(DFLOAT):=[ [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0] ]
--R
--R
@@ -827,7 +859,7 @@ b:PRIMARR(DFLOAT):=[ [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0] ]
--R Type: PrimitiveArray(DoubleFloat)
--E 62
---S 63 of 140
+--S 63 of 148
dcopy(3,a,1,b,1)
--R
--R
@@ -835,7 +867,7 @@ dcopy(3,a,1,b,1)
--R Type: PrimitiveArray(DoubleFloat)
--E 63
---S 64 of 140
+--S 64 of 148
b:PRIMARR(DFLOAT):=[ [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0] ]
--R
--R
@@ -843,7 +875,7 @@ b:PRIMARR(DFLOAT):=[ [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0] ]
--R Type: PrimitiveArray(DoubleFloat)
--E 64
---S 65 of 140
+--S 65 of 148
dcopy(7,a,1,b,1)
--R
--R
@@ -851,7 +883,7 @@ dcopy(7,a,1,b,1)
--R Type: PrimitiveArray(DoubleFloat)
--E 65
---S 66 of 140
+--S 66 of 148
b:PRIMARR(DFLOAT):=[ [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0] ]
--R
--R
@@ -859,7 +891,7 @@ b:PRIMARR(DFLOAT):=[ [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0] ]
--R Type: PrimitiveArray(DoubleFloat)
--E 66
---S 67 of 140
+--S 67 of 148
dcopy(8,a,1,b,1)
--R
--R
@@ -867,7 +899,7 @@ dcopy(8,a,1,b,1)
--R Type: PrimitiveArray(DoubleFloat)
--E 67
---S 68 of 140
+--S 68 of 148
b:PRIMARR(DFLOAT):=[ [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0] ]
--R
--R
@@ -875,7 +907,7 @@ b:PRIMARR(DFLOAT):=[ [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0] ]
--R Type: PrimitiveArray(DoubleFloat)
--E 68
---S 69 of 140
+--S 69 of 148
dcopy(3,a,3,b,3)
--R
--R
@@ -883,7 +915,7 @@ dcopy(3,a,3,b,3)
--R Type: PrimitiveArray(DoubleFloat)
--E 69
---S 70 of 140
+--S 70 of 148
b:PRIMARR(DFLOAT):=[ [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0] ]
--R
--R
@@ -891,7 +923,7 @@ b:PRIMARR(DFLOAT):=[ [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0] ]
--R Type: PrimitiveArray(DoubleFloat)
--E 70
---S 71 of 140
+--S 71 of 148
dcopy(4,a,2,b,2)
--R
--R
@@ -899,7 +931,7 @@ dcopy(4,a,2,b,2)
--R Type: PrimitiveArray(DoubleFloat)
--E 71
---S 72 of 140
+--S 72 of 148
b:PRIMARR(DFLOAT):=[ [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0] ]
--R
--R
@@ -907,7 +939,7 @@ b:PRIMARR(DFLOAT):=[ [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0] ]
--R Type: PrimitiveArray(DoubleFloat)
--E 72
---S 73 of 140
+--S 73 of 148
dcopy(5,a,2,b,2)
--R
--R
@@ -915,7 +947,7 @@ dcopy(5,a,2,b,2)
--R Type: PrimitiveArray(DoubleFloat)
--E 73
---S 74 of 140
+--S 74 of 148
b:PRIMARR(DFLOAT):=[ [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0] ]
--R
--R
@@ -923,7 +955,7 @@ b:PRIMARR(DFLOAT):=[ [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0] ]
--R Type: PrimitiveArray(DoubleFloat)
--E 74
---S 75 of 140
+--S 75 of 148
dcopy(3,a,2,b,2)
--R
--R
@@ -931,7 +963,7 @@ dcopy(3,a,2,b,2)
--R Type: PrimitiveArray(DoubleFloat)
--E 75
---S 76 of 140
+--S 76 of 148
a:PRIMARR(DFLOAT):=[ [ 1.0, 2.0, 3.0] ]
--R
--R
@@ -939,7 +971,7 @@ a:PRIMARR(DFLOAT):=[ [ 1.0, 2.0, 3.0] ]
--R Type: PrimitiveArray(DoubleFloat)
--E 76
---S 77 of 140
+--S 77 of 148
b:PRIMARR(DFLOAT):=[ [ 1.0, 2.0, 3.0, 4.0, 5.0] ]
--R
--R
@@ -947,7 +979,7 @@ b:PRIMARR(DFLOAT):=[ [ 1.0, 2.0, 3.0, 4.0, 5.0] ]
--R Type: PrimitiveArray(DoubleFloat)
--E 77
---S 78 of 140
+--S 78 of 148
dcopy(3,a,1,b,1)
--R
--R
@@ -955,7 +987,7 @@ dcopy(3,a,1,b,1)
--R Type: PrimitiveArray(DoubleFloat)
--E 78
---S 79 of 140
+--S 79 of 148
b:PRIMARR(DFLOAT):=[ [ 1.0, 2.0, 3.0, 4.0, 5.0] ]
--R
--R
@@ -963,7 +995,7 @@ b:PRIMARR(DFLOAT):=[ [ 1.0, 2.0, 3.0, 4.0, 5.0] ]
--R Type: PrimitiveArray(DoubleFloat)
--E 79
---S 80 of 140
+--S 80 of 148
dcopy(3,a,1,b,2)
--R
--R
@@ -971,7 +1003,7 @@ dcopy(3,a,1,b,2)
--R Type: PrimitiveArray(DoubleFloat)
--E 80
---S 81 of 140
+--S 81 of 148
a:PRIMARR(DFLOAT):=[ [ 1.0, 2.0, 3.0, 4.0, 5.0] ]
--R
--R
@@ -979,7 +1011,7 @@ a:PRIMARR(DFLOAT):=[ [ 1.0, 2.0, 3.0, 4.0, 5.0] ]
--R Type: PrimitiveArray(DoubleFloat)
--E 81
---S 82 of 140
+--S 82 of 148
b:PRIMARR(DFLOAT):=[ [ 1.0, 2.0, 3.0] ]
--R
--R
@@ -987,7 +1019,7 @@ b:PRIMARR(DFLOAT):=[ [ 1.0, 2.0, 3.0] ]
--R Type: PrimitiveArray(DoubleFloat)
--E 82
---S 83 of 140
+--S 83 of 148
dcopy(5,a,1,b,1)
--R
--R
@@ -997,63 +1029,63 @@ dcopy(5,a,1,b,1)
)clear all
---S 84 of 140
+--S 84 of 148
a:PRIMARR(DFLOAT):=[ [ 1.0, 2.0, 3.0, 4.0, 5.0] ]
--R
--R (1) [1.,2.,3.,4.,5.]
--R Type: PrimitiveArray(DoubleFloat)
--E 84
---S 85 of 140
+--S 85 of 148
b:PRIMARR(DFLOAT):=[ [ 5.0, 6.0, 7.0, 8.0, 9.0] ]
--R
--R (2) [5.,6.,7.,8.,9.]
--R Type: PrimitiveArray(DoubleFloat)
--E 85
---S 86 of 140
+--S 86 of 148
ddot(0,a,1,b,1)
--R
--R (3) 0.
--R Type: DoubleFloat
--E 86
---S 87 of 140
+--S 87 of 148
ddot(3,a,1,b,1)
--R
--R (4) 38.
--R Type: DoubleFloat
--E 87
---S 88 of 140
+--S 88 of 148
ddot(3,a,1,b,2)
--R
--R (5) 46.
--R Type: DoubleFloat
--E 88
---S 89 of 140
+--S 89 of 148
ddot(3,a,2,b,1)
--R
--R (6) 58.
--R Type: DoubleFloat
--E 89
---S 90 of 140
+--S 90 of 148
ddot(3,a,1,b,-2)
--R
--R (7) 38.
--R Type: DoubleFloat
--E 90
---S 91 of 140
+--S 91 of 148
ddot(3,a,-2,b,1)
--R
--R (8) 50.
--R Type: DoubleFloat
--E 91
---S 92 of 140
+--S 92 of 148
ddot(3,a,-2,b,-2)
--R
--R (9) 71.
@@ -1062,28 +1094,28 @@ ddot(3,a,-2,b,-2)
)clear all
---S 93 of 140
+--S 93 of 148
a:PRIMARR(DFLOAT):=[ [ 3.0, -4.0, 5.0, -7.0, 9.0] ]
--R
--R (1) [3.,- 4.,5.,- 7.,9.]
--R Type: PrimitiveArray(DoubleFloat)
--E 93
---S 94 of 140
+--S 94 of 148
dnrm2(3,a,1)
--R
--R (2) 7.0710678118654755
--R Type: DoubleFloat
--E 94
---S 95 of 140
+--S 95 of 148
dnrm2(5,a,1)
--R
--R (3) 13.416407864998739
--R Type: DoubleFloat
--E 95
---S 96 of 140
+--S 96 of 148
dnrm2(3,a,2)
--R
--R (4) 10.723805294763608
@@ -1091,7 +1123,7 @@ dnrm2(3,a,2)
--E 96
)clear all
---S 97 of 140
+--S 97 of 148
a:MATRIX(DFLOAT):=[[6,5,0],[5,1,4],[0,4,3]]
--R
--R +6. 5. 0.+
@@ -1102,7 +1134,7 @@ a:MATRIX(DFLOAT):=[[6,5,0],[5,1,4],[0,4,3]]
--R Type: Matrix(DoubleFloat)
--E 97
---S 98 of 140
+--S 98 of 148
t1:=drotg(elt(a,1,1),elt(a,1,2),0.0,0.0)
--R
--R (2)
@@ -1111,7 +1143,7 @@ t1:=drotg(elt(a,1,1),elt(a,1,2),0.0,0.0)
--R Type: PrimitiveArray(DoubleFloat)
--E 98
---S 99 of 140
+--S 99 of 148
g1:MATRIX(DFLOAT):=[[elt(t1,2), elt(t1,3),0.0],_
[-elt(t1,3),elt(t1,2),0.0],_
[0.0, 0.0, 1.0]]
@@ -1125,7 +1157,7 @@ g1:MATRIX(DFLOAT):=[[elt(t1,2), elt(t1,3),0.0],_
--R Type: Matrix(DoubleFloat)
--E 99
---S 100 of 140
+--S 100 of 148
t2:=g1*a
--R
--R + 7.810249675906654 4.4812907976513596 2.5607375986579197+
@@ -1136,7 +1168,7 @@ t2:=g1*a
--R Type: Matrix(DoubleFloat)
--E 100
---S 101 of 140
+--S 101 of 148
t3:=drotg(elt(t2,2,2),elt(a,3,2),0.0,0.0)
--R
--R (5)
@@ -1145,7 +1177,7 @@ t3:=drotg(elt(t2,2,2),elt(a,3,2),0.0,0.0)
--R Type: PrimitiveArray(DoubleFloat)
--E 101
---S 102 of 140
+--S 102 of 148
g2:MATRIX(DFLOAT):=[[1.0, 0.0, 0.0],_
[0.0, elt(t3,2),elt(t3,3)],_
[0.0,-elt(t3,3),elt(t3,2)]]
@@ -1159,7 +1191,7 @@ g2:MATRIX(DFLOAT):=[[1.0, 0.0, 0.0],_
--R Type: Matrix(DoubleFloat)
--E 102
---S 103 of 140
+--S 103 of 148
g2*g1*a
--R
--R + 7.810249675906654 4.4812907976513596 2.5607375986579197 +
@@ -1170,7 +1202,7 @@ g2*g1*a
--R Type: Matrix(DoubleFloat)
--E 103
---S 104 of 140
+--S 104 of 148
q:=transpose(g1)*transpose(g2)
--R
--R +0.76822127959737585 0.33265417936007158 0.54697098874441952 +
@@ -1183,21 +1215,21 @@ q:=transpose(g1)*transpose(g2)
)clear all
---S 105 of 140
+--S 105 of 148
dx:PRIMARR(DFLOAT):=[[6,0, 1.0, 4.0, -1.0, -1.0]]
--R
--R (1) [6.,0.,1.,4.,- 1.,- 1.]
--R Type: PrimitiveArray(DoubleFloat)
--E 105
---S 106 of 140
+--S 106 of 148
dy:PRIMARR(DFLOAT):=[[5.0, 1.0, -4.0, 4.0, -4.0]]
--R
--R (2) [5.,1.,- 4.,4.,- 4.]
--R Type: PrimitiveArray(DoubleFloat)
--E 106
---S 107 of 140
+--S 107 of 148
drot(5,dx,1,dy,1,0.707106781,0.707106781) -- rotate by 45 degrees
--R
--R (3)
@@ -1212,7 +1244,7 @@ drot(5,dx,1,dy,1,0.707106781,0.707106781) -- rotate by 45 degrees
--R Type: List(PrimitiveArray(DoubleFloat))
--E 107
---S 108 of 140
+--S 108 of 148
[dx,dy] -- note that the input arguments, dx and dy were modified
--R
--R (4)
@@ -1227,7 +1259,7 @@ drot(5,dx,1,dy,1,0.707106781,0.707106781) -- rotate by 45 degrees
--R Type: List(PrimitiveArray(DoubleFloat))
--E 108
---S 109 of 140
+--S 109 of 148
drot(5,dx,1,dy,1,0.707106781,-0.707106781) -- rotate by -45 degrees
--R
--R (5)
@@ -1242,7 +1274,7 @@ drot(5,dx,1,dy,1,0.707106781,-0.707106781) -- rotate by -45 degrees
--R Type: List(PrimitiveArray(DoubleFloat))
--E 109
---S 110 of 140
+--S 110 of 148
[dx,dy] -- note that the input arguments, dx and dy were modified
--R
--R (6)
@@ -1257,21 +1289,21 @@ drot(5,dx,1,dy,1,0.707106781,-0.707106781) -- rotate by -45 degrees
--R Type: List(PrimitiveArray(DoubleFloat))
--E 110
---S 111 of 140
+--S 111 of 148
dx:PRIMARR(DFLOAT):=[[6,0, 1.0, 4.0, -1.0, -1.0]]
--R
--R (7) [6.,0.,1.,4.,- 1.,- 1.]
--R Type: PrimitiveArray(DoubleFloat)
--E 111
---S 112 of 140
+--S 112 of 148
dy:PRIMARR(DFLOAT):=[[5.0, 1.0, -4.0, 4.0, -4.0]]
--R
--R (8) [5.,1.,- 4.,4.,- 4.]
--R Type: PrimitiveArray(DoubleFloat)
--E 112
---S 113 of 140
+--S 113 of 148
drot(5,dx,1,dy,1,0.707106781,0.707106781) -- rotate by 45 degrees
--R
--R (9)
@@ -1286,7 +1318,7 @@ drot(5,dx,1,dy,1,0.707106781,0.707106781) -- rotate by 45 degrees
--R Type: List(PrimitiveArray(DoubleFloat))
--E 113
---S 114 of 140
+--S 114 of 148
drot(5,dx,1,dy,1,0.707106781,0.707106781) -- rotate to 90 degrees
--R
--R (10)
@@ -1301,7 +1333,7 @@ drot(5,dx,1,dy,1,0.707106781,0.707106781) -- rotate to 90 degrees
--R Type: List(PrimitiveArray(DoubleFloat))
--E 114
---S 115 of 140
+--S 115 of 148
drot(5,dx,1,dy,1,0.707106781,0.707106781) -- rotate to 135 degrees
--R
--R (11)
@@ -1316,7 +1348,7 @@ drot(5,dx,1,dy,1,0.707106781,0.707106781) -- rotate to 135 degrees
--R Type: List(PrimitiveArray(DoubleFloat))
--E 115
---S 116 of 140
+--S 116 of 148
drot(5,dx,1,dy,1,0.707106781,0.707106781) -- rotate to 180 degrees
--R
--R (12)
@@ -1331,7 +1363,7 @@ drot(5,dx,1,dy,1,0.707106781,0.707106781) -- rotate to 180 degrees
--R Type: List(PrimitiveArray(DoubleFloat))
--E 116
---S 117 of 140
+--S 117 of 148
drot(5,dx,1,dy,1,0.707106781,0.707106781) -- rotate to 225 degrees
--R
--R (13)
@@ -1346,7 +1378,7 @@ drot(5,dx,1,dy,1,0.707106781,0.707106781) -- rotate to 225 degrees
--R Type: List(PrimitiveArray(DoubleFloat))
--E 117
---S 118 of 140
+--S 118 of 148
drot(5,dx,1,dy,1,0.707106781,0.707106781) -- rotate to 270 degrees
--R
--R (14)
@@ -1361,7 +1393,7 @@ drot(5,dx,1,dy,1,0.707106781,0.707106781) -- rotate to 270 degrees
--R Type: List(PrimitiveArray(DoubleFloat))
--E 118
---S 119 of 140
+--S 119 of 148
drot(5,dx,1,dy,1,0.707106781,0.707106781) -- rotate to 315 degrees
--R
--R (15)
@@ -1376,7 +1408,7 @@ drot(5,dx,1,dy,1,0.707106781,0.707106781) -- rotate to 315 degrees
--R Type: List(PrimitiveArray(DoubleFloat))
--E 119
---S 120 of 140
+--S 120 of 148
drot(5,dx,1,dy,1,0.707106781,0.707106781) -- rotate to 360 degrees
--R
--R (16)
@@ -1391,7 +1423,7 @@ drot(5,dx,1,dy,1,0.707106781,0.707106781) -- rotate to 360 degrees
--R Type: List(PrimitiveArray(DoubleFloat))
--E 120
---S 121 of 140
+--S 121 of 148
[dx,dy] -- note that the input arguments, dx and dy were modified
--R
--R (17)
@@ -1407,42 +1439,42 @@ drot(5,dx,1,dy,1,0.707106781,0.707106781) -- rotate to 360 degrees
--E 121
)clear all
---S 122 of 140
+--S 122 of 148
dx:PRIMARR(DFLOAT):=[[1.0, 2.0, 3.0, 4.0, 5.0, 6.0]]
--R
--R (1) [1.,2.,3.,4.,5.,6.]
--R Type: PrimitiveArray(DoubleFloat)
--E 122
---S 123 of 140
+--S 123 of 148
dscal(6,2.0,dx,1)
--R
--R (2) [2.,4.,6.,8.,10.,12.]
--R Type: PrimitiveArray(DoubleFloat)
--E 123
---S 124 of 140
+--S 124 of 148
dx
--R
--R (3) [2.,4.,6.,8.,10.,12.]
--R Type: PrimitiveArray(DoubleFloat)
--E 124
---S 125 of 140
+--S 125 of 148
dx:PRIMARR(DFLOAT):=[[1.0, 2.0, 3.0, 4.0, 5.0, 6.0]]
--R
--R (4) [1.,2.,3.,4.,5.,6.]
--R Type: PrimitiveArray(DoubleFloat)
--E 125
---S 126 of 140
+--S 126 of 148
dscal(3,0.5,dx,1)
--R
--R (5) [0.5,1.,1.5,4.,5.,6.]
--R Type: PrimitiveArray(DoubleFloat)
--E 126
---S 127 of 140
+--S 127 of 148
dx
--R
--R (6) [0.5,1.,1.5,4.,5.,6.]
@@ -1451,63 +1483,63 @@ dx
)clear all
---S 128 of 140
+--S 128 of 148
dx:PRIMARR(DFLOAT):=[[1.0, 2.0, 3.0, 4.0, 5.0]]
--R
--R (1) [1.,2.,3.,4.,5.]
--R Type: PrimitiveArray(DoubleFloat)
--E 128
---S 129 of 140
+--S 129 of 148
dy:PRIMARR(DFLOAT):=[[9.0, 8.0, 7.0, 6.0, -5.0]]
--R
--R (2) [9.,8.,7.,6.,- 5.]
--R Type: PrimitiveArray(DoubleFloat)
--E 129
---S 130 of 140
+--S 130 of 148
dswap(5,dx,1,dy,1)
--R
--R (3) [[9.,8.,7.,6.,- 5.],[1.,2.,3.,4.,5.]]
--R Type: List(PrimitiveArray(DoubleFloat))
--E 130
---S 131 of 140
+--S 131 of 148
dx:PRIMARR(DFLOAT):=[[1.0, 2.0, 3.0, 4.0, 5.0]]
--R
--R (4) [1.,2.,3.,4.,5.]
--R Type: PrimitiveArray(DoubleFloat)
--E 131
---S 132 of 140
+--S 132 of 148
dy:PRIMARR(DFLOAT):=[[9.0, 8.0, 7.0, 6.0, -5.0]]
--R
--R (5) [9.,8.,7.,6.,- 5.]
--R Type: PrimitiveArray(DoubleFloat)
--E 132
---S 133 of 140
+--S 133 of 148
dswap(3,dx,2,dy,2)
--R
--R (6) [[9.,2.,7.,4.,- 5.],[1.,8.,3.,6.,5.]]
--R Type: List(PrimitiveArray(DoubleFloat))
--E 133
---S 134 of 140
+--S 134 of 148
dx:PRIMARR(DFLOAT):=[[1.0, 2.0, 3.0, 4.0, 5.0]]
--R
--R (7) [1.,2.,3.,4.,5.]
--R Type: PrimitiveArray(DoubleFloat)
--E 134
---S 135 of 140
+--S 135 of 148
dy:PRIMARR(DFLOAT):=[[9.0, 8.0, 7.0, 6.0, -5.0]]
--R
--R (8) [9.,8.,7.,6.,- 5.]
--R Type: PrimitiveArray(DoubleFloat)
--E 135
---S 136 of 140
+--S 136 of 148
dswap(5,dx,1,dy,-1)
--R
--R (9) [[9.,8.,7.,6.,- 5.],[1.,2.,3.,4.,5.]]
@@ -1516,34 +1548,93 @@ dswap(5,dx,1,dy,-1)
)clear all
---S 137 of 140
+--S 137 of 148
d:PRIMARR(COMPLEX(DFLOAT)):=[[1.0+2.0*%i,-3.0+4.0*%i,5.0-6.0*%i]]
--R
--R (1) [1. + 2. %i,- 3. + 4. %i,5. - 6. %i]
--R Type: PrimitiveArray(Complex(DoubleFloat))
--E 137
---S 138 of 140
+--S 138 of 148
dzasum(3,d,1) -- 21.0
--R
--R (2) 21.
--R Type: DoubleFloat
--E 138
---S 139 of 140
+--S 139 of 148
dzasum(3,d,2) -- 14.0
--R
--R (3) 14.
--R Type: DoubleFloat
--E 139
---S 140 of 140
+--S 140 of 148
dzasum(-3,d,1) -- 0.0
--R
--R (4) 0.
--R Type: DoubleFloat
--E 140
+)clear all
+
+--S 141 of 148
+a:PRIMARR(COMPLEX(DFLOAT)):=_
+ [[3.+4.*%i, -4.+5.*%i, 5.+6.*%i, 7.-8.*%i, -9.-2.*%i]]
+--R
+--R (1) [3. + 4. %i,- 4. + 5. %i,5. + 6. %i,7. - 8. %i,- 9. - 2. %i]
+--R Type: PrimitiveArray(Complex(DoubleFloat))
+--E 141
+
+--S 142 of 148
+dznrm2(5,a,1) -- should be 18.028
+--R
+--R (2) 18.027756377319946
+--R Type: DoubleFloat
+--E 142
+
+--S 143 of 148
+dznrm2(3,a,2) -- should be 13.077
+--R
+--R (3) 13.076696830622021
+--R Type: DoubleFloat
+--E 143
+
+--S 144 of 148
+dznrm2(3,a,1) -- should be 11.269
+--R
+--R (4) 11.269427669584644
+--R Type: DoubleFloat
+--E 144
+
+--S 145 of 148
+dznrm2(3,a,-1) -- should be 0.0
+--R
+--R (5) 0.
+--R Type: DoubleFloat
+--E 145
+
+--S 146 of 148
+dznrm2(-3,a,-1) -- should be 0.0
+--R
+--R (6) 0.
+--R Type: DoubleFloat
+--E 146
+
+--S 147 of 148
+dznrm2(1,a,1) -- should be 5.0
+--R
+--R (7) 5.
+--R Type: DoubleFloat
+--E 147
+
+--S 148 of 148
+dznrm2(1,a,2) -- should be 5.0
+--R
+--R (8) 5.
+--R Type: DoubleFloat
+--E 148
+
)spool
)lisp (bye)
\end{chunk}
@@ -1740,6 +1831,21 @@ BlasLevelOne() : Exports == Implementation where
++X dzasum(3,d,2) -- 14.0
++X dzasum(-3,d,1) -- 0.0
+ dznrm2: (SI, PCDF, SI) -> DF
+ ++ dznrm2 returns the norm of a complex vector. It computes
+ ++ sqrt(sum(v*conjugate(v)))
+ ++
+ ++X a:PRIMARR(COMPLEX(DFLOAT))
+ ++X a:=[[3.+4.*%i,-4.+5.*%i,5.+6.*%i,7.-8.*%i,-9.-2.*%i]]
+ ++X dznrm2(5,a,1) -- should be 18.028
+ ++X dznrm2(3,a,2) -- should be 13.077
+ ++X dznrm2(3,a,1) -- should be 11.269
+ ++X dznrm2(3,a,-1) -- should be 0.0
+ ++X dznrm2(-3,a,-1) -- should be 0.0
+ ++X dznrm2(1,a,1) -- should be 5.0
+ ++X dznrm2(1,a,2) -- should be 5.0
+
+
Implementation == add
dcabs1(z:CDF):DF ==
@@ -1764,6 +1870,8 @@ BlasLevelOne() : Exports == Implementation where
DSWAP(n,dx,incx,dy,incx)$Lisp
dzasum(n:SI,dz:PCDF,incx:SI):DF ==
DZASUMSPAD(n,dz,incx)$Lisp
+ dznrm2(n:SI,dz:PCDF,incx:SI):DF ==
+ DZNRM2SPAD(n,dz,incx)$Lisp
\end{chunk}
\begin{chunk}{BLAS1.dotabb}
@@ -6917,6 +7025,63 @@ code standard so we need to create thunks to do the data translation.
)set message auto off
)clear all
+--S 1 of 8
+a:PRIMARR(COMPLEX(DFLOAT)):=_
+ [[3.+4.*%i, -4.+5.*%i, 5.+6.*%i, 7.-8.*%i, -9.-2.*%i]]
+--R
+--R (1) [3. + 4. %i,- 4. + 5. %i,5. + 6. %i,7. - 8. %i,- 9. - 2. %i]
+--R Type: PrimitiveArray(Complex(DoubleFloat))
+--E 1
+
+--S 2 of 8
+dznrm2(5,a,1) -- should be 18.028
+--R
+--R (2) 18.027756377319946
+--R Type: DoubleFloat
+--E 2
+
+--S 3 of 8
+dznrm2(3,a,2) -- should be 13.077
+--R
+--R (3) 13.076696830622021
+--R Type: DoubleFloat
+--E 3
+
+--S 4 of 8
+dznrm2(3,a,1) -- should be 11.269
+--R
+--R (4) 11.269427669584644
+--R Type: DoubleFloat
+--E 4
+
+--S 5 of 8
+dznrm2(3,a,-1) -- should be 0.0
+--R
+--R (5) 0.
+--R Type: DoubleFloat
+--E 5
+
+--S 6 of 8
+dznrm2(-3,a,-1) -- should be 0.0
+--R
+--R (6) 0.
+--R Type: DoubleFloat
+--E 6
+
+--S 7 of 8
+dznrm2(1,a,1) -- should be 5.0
+--R
+--R (7) 5.
+--R Type: DoubleFloat
+--E 7
+
+--S 8 of 8
+dznrm2(1,a,2) -- should be 5.0
+--R
+--R (8) 5.
+--R Type: DoubleFloat
+--E 8
+
)spool
)lisp (bye)
\end{chunk}
@@ -6925,6 +7090,46 @@ code standard so we need to create thunks to do the data translation.
dznrm2 examples
====================================================================
+dznrm2 computes the complex norm of the input vector.
+For each element it computes the sum
+ a.i*conjugate(a.i)
+for all i. Then it returns the square root of the final sum.
+
+If the count or increment are negative, the result is 0.0
+
+
+a:PRIMARR(COMPLEX(DFLOAT)):=_
+ [[3.+4.*%i, -4.+5.*%i, 5.+6.*%i, 7.-8.*%i, -9.-2.*%i]]
+
+ [3. + 4. %i,- 4. + 5. %i,5. + 6. %i,7. - 8. %i,- 9. - 2. %i]
+
+dznrm2(5,a,1)
+
+ 18.027756377319946
+
+dznrm2(3,a,2)
+
+ 13.076696830622021
+
+dznrm2(3,a,1)
+
+ 11.269427669584644
+
+dznrm2(3,a,-1)
+
+ 0.
+
+dznrm2(-3,a,-1)
+
+ 0.
+
+dznrm2(1,a,1)
+
+ 5.
+
+dznrm2(1,a,2)
+ 5.
+
====================================================================
Man Page Details
====================================================================
@@ -7045,65 +7250,153 @@ NOTES
\end{chunk}
+\begin{chunk}{dznrm2 example}
+ program dznrm2EX
+* Tim Daly May 8, 2012
+* unit tests for BLAS dznrm2
+ complex*16 a(5)
+ double precision c
+ a(1) = ( 3.0D0, 4.0D0)
+ a(2) = (-4.0D0, 5.0D0)
+ a(3) = ( 5.0D0, 6.0D0)
+ a(4) = ( 7.0D0,-8.0D0)
+ a(5) = (-9.0D0,-2.0D0)
+ write(6,100)a(1),a(2),a(3),a(4),a(5)
+ 100 format("a=(/ (",f6.3,f6.3,"),(",f6.3,f6.3"),(",f6.3,f6.3"),",/,
+ C " (",f6.3,f6.3,"),(",f6.3,f6.3") /)")
+ c=dznrm2(5,a,1)
+ write(6,200)c
+ 200 format("should be 18.028",/,"c=",f6.3)
+ c=dznrm2(3,a,2)
+ write(6,201)c
+ 201 format("should be 13.077",/,"c=",f6.3)
+ c=dznrm2(3,a,1)
+ write(6,202)c
+ 202 format("should be 11.269",/,"c=",f6.3)
+ c=dznrm2(3,a,-1)
+ write(6,203)c
+ 203 format("should be 0.000",/,"c=",f6.3)
+ c=dznrm2(-3,a,-1)
+ write(6,204)c
+ 204 format("should be 0.000",/,"c=",f6.3)
+ c=dznrm2(1,a,1)
+ write(6,205)c
+ 205 format("should be 5.000",/,"c=",f6.3)
+ c=dznrm2(1,a,2)
+ write(6,206)c
+ 206 format("should be 5.000",/,"c=",f6.3)
+ stop
+ end
+\end{chunk}
+
+\begin{verbatim}
+gcc -o dznrm2EX dznrm2EX.f -lgfortran dznrm2.o && ./dznrm2EX
+a=(/ ( 3.000 4.000),(-4.000 5.000),( 5.000 6.000),
+ ( 7.000-8.000),(-9.000-2.000) /)
+should be 18.028
+c=18.028
+should be 13.077
+c=13.077
+should be 11.269
+c=11.269
+should be 0.000
+c= 0.000
+should be 0.000
+c= 0.000
+should be 5.000
+c= 5.000
+should be 5.000
+c= 5.000
+\end{verbatim}
+
+Spad represents complex numbers as a pair where the car is the real
+part and the cons is the imaginary part. BLAS wants a complex number
+in fortran format. So we have a design choice to make. Either we could
+write all of the BLAS code using Spad internal representation or we
+could follow the BLAS code standard. I've decided to follow the BLAS
+code standard so we need to create thunks to do the data translation.
+
\begin{chunk}{BLAS 1 dznrm2}
-(let* ((one 1.0) (zero 0.0))
- (declare (type (double-float 1.0 1.0) one)
- (type (double-float 0.0 0.0) zero))
- (defun dznrm2 (n x incx)
- (declare (type (simple-array (complex double-float) (*)) x)
- (type fixnum incx n))
- (f2cl-lib:with-multi-array-data
- ((x (complex double-float) x-%data% x-%offset%))
- (prog ((norm 0.0) (scale 0.0) (ssq 0.0) (temp 0.0) (ix 0) (dznrm2 0.0))
- (declare (type fixnum ix)
- (type (double-float) norm scale ssq temp dznrm2))
- (cond
- ((or (< n 1) (< incx 1))
- (setf norm zero))
- (t
- (setf scale zero)
- (setf ssq one)
- (f2cl-lib:fdo (ix 1 (f2cl-lib:int-add ix incx))
- ((> ix
- (f2cl-lib:int-add 1
- (f2cl-lib:int-mul
- (the fixnum (1- n))
- incx)))
- nil)
- (tagbody
- (cond
- ((/=
- (coerce (realpart (f2cl-lib:fref x (ix) ((1 *)))) 'double-float)
- zero)
- (setf temp
- (abs
- (coerce (realpart
- (f2cl-lib:fref x-%data% (ix) ((1 *)) x-%offset%))
- 'double-float)))
- (cond
- ((< scale temp)
- (setf ssq (+ one (* ssq (expt (/ scale temp) 2))))
- (setf scale temp))
- (t
- (setf ssq (+ ssq (expt (/ temp scale) 2)))))))
- (cond
- ((/= (f2cl-lib:dimag (f2cl-lib:fref x (ix) ((1 *)))) zero)
- (setf temp
- (abs
- (f2cl-lib:dimag
- (f2cl-lib:fref x-%data% (ix) ((1 *)) x-%offset%))))
- (cond
- ((< scale temp)
- (setf ssq (+ one (* ssq (expt (/ scale temp) 2))))
- (setf scale temp))
- (t
- (setf ssq (+ ssq (expt (/ temp scale) 2)))))))))
- (setf norm (* scale (f2cl-lib:fsqrt ssq)))))
- (setf dznrm2 norm)
- end_label
- (return (values dznrm2 nil nil nil))))))
+(defun dznrm2Spad (n zx incx)
+; Tim Daly May 8, 2012
+ (let (result vec)
+ (dotimes (i (length zx))
+ (push (complex (car (svref zx i)) (cdr (svref zx i))) result))
+ (setq vec (make-array (length result) :initial-contents (nreverse result)))
+ (dznrm2 n vec incx)))
+(defun dznrm2 (n x incx)
+; Tim Daly May 8, 2012
+ (declare (type (simple-array (complex double-float) (*)) x)
+ (type fixnum incx n))
+ (let ((scale 0.0d0) (ssq 0.0d0) (temp 0.0d0)
+ (dznrm2 0.0d0) (limitx (min (* n incx) (length x))))
+ (declare (type fixnum limitx) (type (double-float) scale ssq temp dznrm2))
+ (when (and (>= n 1) (>= incx 1))
+ (do ((ix 0 (the fixnum (+ ix incx))))
+ ((>= ix limitx))
+ (when (/= (the double-float (realpart
+ (the (complex double-float) (svref x ix))))
+ 0.0d0)
+ (setf temp
+ (the double-float (abs
+ (the double-float (realpart
+ (the (complex double-float) (svref x ix)))))))
+ (cond
+ ((< scale temp)
+ (setf ssq (+ 1.0d0
+ (the double-float (*
+ ssq
+ (the double-float (*
+ (the double-float (/ scale temp))
+ (the double-float (/ scale temp))))))))
+ (setf scale temp))
+ (t
+ (setf ssq (+ ssq (*
+ (the double-float (/ temp scale))
+ (the double-float (/ temp scale))))))))
+ (when (/= (the double-float (imagpart
+ (the (complex double-float) (svref x ix)))) 0.0d0)
+ (setf temp
+ (the double-float (abs
+ (the double-float (imagpart
+ (the (complex double-float) (svref x ix)))))))
+ (cond
+ ((< scale temp)
+ (setf ssq (+ 1.0d0 (* ssq (*
+ (the double-float (/ scale temp))
+ (the double-float (/ scale temp))))))
+ (setf scale temp))
+ (t
+ (setf ssq (+ ssq (*
+ (the double-float (/ temp scale))
+ (the double-float (/ temp scale)))))))))
+ (setf dznrm2 (the double-float (* scale (the double-float (sqrt ssq))))))
+ dznrm2))
+
+\end{chunk}
+
+\begin{chunk}{BLAS 1 dznrm2 lisp test}
+(load "dznrm2.lisp")
+(setq a (vector #C(3.0d0 4.0d0) #C(-4.0d0 5.0d0) #C(5.0d0 6.0d0)
+ #C(7.0d0 -8.0d0) #C(-9.0d0 -2.0d0)))
+; #(#C(3.0 4.0) #C(-4.0 5.0) #C(5.0 6.0) #C(7.0 -8.0) #C(-9.0 -2.0))
+(dznrm2 5 a 1)
+; 18.027756377319946
+(dznrm2 3 a 2)
+; 13.076696830622023
+(dznrm2 3 a 1)
+; 11.269427669584648
+(dznrm2 3 a -1)
+; 0.0
+(dznrm2 -3 a -1)
+; 0.0
+(dznrm2 1 a 1)
+; 5.0
+(dznrm2 1 a 2)
+; 5.0
\end{chunk}
+
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{icamax BLAS}
%\pagehead{icamax}{icamax}
@@ -138913,12 +139206,12 @@ Warning: Types of argument 1 in call to ZLARFB do not match.
\getchunk{BLAS 1 dscal}
\getchunk{BLAS 1 dswap}
\getchunk{BLAS 1 dzasum}
+\getchunk{BLAS 1 dznrm2}
\end{chunk}
\begin{chunk}{untested}
\getchunk{BLAS lsame}
\getchunk{BLAS xerbla}
-\getchunk{BLAS 1 dznrm2}
\getchunk{BLAS 1 icamax}
\getchunk{BLAS 1 idamax}
\getchunk{BLAS 1 isamax}
diff --git a/books/bookvolbib.bib b/books/bookvolbib.bib
index 36bbdd6..9023eee 100644
--- a/books/bookvolbib.bib
+++ b/books/bookvolbib.bib
@@ -177,6 +177,66 @@ Aggressive Early Deflation},
Month = {June},
Year = {2006}}
+@article{REF-LAW79
+ Author = {C.L. Lawson, R.J. Hanson, D.R. Kincaid, F.T. Krogh},
+ Date-Added = {2012-05-07 05:32:45 -0500},
+ Date-Modified = {2012-05-07 05:33:48 -0500},
+ Journal = {ACM Transactions on Mathematical Software},
+ Pages = {303-323},
+ Title = {Basic Linear Algebra Subprograms for Fortran Usage},
+ Volume = {5},
+ Number = {3},
+ Month = {September},
+ Year = {1979}}
+
+@article{REF-DOU88,
+ Author = {Jack J. Dongarra, Jeremy Du Croz, Sven Hammarling, Richard J. Hanson},
+ Date-Added = {2012-05-07 05:32:45 -0500},
+ Date-Modified = {2012-05-07 05:33:48 -0500},
+ Journal = {ACM Transactions on Mathematical Software},
+ Pages = {1-17},
+ Title = {An Extended Set of FORTRAN Basic Linear Algebra Subprograms},
+ Volume = {14},
+ Number = {1},
+ Month = {March},
+ Year = {1988}}
+
+@article{REF-DOU88a,
+ Author = {Jack J. Dongarra, Jeremy Du Croz, Sven Hammarling, Richard J. Hanson},
+ Date-Added = {2012-05-07 05:32:45 -0500},
+ Date-Modified = {2012-05-07 05:33:48 -0500},
+ Journal = {ACM Transactions on Mathematical Software},
+ Pages = {18-32},
+ Title = {An Extended Set of FORTRAN Basic Linear Algebra Subprograms: Model Implementation and Test Programs},
+ Volume = {14},
+ Number = {1},
+ Month = {March},
+ Year = {1988}}
+
+@article{REF-DOU90,
+ Author = {Jack J. Dongarra, Jeremy Du Croz, Sven Hammarling, Iain S. Duff},
+ Date-Added = {2012-05-07 05:32:45 -0500},
+ Date-Modified = {2012-05-07 05:33:48 -0500},
+ Journal = {ACM Transactions on Mathematical Software},
+ Pages = {1-17},
+ Title = {A Set of Level 3 Basic Linear Algebra Subprograms},
+ Volume = {16},
+ Number = {1},
+ Month = {March},
+ Year = {1990}}
+
+@article{REF-DOU90a,
+ Author = {Jack J. Dongarra, Jeremy Du Croz, Sven Hammarling, Iain S. Duff},
+ Date-Added = {2012-05-07 05:32:45 -0500},
+ Date-Modified = {2012-05-07 05:33:48 -0500},
+ Journal = {ACM Transactions on Mathematical Software},
+ Pages = {18-28},
+ Title = {ALGORITHM 679: A Set of Level 3 Basic Linear Algebra Subprograms: Model Implementation and Test Programs},
+ Volume = {16},
+ Number = {1},
+ Month = {March},
+ Year = {1990}}
+
@article{REF-Hig88,
Author = {N. J. Higham},
Date-Added = {2012-04-22 05:32:45 -0500},
diff --git a/books/bookvolbib.pamphlet b/books/bookvolbib.pamphlet
index a722655..804c802 100644
--- a/books/bookvolbib.pamphlet
+++ b/books/bookvolbib.pamphlet
@@ -1252,6 +1252,28 @@ A.K Peters, Natick, MA. (2003) ISBN 1-56881-134-9
\bibitem[DA98]{DA98}
Dalmas, Stephane and Arsac, Olivier ``The INRIA OpenMath Library''
Projet SAFIR, INRIA Sophia Antipolis Nov 25, 1998
+\bibitem[REF-DON88]{REF-DON88}
+Jack J. Dongarra, Jeremy Du Croz, Sven Hammarling, Richard J. Hanson
+``An Extended Set of FORTRAN Basic Linear Algebra Subroutines''
+ACM Transactions on Mathematical Software, Vol 14, No 1, March 1988,
+pp 1-17
+\bibitem[REF-DON88a]{REF-DON88a}
+Jack J. Dongarra, Jeremy Du Croz, Sven Hammarling, Richard J. Hanson
+``ALGORITHM 656: An Extended Set of Basic Linear Algebra Subprograms:
+Model Implementation and Test Programs''
+ACM Transactions on Mathematical Software, Vol 14, No 1, March 1988,
+pp 18-32
+\bibitem[REF-DON90]{REF-DON90}
+Jack J. Dongarra, Jeremy Du Croz, Sven Hammarling, Iain S. Duff
+``A Set of Level 3 Basic Linear Algebra Subprograms''
+ACM Transactions on Mathematical Software, Vol 16, No 1, March 1990,
+pp 1-17
+\bibitem[REF-DON90a]{REF-DON90a}
+Jack J. Dongarra, Jeremy Du Croz, Sven Hammarling, Iain S. Duff
+``ALGORITHM 679: A Set of Level 3 Basic Linear Algebra Subprograms:
+Model Implementation and Test Programs''
+ACM Transactions on Mathematical Software, Vol 16, No 1, March 1990,
+pp 18-28
\bibitem[Fl01]{Fl01}
Fletcher, John P. ``Symbolic processing of Clifford Numbers in C++'',
Paper 25, AGACSE 2001.
@@ -1340,6 +1362,11 @@ Lamport, Leslie,
{\it LaTeX: A Document Preparation System,} \\
Reading, Massachusetts, Addison-Wesley Publishing Company, Inc.,
1986. ISBN 0-201-15790-X
+\bibitem[REF-LAW79]{REF-LAW79}
+Lawson, C.L., Hanson R.J., Kincaid, D.R., Krogh, F.T.
+``Algorithm 539: Basic linear algebra subprograms for FORTRAN usage''
+ACM Transactions on Mathematical Software, Vol 5 No 3 September 1979
+pp 308-323
\bibitem[LR88]{LR88}
Le Brigand, D. and Risler, J.J.
``Algorithme de Brill-Noether et codes de Goppa''
diff --git a/changelog b/changelog
index 625da0c..673b835 100644
--- a/changelog
+++ b/changelog
@@ -1,3 +1,7 @@
+20120508 tpd src/axiom-website/patches.html 20120508.01.tpd.patch
+20120508 tpd books/bookvolbib update references
+20120508 tpd books/bookvolbib.bib update references
+20120508 tpd books/bookvol10.5 BLAS1 dznrm2
20120507 tpd src/axiom-website/patches.html 20120507.02.tpd.patch
20120507 tpd books/bookvol10.5 BLAS1 dzasum
20120507 tpd src/axiom-website/patches.html 20120507.01.tpd.patch
diff --git a/src/axiom-website/patches.html b/src/axiom-website/patches.html
index 53fc6de..e79d5af 100644
--- a/src/axiom-website/patches.html
+++ b/src/axiom-website/patches.html
@@ -3910,5 +3910,7 @@ books/bookvol10.5 BLAS1 dscal
books/bookvol10.5 BLAS1 dswap
20120507.02.tpd.patch
books/bookvol10.5 BLAS1 dzasum
+20120508.01.tpd.patch
+books/bookvol10.5 BLAS1 dznrm2