LAPACK  3.4.2 LAPACK: Linear Algebra PACKage
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## Functions/Subroutines

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/Subroutine Documentation

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

DASUM

Purpose:
`    DASUM takes the sum of the absolute values.`
Date:
November 2011
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(*)```

Definition at line 52 of file dasum.f.

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 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.```
Date:
November 2011
Further Details:
```     jack dongarra, linpack, 3/11/78.
modified 12/3/93, array(1) declarations changed to array(*)```

Definition at line 53 of file daxpy.f.

 DOUBLE PRECISION function dcabs1 ( complex*16 Z )

DCABS1

Purpose:
` DCABS1 computes absolute value of a double complex number `
Date:
November 2011

Definition at line 40 of file dcabs1.f.

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 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 one.```
Date:
November 2011
Further Details:
```     jack dongarra, linpack, 3/11/78.
modified 12/3/93, array(1) declarations changed to array(*)```

Definition at line 52 of file dcopy.f.

 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.```
Date:
November 2011
Further Details:
```     jack dongarra, linpack, 3/11/78.
modified 12/3/93, array(1) declarations changed to array(*)```

Definition at line 52 of file ddot.f.

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 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 )```
Date:
November 2011
Further Details:
```  -- This version written on 25-October-1982.
Modified on 14-October-1993 to inline the call to DLASSQ.
Sven Hammarling, Nag Ltd.```

Definition at line 55 of file dnrm2.f.

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 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.`
Date:
November 2011
Further Details:
```     jack dongarra, linpack, 3/11/78.
modified 12/3/93, array(1) declarations changed to array(*)```

Definition at line 52 of file drot.f.

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

DROTG

Purpose:
`    DROTG construct givens plane rotation.`
Date:
November 2011
Further Details:
`     jack dongarra, linpack, 3/11/78.`

Definition at line 47 of file drotg.f.

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 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:
 [in] N ``` N is INTEGER number of elements in input vector(s)``` [in,out] DX ``` DX is DOUBLE PRECISION array, dimension N double precision vector with N elements``` [in] INCX ``` INCX is INTEGER storage spacing between elements of DX``` [in,out] DY ``` DY is DOUBLE PRECISION array, dimension N double precision vector with N elements``` [in] INCY ``` INCY is INTEGER storage spacing between elements of DY``` [in,out] DPARAM ``` DPARAM is DOUBLE PRECISION array, dimension 5 DPARAM(1)=DFLAG DPARAM(2)=DH11 DPARAM(3)=DH21 DPARAM(4)=DH12 DPARAM(5)=DH22```
Date:
November 2011

Definition at line 99 of file drotm.f.

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 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:
 [in,out] DD1 ` DD1 is DOUBLE PRECISION` [in,out] DD2 ` DD2 is DOUBLE PRECISION` [in,out] DX1 ` DX1 is DOUBLE PRECISION` [in] DY1 ` DY1 is DOUBLE PRECISION` [in,out] DPARAM ``` DPARAM is DOUBLE PRECISION array, dimension 5 DPARAM(1)=DFLAG DPARAM(2)=DH11 DPARAM(3)=DH21 DPARAM(4)=DH12 DPARAM(5)=DH22```
Date:
November 2011

Definition at line 91 of file drotmg.f.

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 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 one.```
Date:
November 2011
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(*)```

Definition at line 54 of file dscal.f.

 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:
 [in] N ``` N is INTEGER number of elements in input vector(s)``` [in] SX ``` SX is REAL array, dimension(N) single precision vector with N elements``` [in] INCX ``` INCX is INTEGER storage spacing between elements of SX``` [in] SY ``` SY is REAL array, dimension(N) single precision vector with N elements``` [in] 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)```
Date:
November 2011
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)```

Definition at line 120 of file dsdot.f.

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

DSWAP

Purpose:
```    interchanges two vectors.
uses unrolled loops for increments equal one.```
Date:
November 2011
Further Details:
```     jack dongarra, linpack, 3/11/78.
modified 12/3/93, array(1) declarations changed to array(*)```

Definition at line 52 of file dswap.f.

 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:
 [in] 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.``` [in] 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.``` [in] 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.``` [in] N ``` N is INTEGER On entry, N specifies the order of the matrix A. N must be at least zero.``` [in] A ``` A is DOUBLE PRECISION array of 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.``` [in] 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 ).``` [in,out] X ``` X is DOUBLE PRECISION array of 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.``` [in] 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.```
Date:
November 2011

Definition at line 144 of file dtrsv.f.

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 DOUBLE PRECISION function dzasum ( integer N, complex*16, dimension(*) ZX, integer INCX )

DZASUM

Purpose:
`    DZASUM takes the sum of the absolute values.`
Date:
November 2011
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(*)```

Definition at line 52 of file dzasum.f.

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 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 )```
Date:
November 2011
Further Details:
```  -- This version written on 25-October-1982.
Modified on 14-October-1993 to inline the call to ZLASSQ.
Sven Hammarling, Nag Ltd.```

Definition at line 55 of file dznrm2.f.

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