# la_heamv - Man Page

la_heamv: matrix-vector multiply |A| * |x|, Hermitian/symmetric

## Synopsis

### Functions

subroutine **cla_heamv** (uplo, n, alpha, a, lda, x, incx, beta, y, incy)**CLA_HEAMV** computes a matrix-vector product using a Hermitian indefinite matrix to calculate error bounds.

subroutine **cla_syamv** (uplo, n, alpha, a, lda, x, incx, beta, y, incy)**CLA_SYAMV** computes a matrix-vector product using a symmetric indefinite matrix to calculate error bounds.

subroutine **dla_syamv** (uplo, n, alpha, a, lda, x, incx, beta, y, incy)**DLA_SYAMV** computes a matrix-vector product using a symmetric indefinite matrix to calculate error bounds.

subroutine **sla_syamv** (uplo, n, alpha, a, lda, x, incx, beta, y, incy)**SLA_SYAMV** computes a matrix-vector product using a symmetric indefinite matrix to calculate error bounds.

subroutine **zla_heamv** (uplo, n, alpha, a, lda, x, incx, beta, y, incy)**ZLA_HEAMV** computes a matrix-vector product using a Hermitian indefinite matrix to calculate error bounds.

subroutine **zla_syamv** (uplo, n, alpha, a, lda, x, incx, beta, y, incy)**ZLA_SYAMV** computes a matrix-vector product using a symmetric indefinite matrix to calculate error bounds.

## Detailed Description

## Function Documentation

### subroutine cla_heamv (integer uplo, integer n, real alpha, complex, dimension( lda, * ) a, integer lda, complex, dimension( * ) x, integer incx, real beta, real, dimension( * ) y, integer incy)

**CLA_HEAMV** computes a matrix-vector product using a Hermitian indefinite matrix to calculate error bounds.

**Purpose:**

CLA_SYAMV performs the matrix-vector operation y := alpha*abs(A)*abs(x) + beta*abs(y), where alpha and beta are scalars, x and y are vectors and A is an n by n symmetric matrix. This function is primarily used in calculating error bounds. To protect against underflow during evaluation, components in the resulting vector are perturbed away from zero by (N+1) times the underflow threshold. To prevent unnecessarily large errors for block-structure embedded in general matrices, 'symbolically' zero components are not perturbed. A zero entry is considered 'symbolic' if all multiplications involved in computing that entry have at least one zero multiplicand.

**Parameters***UPLO*UPLO is INTEGER On entry, UPLO specifies whether the upper or lower triangular part of the array A is to be referenced as follows: UPLO = BLAS_UPPER Only the upper triangular part of A is to be referenced. UPLO = BLAS_LOWER Only the lower triangular part of A is to be referenced. Unchanged on exit.

*N*N is INTEGER On entry, N specifies the number of columns of the matrix A. N must be at least zero. Unchanged on exit.

*ALPHA*ALPHA is REAL . On entry, ALPHA specifies the scalar alpha. Unchanged on exit.

*A*A is COMPLEX array, dimension ( LDA, n ). Before entry, the leading m by n part of the array A must contain the matrix of coefficients. Unchanged on exit.

*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 ). Unchanged on exit.

*X*X is COMPLEX array, dimension ( 1 + ( n - 1 )*abs( INCX ) ) Before entry, the incremented array X must contain the vector x. Unchanged on exit.

*INCX*INCX is INTEGER On entry, INCX specifies the increment for the elements of X. INCX must not be zero. Unchanged on exit.

*BETA*BETA is REAL . On entry, BETA specifies the scalar beta. When BETA is supplied as zero then Y need not be set on input. Unchanged on exit.

*Y*Y is REAL array, dimension ( 1 + ( n - 1 )*abs( INCY ) ) Before entry with BETA non-zero, the incremented array Y must contain the vector y. On exit, Y is overwritten by the updated vector y.

*INCY*INCY is INTEGER On entry, INCY specifies the increment for the elements of Y. INCY must not be zero. Unchanged on exit.

**Author**Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

**Further Details:**

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. -- Modified for the absolute-value product, April 2006 Jason Riedy, UC Berkeley

Definition at line **176** of file **cla_heamv.f**.

### subroutine cla_syamv (integer uplo, integer n, real alpha, complex, dimension( lda, * ) a, integer lda, complex, dimension( * ) x, integer incx, real beta, real, dimension( * ) y, integer incy)

**CLA_SYAMV** computes a matrix-vector product using a symmetric indefinite matrix to calculate error bounds.

**Purpose:**

CLA_SYAMV performs the matrix-vector operation y := alpha*abs(A)*abs(x) + beta*abs(y), where alpha and beta are scalars, x and y are vectors and A is an n by n symmetric matrix. This function is primarily used in calculating error bounds. To protect against underflow during evaluation, components in the resulting vector are perturbed away from zero by (N+1) times the underflow threshold. To prevent unnecessarily large errors for block-structure embedded in general matrices, 'symbolically' zero components are not perturbed. A zero entry is considered 'symbolic' if all multiplications involved in computing that entry have at least one zero multiplicand.

**Parameters***UPLO*UPLO is INTEGER On entry, UPLO specifies whether the upper or lower triangular part of the array A is to be referenced as follows: UPLO = BLAS_UPPER Only the upper triangular part of A is to be referenced. UPLO = BLAS_LOWER Only the lower triangular part of A is to be referenced. Unchanged on exit.

*N*N is INTEGER On entry, N specifies the number of columns of the matrix A. N must be at least zero. Unchanged on exit.

*ALPHA*ALPHA is REAL . On entry, ALPHA specifies the scalar alpha. Unchanged on exit.

*A*A is COMPLEX array, dimension ( LDA, n ). Before entry, the leading m by n part of the array A must contain the matrix of coefficients. Unchanged on exit.

*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 ). Unchanged on exit.

*X*X is COMPLEX array, dimension ( 1 + ( n - 1 )*abs( INCX ) ) Before entry, the incremented array X must contain the vector x. Unchanged on exit.

*INCX*INCX is INTEGER On entry, INCX specifies the increment for the elements of X. INCX must not be zero. Unchanged on exit.

*BETA*BETA is REAL . On entry, BETA specifies the scalar beta. When BETA is supplied as zero then Y need not be set on input. Unchanged on exit.

*Y*Y is REAL array, dimension ( 1 + ( n - 1 )*abs( INCY ) ) Before entry with BETA non-zero, the incremented array Y must contain the vector y. On exit, Y is overwritten by the updated vector y.

*INCY*INCY is INTEGER On entry, INCY specifies the increment for the elements of Y. INCY must not be zero. Unchanged on exit.

**Author**Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

**Further Details:**

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. -- Modified for the absolute-value product, April 2006 Jason Riedy, UC Berkeley

Definition at line **177** of file **cla_syamv.f**.

### subroutine dla_syamv (integer uplo, integer n, double precision alpha, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( * ) x, integer incx, double precision beta, double precision, dimension( * ) y, integer incy)

**DLA_SYAMV** computes a matrix-vector product using a symmetric indefinite matrix to calculate error bounds.

**Purpose:**

DLA_SYAMV performs the matrix-vector operation y := alpha*abs(A)*abs(x) + beta*abs(y), where alpha and beta are scalars, x and y are vectors and A is an n by n symmetric matrix. This function is primarily used in calculating error bounds. To protect against underflow during evaluation, components in the resulting vector are perturbed away from zero by (N+1) times the underflow threshold. To prevent unnecessarily large errors for block-structure embedded in general matrices, 'symbolically' zero components are not perturbed. A zero entry is considered 'symbolic' if all multiplications involved in computing that entry have at least one zero multiplicand.

**Parameters***UPLO*UPLO is INTEGER On entry, UPLO specifies whether the upper or lower triangular part of the array A is to be referenced as follows: UPLO = BLAS_UPPER Only the upper triangular part of A is to be referenced. UPLO = BLAS_LOWER Only the lower triangular part of A is to be referenced. Unchanged on exit.

*N*N is INTEGER On entry, N specifies the number of columns of the matrix A. N must be at least zero. Unchanged on exit.

*ALPHA*ALPHA is DOUBLE PRECISION . On entry, ALPHA specifies the scalar alpha. Unchanged on exit.

*A*A is DOUBLE PRECISION array, dimension ( LDA, n ). Before entry, the leading m by n part of the array A must contain the matrix of coefficients. Unchanged on exit.

*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 ). Unchanged on exit.

*X*X is DOUBLE PRECISION array, dimension ( 1 + ( n - 1 )*abs( INCX ) ) Before entry, the incremented array X must contain the vector x. Unchanged on exit.

*INCX*INCX is INTEGER On entry, INCX specifies the increment for the elements of X. INCX must not be zero. Unchanged on exit.

*BETA*BETA is DOUBLE PRECISION . On entry, BETA specifies the scalar beta. When BETA is supplied as zero then Y need not be set on input. Unchanged on exit.

*Y*Y is DOUBLE PRECISION array, dimension ( 1 + ( n - 1 )*abs( INCY ) ) Before entry with BETA non-zero, the incremented array Y must contain the vector y. On exit, Y is overwritten by the updated vector y.

*INCY*INCY is INTEGER On entry, INCY specifies the increment for the elements of Y. INCY must not be zero. Unchanged on exit.

**Author**Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

**Further Details:**

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. -- Modified for the absolute-value product, April 2006 Jason Riedy, UC Berkeley

Definition at line **175** of file **dla_syamv.f**.

### subroutine sla_syamv (integer uplo, integer n, real alpha, real, dimension( lda, * ) a, integer lda, real, dimension( * ) x, integer incx, real beta, real, dimension( * ) y, integer incy)

**SLA_SYAMV** computes a matrix-vector product using a symmetric indefinite matrix to calculate error bounds.

**Purpose:**

SLA_SYAMV performs the matrix-vector operation y := alpha*abs(A)*abs(x) + beta*abs(y), where alpha and beta are scalars, x and y are vectors and A is an n by n symmetric matrix. This function is primarily used in calculating error bounds. To protect against underflow during evaluation, components in the resulting vector are perturbed away from zero by (N+1) times the underflow threshold. To prevent unnecessarily large errors for block-structure embedded in general matrices, 'symbolically' zero components are not perturbed. A zero entry is considered 'symbolic' if all multiplications involved in computing that entry have at least one zero multiplicand.

**Parameters***UPLO**N**ALPHA*ALPHA is REAL . On entry, ALPHA specifies the scalar alpha. Unchanged on exit.

*A*A is REAL array, dimension ( LDA, n ). Before entry, the leading m by n part of the array A must contain the matrix of coefficients. Unchanged on exit.

*LDA**X*X is REAL array, dimension ( 1 + ( n - 1 )*abs( INCX ) ) Before entry, the incremented array X must contain the vector x. Unchanged on exit.

*INCX**BETA*BETA is REAL . On entry, BETA specifies the scalar beta. When BETA is supplied as zero then Y need not be set on input. Unchanged on exit.

*Y*Y is REAL array, dimension ( 1 + ( n - 1 )*abs( INCY ) ) Before entry with BETA non-zero, the incremented array Y must contain the vector y. On exit, Y is overwritten by the updated vector y.

*INCY***Author**Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

**Further Details:**

Definition at line **175** of file **sla_syamv.f**.

### subroutine zla_heamv (integer uplo, integer n, double precision alpha, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( * ) x, integer incx, double precision beta, double precision, dimension( * ) y, integer incy)

**ZLA_HEAMV** computes a matrix-vector product using a Hermitian indefinite matrix to calculate error bounds.

**Purpose:**

ZLA_SYAMV performs the matrix-vector operation y := alpha*abs(A)*abs(x) + beta*abs(y), where alpha and beta are scalars, x and y are vectors and A is an n by n symmetric matrix. This function is primarily used in calculating error bounds. To protect against underflow during evaluation, components in the resulting vector are perturbed away from zero by (N+1) times the underflow threshold. To prevent unnecessarily large errors for block-structure embedded in general matrices, 'symbolically' zero components are not perturbed. A zero entry is considered 'symbolic' if all multiplications involved in computing that entry have at least one zero multiplicand.

**Parameters***UPLO**N**ALPHA*ALPHA is DOUBLE PRECISION . On entry, ALPHA specifies the scalar alpha. Unchanged on exit.

*A*A is COMPLEX*16 array, dimension ( LDA, n ). Before entry, the leading m by n part of the array A must contain the matrix of coefficients. Unchanged on exit.

*LDA**X*X is COMPLEX*16 array, dimension at least ( 1 + ( n - 1 )*abs( INCX ) ) Before entry, the incremented array X must contain the vector x. Unchanged on exit.

*INCX**BETA*BETA is DOUBLE PRECISION . On entry, BETA specifies the scalar beta. When BETA is supplied as zero then Y need not be set on input. Unchanged on exit.

*Y*Y is DOUBLE PRECISION array, dimension ( 1 + ( n - 1 )*abs( INCY ) ) Before entry with BETA non-zero, the incremented array Y must contain the vector y. On exit, Y is overwritten by the updated vector y.

*INCY***Author**Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

**Further Details:**

Definition at line **176** of file **zla_heamv.f**.

### subroutine zla_syamv (integer uplo, integer n, double precision alpha, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( * ) x, integer incx, double precision beta, double precision, dimension( * ) y, integer incy)

**ZLA_SYAMV** computes a matrix-vector product using a symmetric indefinite matrix to calculate error bounds.

**Purpose:**

ZLA_SYAMV performs the matrix-vector operation y := alpha*abs(A)*abs(x) + beta*abs(y), where alpha and beta are scalars, x and y are vectors and A is an n by n symmetric matrix. This function is primarily used in calculating error bounds. To protect against underflow during evaluation, components in the resulting vector are perturbed away from zero by (N+1) times the underflow threshold. To prevent unnecessarily large errors for block-structure embedded in general matrices, 'symbolically' zero components are not perturbed. A zero entry is considered 'symbolic' if all multiplications involved in computing that entry have at least one zero multiplicand.

**Parameters***UPLO**N**ALPHA*ALPHA is DOUBLE PRECISION . On entry, ALPHA specifies the scalar alpha. Unchanged on exit.

*A*A is COMPLEX*16 array, dimension ( LDA, n ). Before entry, the leading m by n part of the array A must contain the matrix of coefficients. Unchanged on exit.

*LDA**X*X is COMPLEX*16 array, dimension at least ( 1 + ( n - 1 )*abs( INCX ) ) Before entry, the incremented array X must contain the vector x. Unchanged on exit.

*INCX**BETA*BETA is DOUBLE PRECISION . On entry, BETA specifies the scalar beta. When BETA is supplied as zero then Y need not be set on input. Unchanged on exit.

*Y*Y is DOUBLE PRECISION array, dimension ( 1 + ( n - 1 )*abs( INCY ) ) Before entry with BETA non-zero, the incremented array Y must contain the vector y. On exit, Y is overwritten by the updated vector y.

*INCY***Author**Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

**Further Details:**

Definition at line **177** of file **zla_syamv.f**.

## Author

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