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MAGMA
2.7.1
Matrix Algebra for GPU and Multicore Architectures
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Functions | |
magma_int_t | magma_dlaln2 (magma_int_t trans, magma_int_t na, magma_int_t nw, double smin, double ca, const double *A, magma_int_t lda, double d1, double d2, const double *B, magma_int_t ldb, double wr, double wi, double *X, magma_int_t ldx, double *scale, double *xnorm, magma_int_t *info) |
DLALN2 solves a system of the form (ca A - w D) X = s B or (ca A**T - w D) X = s B with possible scaling ("s") and perturbation of A. More... | |
magma_int_t | magma_slaln2 (magma_int_t trans, magma_int_t na, magma_int_t nw, float smin, float ca, const float *A, magma_int_t lda, float d1, float d2, const float *B, magma_int_t ldb, float wr, float wi, float *X, magma_int_t ldx, float *scale, float *xnorm, magma_int_t *info) |
SLALN2 solves a system of the form (ca A - w D) X = s B or (ca A**T - w D) X = s B with possible scaling ("s") and perturbation of A. More... | |
magma_int_t magma_dlaln2 | ( | magma_int_t | trans, |
magma_int_t | na, | ||
magma_int_t | nw, | ||
double | smin, | ||
double | ca, | ||
const double * | A, | ||
magma_int_t | lda, | ||
double | d1, | ||
double | d2, | ||
const double * | B, | ||
magma_int_t | ldb, | ||
double | wr, | ||
double | wi, | ||
double * | X, | ||
magma_int_t | ldx, | ||
double * | scale, | ||
double * | xnorm, | ||
magma_int_t * | info | ||
) |
DLALN2 solves a system of the form (ca A - w D) X = s B or (ca A**T - w D) X = s B with possible scaling ("s") and perturbation of A.
(A**T means A-transpose.)
A is an NA x NA real matrix, ca is a real scalar, D is an NA x NA real diagonal matrix, w is a real or complex value, and X and B are NA x 1 matrices – real if w is real, complex if w is complex. NA may be 1 or 2.
If w is complex, X and B are represented as NA x 2 matrices, the first column of each being the real part and the second being the imaginary part.
"s" is a scaling factor (.LE. 1), computed by DLALN2, which is so chosen that X can be computed without overflow. X is further scaled if necessary to assure that norm(ca A - w D)*norm(X) is less than overflow.
If both singular values of (ca A - w D) are less than SMIN, SMIN*identity will be used instead of (ca A - w D). If only one singular value is less than SMIN, one element of (ca A - w D) will be perturbed enough to make the smallest singular value roughly SMIN. If both singular values are at least SMIN, (ca A - w D) will not be perturbed. In any case, the perturbation will be at most some small multiple of max( SMIN, ulp*norm(ca A - w D) ). The singular values are computed by infinity-norm approximations, and thus will only be correct to a factor of 2 or so.
Note: all input quantities are assumed to be smaller than overflow by a reasonable factor. (See BIGNUM.)
[in] | trans | LOGICAL = true (1): A**T will be used. = false (0): A will be used (not transposed.) |
[in] | na | INTEGER The size of the matrix A. It may (only) be 1 or 2. |
[in] | nw | INTEGER 1 if "w" is real, 2 if "w" is complex. It may only be 1 or 2. |
[in] | smin | DOUBLE PRECISION The desired lower bound on the singular values of A. This should be a safe distance away from underflow or overflow, say, between (underflow/machine precision) and (machine precision * overflow ). (See BIGNUM and ULP.) |
[in] | ca | DOUBLE PRECISION The coefficient c, which A is multiplied by. |
[in] | A | DOUBLE PRECISION array, dimension (LDA,NA) The NA x NA matrix A. |
[in] | lda | INTEGER The leading dimension of A. It must be at least NA. |
[in] | d1 | DOUBLE PRECISION The 1,1 element in the diagonal matrix D. |
[in] | d2 | DOUBLE PRECISION The 2,2 element in the diagonal matrix D. Not used if NW=1. |
[in] | B | DOUBLE PRECISION array, dimension (LDB,NW) The NA x NW matrix B (right-hand side). If NW=2 ("w" is complex), column 1 contains the real part of B and column 2 contains the imaginary part. |
[in] | ldb | INTEGER The leading dimension of B. It must be at least NA. |
[in] | wr | DOUBLE PRECISION The real part of the scalar "w". |
[in] | wi | DOUBLE PRECISION The imaginary part of the scalar "w". Not used if NW=1. |
[out] | X | DOUBLE PRECISION array, dimension (LDX,NW) The NA x NW matrix X (unknowns), as computed by DLALN2. If NW=2 ("w" is complex), on exit, column 1 will contain the real part of X and column 2 will contain the imaginary part. |
[in] | ldx | INTEGER The leading dimension of X. It must be at least NA. |
[out] | scale | DOUBLE PRECISION The scale factor that B must be multiplied by to insure that overflow does not occur when computing X. Thus, (ca A - w D) X will be SCALE*B, not B (ignoring perturbations of A.) It will be at most 1. |
[out] | xnorm | DOUBLE PRECISION The infinity-norm of X, when X is regarded as an NA x NW real matrix. |
[out] | info | INTEGER An error flag. It will be set to zero if no error occurs, a negative number if an argument is in error, or a positive number if ca A - w D had to be perturbed. The possible values are:
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magma_int_t magma_slaln2 | ( | magma_int_t | trans, |
magma_int_t | na, | ||
magma_int_t | nw, | ||
float | smin, | ||
float | ca, | ||
const float * | A, | ||
magma_int_t | lda, | ||
float | d1, | ||
float | d2, | ||
const float * | B, | ||
magma_int_t | ldb, | ||
float | wr, | ||
float | wi, | ||
float * | X, | ||
magma_int_t | ldx, | ||
float * | scale, | ||
float * | xnorm, | ||
magma_int_t * | info | ||
) |
SLALN2 solves a system of the form (ca A - w D) X = s B or (ca A**T - w D) X = s B with possible scaling ("s") and perturbation of A.
(A**T means A-transpose.)
A is an NA x NA real matrix, ca is a real scalar, D is an NA x NA real diagonal matrix, w is a real or complex value, and X and B are NA x 1 matrices – real if w is real, complex if w is complex. NA may be 1 or 2.
If w is complex, X and B are represented as NA x 2 matrices, the first column of each being the real part and the second being the imaginary part.
"s" is a scaling factor (.LE. 1), computed by SLALN2, which is so chosen that X can be computed without overflow. X is further scaled if necessary to assure that norm(ca A - w D)*norm(X) is less than overflow.
If both singular values of (ca A - w D) are less than SMIN, SMIN*identity will be used instead of (ca A - w D). If only one singular value is less than SMIN, one element of (ca A - w D) will be perturbed enough to make the smallest singular value roughly SMIN. If both singular values are at least SMIN, (ca A - w D) will not be perturbed. In any case, the perturbation will be at most some small multiple of max( SMIN, ulp*norm(ca A - w D) ). The singular values are computed by infinity-norm approximations, and thus will only be correct to a factor of 2 or so.
Note: all input quantities are assumed to be smaller than overflow by a reasonable factor. (See BIGNUM.)
[in] | trans | LOGICAL = true (1): A**T will be used. = false (0): A will be used (not transposed.) |
[in] | na | INTEGER The size of the matrix A. It may (only) be 1 or 2. |
[in] | nw | INTEGER 1 if "w" is real, 2 if "w" is complex. It may only be 1 or 2. |
[in] | smin | REAL The desired lower bound on the singular values of A. This should be a safe distance away from underflow or overflow, say, between (underflow/machine precision) and (machine precision * overflow ). (See BIGNUM and ULP.) |
[in] | ca | REAL The coefficient c, which A is multiplied by. |
[in] | A | REAL array, dimension (LDA,NA) The NA x NA matrix A. |
[in] | lda | INTEGER The leading dimension of A. It must be at least NA. |
[in] | d1 | REAL The 1,1 element in the diagonal matrix D. |
[in] | d2 | REAL The 2,2 element in the diagonal matrix D. Not used if NW=1. |
[in] | B | REAL array, dimension (LDB,NW) The NA x NW matrix B (right-hand side). If NW=2 ("w" is complex), column 1 contains the real part of B and column 2 contains the imaginary part. |
[in] | ldb | INTEGER The leading dimension of B. It must be at least NA. |
[in] | wr | REAL The real part of the scalar "w". |
[in] | wi | REAL The imaginary part of the scalar "w". Not used if NW=1. |
[out] | X | REAL array, dimension (LDX,NW) The NA x NW matrix X (unknowns), as computed by SLALN2. If NW=2 ("w" is complex), on exit, column 1 will contain the real part of X and column 2 will contain the imaginary part. |
[in] | ldx | INTEGER The leading dimension of X. It must be at least NA. |
[out] | scale | REAL The scale factor that B must be multiplied by to insure that overflow does not occur when computing X. Thus, (ca A - w D) X will be SCALE*B, not B (ignoring perturbations of A.) It will be at most 1. |
[out] | xnorm | REAL The infinity-norm of X, when X is regarded as an NA x NW real matrix. |
[out] | info | INTEGER An error flag. It will be set to zero if no error occurs, a negative number if an argument is in error, or a positive number if ca A - w D had to be perturbed. The possible values are:
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