la_blas Module Reference

Data Types
interface	axpy
	AXPY: constant times a vector plus a vector. More...
interface	copy
	COPY: copies a vector x to a vector y. More...
interface	dot
	DOT: forms the dot product of two vectors. uses unrolled loops for increments equal to one. More...
interface	dotc
	DOTC: forms the dot product of two complex vectors DOTC = X^H * Y. More...
interface	dotu
	DOTU: forms the dot product of two complex vectors DOTU = X^T * Y. More...
interface	gbmv
	GBMV: performs one of the matrix-vector operations y := alpha*A*x + beta*y, or y := alpha*A**T*x + beta*y, or y := alpha*A**H*x + beta*y, where alpha and beta are scalars, x and y are vectors and A is an m by n band matrix, with kl sub-diagonals and ku super-diagonals. More...
interface	gemm
	GEMM: performs one of the matrix-matrix operations C := alpha*op( A )*op( B ) + beta*C, where op( X ) is one of op( X ) = X or op( X ) = X**T or op( X ) = X**H, alpha and beta are scalars, and A, B and C are matrices, with op( A ) an m by k matrix, op( B ) a k by n matrix and C an m by n matrix. More...
interface	gemv
	GEMV: performs one of the matrix-vector operations y := alpha*A*x + beta*y, or y := alpha*A**T*x + beta*y, or y := alpha*A**H*x + beta*y, where alpha and beta are scalars, x and y are vectors and A is an m by n matrix. More...
interface	ger
	GER: performs the rank 1 operation A := alpha*x*y**T + A, where alpha is a scalar, x is an m element vector, y is an n element vector and A is an m by n matrix. More...
interface	gerc
	GERC: performs the rank 1 operation A := alpha*x*y**H + A, where alpha is a scalar, x is an m element vector, y is an n element vector and A is an m by n matrix. More...
interface	geru
	GERU: performs the rank 1 operation A := alpha*x*y**T + A, where alpha is a scalar, x is an m element vector, y is an n element vector and A is an m by n matrix. More...
interface	hbmv
	HBMV: performs the matrix-vector operation y := alpha*A*x + beta*y, where alpha and beta are scalars, x and y are n element vectors and A is an n by n hermitian band matrix, with k super-diagonals. More...
interface	hemm
	HEMM: performs one of the matrix-matrix operations C := alpha*A*B + beta*C, or C := alpha*B*A + beta*C, where alpha and beta are scalars, A is an hermitian matrix and B and C are m by n matrices. More...
interface	hemv
	HEMV: performs the matrix-vector operation y := alpha*A*x + beta*y, where alpha and beta are scalars, x and y are n element vectors and A is an n by n hermitian matrix. More...
interface	her
	HER: performs the hermitian rank 1 operation A := alpha*x*x**H + A, where alpha is a real scalar, x is an n element vector and A is an n by n hermitian matrix. More...
interface	her2
	HER2: performs the hermitian rank 2 operation A := alpha*x*y**H + conjg( alpha )*y*x**H + A, where alpha is a scalar, x and y are n element vectors and A is an n by n hermitian matrix. More...
interface	her2k
	HER2K: performs one of the hermitian rank 2k operations C := alpha*A*B**H + conjg( alpha )*B*A**H + beta*C, or C := alpha*A**H*B + conjg( alpha )*B**H*A + beta*C, where alpha and beta are scalars with beta real, C is an n by n hermitian matrix and A and B are n by k matrices in the first case and k by n matrices in the second case. More...
interface	herk
	HERK: performs one of the hermitian rank k operations C := alpha*A*A**H + beta*C, or C := alpha*A**H*A + beta*C, where alpha and beta are real scalars, C is an n by n hermitian matrix and A is an n by k matrix in the first case and a k by n matrix in the second case. More...
interface	hpmv
	HPMV: performs the matrix-vector operation y := alpha*A*x + beta*y, where alpha and beta are scalars, x and y are n element vectors and A is an n by n hermitian matrix, supplied in packed form. More...
interface	hpr
	HPR: performs the hermitian rank 1 operation A := alpha*x*x**H + A, where alpha is a real scalar, x is an n element vector and A is an n by n hermitian matrix, supplied in packed form. More...
interface	hpr2
	HPR2: performs the hermitian rank 2 operation A := alpha*x*y**H + conjg( alpha )*y*x**H + A, where alpha is a scalar, x and y are n element vectors and A is an n by n hermitian matrix, supplied in packed form. More...
interface	nrm2
	! More...
interface	rot
	ROT: applies a plane rotation. More...
interface	rotg
	! More...
interface	rotm
	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 >= 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._dp DFLAG=0._dp DFLAG=1._dp DFLAG=-2.D0 (DH11 DH12) (1._dp DH12) (DH11 1._dp) (1._dp 0._dp) H=( ) ( ) ( ) ( ) (DH21 DH22), (DH21 1._dp), (-1._dp DH22), (0._dp 1._dp). SEE ROTMG FOR A DESCRIPTION OF DATA STORAGE IN DPARAM. More...
interface	rotmg
	CONSTRUCT THE MODIFIED GIVENS TRANSFORMATION MATRIX H WHICH ZEROS THE SECOND COMPONENT OF THE 2-VECTOR (SQRT(DD1)*DX1,SQRT(DD2) DY2)**T. WITH DPARAM(1)=DFLAG, H HAS ONE OF THE FOLLOWING FORMS.. DFLAG=-1._dp DFLAG=0._dp DFLAG=1._dp DFLAG=-2.D0 (DH11 DH12) (1._dp DH12) (DH11 1._dp) (1._dp 0._dp) H=( ) ( ) ( ) ( ) (DH21 DH22), (DH21 1._dp), (-1._dp DH22), (0._dp 1._dp). LOCATIONS 2-4 OF DPARAM CONTAIN DH11, DH21, DH12, AND DH22 RESPECTIVELY. (VALUES OF 1._dp, -1._dp, OR 0._dp 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. More...
interface	sbmv
	SBMV: performs the matrix-vector operation y := alpha*A*x + beta*y, where alpha and beta are scalars, x and y are n element vectors and A is an n by n symmetric band matrix, with k super-diagonals. More...
interface	scal
	SCAL: scales a vector by a constant. More...
interface	sdot
	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 SDOT: = sum for I = 0 to N-1 of SX(LX+I*INCX) * SY(LY+I*INCY), where LX = 1 if INCX >= 0, else LX = 1+(1-N)*INCX, and LY is defined in a similar way using INCY. More...
interface	spmv
	SPMV: performs the matrix-vector operation y := alpha*A*x + beta*y, where alpha and beta are scalars, x and y are n element vectors and A is an n by n symmetric matrix, supplied in packed form. More...
interface	spr
	SPR: performs the symmetric rank 1 operation A := alpha*x*x**T + A, where alpha is a real scalar, x is an n element vector and A is an n by n symmetric matrix, supplied in packed form. More...
interface	spr2
	SPR2: performs the symmetric rank 2 operation A := alpha*x*y**T + alpha*y*x**T + A, where alpha is a scalar, x and y are n element vectors and A is an n by n symmetric matrix, supplied in packed form. More...
interface	srot
	SROT: applies a plane rotation, where the cos and sin (c and s) are real and the vectors cx and cy are complex. jack dongarra, linpack, 3/11/78. More...
interface	sscal
	SSCAL: scales a complex vector by a real constant. More...
interface	swap
	SWAP: interchanges two vectors. More...
interface	symm
	SYMM: performs one of the matrix-matrix operations C := alpha*A*B + beta*C, or C := alpha*B*A + beta*C, where alpha and beta are scalars, A is a symmetric matrix and B and C are m by n matrices. More...
interface	symv
	SYMV: performs the matrix-vector operation y := alpha*A*x + beta*y, where alpha and beta are scalars, x and y are n element vectors and A is an n by n symmetric matrix. More...
interface	syr
	SYR: performs the symmetric rank 1 operation A := alpha*x*x**T + A, where alpha is a real scalar, x is an n element vector and A is an n by n symmetric matrix. More...
interface	syr2
	SYR2: performs the symmetric rank 2 operation A := alpha*x*y**T + alpha*y*x**T + A, where alpha is a scalar, x and y are n element vectors and A is an n by n symmetric matrix. More...
interface	syr2k
	SYR2K: performs one of the symmetric rank 2k operations C := alpha*A*B**T + alpha*B*A**T + beta*C, or C := alpha*A**T*B + alpha*B**T*A + beta*C, where alpha and beta are scalars, C is an n by n symmetric matrix and A and B are n by k matrices in the first case and k by n matrices in the second case. More...
interface	syrk
	SYRK: performs one of the symmetric rank k operations C := alpha*A*A**T + beta*C, or C := alpha*A**T*A + beta*C, where alpha and beta are scalars, C is an n by n symmetric matrix and A is an n by k matrix in the first case and a k by n matrix in the second case. More...
interface	tbmv
	TBMV: performs one of the matrix-vector operations x := A*x, or x := A**T*x, or x := A**H*x, where x is an n element vector and A is an n by n unit, or non-unit, upper or lower triangular band matrix, with ( k + 1 ) diagonals. More...
interface	tbsv
	TBSV: solves one of the systems of equations A*x = b, or A**T*x = b, or A**H*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 band matrix, with ( k + 1 ) diagonals. No test for singularity or near-singularity is included in this routine. Such tests must be performed before calling this routine. More...
interface	tpmv
	TPMV: performs one of the matrix-vector operations x := A*x, or x := A**T*x, or x := A**H*x, where x is an n element vector and A is an n by n unit, or non-unit, upper or lower triangular matrix, supplied in packed form. More...
interface	tpsv
	TPSV: solves one of the systems of equations A*x = b, or A**T*x = b, or A**H*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, supplied in packed form. No test for singularity or near-singularity is included in this routine. Such tests must be performed before calling this routine. More...
interface	trmm
	TRMM: performs one of the matrix-matrix operations B := alpha*op( A )*B, or B := alpha*B*op( A ) where alpha is a scalar, B is an m by n matrix, A is a unit, or non-unit, upper or lower triangular matrix and op( A ) is one of op( A ) = A or op( A ) = A**T or op( A ) = A**H. More...
interface	trmv
	TRMV: performs one of the matrix-vector operations x := A*x, or x := A**T*x, or x := A**H*x, where x is an n element vector and A is an n by n unit, or non-unit, upper or lower triangular matrix. More...
interface	trsm
	TRSM: solves one of the matrix equations op( A )*X = alpha*B, or X*op( A ) = alpha*B, where alpha is a scalar, X and B are m by n matrices, A is a unit, or non-unit, upper or lower triangular matrix and op( A ) is one of op( A ) = A or op( A ) = A**T or op( A ) = A**H. The matrix X is overwritten on B. More...
interface	trsv
	TRSV: solves one of the systems of equations A*x = b, or A**T*x = b, or A**H*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. More...