Document revision date: 30 March 2001 | |
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The conjugated versions of this routine, BLAS1$VCDOTC, BLAS1$VZDOTC, and BLAS1$VWDOTC return the dot product of the conjugate of the first n-element vector with a second n-element vector, as follows:
Vectors x and y contain n elements that are accessed from arrays x and y by stepping incx and incy elements at a time. The vectors x and y can be rows or columns of a matrix. Both forward and backward indexing are permitted.
The routine name determines the data type you should specify for arguments x and y. Specify the same data type for these arguments.
Rounding in BLAS1$VxDOTx occurs in a different order than in a sequential evaluation of the dot product. The final result may differ from the result of a sequential evaluation.
C C To compute the dot product of two vectors, x and y, C and return the result in DOTPR: C INTEGER INCX,INCY REAL X(20),Y(20),DOTPR INCX = 1 INCY = 1 N = 20 DOTPR = BLAS1$VSDOT(N,X,INCX,Y,INCY) |
The Obtain the Euclidean Norm of a Vector routine obtains the Euclidean norm of an n-element vector x , expressed as follows:
BLAS1$VSNRM2 n ,x ,incxBLAS1$VDNRM2 n ,x ,incx
BLAS1$VGNRM2 n ,x ,incx
BLAS1$VSCNRM2 n ,x ,incx
BLAS1$VDZNRM2 n ,x ,incx
BLAS1$VGWNRM2 n ,x ,incx
Use BLAS1$VSNRM2 for single-precision real operations.
Use BLAS1$VDNRM2 for double-precision real (D-floating) operations.
Use BLAS1$VGNRM2 for double-precision real (G-floating) operations. Use BLAS1$VSCNRM2 for single-precision complex operations.
Use BLAS1$VDZNRM2 for double-precision complex (D-floating) operations.
Use BLAS1$VGWNRM2 for double-precision complex (G-floating) operations.
OpenVMS usage: floating_point type: F_floating, D_floating, or G_floating real access: write only mechanism: by value
The function value, called e_norm, is the Euclidean norm of the vector x . The data type of the function value is a real number; for the BLAS1$VSCNRM2, BLAS1$VDZNRM2, and BLAS1$VGWNRM2 routines, the data type of the function value is the real data type corresponding to the complex argument data type.
n
OpenVMS usage: longword_signed type: longword integer (signed) access: read only mechanism: by reference
Number of elements in vector x to be processed. The n argument is the address of a signed longword integer containing the number of elements.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:
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$VSNRM2 | F-floating real |
BLAS1$VDNRM2 | D-floating real |
BLAS1$VGNRM2 | G-floating real |
BLAS1$VSCNRM2 | F-floating complex |
BLAS1$VDZNRM2 | D-floating complex |
BLAS1$VGWNRM2 | G-floating complex |
If n is less than or equal to 0, then e_norm is 0.0.
OpenVMS usage: | longword_signed |
type: | longword integer (signed) |
access: | read only |
mechanism: | by reference |
where:
x | = | array specified in x |
i | = | element of the vector x |
incx | = | increment argument for the array x specified in incx |
If you specify a negative value for incx, it is interpreted as the absolute value of incx.
BLAS1$VxNRM2 obtains the Euclidean norm of an n-element vector x , expressed as follows:
Vector x contains n elements that are accessed from array x by stepping incx elements at a time. The vector x is a real or complex single-precision or double-precision (D and G) n-element vector. The vector can be a row or a column of a matrix. Both forward and backward indexing are permitted.
The public-domain BLAS Level 1 xNRM2 routines require a positive value for incx. The Run-Time Library BLAS Level 1 routines interpret a negative value for incx as the absolute value of incx.
The algorithm does not provide a special case for incx = 0. Therefore, specifying 0 for incx has the effect of using vector operations to set e_norm as follows:
e_norm = n0.5*|x[1]|
For BLAS1$VDNRM2, BLAS1$VGNRM2, BLAS1$VDZNRM2, and BLAS1$VGWNRM2 (the double-precision routines), the elements of the vector x are scaled to avoid intermediate overflow or underflow. BLAS1$VSNRM2 and BLAS1$VSCNRM2 (the single-precision routines) use a backup data type to avoid intermediate overflow or underflow.
Rounding in BLAS1$VxNRM2 occurs in a different order than in a sequential evaluation of the Euclidean norm. The final result may differ from the result of a sequential evaluation.
C C To obtain the Euclidean norm of the vector x: C INTEGER INCX,N REAL X(20),E_NORM INCX = 1 N = 20 E_NORM = BLAS1$VSNRM2(N,X,INCX) |
The Apply a Givens Plane Rotation routine applies a Givens plane rotation to a pair of n-element vectors x and y .
BLAS1$VSROT n ,x ,incx ,y ,incy ,c ,sBLAS1$VDROT n ,x ,incx ,y ,incy ,c ,s
BLAS1$VGROT n ,x ,incx ,y ,incy ,c ,s
BLAS1$VCSROT n ,x ,incx ,y ,incy ,c ,s
BLAS1$VZDROT n ,x ,incx ,y ,incy ,c ,s
BLAS1$VWGROT n ,x ,incx ,y ,incy ,c ,s
Use BLAS1$VSROT for single-precision real operations.
Use BLAS1$VDROT for double-precision real (D-floating) operations.
Use BLAS1$VGROT for double-precision real (G-floating) operations. Use BLAS1$VCSROT for single-precision complex operations.
Use BLAS1$VZDROT for double-precision complex (D-floating) operations.
Use BLAS1$VWGROT for double-precision complex (G-floating) operations.
BLAS1$VCSROT, BLAS1$VZDROT, and BLAS1$VWGROT are real rotations applied to a complex vector.
None.
n
OpenVMS usage: longword_signed type: longword integer (signed) access: read only mechanism: by reference
Number of elements in vectors x and y to be rotated. The n argument is the address of a signed longword integer containing the number of elements to be rotated. If n is less than or equal to 0, then x and y are 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: modify 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. On entry, this argument is an array of length at least:
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$VSROT | F-floating real |
BLAS1$VDROT | D-floating real |
BLAS1$VGROT | G-floating real |
BLAS1$VCSROT | F-floating complex |
BLAS1$VZDROT | D-floating complex |
BLAS1$VWGROT | G-floating complex |
If n is less than or equal to 0, then x and y are unchanged. If c equals 1.0 and s equals 0, then x and y are unchanged. If any element of x shares a memory location with an element of y , then the results are unpredictable.
On exit, x contains the rotated vector x , as follows:
where:
x | = | array x specified in x |
y | = | array y specified in y |
i | = | i = 1,2,...,n |
c | = | rotation element generated by the BLAS1$VxROTG routines |
s | = | rotation element generated by the BLAS1$VxROTG routines |
OpenVMS usage: | longword_signed |
type: | longword integer (signed) |
access: | read only |
mechanism: | by reference |
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:
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 |
OpenVMS usage: | floating_point or complex_number |
type: | F_floating, D_floating, G_floating real or F_floating, D_floating, G_floating complex |
access: | modify |
mechanism: | by reference, array reference |
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 y |
---|---|
BLAS1$VSROT | F-floating real |
BLAS1$VDROT | D-floating real |
BLAS1$VGROT | G-floating real |
BLAS1$VCSROT | F-floating complex |
BLAS1$VZDROT | D-floating complex |
BLAS1$VWGROT | G-floating complex |
If n is less than or equal to 0, then x and y are unchanged. If c equals 1.0 and s equals 0, then x and y are unchanged. If any element of x shares a memory location with an element of y , then the results are unpredictable.
On exit, y contains the rotated vector y , as follows:
where:
x | = | array x specified in x |
y | = | array y specified in y |
i | = | i = 1,2,...,n |
c | = | real rotation element (can be generated by the BLAS1$VxROTG routines) |
s | = | complex rotation element (can be generated by the BLAS1$VxROTG routines) |
OpenVMS usage: | longword_signed |
type: | longword integer (signed) |
access: | read only |
mechanism: | by reference |
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:
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 |
OpenVMS usage: | floating_point |
type: | F_floating, D_floating, or G_floating real |
access: | read only |
mechanism: | by reference |
Specify the data type (which is always real) as follows:
Routine | Data Type for c |
---|---|
BLAS1$VSROT and BLAS1$VCSROT | F-floating real |
BLAS1$VDROT and BLAS1$VZDROT | D-floating real |
BLAS1$VGROT and BLAS1$VWGROT | G-floating real |
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 |
Specify the data type (which can be either real or complex) as follows:
Routine | Data Type for s |
---|---|
BLAS1$VSROT and BLAS1$VCSROT | F-floating real or F-floating complex |
BLAS1$VDROT and BLAS1$VZDROT | D-floating real or D-floating complex |
BLAS1$VGROT and BLAS1$VWGROT | G-floating real or G-floating complex |
BLAS1$VSROT, BLAS1$VDROT, and BLAS1$VGROT apply a real Givens plane rotation to a pair of real vectors. BLAS1$VCSROT, BLAS1$VZDROT, and BLAS1$VWGROT apply a real Givens plane rotation to a pair of complex vectors. The vectors x and y are real or complex single-precision or double-precision (D and G) vectors. The vectors can be rows or columns of a matrix. Both forward and backward indexing are permitted. The routine name determines the data type you should specify for arguments x and y. Specify the same data type for each of these arguments.The Givens plane rotation is applied to n elements, where the elements to be rotated are contained in vectors x and y (i equals 1,2,...,n). These elements are accessed from arrays x and y by stepping incx and incy elements at a time. The cosine and sine of the angle of rotation are c and s, respectively. The arguments c and s are usually generated by the BLAS Level 1 routine BLAS1$VxROTG, using a=x and b=y :
The BLAS1$VxROT routines can be used to introduce zeros selectively into a matrix.
C C To rotate the first two rows of a matrix and zero C out the element in the first column of the second row: C INTEGER INCX,N REAL X(20,20),A,B,C,S INCX = 20 N = 20 A = X(1,1) B = X(2,1) CALL BLAS1$VSROTG(A,B,C,S) CALL BLAS1$VSROT(N,X,INCX,X(2,1),INCX,C,S) |
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