|
double precision function | dasum (N, DX, INCX) |
| DASUM More...
|
|
subroutine | daxpy (N, DA, DX, INCX, DY, INCY) |
| DAXPY More...
|
|
double precision function | dcabs1 (Z) |
| DCABS1 More...
|
|
subroutine | dcopy (N, DX, INCX, DY, INCY) |
| DCOPY More...
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|
double precision function | ddot (N, DX, INCX, DY, INCY) |
| DDOT More...
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|
double precision function | dnrm2 (N, X, INCX) |
| DNRM2 More...
|
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subroutine | drot (N, DX, INCX, DY, INCY, C, S) |
| DROT More...
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subroutine | drotg (DA, DB, C, S) |
| DROTG More...
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subroutine | drotm (N, DX, INCX, DY, INCY, DPARAM) |
| DROTM More...
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subroutine | drotmg (DD1, DD2, DX1, DY1, DPARAM) |
| DROTMG More...
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subroutine | dscal (N, DA, DX, INCX) |
| DSCAL More...
|
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double precision function | dsdot (N, SX, INCX, SY, INCY) |
| DSDOT More...
|
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subroutine | dswap (N, DX, INCX, DY, INCY) |
| DSWAP More...
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subroutine | dtrsv (UPLO, TRANS, DIAG, N, A, LDA, X, INCX) |
| DTRSV More...
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double precision function | dzasum (N, ZX, INCX) |
| DZASUM More...
|
|
double precision function | dznrm2 (N, X, INCX) |
| DZNRM2 More...
|
|
This is the group of double LEVEL 1 BLAS routines.
double precision function dasum |
( |
integer |
N, |
|
|
double precision, dimension(*) |
DX, |
|
|
integer |
INCX |
|
) |
| |
DASUM
- Purpose:
DASUM takes the sum of the absolute values.
- Author
- Univ. of Tennessee
-
Univ. of California Berkeley
-
Univ. of Colorado Denver
-
NAG Ltd.
- 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(*)
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.
- Author
- Univ. of Tennessee
-
Univ. of California Berkeley
-
Univ. of Colorado Denver
-
NAG Ltd.
- Date
- November 2011
- 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
- Author
- Univ. of Tennessee
-
Univ. of California Berkeley
-
Univ. of Colorado Denver
-
NAG Ltd.
- Date
- November 2015
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.
- Author
- Univ. of Tennessee
-
Univ. of California Berkeley
-
Univ. of Colorado Denver
-
NAG Ltd.
- Date
- November 2011
- 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.
- Author
- Univ. of Tennessee
-
Univ. of California Berkeley
-
Univ. of Colorado Denver
-
NAG Ltd.
- Date
- November 2011
- 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 )
- Author
- Univ. of Tennessee
-
Univ. of California Berkeley
-
Univ. of Colorado Denver
-
NAG Ltd.
- 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.
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.
- Author
- Univ. of Tennessee
-
Univ. of California Berkeley
-
Univ. of Colorado Denver
-
NAG Ltd.
- Date
- November 2011
- 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.
- Author
- Univ. of Tennessee
-
Univ. of California Berkeley
-
Univ. of Colorado Denver
-
NAG Ltd.
- Date
- November 2011
- 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
-
[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 |
- Author
- Univ. of Tennessee
-
Univ. of California Berkeley
-
Univ. of Colorado Denver
-
NAG Ltd.
- Date
- November 2011
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 |
- Author
- Univ. of Tennessee
-
Univ. of California Berkeley
-
Univ. of Colorado Denver
-
NAG Ltd.
- Date
- November 2011
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.
- Author
- Univ. of Tennessee
-
Univ. of California Berkeley
-
Univ. of Colorado Denver
-
NAG Ltd.
- 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(*)
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)
- Author
- Univ. of Tennessee
-
Univ. of California Berkeley
-
Univ. of Colorado Denver
-
NAG Ltd.
- 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)
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.
- Author
- Univ. of Tennessee
-
Univ. of California Berkeley
-
Univ. of Colorado Denver
-
NAG Ltd.
- Date
- November 2011
- 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
-
[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. |
- Author
- Univ. of Tennessee
-
Univ. of California Berkeley
-
Univ. of Colorado Denver
-
NAG Ltd.
- Date
- November 2011
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.
- Author
- Univ. of Tennessee
-
Univ. of California Berkeley
-
Univ. of Colorado Denver
-
NAG Ltd.
- Date
- November 2015
- 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 )
- Author
- Univ. of Tennessee
-
Univ. of California Berkeley
-
Univ. of Colorado Denver
-
NAG Ltd.
- 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.