double_blas_level1(3) LAPACK double_blas_level1(3)

NAME¶

double_blas_level1

SYNOPSIS¶

Functions¶

double precision function dasum (N, DX, INCX)
DASUM subroutine daxpy (N, DA, DX, INCX, DY, INCY)
DAXPY double precision function dcabs1 (Z)
DCABS1 subroutine dcopy (N, DX, INCX, DY, INCY)
DCOPY double precision function ddot (N, DX, INCX, DY, INCY)
DDOT double precision function dnrm2 (N, X, INCX)
DNRM2 subroutine drot (N, DX, INCX, DY, INCY, C, S)
DROT subroutine drotg (DA, DB, C, S)
DROTG subroutine drotm (N, DX, INCX, DY, INCY, DPARAM)
DROTM subroutine drotmg (DD1, DD2, DX1, DY1, DPARAM)
DROTMG subroutine dscal (N, DA, DX, INCX)
DSCAL double precision function dsdot (N, SX, INCX, SY, INCY)
DSDOT subroutine dswap (N, DX, INCX, DY, INCY)
DSWAP subroutine dtrsv (UPLO, TRANS, DIAG, N, A, LDA, X, INCX)
DTRSV double precision function dzasum (N, ZX, INCX)
DZASUM double precision function dznrm2 (N, X, INCX)
DZNRM2

Detailed Description¶

This is the group of double LEVEL 1 BLAS routines.

Function Documentation¶

double precision function dasum (integer N, double precision, dimension(*) DX, integer INCX)¶

DASUM

Purpose:

```    DASUM takes the sum of the absolute values.
```

Parameters:

N

```          N is INTEGER
number of elements in input vector(s)
```

DX

```          DX is DOUBLE PRECISION array, dimension ( 1 + ( N - 1 )*abs( INCX ) )
```

INCX

```          INCX is INTEGER
storage spacing between elements of DX
```

Author:

Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

Date:

November 2017

Further Details:

```     jack dongarra, linpack, 3/11/78.
modified 3/93 to return if incx .le. 0.
modified 12/3/93, array(1) declarations changed to array(*)
```

subroutine daxpy (integer N, double precision DA, double precision, dimension(*) DX, integer INCX, double precision, dimension(*) DY, integer INCY)¶

DAXPY

Purpose:

```    DAXPY constant times a vector plus a vector.
uses unrolled loops for increments equal to one.
```

Parameters:

N

```          N is INTEGER
number of elements in input vector(s)
```

DA

```          DA is DOUBLE PRECISION
On entry, DA specifies the scalar alpha.
```

DX

```          DX is DOUBLE PRECISION array, dimension ( 1 + ( N - 1 )*abs( INCX ) )
```

INCX

```          INCX is INTEGER
storage spacing between elements of DX
```

DY

```          DY is DOUBLE PRECISION array, dimension ( 1 + ( N - 1 )*abs( INCY ) )
```

INCY

```          INCY is INTEGER
storage spacing between elements of DY
```

Author:

Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

Date:

November 2017

Further Details:

```     jack dongarra, linpack, 3/11/78.
modified 12/3/93, array(1) declarations changed to array(*)
```

double precision function dcabs1 (complex*16 Z)¶

DCABS1

Purpose:

``` DCABS1 computes |Re(.)| + |Im(.)| of a double complex number
```

Parameters:

Z

```          Z is COMPLEX*16
```

Author:

Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

Date:

November 2017

subroutine dcopy (integer N, double precision, dimension(*) DX, integer INCX, double precision, dimension(*) DY, integer INCY)¶

DCOPY

Purpose:

```    DCOPY copies a vector, x, to a vector, y.
uses unrolled loops for increments equal to 1.
```

Parameters:

N

```          N is INTEGER
number of elements in input vector(s)
```

DX

```          DX is DOUBLE PRECISION array, dimension ( 1 + ( N - 1 )*abs( INCX ) )
```

INCX

```          INCX is INTEGER
storage spacing between elements of DX
```

DY

```          DY is DOUBLE PRECISION array, dimension ( 1 + ( N - 1 )*abs( INCY ) )
```

INCY

```          INCY is INTEGER
storage spacing between elements of DY
```

Author:

Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

Date:

November 2017

Further Details:

```     jack dongarra, linpack, 3/11/78.
modified 12/3/93, array(1) declarations changed to array(*)
```

double precision function ddot (integer N, double precision, dimension(*) DX, integer INCX, double precision, dimension(*) DY, integer INCY)¶

DDOT

Purpose:

```    DDOT forms the dot product of two vectors.
uses unrolled loops for increments equal to one.
```

Parameters:

N

```          N is INTEGER
number of elements in input vector(s)
```

DX

```          DX is DOUBLE PRECISION array, dimension ( 1 + ( N - 1 )*abs( INCX ) )
```

INCX

```          INCX is INTEGER
storage spacing between elements of DX
```

DY

```          DY is DOUBLE PRECISION array, dimension ( 1 + ( N - 1 )*abs( INCY ) )
```

INCY

```          INCY is INTEGER
storage spacing between elements of DY
```

Author:

Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

Date:

November 2017

Further Details:

```     jack dongarra, linpack, 3/11/78.
modified 12/3/93, array(1) declarations changed to array(*)
```

double precision function dnrm2 (integer N, double precision, dimension(*) X, integer INCX)¶

DNRM2

Purpose:

``` DNRM2 returns the euclidean norm of a vector via the function
name, so that
DNRM2 := sqrt( x'*x )
```

Parameters:

N

```          N is INTEGER
number of elements in input vector(s)
```

X

```          X is DOUBLE PRECISION array, dimension ( 1 + ( N - 1 )*abs( INCX ) )
```

INCX

```          INCX is INTEGER
storage spacing between elements of DX
```

Author:

Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

Date:

November 2017

Further Details:

```  -- This version written on 25-October-1982.
Modified on 14-October-1993 to inline the call to DLASSQ.
Sven Hammarling, Nag Ltd.
```

subroutine drot (integer N, double precision, dimension(*) DX, integer INCX, double precision, dimension(*) DY, integer INCY, double precision C, double precision S)¶

DROT

Purpose:

```    DROT applies a plane rotation.
```

Parameters:

N

```          N is INTEGER
number of elements in input vector(s)
```

DX

```          DX is DOUBLE PRECISION array, dimension ( 1 + ( N - 1 )*abs( INCX ) )
```

INCX

```          INCX is INTEGER
storage spacing between elements of DX
```

DY

```          DY is DOUBLE PRECISION array, dimension ( 1 + ( N - 1 )*abs( INCY ) )
```

INCY

```          INCY is INTEGER
storage spacing between elements of DY
```

C

```          C is DOUBLE PRECISION
```

S

```          S is DOUBLE PRECISION
```

Author:

Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

Date:

November 2017

Further Details:

```     jack dongarra, linpack, 3/11/78.
modified 12/3/93, array(1) declarations changed to array(*)
```

subroutine drotg (double precision DA, double precision DB, double precision C, double precision S)¶

DROTG

Purpose:

```    DROTG construct givens plane rotation.
```

Parameters:

DA

```          DA is DOUBLE PRECISION
```

DB

```          DB is DOUBLE PRECISION
```

C

```          C is DOUBLE PRECISION
```

S

```          S is DOUBLE PRECISION
```

Author:

Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

Date:

November 2017

Further Details:

```     jack dongarra, linpack, 3/11/78.
```

subroutine drotm (integer N, double precision, dimension(*) DX, integer INCX, double precision, dimension(*) DY, integer INCY, double precision, dimension(5) DPARAM)¶

DROTM

Purpose:

```    APPLY THE MODIFIED GIVENS TRANSFORMATION, H, TO THE 2 BY N MATRIX
(DX**T) , WHERE **T INDICATES TRANSPOSE. THE ELEMENTS OF DX ARE IN
(DY**T)
DX(LX+I*INCX), I = 0 TO N-1, WHERE LX = 1 IF INCX .GE. 0, ELSE
LX = (-INCX)*N, AND SIMILARLY FOR SY USING LY AND INCY.
WITH DPARAM(1)=DFLAG, H HAS ONE OF THE FOLLOWING FORMS..
DFLAG=-1.D0     DFLAG=0.D0        DFLAG=1.D0     DFLAG=-2.D0
(DH11  DH12)    (1.D0  DH12)    (DH11  1.D0)    (1.D0  0.D0)
H=(          )    (          )    (          )    (          )
(DH21  DH22),   (DH21  1.D0),   (-1.D0 DH22),   (0.D0  1.D0).
SEE DROTMG FOR A DESCRIPTION OF DATA STORAGE IN DPARAM.
```

Parameters:

N

```          N is INTEGER
number of elements in input vector(s)
```

DX

```          DX is DOUBLE PRECISION array, dimension ( 1 + ( N - 1 )*abs( INCX ) )
```

INCX

```          INCX is INTEGER
storage spacing between elements of DX
```

DY

```          DY is DOUBLE PRECISION array, dimension ( 1 + ( N - 1 )*abs( INCY ) )
```

INCY

```          INCY is INTEGER
storage spacing between elements of DY
```

DPARAM

```          DPARAM is DOUBLE PRECISION array, dimension (5)
DPARAM(1)=DFLAG
DPARAM(2)=DH11
DPARAM(3)=DH21
DPARAM(4)=DH12
DPARAM(5)=DH22
```

Author:

Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

Date:

November 2017

subroutine drotmg (double precision DD1, double precision DD2, double precision DX1, double precision DY1, double precision, dimension(5) DPARAM)¶

DROTMG

Purpose:

```    CONSTRUCT THE MODIFIED GIVENS TRANSFORMATION MATRIX H WHICH ZEROS
THE SECOND COMPONENT OF THE 2-VECTOR  (DSQRT(DD1)*DX1,DSQRT(DD2)*>    DY2)**T.
WITH DPARAM(1)=DFLAG, H HAS ONE OF THE FOLLOWING FORMS..
DFLAG=-1.D0     DFLAG=0.D0        DFLAG=1.D0     DFLAG=-2.D0
(DH11  DH12)    (1.D0  DH12)    (DH11  1.D0)    (1.D0  0.D0)
H=(          )    (          )    (          )    (          )
(DH21  DH22),   (DH21  1.D0),   (-1.D0 DH22),   (0.D0  1.D0).
LOCATIONS 2-4 OF DPARAM CONTAIN DH11, DH21, DH12, AND DH22
RESPECTIVELY. (VALUES OF 1.D0, -1.D0, OR 0.D0 IMPLIED BY THE
VALUE OF DPARAM(1) ARE NOT STORED IN DPARAM.)
THE VALUES OF GAMSQ AND RGAMSQ SET IN THE DATA STATEMENT MAY BE
INEXACT.  THIS IS OK AS THEY ARE ONLY USED FOR TESTING THE SIZE
OF DD1 AND DD2.  ALL ACTUAL SCALING OF DATA IS DONE USING GAM.
```

Parameters:

DD1

```          DD1 is DOUBLE PRECISION
```

DD2

```          DD2 is DOUBLE PRECISION
```

DX1

```          DX1 is DOUBLE PRECISION
```

DY1

```          DY1 is DOUBLE PRECISION
```

DPARAM

```          DPARAM is DOUBLE PRECISION array, dimension (5)
DPARAM(1)=DFLAG
DPARAM(2)=DH11
DPARAM(3)=DH21
DPARAM(4)=DH12
DPARAM(5)=DH22
```

Author:

Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

Date:

November 2017

subroutine dscal (integer N, double precision DA, double precision, dimension(*) DX, integer INCX)¶

DSCAL

Purpose:

```    DSCAL scales a vector by a constant.
uses unrolled loops for increment equal to 1.
```

Parameters:

N

```          N is INTEGER
number of elements in input vector(s)
```

DA

```          DA is DOUBLE PRECISION
On entry, DA specifies the scalar alpha.
```

DX

```          DX is DOUBLE PRECISION array, dimension ( 1 + ( N - 1 )*abs( INCX ) )
```

INCX

```          INCX is INTEGER
storage spacing between elements of DX
```

Author:

Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

Date:

November 2017

Further Details:

```     jack dongarra, linpack, 3/11/78.
modified 3/93 to return if incx .le. 0.
modified 12/3/93, array(1) declarations changed to array(*)
```

double precision function dsdot (integer N, real, dimension(*) SX, integer INCX, real, dimension(*) SY, integer INCY)¶

DSDOT

Purpose:

``` Compute the inner product of two vectors with extended
precision accumulation and result.
Returns D.P. dot product accumulated in D.P., for S.P. SX and SY
DSDOT = sum for I = 0 to N-1 of  SX(LX+I*INCX) * SY(LY+I*INCY),
where LX = 1 if INCX .GE. 0, else LX = 1+(1-N)*INCX, and LY is
defined in a similar way using INCY.
```

Parameters:

N

```          N is INTEGER
number of elements in input vector(s)
```

SX

```          SX is REAL array, dimension(N)
single precision vector with N elements
```

INCX

```          INCX is INTEGER
storage spacing between elements of SX
```

SY

```          SY is REAL array, dimension(N)
single precision vector with N elements
```

INCY

```          INCY is INTEGER
storage spacing between elements of SY
```

Returns:

DSDOT

```          DSDOT is DOUBLE PRECISION
DSDOT  double precision dot product (zero if N.LE.0)
```

Author:

Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

Date:

December 2016

Further Details:

```
```

References:

```  C. L. Lawson, R. J. Hanson, D. R. Kincaid and F. T.
Krogh, Basic linear algebra subprograms for Fortran
usage, Algorithm No. 539, Transactions on Mathematical
Software 5, 3 (September 1979), pp. 308-323.
REVISION HISTORY  (YYMMDD)
791001  DATE WRITTEN
890831  Modified array declarations.  (WRB)
890831  REVISION DATE from Version 3.2
891214  Prologue converted to Version 4.0 format.  (BAB)
920310  Corrected definition of LX in DESCRIPTION.  (WRB)
920501  Reformatted the REFERENCES section.  (WRB)
070118  Reformat to LAPACK style (JL)
```

subroutine dswap (integer N, double precision, dimension(*) DX, integer INCX, double precision, dimension(*) DY, integer INCY)¶

DSWAP

Purpose:

```    DSWAP interchanges two vectors.
uses unrolled loops for increments equal to 1.
```

Parameters:

N

```          N is INTEGER
number of elements in input vector(s)
```

DX

```          DX is DOUBLE PRECISION array, dimension ( 1 + ( N - 1 )*abs( INCX ) )
```

INCX

```          INCX is INTEGER
storage spacing between elements of DX
```

DY

```          DY is DOUBLE PRECISION array, dimension ( 1 + ( N - 1 )*abs( INCY ) )
```

INCY

```          INCY is INTEGER
storage spacing between elements of DY
```

Author:

Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

Date:

November 2017

Further Details:

```     jack dongarra, linpack, 3/11/78.
modified 12/3/93, array(1) declarations changed to array(*)
```

subroutine dtrsv (character UPLO, character TRANS, character DIAG, integer N, double precision, dimension(lda,*) A, integer LDA, double precision, dimension(*) X, integer INCX)¶

DTRSV

Purpose:

``` DTRSV  solves one of the systems of equations
A*x = b,   or   A**T*x = b,
where b and x are n element vectors and A is an n by n unit, or
non-unit, upper or lower triangular matrix.
No test for singularity or near-singularity is included in this
routine. Such tests must be performed before calling this routine.
```

Parameters:

UPLO

```          UPLO is CHARACTER*1
On entry, UPLO specifies whether the matrix is an upper or
lower triangular matrix as follows:
UPLO = 'U' or 'u'   A is an upper triangular matrix.
UPLO = 'L' or 'l'   A is a lower triangular matrix.
```

TRANS

```          TRANS is CHARACTER*1
On entry, TRANS specifies the equations to be solved as
follows:
TRANS = 'N' or 'n'   A*x = b.
TRANS = 'T' or 't'   A**T*x = b.
TRANS = 'C' or 'c'   A**T*x = b.
```

DIAG

```          DIAG is CHARACTER*1
On entry, DIAG specifies whether or not A is unit
triangular as follows:
DIAG = 'U' or 'u'   A is assumed to be unit triangular.
DIAG = 'N' or 'n'   A is not assumed to be unit
triangular.
```

N

```          N is INTEGER
On entry, N specifies the order of the matrix A.
N must be at least zero.
```

A

```          A is DOUBLE PRECISION array, dimension ( LDA, N )
Before entry with  UPLO = 'U' or 'u', the leading n by n
upper triangular part of the array A must contain the upper
triangular matrix and the strictly lower triangular part of
A is not referenced.
Before entry with UPLO = 'L' or 'l', the leading n by n
lower triangular part of the array A must contain the lower
triangular matrix and the strictly upper triangular part of
A is not referenced.
Note that when  DIAG = 'U' or 'u', the diagonal elements of
A are not referenced either, but are assumed to be unity.
```

LDA

```          LDA is INTEGER
On entry, LDA specifies the first dimension of A as declared
in the calling (sub) program. LDA must be at least
max( 1, n ).
```

X

```          X is DOUBLE PRECISION array, dimension at least
( 1 + ( n - 1 )*abs( INCX ) ).
Before entry, the incremented array X must contain the n
element right-hand side vector b. On exit, X is overwritten
with the solution vector x.
```

INCX

```          INCX is INTEGER
On entry, INCX specifies the increment for the elements of
X. INCX must not be zero.
Level 2 Blas routine.
-- Written on 22-October-1986.
Jack Dongarra, Argonne National Lab.
Jeremy Du Croz, Nag Central Office.
Sven Hammarling, Nag Central Office.
Richard Hanson, Sandia National Labs.
```

Author:

Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

Date:

December 2016

double precision function dzasum (integer N, complex*16, dimension(*) ZX, integer INCX)¶

DZASUM

Purpose:

```    DZASUM takes the sum of the (|Re(.)| + |Im(.)|)'s of a complex vector and
returns a single precision result.
```

Parameters:

N

```          N is INTEGER
number of elements in input vector(s)
```

ZX

```          ZX is COMPLEX*16 array, dimension ( 1 + ( N - 1 )*abs( INCX ) )
```

INCX

```          INCX is INTEGER
storage spacing between elements of ZX
```

Author:

Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

Date:

November 2017

Further Details:

```     jack dongarra, 3/11/78.
modified 3/93 to return if incx .le. 0.
modified 12/3/93, array(1) declarations changed to array(*)
```

double precision function dznrm2 (integer N, complex*16, dimension(*) X, integer INCX)¶

DZNRM2

Purpose:

``` DZNRM2 returns the euclidean norm of a vector via the function
name, so that
DZNRM2 := sqrt( x**H*x )
```

Parameters:

N

```          N is INTEGER
number of elements in input vector(s)
```

X

```          X is COMPLEX*16 array, dimension (N)
complex vector with N elements
```

INCX

```          INCX is INTEGER
storage spacing between elements of X
```

Author:

Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

Date:

November 2017

Further Details:

```  -- This version written on 25-October-1982.
Modified on 14-October-1993 to inline the call to ZLASSQ.
Sven Hammarling, Nag Ltd.
```

Author¶

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