OpenVMS VAX RTL Mathematics (MTH$) Manual

Updated: 12 December 1998

OpenVMS VAX RTL Mathematics (MTH$) Manual

Contents

Index

y(1+(i-1)*incy)

where:

y = array specified in y

i = element of the vector y

incy = increment argument for the array y specified in incy

If incy is less than 0, then y is referenced backward in array y; that is, (y[i]) is is referenced in:

y(1+(n-i)*|incy|)

where:

y = array specified in y

n = number of vector elements specified in n

i = element of the vector y

incy = increment argument for the array y specified in incy

Description

BLAS1$VxAXPY multiplies a vector x by a scalar, adds to a vector y , and stores the result in the vector y . This is expressed as follows:
y <- ax + y
where a is a scalar number and x and y are real or complex single-precision or double-precision (D and G) n-element vectors. The vectors can be rows or columns of a matrix. Both forward and backward indexing are permitted. Vectors x and y contain n elements that are accessed from arrays x and y by stepping incx and incy elements at a time.
The routine name determines the data type you should specify for arguments a, x, and y. Specify the same data type for each of these arguments.
The algorithm does not provide a special case for incx = 0. Therefore, specifying 0 for incx has the effect of adding the constant a*x[1] to all elements of the vector y using vector operations.

Example


C C To compute y=y+2.0*x using SAXPY: C INTEGER N,INCX,INCY REAL X(20), Y(20),A INCX = 1 INCY = 1 A = 2.0 N = 20 CALL BLAS1$VSAXPY(N,A,X,INCX,Y,INCY)

BLAS1$VxCOPY

The Copy a Vector routine copies n elements of the vector x to the vector y .

Format

BLAS1$VSCOPY n ,x ,incx ,y ,incy

BLAS1$VDCOPY n ,x ,incx ,y ,incy

BLAS1$VCCOPY n ,x ,incx ,y ,incy

BLAS1$VZCOPY n ,x ,incx ,y ,incy
Use BLAS1$VSCOPY for single-precision real operations.
Use BLAS1$VDCOPY for double-precision real (D or G) operations. Use BLAS1$VCCOPY for single-precision complex operations.
Use BLAS1$VZCOPY for double-precision complex (D or G) operations.

RETURNS

None.

Arguments

n

OpenVMS usage: longword_signed

type: longword integer (signed)

access: read only

mechanism: by reference

Number of elements in vector x to be copied. The n argument is the address of a signed longword integer containing the number of elements in vector x . If n is less than or equal to 0, then y is unchanged.
x

OpenVMS usage: floating_point or complex_number

type: F_floating, D_floating, G_floating real or F_floating, D_floating, G_floating complex

access: read only

mechanism: by reference, array reference

Array containing the elements to be accessed. All elements of array x are accessed only if the increment argument of x, called incx, is 1. The x argument is the address of a floating-point or floating-point complex number that is this array. This argument is an array of length at least:
1+(n-1)*|incx|
where:

n = number of vector elements specified in n

incx = increment argument for the array x specified in incx

Specify the data type as follows:

Routine Data Type for x

BLAS1$VSCOPY F-floating real

BLAS1$VDCOPY D-floating or G-floating real

BLAS1$VCCOPY F-floating complex

BLAS1$VZCOPY D-floating or G-floating complex

incx

OpenVMS usage: longword_signed

type: longword integer (signed)

access: read only

mechanism: by reference

Increment argument for the array x. The incx argument is the address of a signed longword integer containing the increment argument. If incx is greater than or equal to 0, then x is referenced forward in array x; that is, x[i] is referenced in:
x(1+(i-1)*incx)
where:

x = array specified in x

i = element of the vector x

incx = increment argument for the array x specified in incx

If incx is less than 0, then x is referenced backward in array x; that is, x[i] is referenced in:
x(1+(n-i)*|incx|)
where:

x = array specified in x

n = number of vector elements specified in n

i = element of the vector x

incx = increment argument for the array x specified in incx

y

OpenVMS usage: floating_point or complex_number

type: F_floating, D_floating, G_floating real or F_floating, D_floating, G_floating complex

access: write only

mechanism: by reference, array reference

Array that receives the copied elements. All elements of array y receive the copied elements only if the increment argument of y, called incy, is 1. The y argument is the address of a floating-point or floating-point complex number that is this array. This argument is an array of length at least:
1+(n-1)*|incy|
where:

n = number of vector elements specified in n

incy = increment argument for the array y specified in incy

Specify the data type as follows:

Routine Data Type for y

BLAS1$VSCOPY F-floating real

BLAS1$VDCOPY D-floating or G-floating real

BLAS1$VCCOPY F-floating complex

BLAS1$VZCOPY D-floating or G-floating complex

If n is less than or equal to 0, then y is unchanged. If incx is equal to 0, then each y[i] is set to x[1] . If incy is equal to 0, then y[i] is set to the last referenced element of x . If any element of x shares a memory location with an element of y , the results are unpredictable. (See the Description section for a special case that does not cause unpredictable results when the same memory location is shared by input and output.)
incy

OpenVMS usage: longword_signed

type: longword integer (signed)

access: read only

mechanism: by reference

Increment argument for the array y. The incy argument is the address of a signed longword integer containing the increment argument. If incy is greater than or equal to 0, then y is referenced forward in array y; that is, y[i] is referenced in:
y(1+(i-1)*incy)
where:

y = array specified in y

i = element of the vector y

If incy is less than 0, then y is referenced backward in array y; that is, y[i] is referenced in:
y(1+(n-i)*|incy|)
where:

y = array specified in y

n = number of vector elements specified in n

i = element of the vector y

incy = increment argument for the array y specified in incy

Routine	Data Type for x
BLAS1$VSCOPY	F-floating real
BLAS1$VDCOPY	D-floating or G-floating real
BLAS1$VCCOPY	F-floating complex
BLAS1$VZCOPY	D-floating or G-floating complex

Routine	Data Type for y
BLAS1$VSCOPY	F-floating real
BLAS1$VDCOPY	D-floating or G-floating real
BLAS1$VCCOPY	F-floating complex
BLAS1$VZCOPY	D-floating or G-floating complex

Description

BLAS1$VSCOPY, BLAS1$VDCOPY, BLAS1$VCCOPY, and BLAS1$VZCOPY copy n elements of the vector x to the vector y . Vector x contains n elements that are accessed from array x by stepping incx elements at a time. Both x and y are real or complex single-precision or double-precision (D and G) n-element vectors. The vectors can be rows or columns of a matrix. Both forward and backward indexing are permitted.
If you specify 0 for incx, BLAS1$VxCOPY initializes all elements of y to a constant.
If you specify --incx for incy, the vector x is stored in reverse order in y . In this case, the call format is as follows:
CALL BLAS1$VxCOPY (N,X,INCX,Y,-INCX)
It is possible to move the contents of a vector up or down within itself and not cause unpredictable results even though the same memory location is shared between input and output. To do this when i is greater than j, call the routine BLAS1$VxCOPY with incx = incy > 0 as follows:
CALL BLAS1$VxCOPY (N,X(I),INCX,X(J),INCX)
The preceding call to BLAS1$VxCOPY moves:
x(i),x(i+1*incx),...x(i+(n-1)*incx)
to
x(j),x(j+1*incx),...x(j+(n-1)*incx)
If i is less than j, specify a negative value for incx and incy in the call to BLAS1$VxCOPY, as follows. The parts that do not overlap are unchanged.
CALL BLAS1$VxCOPY (N,X(I),-INCX,X(J),-INCX)
Note
BLAS1$VxCOPY does not perform floating operations on the input data. Therefore, floating reserved operands are not detected by BLAS1$VxCOPY.

Example


C C To copy a vector x to a vector y using BLAS1$VSCOPY: C INTEGER N,INCX,INCY REAL X(20),Y(20) INCX = 1 INCY = 1 N = 20 CALL BLAS1$VSCOPY(N,X,INCX,Y,INCY) C C To move the contents of X(1),X(3),X(5),...,X(2N-1) C to X(3),X(5),...,X(2N+1) and leave x unchanged: C CALL BLAS1$VSCOPY(N,X,-2,X(3),-2)) C C To move the contents of X(2),X(3),...,X(100) to C X(1),X(2),...,X(99)and leave x(100) unchanged: C CALL BLAS1$VSCOPY(99,X(2),1,X,1)) C C To move the contents of X(1),X(2),X(3),...,X(N) to C Y(N),Y(N-1),...,Y C CALL BLAS1$VSCOPY(N,X,1,Y,-1))

C 
C To copy a vector x to a vector y using BLAS1$VSCOPY: 
C 
        INTEGER N,INCX,INCY 
        REAL X(20),Y(20) 
        INCX = 1 
        INCY = 1 
        N = 20 
        CALL BLAS1$VSCOPY(N,X,INCX,Y,INCY) 
C 
C To move the contents of X(1),X(3),X(5),...,X(2N-1) 
C to X(3),X(5),...,X(2N+1) and leave x unchanged: 
C 
        CALL BLAS1$VSCOPY(N,X,-2,X(3),-2)) 
C 
C To move the contents of X(2),X(3),...,X(100) to 
C X(1),X(2),...,X(99)and leave x(100) unchanged: 
C 
        CALL BLAS1$VSCOPY(99,X(2),1,X,1)) 
C 
C To move the contents of X(1),X(2),X(3),...,X(N) to 
C Y(N),Y(N-1),...,Y 
C 
        CALL BLAS1$VSCOPY(N,X,1,Y,-1))

BLAS1$VxDOTx

The Obtain the Inner Product of Two Vectors routine returns the dot product of two n-element vectors, x and y .

Format

BLAS1$VSDOT n ,x ,incx ,y ,incy

BLAS1$VDDOT n ,x ,incx ,y ,incy

BLAS1$VGDOT n ,x ,incx ,y ,incy

BLAS1$VCDOTU n ,x ,incx ,y ,incy

BLAS1$VCDOTC n ,x ,incx ,y ,incy

BLAS1$VZDOTU n ,x ,incx ,y ,incy

BLAS1$VWDOTU n ,x ,incx ,y ,incy

BLAS1$VZDOTC n ,x ,incx ,y ,incy

BLAS1$VWDOTC n ,x ,incx ,y ,incy
Use BLAS1$VSDOT to obtain the inner product of two single-precision real vectors. Use BLAS1$VDDOT to obtain the inner product of two double-precision (D-floating) real vectors. Use BLAS1$VGDOT to obtain the inner product of two double-precision (G-floating) real vectors. Use BLAS1$VCDOTU to obtain the inner product of two single-precision complex vectors (unconjugated). Use BLAS1$VCDOTC to obtain the inner product of two single-precision complex vectors (conjugated). Use BLAS1$VZDOTU to obtain the inner product of two double-precision (D-floating) complex vectors (unconjugated). Use BLAS1$VWDOTU to obtain the inner product of two double-precision (G-floating) complex vectors (unconjugated). Use BLAS1$VZDOTC to obtain the inner product of two double-precision (D-floating) complex vectors (conjugated). Use BLAS1$VWDOTC to obtain the inner product of two double-precision (G-floating) complex vectors (conjugated).

RETURNS

OpenVMS usage: floating_point or complex_number

type: F_floating, D_floating, G_floating real or F_floating, D_floating, G_floating complex

access: write only

mechanism: by value

The function value, called dotpr, is the dot product of two n-element vectors, x and y . Specify the same data type for dotpr and the argument x.

Arguments

n

OpenVMS usage: longword_signed

type: longword integer (signed)

access: read only

mechanism: by reference

Number of elements in vector x . The n argument is the address of a signed longword integer containing the number of elements. If you specify a value for n that is less than or equal to 0, then the value of dotpr is 0.0.
x

OpenVMS usage: floating_point or complex_number

type: F_floating, D_floating, G_floating real or F_floating, D_floating, G_floating complex

access: read only

mechanism: by reference, array reference

Array containing the elements to be accessed. All elements of array x are accessed only if the increment argument of x, called incx, is 1. The x argument is the address of a floating-point or floating-point complex number that is this array. This argument is an array of length at least:
1+(n-1)*|incx|
where:

n = number of vector elements specified in n

incx = increment argument for the array x specified in incx

Specify the data type as follows:

Routine Data Type for x

BLAS1$VSDOT F-floating real

BLAS1$VDDOT D-floating real

BLAS1$VGDOT G-floating real

BLAS1$VCDOTU and BLAS1$VCDOTC F-floating complex

BLAS1$VZDOTU and BLAS1$VZDOTC D-floating complex

BLAS1$VWDOTU and BLAS1$VWDOTC G-floating complex

incx

OpenVMS usage: longword_signed

type: longword integer (signed)

access: read only

mechanism: by reference

Increment argument for the array x. The incx argument is the address of a signed longword integer containing the increment argument. If incx is greater than 0, then x is referenced forward in array x; that is, x[i] is referenced in:
x(1+(i-1)*incx)
where:

x = array specified in x

i = element of the vector x

incx = increment argument for the array x specified in incx

If incx is less than 0, then x is referenced backward in array x; that is, x[i] is referenced in:
x(1+(n-i)*|incx|)
where:

x = array specified in x

n = number of vector elements specified in n

i = element of the vector x

incx = increment argument for the array x specified in incx

y

OpenVMS usage: floating_point or complex_number

type: F_floating, D_floating, G_floating real or F_floating, D_floating, G_floating complex

access: read only

mechanism: by reference, array reference

Array containing the elements to be accessed. All elements of array y are accessed only if the increment argument of y, called incy, is 1. The y argument is the address of a floating-point or floating-point complex number that is this array. This argument is an array of length at least:
1+(n-1)*|incy|
where:

n = number of vector elements specified in n

incy = increment argument for the array y specified in incy

Specify the data type as follows:

Routine Data Type for y

BLAS1$VSDOT F-floating real

BLAS1$VDDOT D-floating real

BLAS1$VGDOT G-floating real

BLAS1$VCDOTU and BLAS1$VCDOTC F-floating complex

BLAS1$VZDOTU and BLAS1$VZDOTC D-floating complex

BLAS1$VWDOTU and BLAS1$VWDOTC G-floating complex

incy

OpenVMS usage: longword_signed

type: longword integer (signed)

access: read only

mechanism: by reference

Increment argument for the array y. The incy argument is the address of a signed longword integer containing the increment argument. If incy is greater than or equal to 0, then y is referenced forward in array y; that is, y[i] is referenced in:
y(1+(i-1)*incy)
where:

y = array specified in y

i = element of the vector y

incy = increment argument for the array y specified in incy

If incy is less than 0, then y is referenced backward in array y; that is, y[i] is referenced in:
y(1+(n-i)*|incy|)
where:

y = array specified in y

n = number of vector elements specified in n

i = element of the vector y

incy = increment argument for the array y specified in incy

Routine	Data Type for x
BLAS1$VSDOT	F-floating real
BLAS1$VDDOT	D-floating real
BLAS1$VGDOT	G-floating real
BLAS1$VCDOTU and BLAS1$VCDOTC	F-floating complex
BLAS1$VZDOTU and BLAS1$VZDOTC	D-floating complex
BLAS1$VWDOTU and BLAS1$VWDOTC	G-floating complex

Routine	Data Type for y
BLAS1$VSDOT	F-floating real
BLAS1$VDDOT	D-floating real
BLAS1$VGDOT	G-floating real
BLAS1$VCDOTU and BLAS1$VCDOTC	F-floating complex
BLAS1$VZDOTU and BLAS1$VZDOTC	D-floating complex
BLAS1$VWDOTU and BLAS1$VWDOTC	G-floating complex

Description

The unconjugated versions of this routine, BLAS1$VSDOT, BLAS1$VDDOT, BLAS1$VGDOT, BLAS1$VCDOTU, BLAS1$VZDOTU, and BLAS1$VWDOTU return the dot product of two n-element vectors, x and y , expressed as follows:
x· y = x[1]y[1] + x[2]y[2] + ... + x[n]y[n]
The conjugated versions of this routine, BLAS1$VCDOTC, BLAS1$VZDOTC, and BLAS1$VWDOTC return the dot product of the conjugate of the first n-element vector with a second n-element vector, as follows:

Vectors x and y contain n elements that are accessed from arrays x and y by stepping incx and incy elements at a time. The vectors x and y can be rows or columns of a matrix. Both forward and backward indexing are permitted.

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y	=	array specified in y
i	=	element of the vector y
incy	=	increment argument for the array y specified in incy

y	=	array specified in y
n	=	number of vector elements specified in n
i	=	element of the vector y
incy	=	increment argument for the array y specified in incy

OpenVMS usage:	longword_signed
type:	longword integer (signed)
access:	read only
mechanism:	by reference

OpenVMS usage:	floating_point or complex_number
type:	F_floating, D_floating, G_floating real or F_floating, D_floating, G_floating complex
access:	read only
mechanism:	by reference, array reference

n	=	number of vector elements specified in n
incx	=	increment argument for the array x specified in incx

x	=	array specified in x
i	=	element of the vector x
incx	=	increment argument for the array x specified in incx